0.00/0.01	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.01	% app-encoded or not : app
0.00/0.01	% Variant    : fo
0.00/0.01	% Ordering    : rpo6
0.00/0.01	% Command    : 
0.00/0.01	#!/bin/sh
0.00/0.01	
0.00/0.01	./zipperposition.native ${1:+"$1"} \
0.00/0.01	  -i tptp \
0.00/0.01	  -o tptp \
0.00/0.01	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.01	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.01	  --no-ho \
0.00/0.01	  --no-avatar \
0.00/0.01	  --no-induction \
0.00/0.01	  --no-unif-pattern \
0.00/0.01	  --ord $2 \
0.00/0.01	  --simultaneous-sup false \
0.00/0.01	  --no-max-vars \
0.00/0.01	  --no-fool
0.00/0.20	% Computer   : n080.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 18:00:38 CST 2018
5.43/5.65	% done 2876 iterations in 5.440s
5.43/5.65	% SZS status Theorem for 'stdin'
5.43/5.65	% SZS output start Refutation
5.43/5.65	tff(zf_stmt_9, conjecture,
5.43/5.65	  (((![R:app_encode_fun(a,app_encode_fun(a,app_encode_fun(a,$o)))]:
5.43/5.65	       ((![Xa:a,Xb:a,Xc:a]:
5.43/5.65	           ((((Xa = c0) & (Xb = Xc)) | ((Xb = c0) & (Xa = Xc)) | 
5.43/5.65	             (?[Xx1:a,Xx2:a,Xy1:a,Xy2:a,Xz1:a,Xz2:a]:
5.43/5.65	                ((Xa =
5.43/5.65	                  app_encode_app(a,a,
5.43/5.65	                                 app_encode_app(a,app_encode_fun(a,a),cP,Xx1),
5.43/5.65	                                 Xx2)) & 
5.43/5.65	                 (Xb =
5.43/5.65	                  app_encode_app(a,a,
5.43/5.65	                                 app_encode_app(a,app_encode_fun(a,a),cP,Xy1),
5.43/5.65	                                 Xy2)) & 
5.43/5.65	                 (Xc =
5.43/5.65	                  app_encode_app(a,a,
5.43/5.65	                                 app_encode_app(a,app_encode_fun(a,a),cP,Xz1),
5.43/5.65	                                 Xz2)) & 
5.43/5.65	                 app_encode_app(a,$o,
5.43/5.65	                                app_encode_app(a,app_encode_fun(a,$o),
5.43/5.65	                                               app_encode_app(a,
5.43/5.65	                                                              app_encode_fun(
5.43/5.65	                                                              a,
5.43/5.65	                                                              app_encode_fun(
5.43/5.65	                                                              a,$o)),R,Xx1),
5.43/5.65	                                               Xy1),
5.43/5.65	                                Xz1) & 
5.43/5.65	                 app_encode_app(a,$o,
5.43/5.65	                                app_encode_app(a,app_encode_fun(a,$o),
5.43/5.65	                                               app_encode_app(a,
5.43/5.65	                                                              app_encode_fun(
5.43/5.65	                                                              a,
5.43/5.65	                                                              app_encode_fun(
5.43/5.65	                                                              a,$o)),R,Xx2),
5.43/5.65	                                               Xy2),
5.43/5.65	                                Xz2)))) =>
5.43/5.65	            app_encode_app(a,$o,
5.43/5.65	                           app_encode_app(a,app_encode_fun(a,$o),
5.43/5.65	                                          app_encode_app(a,
5.43/5.65	                                                         app_encode_fun(
5.43/5.65	                                                         a,
5.43/5.65	                                                         app_encode_fun(a,$o)),
5.43/5.65	                                                         R,Xa),
5.43/5.65	                                          Xb),
5.43/5.65	                           Xc))) =>
5.43/5.65	        app_encode_app(a,$o,
5.43/5.65	                       app_encode_app(a,app_encode_fun(a,$o),
5.43/5.65	                                      app_encode_app(a,
5.43/5.65	                                                     app_encode_fun(a,
5.43/5.65	                                                                    app_encode_fun(
5.43/5.65	                                                                    a,$o)),
5.43/5.65	                                                     R,x),
5.43/5.65	                                      y),
5.43/5.65	                       y))) & 
5.43/5.65	    (![R:app_encode_fun(a,app_encode_fun(a,app_encode_fun(a,$o)))]:
5.43/5.65	       ((![Xa:a,Xb:a,Xc:a]:
5.43/5.65	           ((((Xa = c0) & (Xb = Xc)) | ((Xb = c0) & (Xa = Xc)) | 
5.43/5.65	             (?[Xx1:a,Xx2:a,Xy1:a,Xy2:a,Xz1:a,Xz2:a]:
5.43/5.65	                ((Xa =
5.43/5.65	                  app_encode_app(a,a,
5.43/5.65	                                 app_encode_app(a,app_encode_fun(a,a),cP,Xx1),
5.43/5.65	                                 Xx2)) & 
5.43/5.65	                 (Xb =
5.43/5.65	                  app_encode_app(a,a,
5.43/5.65	                                 app_encode_app(a,app_encode_fun(a,a),cP,Xy1),
5.43/5.65	                                 Xy2)) & 
5.43/5.65	                 (Xc =
5.43/5.65	                  app_encode_app(a,a,
5.43/5.65	                                 app_encode_app(a,app_encode_fun(a,a),cP,Xz1),
5.43/5.65	                                 Xz2)) & 
5.43/5.65	                 app_encode_app(a,$o,
5.43/5.65	                                app_encode_app(a,app_encode_fun(a,$o),
5.43/5.65	                                               app_encode_app(a,
5.43/5.65	                                                              app_encode_fun(
5.43/5.65	                                                              a,
5.43/5.65	                                                              app_encode_fun(
5.43/5.65	                                                              a,$o)),R,Xx1),
5.43/5.65	                                               Xy1),
5.43/5.65	                                Xz1) & 
5.43/5.65	                 app_encode_app(a,$o,
5.43/5.65	                                app_encode_app(a,app_encode_fun(a,$o),
5.43/5.65	                                               app_encode_app(a,
5.43/5.65	                                                              app_encode_fun(
5.43/5.65	                                                              a,
5.43/5.65	                                                              app_encode_fun(
5.43/5.65	                                                              a,$o)),R,Xx2),
5.43/5.65	                                               Xy2),
5.43/5.65	                                Xz2)))) =>
5.43/5.65	            app_encode_app(a,$o,
5.43/5.65	                           app_encode_app(a,app_encode_fun(a,$o),
5.43/5.65	                                          app_encode_app(a,
5.43/5.65	                                                         app_encode_fun(
5.43/5.65	                                                         a,
5.43/5.65	                                                         app_encode_fun(a,$o)),
5.43/5.65	                                                         R,Xa),
5.43/5.65	                                          Xb),
5.43/5.65	                           Xc))) =>
5.43/5.65	        app_encode_app(a,$o,
5.43/5.65	                       app_encode_app(a,app_encode_fun(a,$o),
5.43/5.65	                                      app_encode_app(a,
5.43/5.65	                                                     app_encode_fun(a,
5.43/5.65	                                                                    app_encode_fun(
5.43/5.65	                                                                    a,$o)),
5.43/5.65	                                                     R,w),
5.43/5.65	                                      z),
5.43/5.65	                       z)))) =>
5.43/5.65	   (![R:app_encode_fun(a,app_encode_fun(a,app_encode_fun(a,$o)))]:
5.43/5.65	      ((![Xa:a,Xb:a,Xc:a]:
5.43/5.65	          ((((Xa = c0) & (Xb = Xc)) | ((Xb = c0) & (Xa = Xc)) | 
5.43/5.65	            (?[Xx1:a,Xx2:a,Xy1:a,Xy2:a,Xz1:a,Xz2:a]:
5.43/5.65	               ((Xa =
5.43/5.65	                 app_encode_app(a,a,
5.43/5.65	                                app_encode_app(a,app_encode_fun(a,a),cP,Xx1),
5.43/5.65	                                Xx2)) & 
5.43/5.65	                (Xb =
5.43/5.65	                 app_encode_app(a,a,
5.43/5.65	                                app_encode_app(a,app_encode_fun(a,a),cP,Xy1),
5.43/5.65	                                Xy2)) & 
5.43/5.65	                (Xc =
5.43/5.65	                 app_encode_app(a,a,
5.43/5.65	                                app_encode_app(a,app_encode_fun(a,a),cP,Xz1),
5.43/5.65	                                Xz2)) & 
5.43/5.65	                app_encode_app(a,$o,
5.43/5.65	                               app_encode_app(a,app_encode_fun(a,$o),
5.43/5.65	                                              app_encode_app(a,
5.43/5.65	                                                             app_encode_fun(
5.43/5.65	                                                             a,
5.43/5.65	                                                             app_encode_fun(
5.43/5.65	                                                             a,$o)),R,Xx1),
5.43/5.65	                                              Xy1),
5.43/5.65	                               Xz1) & 
5.43/5.65	                app_encode_app(a,$o,
5.43/5.65	                               app_encode_app(a,app_encode_fun(a,$o),
5.43/5.65	                                              app_encode_app(a,
5.43/5.65	                                                             app_encode_fun(
5.43/5.65	                                                             a,
5.43/5.65	                                                             app_encode_fun(
5.43/5.65	                                                             a,$o)),R,Xx2),
5.43/5.65	                                              Xy2),
5.43/5.65	                               Xz2)))) =>
5.43/5.65	           app_encode_app(a,$o,
5.43/5.65	                          app_encode_app(a,app_encode_fun(a,$o),
5.43/5.65	                                         app_encode_app(a,
5.43/5.65	                                                        app_encode_fun(
5.43/5.65	                                                        a,
5.43/5.65	                                                        app_encode_fun(a,$o)),
5.43/5.65	                                                        R,Xa),
5.43/5.65	                                         Xb),
5.43/5.65	                          Xc))) =>
5.43/5.65	       app_encode_app(a,$o,
5.43/5.65	                      app_encode_app(a,app_encode_fun(a,$o),
5.43/5.65	                                     app_encode_app(a,
5.43/5.65	                                                    app_encode_fun(a,
5.43/5.65	                                                                   app_encode_fun(
5.43/5.65	                                                                   a,$o)),
5.43/5.65	                                                    R,
5.43/5.65	                                                    app_encode_app(a,a,
5.43/5.65	                                                                   app_encode_app(
5.43/5.65	                                                                   a,
5.43/5.65	                                                                   app_encode_fun(
5.43/5.65	                                                                   a,a),cP,x),
5.43/5.65	                                                                   w)),
5.43/5.65	                                     app_encode_app(a,a,
5.43/5.65	                                                    app_encode_app(a,
5.43/5.65	                                                                   app_encode_fun(
5.43/5.65	                                                                   a,a),cP,y),
5.43/5.65	                                                    z)),
5.43/5.65	                      app_encode_app(a,a,
5.43/5.65	                                     app_encode_app(a,app_encode_fun(a,a),cP,
5.43/5.65	                                                    y),
5.43/5.65	                                     z)))))).
5.43/5.65	tff(zf_stmt_0, negated_conjecture,
5.43/5.65	  (~
5.43/5.65	    (((![R:app_encode_fun(a,app_encode_fun(a,app_encode_fun(a,$o)))]:
5.43/5.65	         ((![Xa:a,Xb:a,Xc:a]:
5.43/5.65	             ((((Xa = c0) & (Xb = Xc)) | ((Xb = c0) & (Xa = Xc)) | 
5.43/5.65	               (?[Xx1:a,Xx2:a,Xy1:a,Xy2:a,Xz1:a,Xz2:a]:
5.43/5.65	                  ((Xa =
5.43/5.65	                    app_encode_app(a,a,
5.43/5.65	                                   app_encode_app(a,app_encode_fun(a,a),cP,
5.43/5.65	                                                  Xx1),
5.43/5.65	                                   Xx2)) & 
5.43/5.65	                   (Xb =
5.43/5.65	                    app_encode_app(a,a,
5.43/5.65	                                   app_encode_app(a,app_encode_fun(a,a),cP,
5.43/5.65	                                                  Xy1),
5.43/5.65	                                   Xy2)) & 
5.43/5.65	                   (Xc =
5.43/5.65	                    app_encode_app(a,a,
5.43/5.65	                                   app_encode_app(a,app_encode_fun(a,a),cP,
5.43/5.65	                                                  Xz1),
5.43/5.65	                                   Xz2)) & 
5.43/5.65	                   app_encode_app(a,$o,
5.43/5.65	                                  app_encode_app(a,app_encode_fun(a,$o),
5.43/5.65	                                                 app_encode_app(a,
5.43/5.65	                                                                app_encode_fun(
5.43/5.65	                                                                a,
5.43/5.65	                                                                app_encode_fun(
5.43/5.65	                                                                a,$o)),R,Xx1),
5.43/5.65	                                                 Xy1),
5.43/5.65	                                  Xz1) & 
5.43/5.65	                   app_encode_app(a,$o,
5.43/5.65	                                  app_encode_app(a,app_encode_fun(a,$o),
5.43/5.65	                                                 app_encode_app(a,
5.43/5.65	                                                                app_encode_fun(
5.43/5.65	                                                                a,
5.43/5.65	                                                                app_encode_fun(
5.43/5.65	                                                                a,$o)),R,Xx2),
5.43/5.65	                                                 Xy2),
5.43/5.65	                                  Xz2)))) =>
5.43/5.65	              app_encode_app(a,$o,
5.43/5.65	                             app_encode_app(a,app_encode_fun(a,$o),
5.43/5.65	                                            app_encode_app(a,
5.43/5.65	                                                           app_encode_fun(
5.43/5.65	                                                           a,
5.43/5.65	                                                           app_encode_fun(
5.43/5.65	                                                           a,$o)),R,Xa),
5.43/5.65	                                            Xb),
5.43/5.65	                             Xc))) =>
5.43/5.65	          app_encode_app(a,$o,
5.43/5.65	                         app_encode_app(a,app_encode_fun(a,$o),
5.43/5.65	                                        app_encode_app(a,
5.43/5.65	                                                       app_encode_fun(
5.43/5.65	                                                       a,app_encode_fun(a,$o)),
5.43/5.65	                                                       R,x),
5.43/5.65	                                        y),
5.43/5.65	                         y))) & 
5.43/5.65	      (![R:app_encode_fun(a,app_encode_fun(a,app_encode_fun(a,$o)))]:
5.43/5.65	         ((![Xa:a,Xb:a,Xc:a]:
5.43/5.65	             ((((Xa = c0) & (Xb = Xc)) | ((Xb = c0) & (Xa = Xc)) | 
5.43/5.65	               (?[Xx1:a,Xx2:a,Xy1:a,Xy2:a,Xz1:a,Xz2:a]:
5.43/5.65	                  ((Xa =
5.43/5.65	                    app_encode_app(a,a,
5.43/5.65	                                   app_encode_app(a,app_encode_fun(a,a),cP,
5.43/5.65	                                                  Xx1),
5.43/5.65	                                   Xx2)) & 
5.43/5.65	                   (Xb =
5.43/5.65	                    app_encode_app(a,a,
5.43/5.65	                                   app_encode_app(a,app_encode_fun(a,a),cP,
5.43/5.65	                                                  Xy1),
5.43/5.65	                                   Xy2)) & 
5.43/5.65	                   (Xc =
5.43/5.65	                    app_encode_app(a,a,
5.43/5.65	                                   app_encode_app(a,app_encode_fun(a,a),cP,
5.43/5.65	                                                  Xz1),
5.43/5.65	                                   Xz2)) & 
5.43/5.65	                   app_encode_app(a,$o,
5.43/5.65	                                  app_encode_app(a,app_encode_fun(a,$o),
5.43/5.65	                                                 app_encode_app(a,
5.43/5.65	                                                                app_encode_fun(
5.43/5.65	                                                                a,
5.43/5.65	                                                                app_encode_fun(
5.43/5.65	                                                                a,$o)),R,Xx1),
5.43/5.65	                                                 Xy1),
5.43/5.65	                                  Xz1) & 
5.43/5.65	                   app_encode_app(a,$o,
5.43/5.65	                                  app_encode_app(a,app_encode_fun(a,$o),
5.43/5.65	                                                 app_encode_app(a,
5.43/5.65	                                                                app_encode_fun(
5.43/5.65	                                                                a,
5.43/5.65	                                                                app_encode_fun(
5.43/5.65	                                                                a,$o)),R,Xx2),
5.43/5.65	                                                 Xy2),
5.43/5.65	                                  Xz2)))) =>
5.43/5.65	              app_encode_app(a,$o,
5.43/5.65	                             app_encode_app(a,app_encode_fun(a,$o),
5.43/5.65	                                            app_encode_app(a,
5.43/5.65	                                                           app_encode_fun(
5.43/5.65	                                                           a,
5.43/5.65	                                                           app_encode_fun(
5.43/5.65	                                                           a,$o)),R,Xa),
5.43/5.65	                                            Xb),
5.43/5.65	                             Xc))) =>
5.43/5.65	          app_encode_app(a,$o,
5.43/5.65	                         app_encode_app(a,app_encode_fun(a,$o),
5.43/5.65	                                        app_encode_app(a,
5.43/5.65	                                                       app_encode_fun(
5.43/5.65	                                                       a,app_encode_fun(a,$o)),
5.43/5.65	                                                       R,w),
5.43/5.65	                                        z),
5.43/5.65	                         z)))) =>
5.43/5.65	     (![R:app_encode_fun(a,app_encode_fun(a,app_encode_fun(a,$o)))]:
5.43/5.65	        ((![Xa:a,Xb:a,Xc:a]:
5.43/5.65	            ((((Xa = c0) & (Xb = Xc)) | ((Xb = c0) & (Xa = Xc)) | 
5.43/5.65	              (?[Xx1:a,Xx2:a,Xy1:a,Xy2:a,Xz1:a,Xz2:a]:
5.43/5.65	                 ((Xa =
5.43/5.65	                   app_encode_app(a,a,
5.43/5.65	                                  app_encode_app(a,app_encode_fun(a,a),cP,Xx1),
5.43/5.65	                                  Xx2)) & 
5.43/5.65	                  (Xb =
5.43/5.65	                   app_encode_app(a,a,
5.43/5.65	                                  app_encode_app(a,app_encode_fun(a,a),cP,Xy1),
5.43/5.65	                                  Xy2)) & 
5.43/5.65	                  (Xc =
5.43/5.65	                   app_encode_app(a,a,
5.43/5.65	                                  app_encode_app(a,app_encode_fun(a,a),cP,Xz1),
5.43/5.65	                                  Xz2)) & 
5.43/5.65	                  app_encode_app(a,$o,
5.43/5.65	                                 app_encode_app(a,app_encode_fun(a,$o),
5.43/5.65	                                                app_encode_app(a,
5.43/5.65	                                                               app_encode_fun(
5.43/5.65	                                                               a,
5.43/5.65	                                                               app_encode_fun(
5.43/5.65	                                                               a,$o)),R,Xx1),
5.43/5.65	                                                Xy1),
5.43/5.65	                                 Xz1) & 
5.43/5.65	                  app_encode_app(a,$o,
5.43/5.65	                                 app_encode_app(a,app_encode_fun(a,$o),
5.43/5.65	                                                app_encode_app(a,
5.43/5.65	                                                               app_encode_fun(
5.43/5.65	                                                               a,
5.43/5.65	                                                               app_encode_fun(
5.43/5.65	                                                               a,$o)),R,Xx2),
5.43/5.65	                                                Xy2),
5.43/5.65	                                 Xz2)))) =>
5.43/5.65	             app_encode_app(a,$o,
5.43/5.65	                            app_encode_app(a,app_encode_fun(a,$o),
5.43/5.65	                                           app_encode_app(a,
5.43/5.65	                                                          app_encode_fun(
5.43/5.65	                                                          a,
5.43/5.65	                                                          app_encode_fun(
5.43/5.65	                                                          a,$o)),R,Xa),
5.43/5.65	                                           Xb),
5.43/5.65	                            Xc))) =>
5.43/5.65	         app_encode_app(a,$o,
5.43/5.65	                        app_encode_app(a,app_encode_fun(a,$o),
5.43/5.65	                                       app_encode_app(a,
5.43/5.65	                                                      app_encode_fun(
5.43/5.65	                                                      a,app_encode_fun(a,$o)),
5.43/5.65	                                                      R,
5.43/5.65	                                                      app_encode_app(
5.43/5.65	                                                      a,a,
5.43/5.65	                                                      app_encode_app(
5.43/5.65	                                                      a,app_encode_fun(a,a),
5.43/5.65	                                                      cP,x),w)),
5.43/5.65	                                       app_encode_app(a,a,
5.43/5.65	                                                      app_encode_app(
5.43/5.65	                                                      a,app_encode_fun(a,a),
5.43/5.65	                                                      cP,y),z)),
5.43/5.65	                        app_encode_app(a,a,
5.43/5.65	                                       app_encode_app(a,app_encode_fun(a,a),
5.43/5.66	                                                      cP,y),
5.43/5.66	                                       z))))))).
5.43/5.66	tff('0', plain,
5.43/5.66	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, x), 
5.43/5.66	           y), y)
5.43/5.66	       | sk_Xb1(X0) = sk_Xc1(X0)
5.43/5.66	       | sk_Xa1(X0) = sk_Xc1(X0)
5.43/5.66	       | sk_Xc1(X0)
5.43/5.66	          = app_encode_app(a, a, 
5.43/5.66	              app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz11(X0)), 
5.43/5.66	              sk_Xz21(X0))),
5.43/5.66	    inference('cnf', [status(esa)], [zf_stmt_0])).
5.43/5.66	tff('1', plain,
5.43/5.66	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, x), 
5.43/5.66	           y), y)
5.43/5.66	       | sk_Xb1(X0) = sk_Xc1(X0)
5.43/5.66	       | sk_Xa1(X0) = sk_Xc1(X0)
5.43/5.66	       | sk_Xb1(X0)
5.43/5.66	          = app_encode_app(a, a, 
5.43/5.66	              app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy11(X0)), 
5.43/5.66	              sk_Xy21(X0))),
5.43/5.66	    inference('cnf', [status(esa)], [zf_stmt_0])).
5.43/5.66	tff('2', plain,
5.43/5.66	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, x), 
5.43/5.66	           y), y)
5.43/5.66	       | sk_Xb1(X0) = sk_Xc1(X0)
5.43/5.66	       | sk_Xa1(X0) = sk_Xc1(X0)
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
5.43/5.66	               sk_Xx21(X0)), sk_Xy21(X0)), sk_Xz21(X0))),
5.43/5.66	    inference('cnf', [status(esa)], [zf_stmt_0])).
5.43/5.66	tff('3', plain,
5.43/5.66	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, x), 
5.43/5.66	           y), y)
5.43/5.66	       | sk_Xb1(X0) = sk_Xc1(X0)
5.43/5.66	       | sk_Xa1(X0) = sk_Xc1(X0)
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
5.43/5.66	               sk_Xx11(X0)), sk_Xy11(X0)), sk_Xz11(X0))),
5.43/5.66	    inference('cnf', [status(esa)], [zf_stmt_0])).
5.43/5.66	tff('4', plain,
5.43/5.66	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, x), 
5.43/5.66	           y), y)
5.43/5.66	       | sk_Xb1(X0) = sk_Xc1(X0)
5.43/5.66	       | sk_Xa1(X0) = sk_Xc1(X0)
5.43/5.66	       | sk_Xa1(X0)
5.43/5.66	          = app_encode_app(a, a, 
5.43/5.66	              app_encode_app(a, app_encode_fun(a, a), cP, sk_Xx11(X0)), 
5.43/5.66	              sk_Xx21(X0))),
5.43/5.66	    inference('cnf', [status(esa)], [zf_stmt_0])).
5.43/5.66	tff('5', plain,
5.43/5.66	    ![X2 : a, X3 : a, X4 : a, X5 : a, X6 : a, X7 : a, X8 : a, X9 : a, X10 : a]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             X2), X3), X4)
5.43/5.66	       | X2
5.43/5.66	          != app_encode_app(a, a, 
5.43/5.66	               app_encode_app(a, app_encode_fun(a, a), cP, X5), X6)
5.43/5.66	       | X3
5.43/5.66	          != app_encode_app(a, a, 
5.43/5.66	               app_encode_app(a, app_encode_fun(a, a), cP, X7), X8)
5.43/5.66	       | ~ app_encode_app(a, $o, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	                 sk_R, X5), X7), X9)
5.43/5.66	       | ~ app_encode_app(a, $o, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	                 sk_R, X6), X8), X10)
5.43/5.66	       | X4
5.43/5.66	          != app_encode_app(a, a, 
5.43/5.66	               app_encode_app(a, app_encode_fun(a, a), cP, X9), X10)),
5.43/5.66	    inference('cnf', [status(esa)], [zf_stmt_0])).
5.43/5.66	tff('6', plain,
5.43/5.66	    ![X5 : a, X6 : a, X7 : a, X8 : a, X9 : a, X10 : a]:
5.43/5.66	      (~ app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	               sk_R, X6), X8), X10)
5.43/5.66	       | ~ app_encode_app(a, $o, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	                 sk_R, X5), X7), X9)
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	               sk_R, 
5.43/5.66	               app_encode_app(a, a, 
5.43/5.66	                 app_encode_app(a, app_encode_fun(a, a), cP, X5), X6)), 
5.43/5.66	             app_encode_app(a, a, 
5.43/5.66	               app_encode_app(a, app_encode_fun(a, a), cP, X7), X8)), 
5.43/5.66	           app_encode_app(a, a, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, a), cP, X9), X10))),
5.43/5.66	    inference('simplify', [status(thm)], ['5'])).
5.43/5.66	tff('7', plain,
5.43/5.66	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o))), 
5.43/5.66	      X1 : a, X2 : a, X3 : a, X4 : a]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             sk_Xa1(X0)), 
5.43/5.66	           app_encode_app(a, a, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, a), cP, X4), X3)), 
5.43/5.66	         app_encode_app(a, a, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, a), cP, X2), X1))
5.43/5.66	       | sk_Xa1(X0) = sk_Xc1(X0)
5.43/5.66	       | sk_Xb1(X0) = sk_Xc1(X0)
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
5.43/5.66	               x), y), y)
5.43/5.66	       | ~ app_encode_app(a, $o, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	                 sk_R, sk_Xx11(X0)), X4), X2)
5.43/5.66	       | ~ app_encode_app(a, $o, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	                 sk_R, sk_Xx21(X0)), X3), X1)),
5.43/5.66	    inference('sup+', [status(thm)], ['4', '6'])).
5.43/5.66	tff('8', plain,
5.43/5.66	    ![X0 : a, X1 : a]:
5.43/5.66	      (~ $true
5.43/5.66	       | sk_Xa1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	       | sk_Xb1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	               sk_R, x), y), y)
5.43/5.66	       | ~ app_encode_app(a, $o, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	                 sk_R, sk_Xx21(sk_R)), X1), X0)
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	               sk_R, x), y), y)
5.43/5.66	       | sk_Xb1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	       | sk_Xa1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	               sk_R, sk_Xa1(sk_R)), 
5.43/5.66	             app_encode_app(a, a, 
5.43/5.66	               app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy11(sk_R)), 
5.43/5.66	               X1)), 
5.43/5.66	           app_encode_app(a, a, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz11(sk_R)), X0))),
5.43/5.66	    inference('sup-', [status(thm)], ['3', '7'])).
5.43/5.66	tff('9', plain,
5.43/5.66	    ![X0 : a, X1 : a]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             sk_Xa1(sk_R)), 
5.43/5.66	           app_encode_app(a, a, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy11(sk_R)), X1)), 
5.43/5.66	         app_encode_app(a, a, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz11(sk_R)), X0))
5.43/5.66	       | ~ app_encode_app(a, $o, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	                 sk_R, sk_Xx21(sk_R)), X1), X0)
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	               sk_R, x), y), y)
5.43/5.66	       | sk_Xb1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	       | sk_Xa1(sk_R) = sk_Xc1(sk_R)),
5.43/5.66	    inference('simplify', [status(thm)], ['8'])).
5.43/5.66	tff('10', plain,
5.43/5.66	    (~ $true
5.43/5.66	     | sk_Xa1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	     | sk_Xb1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)
5.43/5.66	     | sk_Xa1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	     | sk_Xb1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             sk_Xa1(sk_R)), 
5.43/5.66	           app_encode_app(a, a, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy11(sk_R)), 
5.43/5.66	             sk_Xy21(sk_R))), 
5.43/5.66	         app_encode_app(a, a, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz11(sk_R)), 
5.43/5.66	           sk_Xz21(sk_R)))),
5.43/5.66	    inference('sup-', [status(thm)], ['2', '9'])).
5.43/5.66	tff('11', plain,
5.43/5.66	    (app_encode_app(a, $o, 
5.43/5.66	       app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	           sk_Xa1(sk_R)), 
5.43/5.66	         app_encode_app(a, a, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy11(sk_R)), 
5.43/5.66	           sk_Xy21(sk_R))), 
5.43/5.66	       app_encode_app(a, a, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz11(sk_R)), 
5.43/5.66	         sk_Xz21(sk_R)))
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)
5.43/5.66	     | sk_Xb1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	     | sk_Xa1(sk_R) = sk_Xc1(sk_R)),
5.43/5.66	    inference('simplify', [status(thm)], ['10'])).
5.43/5.66	tff('12', plain,
5.43/5.66	    (app_encode_app(a, $o, 
5.43/5.66	       app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	           sk_Xa1(sk_R)), sk_Xb1(sk_R)), 
5.43/5.66	       app_encode_app(a, a, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz11(sk_R)), 
5.43/5.66	         sk_Xz21(sk_R)))
5.43/5.66	     | sk_Xa1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	     | sk_Xb1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)
5.43/5.66	     | sk_Xa1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	     | sk_Xb1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)),
5.43/5.66	    inference('sup+', [status(thm)], ['1', '11'])).
5.43/5.66	tff('13', plain,
5.43/5.66	    (app_encode_app(a, $o, 
5.43/5.66	       app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, x), 
5.43/5.66	         y), y)
5.43/5.66	     | sk_Xb1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	     | sk_Xa1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             sk_Xa1(sk_R)), sk_Xb1(sk_R)), 
5.43/5.66	         app_encode_app(a, a, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz11(sk_R)), 
5.43/5.66	           sk_Xz21(sk_R)))),
5.43/5.66	    inference('simplify', [status(thm)], ['12'])).
5.43/5.66	tff('14', plain,
5.43/5.66	    (app_encode_app(a, $o, 
5.43/5.66	       app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	           sk_Xa1(sk_R)), sk_Xb1(sk_R)), sk_Xc1(sk_R))
5.43/5.66	     | sk_Xa1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	     | sk_Xb1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)
5.43/5.66	     | sk_Xa1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	     | sk_Xb1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)),
5.43/5.66	    inference('sup+', [status(thm)], ['0', '13'])).
5.43/5.66	tff('15', plain,
5.43/5.66	    (app_encode_app(a, $o, 
5.43/5.66	       app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, x), 
5.43/5.66	         y), y)
5.43/5.66	     | sk_Xb1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	     | sk_Xa1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             sk_Xa1(sk_R)), sk_Xb1(sk_R)), sk_Xc1(sk_R))),
5.43/5.66	    inference('simplify', [status(thm)], ['14'])).
5.43/5.66	tff('16', plain,
5.43/5.66	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, x), 
5.43/5.66	           y), y)
5.43/5.66	       | ~ app_encode_app(a, $o, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	                 X0, sk_Xa1(X0)), sk_Xb1(X0)), sk_Xc1(X0))),
5.43/5.66	    inference('cnf', [status(esa)], [zf_stmt_0])).
5.43/5.66	tff('17', plain,
5.43/5.66	    (sk_Xa1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	     | sk_Xb1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)),
5.43/5.66	    inference('clc', [status(thm)], ['15', '16'])).
5.43/5.66	tff('18', plain,
5.43/5.66	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, x), 
5.43/5.66	           y), y)
5.43/5.66	       | sk_Xa1(X0) = c0
5.43/5.66	       | sk_Xa1(X0) = sk_Xc1(X0)
5.43/5.66	       | sk_Xc1(X0)
5.43/5.66	          = app_encode_app(a, a, 
5.43/5.66	              app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz11(X0)), 
5.43/5.66	              sk_Xz21(X0))),
5.43/5.66	    inference('cnf', [status(esa)], [zf_stmt_0])).
5.43/5.66	tff('19', plain,
5.43/5.66	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, x), 
5.43/5.66	           y), y)
5.43/5.66	       | sk_Xa1(X0) = c0
5.43/5.66	       | sk_Xa1(X0) = sk_Xc1(X0)
5.43/5.66	       | sk_Xb1(X0)
5.43/5.66	          = app_encode_app(a, a, 
5.43/5.66	              app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy11(X0)), 
5.43/5.66	              sk_Xy21(X0))),
5.43/5.66	    inference('cnf', [status(esa)], [zf_stmt_0])).
5.43/5.66	tff('20', plain,
5.43/5.66	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, x), 
5.43/5.66	           y), y)
5.43/5.66	       | sk_Xa1(X0) = c0
5.43/5.66	       | sk_Xa1(X0) = sk_Xc1(X0)
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
5.43/5.66	               sk_Xx21(X0)), sk_Xy21(X0)), sk_Xz21(X0))),
5.43/5.66	    inference('cnf', [status(esa)], [zf_stmt_0])).
5.43/5.66	tff('21', plain,
5.43/5.66	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, x), 
5.43/5.66	           y), y)
5.43/5.66	       | sk_Xa1(X0) = c0
5.43/5.66	       | sk_Xa1(X0) = sk_Xc1(X0)
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
5.43/5.66	               sk_Xx11(X0)), sk_Xy11(X0)), sk_Xz11(X0))),
5.43/5.66	    inference('cnf', [status(esa)], [zf_stmt_0])).
5.43/5.66	tff('22', plain,
5.43/5.66	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, x), 
5.43/5.66	           y), y)
5.43/5.66	       | sk_Xa1(X0) = c0
5.43/5.66	       | sk_Xa1(X0) = sk_Xc1(X0)
5.43/5.66	       | sk_Xa1(X0)
5.43/5.66	          = app_encode_app(a, a, 
5.43/5.66	              app_encode_app(a, app_encode_fun(a, a), cP, sk_Xx11(X0)), 
5.43/5.66	              sk_Xx21(X0))),
5.43/5.66	    inference('cnf', [status(esa)], [zf_stmt_0])).
5.43/5.66	tff('23', plain,
5.43/5.66	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o))), 
5.43/5.66	      X1 : a, X2 : a, X3 : a, X4 : a]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             sk_Xa1(X0)), 
5.43/5.66	           app_encode_app(a, a, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, a), cP, X4), X3)), 
5.43/5.66	         app_encode_app(a, a, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, a), cP, X2), X1))
5.43/5.66	       | sk_Xa1(X0) = sk_Xc1(X0)
5.43/5.66	       | sk_Xa1(X0) = c0
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
5.43/5.66	               x), y), y)
5.43/5.66	       | ~ app_encode_app(a, $o, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	                 sk_R, sk_Xx11(X0)), X4), X2)
5.43/5.66	       | ~ app_encode_app(a, $o, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	                 sk_R, sk_Xx21(X0)), X3), X1)),
5.43/5.66	    inference('sup+', [status(thm)], ['22', '6'])).
5.43/5.66	tff('24', plain,
5.43/5.66	    ![X0 : a, X1 : a]:
5.43/5.66	      (~ $true
5.43/5.66	       | sk_Xa1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	       | sk_Xa1(sk_R) = c0
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	               sk_R, x), y), y)
5.43/5.66	       | ~ app_encode_app(a, $o, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	                 sk_R, sk_Xx21(sk_R)), X1), X0)
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	               sk_R, x), y), y)
5.43/5.66	       | sk_Xa1(sk_R) = c0
5.43/5.66	       | sk_Xa1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	               sk_R, sk_Xa1(sk_R)), 
5.43/5.66	             app_encode_app(a, a, 
5.43/5.66	               app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy11(sk_R)), 
5.43/5.66	               X1)), 
5.43/5.66	           app_encode_app(a, a, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz11(sk_R)), X0))),
5.43/5.66	    inference('sup-', [status(thm)], ['21', '23'])).
5.43/5.66	tff('25', plain,
5.43/5.66	    ![X0 : a, X1 : a]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             sk_Xa1(sk_R)), 
5.43/5.66	           app_encode_app(a, a, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy11(sk_R)), X1)), 
5.43/5.66	         app_encode_app(a, a, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz11(sk_R)), X0))
5.43/5.66	       | ~ app_encode_app(a, $o, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	                 sk_R, sk_Xx21(sk_R)), X1), X0)
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	               sk_R, x), y), y)
5.43/5.66	       | sk_Xa1(sk_R) = c0
5.43/5.66	       | sk_Xa1(sk_R) = sk_Xc1(sk_R)),
5.43/5.66	    inference('simplify', [status(thm)], ['24'])).
5.43/5.66	tff('26', plain,
5.43/5.66	    (~ $true
5.43/5.66	     | sk_Xa1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	     | sk_Xa1(sk_R) = c0
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)
5.43/5.66	     | sk_Xa1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	     | sk_Xa1(sk_R) = c0
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             sk_Xa1(sk_R)), 
5.43/5.66	           app_encode_app(a, a, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy11(sk_R)), 
5.43/5.66	             sk_Xy21(sk_R))), 
5.43/5.66	         app_encode_app(a, a, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz11(sk_R)), 
5.43/5.66	           sk_Xz21(sk_R)))),
5.43/5.66	    inference('sup-', [status(thm)], ['20', '25'])).
5.43/5.66	tff('27', plain,
5.43/5.66	    (app_encode_app(a, $o, 
5.43/5.66	       app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	           sk_Xa1(sk_R)), 
5.43/5.66	         app_encode_app(a, a, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy11(sk_R)), 
5.43/5.66	           sk_Xy21(sk_R))), 
5.43/5.66	       app_encode_app(a, a, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz11(sk_R)), 
5.43/5.66	         sk_Xz21(sk_R)))
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)
5.43/5.66	     | sk_Xa1(sk_R) = c0
5.43/5.66	     | sk_Xa1(sk_R) = sk_Xc1(sk_R)),
5.43/5.66	    inference('simplify', [status(thm)], ['26'])).
5.43/5.66	tff('28', plain,
5.43/5.66	    (app_encode_app(a, $o, 
5.43/5.66	       app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	           sk_Xa1(sk_R)), sk_Xb1(sk_R)), 
5.43/5.66	       app_encode_app(a, a, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz11(sk_R)), 
5.43/5.66	         sk_Xz21(sk_R)))
5.43/5.66	     | sk_Xa1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	     | sk_Xa1(sk_R) = c0
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)
5.43/5.66	     | sk_Xa1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	     | sk_Xa1(sk_R) = c0
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)),
5.43/5.66	    inference('sup+', [status(thm)], ['19', '27'])).
5.43/5.66	tff('29', plain,
5.43/5.66	    (app_encode_app(a, $o, 
5.43/5.66	       app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, x), 
5.43/5.66	         y), y)
5.43/5.66	     | sk_Xa1(sk_R) = c0
5.43/5.66	     | sk_Xa1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             sk_Xa1(sk_R)), sk_Xb1(sk_R)), 
5.43/5.66	         app_encode_app(a, a, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz11(sk_R)), 
5.43/5.66	           sk_Xz21(sk_R)))),
5.43/5.66	    inference('simplify', [status(thm)], ['28'])).
5.43/5.66	tff('30', plain,
5.43/5.66	    (app_encode_app(a, $o, 
5.43/5.66	       app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	           sk_Xa1(sk_R)), sk_Xb1(sk_R)), sk_Xc1(sk_R))
5.43/5.66	     | sk_Xa1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	     | sk_Xa1(sk_R) = c0
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)
5.43/5.66	     | sk_Xa1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	     | sk_Xa1(sk_R) = c0
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)),
5.43/5.66	    inference('sup+', [status(thm)], ['18', '29'])).
5.43/5.66	tff('31', plain,
5.43/5.66	    (app_encode_app(a, $o, 
5.43/5.66	       app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, x), 
5.43/5.66	         y), y)
5.43/5.66	     | sk_Xa1(sk_R) = c0
5.43/5.66	     | sk_Xa1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             sk_Xa1(sk_R)), sk_Xb1(sk_R)), sk_Xc1(sk_R))),
5.43/5.66	    inference('simplify', [status(thm)], ['30'])).
5.43/5.66	tff('32', plain,
5.43/5.66	    (sk_Xa1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	     | sk_Xa1(sk_R) = c0
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)),
5.43/5.66	    inference('clc', [status(thm)], ['31', '16'])).
5.43/5.66	tff('33', plain,
5.43/5.66	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, x), 
5.43/5.66	           y), y)
5.43/5.66	       | sk_Xa1(X0) = c0
5.43/5.66	       | sk_Xb1(X0) = c0
5.43/5.66	       | sk_Xc1(X0)
5.43/5.66	          = app_encode_app(a, a, 
5.43/5.66	              app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz11(X0)), 
5.43/5.66	              sk_Xz21(X0))),
5.43/5.66	    inference('cnf', [status(esa)], [zf_stmt_0])).
5.43/5.66	tff('34', plain,
5.43/5.66	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, x), 
5.43/5.66	           y), y)
5.43/5.66	       | sk_Xa1(X0) = c0
5.43/5.66	       | sk_Xb1(X0) = c0
5.43/5.66	       | sk_Xb1(X0)
5.43/5.66	          = app_encode_app(a, a, 
5.43/5.66	              app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy11(X0)), 
5.43/5.66	              sk_Xy21(X0))),
5.43/5.66	    inference('cnf', [status(esa)], [zf_stmt_0])).
5.43/5.66	tff('35', plain,
5.43/5.66	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, x), 
5.43/5.66	           y), y)
5.43/5.66	       | sk_Xa1(X0) = c0
5.43/5.66	       | sk_Xb1(X0) = c0
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
5.43/5.66	               sk_Xx21(X0)), sk_Xy21(X0)), sk_Xz21(X0))),
5.43/5.66	    inference('cnf', [status(esa)], [zf_stmt_0])).
5.43/5.66	tff('36', plain,
5.43/5.66	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, x), 
5.43/5.66	           y), y)
5.43/5.66	       | sk_Xa1(X0) = c0
5.43/5.66	       | sk_Xb1(X0) = c0
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
5.43/5.66	               sk_Xx11(X0)), sk_Xy11(X0)), sk_Xz11(X0))),
5.43/5.66	    inference('cnf', [status(esa)], [zf_stmt_0])).
5.43/5.66	tff('37', plain,
5.43/5.66	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, x), 
5.43/5.66	           y), y)
5.43/5.66	       | sk_Xa1(X0) = c0
5.43/5.66	       | sk_Xb1(X0) = c0
5.43/5.66	       | sk_Xa1(X0)
5.43/5.66	          = app_encode_app(a, a, 
5.43/5.66	              app_encode_app(a, app_encode_fun(a, a), cP, sk_Xx11(X0)), 
5.43/5.66	              sk_Xx21(X0))),
5.43/5.66	    inference('cnf', [status(esa)], [zf_stmt_0])).
5.43/5.66	tff('38', plain,
5.43/5.66	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o))), 
5.43/5.66	      X1 : a, X2 : a, X3 : a, X4 : a]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             sk_Xa1(X0)), 
5.43/5.66	           app_encode_app(a, a, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, a), cP, X4), X3)), 
5.43/5.66	         app_encode_app(a, a, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, a), cP, X2), X1))
5.43/5.66	       | sk_Xb1(X0) = c0
5.43/5.66	       | sk_Xa1(X0) = c0
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
5.43/5.66	               x), y), y)
5.43/5.66	       | ~ app_encode_app(a, $o, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	                 sk_R, sk_Xx11(X0)), X4), X2)
5.43/5.66	       | ~ app_encode_app(a, $o, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	                 sk_R, sk_Xx21(X0)), X3), X1)),
5.43/5.66	    inference('sup+', [status(thm)], ['37', '6'])).
5.43/5.66	tff('39', plain,
5.43/5.66	    ![X0 : a, X1 : a]:
5.43/5.66	      (~ $true
5.43/5.66	       | sk_Xb1(sk_R) = c0
5.43/5.66	       | sk_Xa1(sk_R) = c0
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	               sk_R, x), y), y)
5.43/5.66	       | ~ app_encode_app(a, $o, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	                 sk_R, sk_Xx21(sk_R)), X1), X0)
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	               sk_R, x), y), y)
5.43/5.66	       | sk_Xa1(sk_R) = c0
5.43/5.66	       | sk_Xb1(sk_R) = c0
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	               sk_R, sk_Xa1(sk_R)), 
5.43/5.66	             app_encode_app(a, a, 
5.43/5.66	               app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy11(sk_R)), 
5.43/5.66	               X1)), 
5.43/5.66	           app_encode_app(a, a, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz11(sk_R)), X0))),
5.43/5.66	    inference('sup-', [status(thm)], ['36', '38'])).
5.43/5.66	tff('40', plain,
5.43/5.66	    ![X0 : a, X1 : a]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             sk_Xa1(sk_R)), 
5.43/5.66	           app_encode_app(a, a, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy11(sk_R)), X1)), 
5.43/5.66	         app_encode_app(a, a, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz11(sk_R)), X0))
5.43/5.66	       | ~ app_encode_app(a, $o, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	                 sk_R, sk_Xx21(sk_R)), X1), X0)
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	               sk_R, x), y), y)
5.43/5.66	       | sk_Xa1(sk_R) = c0
5.43/5.66	       | sk_Xb1(sk_R) = c0),
5.43/5.66	    inference('simplify', [status(thm)], ['39'])).
5.43/5.66	tff('41', plain,
5.43/5.66	    (~ $true
5.43/5.66	     | sk_Xb1(sk_R) = c0
5.43/5.66	     | sk_Xa1(sk_R) = c0
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)
5.43/5.66	     | sk_Xb1(sk_R) = c0
5.43/5.66	     | sk_Xa1(sk_R) = c0
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             sk_Xa1(sk_R)), 
5.43/5.66	           app_encode_app(a, a, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy11(sk_R)), 
5.43/5.66	             sk_Xy21(sk_R))), 
5.43/5.66	         app_encode_app(a, a, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz11(sk_R)), 
5.43/5.66	           sk_Xz21(sk_R)))),
5.43/5.66	    inference('sup-', [status(thm)], ['35', '40'])).
5.43/5.66	tff('42', plain,
5.43/5.66	    (app_encode_app(a, $o, 
5.43/5.66	       app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	           sk_Xa1(sk_R)), 
5.43/5.66	         app_encode_app(a, a, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy11(sk_R)), 
5.43/5.66	           sk_Xy21(sk_R))), 
5.43/5.66	       app_encode_app(a, a, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz11(sk_R)), 
5.43/5.66	         sk_Xz21(sk_R)))
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)
5.43/5.66	     | sk_Xa1(sk_R) = c0
5.43/5.66	     | sk_Xb1(sk_R) = c0),
5.43/5.66	    inference('simplify', [status(thm)], ['41'])).
5.43/5.66	tff('43', plain,
5.43/5.66	    (app_encode_app(a, $o, 
5.43/5.66	       app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	           sk_Xa1(sk_R)), sk_Xb1(sk_R)), 
5.43/5.66	       app_encode_app(a, a, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz11(sk_R)), 
5.43/5.66	         sk_Xz21(sk_R)))
5.43/5.66	     | sk_Xb1(sk_R) = c0
5.43/5.66	     | sk_Xa1(sk_R) = c0
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)
5.43/5.66	     | sk_Xb1(sk_R) = c0
5.43/5.66	     | sk_Xa1(sk_R) = c0
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)),
5.43/5.66	    inference('sup+', [status(thm)], ['34', '42'])).
5.43/5.66	tff('44', plain,
5.43/5.66	    (app_encode_app(a, $o, 
5.43/5.66	       app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, x), 
5.43/5.66	         y), y)
5.43/5.66	     | sk_Xa1(sk_R) = c0
5.43/5.66	     | sk_Xb1(sk_R) = c0
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             sk_Xa1(sk_R)), sk_Xb1(sk_R)), 
5.43/5.66	         app_encode_app(a, a, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz11(sk_R)), 
5.43/5.66	           sk_Xz21(sk_R)))),
5.43/5.66	    inference('simplify', [status(thm)], ['43'])).
5.43/5.66	tff('45', plain,
5.43/5.66	    (app_encode_app(a, $o, 
5.43/5.66	       app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	           sk_Xa1(sk_R)), sk_Xb1(sk_R)), sk_Xc1(sk_R))
5.43/5.66	     | sk_Xb1(sk_R) = c0
5.43/5.66	     | sk_Xa1(sk_R) = c0
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)
5.43/5.66	     | sk_Xb1(sk_R) = c0
5.43/5.66	     | sk_Xa1(sk_R) = c0
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)),
5.43/5.66	    inference('sup+', [status(thm)], ['33', '44'])).
5.43/5.66	tff('46', plain,
5.43/5.66	    (app_encode_app(a, $o, 
5.43/5.66	       app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, x), 
5.43/5.66	         y), y)
5.43/5.66	     | sk_Xa1(sk_R) = c0
5.43/5.66	     | sk_Xb1(sk_R) = c0
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             sk_Xa1(sk_R)), sk_Xb1(sk_R)), sk_Xc1(sk_R))),
5.43/5.66	    inference('simplify', [status(thm)], ['45'])).
5.43/5.66	tff('47', plain,
5.43/5.66	    (sk_Xb1(sk_R) = c0
5.43/5.66	     | sk_Xa1(sk_R) = c0
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)),
5.43/5.66	    inference('clc', [status(thm)], ['46', '16'])).
5.43/5.66	tff('48', plain,
5.43/5.66	    (~ app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             sk_Xa1(sk_R)), c0), sk_Xc1(sk_R))
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)
5.43/5.66	     | sk_Xa1(sk_R) = c0
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)),
5.43/5.66	    inference('sup-', [status(thm)], ['47', '16'])).
5.43/5.66	tff('49', plain,
5.43/5.66	    (sk_Xa1(sk_R) = c0
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)
5.43/5.66	     | ~ app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	               sk_R, sk_Xa1(sk_R)), c0), sk_Xc1(sk_R))),
5.43/5.66	    inference('simplify', [status(thm)], ['48'])).
5.43/5.66	tff('50', plain,
5.43/5.66	    (~ app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             sk_Xa1(sk_R)), c0), sk_Xa1(sk_R))
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)
5.43/5.66	     | sk_Xa1(sk_R) = c0
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)
5.43/5.66	     | sk_Xa1(sk_R) = c0),
5.43/5.66	    inference('sup-', [status(thm)], ['32', '49'])).
5.43/5.66	tff('51', plain,
5.43/5.66	    ![X2 : a, X3 : a, X4 : a]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             X2), X3), X4)
5.43/5.66	       | X3 != c0
5.43/5.66	       | X2 != X4),
5.43/5.66	    inference('cnf', [status(esa)], [zf_stmt_0])).
5.43/5.66	tff('52', plain,
5.43/5.66	    ![X4 : a]:
5.43/5.66	      app_encode_app(a, $o, 
5.43/5.66	        app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	          app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	            X4), c0), X4),
5.43/5.66	    inference('simplify', [status(thm)], ['51'])).
5.43/5.66	tff('53', plain,
5.43/5.66	    (~ $true
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)
5.43/5.66	     | sk_Xa1(sk_R) = c0
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)
5.43/5.66	     | sk_Xa1(sk_R) = c0),
5.43/5.66	    inference('demod', [status(thm)], ['50', '52'])).
5.43/5.66	tff('54', plain,
5.43/5.66	    (sk_Xa1(sk_R) = c0
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)),
5.43/5.66	    inference('simplify', [status(thm)], ['53'])).
5.43/5.66	tff('55', plain,
5.43/5.66	    (~ app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             c0), sk_Xb1(sk_R)), sk_Xc1(sk_R))
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)),
5.43/5.66	    inference('sup-', [status(thm)], ['54', '16'])).
5.43/5.66	tff('56', plain,
5.43/5.66	    (app_encode_app(a, $o, 
5.43/5.66	       app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, x), 
5.43/5.66	         y), y)
5.43/5.66	     | ~ app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	               sk_R, c0), sk_Xb1(sk_R)), sk_Xc1(sk_R))),
5.43/5.66	    inference('simplify', [status(thm)], ['55'])).
5.43/5.66	tff('57', plain,
5.43/5.66	    (~ app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             c0), sk_Xb1(sk_R)), sk_Xb1(sk_R))
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)
5.43/5.66	     | sk_Xa1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)),
5.43/5.66	    inference('sup-', [status(thm)], ['17', '56'])).
5.43/5.66	tff('58', plain,
5.43/5.66	    ![X2 : a, X3 : a, X4 : a]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             X2), X3), X4)
5.43/5.66	       | X2 != c0
5.43/5.66	       | X3 != X4),
5.43/5.66	    inference('cnf', [status(esa)], [zf_stmt_0])).
5.43/5.66	tff('59', plain,
5.43/5.66	    ![X4 : a]:
5.43/5.66	      app_encode_app(a, $o, 
5.43/5.66	        app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	          app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	            c0), X4), X4),
5.43/5.66	    inference('simplify', [status(thm)], ['58'])).
5.43/5.66	tff('60', plain,
5.43/5.66	    (~ $true
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)
5.43/5.66	     | sk_Xa1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)),
5.43/5.66	    inference('demod', [status(thm)], ['57', '59'])).
5.43/5.66	tff('61', plain,
5.43/5.66	    (sk_Xa1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)),
5.43/5.66	    inference('simplify', [status(thm)], ['60'])).
5.43/5.66	tff('62', plain,
5.43/5.66	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, x), 
5.43/5.66	           y), y)
5.43/5.66	       | sk_Xb1(X0) = sk_Xc1(X0)
5.43/5.66	       | sk_Xb1(X0) = c0
5.43/5.66	       | sk_Xc1(X0)
5.43/5.66	          = app_encode_app(a, a, 
5.43/5.66	              app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz11(X0)), 
5.43/5.66	              sk_Xz21(X0))),
5.43/5.66	    inference('cnf', [status(esa)], [zf_stmt_0])).
5.43/5.66	tff('63', plain,
5.43/5.66	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, x), 
5.43/5.66	           y), y)
5.43/5.66	       | sk_Xb1(X0) = sk_Xc1(X0)
5.43/5.66	       | sk_Xb1(X0) = c0
5.43/5.66	       | sk_Xb1(X0)
5.43/5.66	          = app_encode_app(a, a, 
5.43/5.66	              app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy11(X0)), 
5.43/5.66	              sk_Xy21(X0))),
5.43/5.66	    inference('cnf', [status(esa)], [zf_stmt_0])).
5.43/5.66	tff('64', plain,
5.43/5.66	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, x), 
5.43/5.66	           y), y)
5.43/5.66	       | sk_Xb1(X0) = sk_Xc1(X0)
5.43/5.66	       | sk_Xb1(X0) = c0
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
5.43/5.66	               sk_Xx21(X0)), sk_Xy21(X0)), sk_Xz21(X0))),
5.43/5.66	    inference('cnf', [status(esa)], [zf_stmt_0])).
5.43/5.66	tff('65', plain,
5.43/5.66	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, x), 
5.43/5.66	           y), y)
5.43/5.66	       | sk_Xb1(X0) = sk_Xc1(X0)
5.43/5.66	       | sk_Xb1(X0) = c0
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
5.43/5.66	               sk_Xx11(X0)), sk_Xy11(X0)), sk_Xz11(X0))),
5.43/5.66	    inference('cnf', [status(esa)], [zf_stmt_0])).
5.43/5.66	tff('66', plain,
5.43/5.66	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, x), 
5.43/5.66	           y), y)
5.43/5.66	       | sk_Xb1(X0) = sk_Xc1(X0)
5.43/5.66	       | sk_Xb1(X0) = c0
5.43/5.66	       | sk_Xa1(X0)
5.43/5.66	          = app_encode_app(a, a, 
5.43/5.66	              app_encode_app(a, app_encode_fun(a, a), cP, sk_Xx11(X0)), 
5.43/5.66	              sk_Xx21(X0))),
5.43/5.66	    inference('cnf', [status(esa)], [zf_stmt_0])).
5.43/5.66	tff('67', plain,
5.43/5.66	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o))), 
5.43/5.66	      X1 : a, X2 : a, X3 : a, X4 : a]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             sk_Xa1(X0)), 
5.43/5.66	           app_encode_app(a, a, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, a), cP, X4), X3)), 
5.43/5.66	         app_encode_app(a, a, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, a), cP, X2), X1))
5.43/5.66	       | sk_Xb1(X0) = c0
5.43/5.66	       | sk_Xb1(X0) = sk_Xc1(X0)
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
5.43/5.66	               x), y), y)
5.43/5.66	       | ~ app_encode_app(a, $o, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	                 sk_R, sk_Xx11(X0)), X4), X2)
5.43/5.66	       | ~ app_encode_app(a, $o, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	                 sk_R, sk_Xx21(X0)), X3), X1)),
5.43/5.66	    inference('sup+', [status(thm)], ['66', '6'])).
5.43/5.66	tff('68', plain,
5.43/5.66	    ![X0 : a, X1 : a]:
5.43/5.66	      (~ $true
5.43/5.66	       | sk_Xb1(sk_R) = c0
5.43/5.66	       | sk_Xb1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	               sk_R, x), y), y)
5.43/5.66	       | ~ app_encode_app(a, $o, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	                 sk_R, sk_Xx21(sk_R)), X1), X0)
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	               sk_R, x), y), y)
5.43/5.66	       | sk_Xb1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	       | sk_Xb1(sk_R) = c0
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	               sk_R, sk_Xa1(sk_R)), 
5.43/5.66	             app_encode_app(a, a, 
5.43/5.66	               app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy11(sk_R)), 
5.43/5.66	               X1)), 
5.43/5.66	           app_encode_app(a, a, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz11(sk_R)), X0))),
5.43/5.66	    inference('sup-', [status(thm)], ['65', '67'])).
5.43/5.66	tff('69', plain,
5.43/5.66	    ![X0 : a, X1 : a]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             sk_Xa1(sk_R)), 
5.43/5.66	           app_encode_app(a, a, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy11(sk_R)), X1)), 
5.43/5.66	         app_encode_app(a, a, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz11(sk_R)), X0))
5.43/5.66	       | ~ app_encode_app(a, $o, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	                 sk_R, sk_Xx21(sk_R)), X1), X0)
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	               sk_R, x), y), y)
5.43/5.66	       | sk_Xb1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	       | sk_Xb1(sk_R) = c0),
5.43/5.66	    inference('simplify', [status(thm)], ['68'])).
5.43/5.66	tff('70', plain,
5.43/5.66	    (~ $true
5.43/5.66	     | sk_Xb1(sk_R) = c0
5.43/5.66	     | sk_Xb1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)
5.43/5.66	     | sk_Xb1(sk_R) = c0
5.43/5.66	     | sk_Xb1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             sk_Xa1(sk_R)), 
5.43/5.66	           app_encode_app(a, a, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy11(sk_R)), 
5.43/5.66	             sk_Xy21(sk_R))), 
5.43/5.66	         app_encode_app(a, a, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz11(sk_R)), 
5.43/5.66	           sk_Xz21(sk_R)))),
5.43/5.66	    inference('sup-', [status(thm)], ['64', '69'])).
5.43/5.66	tff('71', plain,
5.43/5.66	    (app_encode_app(a, $o, 
5.43/5.66	       app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	           sk_Xa1(sk_R)), 
5.43/5.66	         app_encode_app(a, a, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy11(sk_R)), 
5.43/5.66	           sk_Xy21(sk_R))), 
5.43/5.66	       app_encode_app(a, a, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz11(sk_R)), 
5.43/5.66	         sk_Xz21(sk_R)))
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)
5.43/5.66	     | sk_Xb1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	     | sk_Xb1(sk_R) = c0),
5.43/5.66	    inference('simplify', [status(thm)], ['70'])).
5.43/5.66	tff('72', plain,
5.43/5.66	    (app_encode_app(a, $o, 
5.43/5.66	       app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	           sk_Xa1(sk_R)), sk_Xb1(sk_R)), 
5.43/5.66	       app_encode_app(a, a, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz11(sk_R)), 
5.43/5.66	         sk_Xz21(sk_R)))
5.43/5.66	     | sk_Xb1(sk_R) = c0
5.43/5.66	     | sk_Xb1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)
5.43/5.66	     | sk_Xb1(sk_R) = c0
5.43/5.66	     | sk_Xb1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)),
5.43/5.66	    inference('sup+', [status(thm)], ['63', '71'])).
5.43/5.66	tff('73', plain,
5.43/5.66	    (app_encode_app(a, $o, 
5.43/5.66	       app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, x), 
5.43/5.66	         y), y)
5.43/5.66	     | sk_Xb1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	     | sk_Xb1(sk_R) = c0
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             sk_Xa1(sk_R)), sk_Xb1(sk_R)), 
5.43/5.66	         app_encode_app(a, a, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz11(sk_R)), 
5.43/5.66	           sk_Xz21(sk_R)))),
5.43/5.66	    inference('simplify', [status(thm)], ['72'])).
5.43/5.66	tff('74', plain,
5.43/5.66	    (app_encode_app(a, $o, 
5.43/5.66	       app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	           sk_Xa1(sk_R)), sk_Xb1(sk_R)), sk_Xc1(sk_R))
5.43/5.66	     | sk_Xb1(sk_R) = c0
5.43/5.66	     | sk_Xb1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)
5.43/5.66	     | sk_Xb1(sk_R) = c0
5.43/5.66	     | sk_Xb1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)),
5.43/5.66	    inference('sup+', [status(thm)], ['62', '73'])).
5.43/5.66	tff('75', plain,
5.43/5.66	    (app_encode_app(a, $o, 
5.43/5.66	       app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, x), 
5.43/5.66	         y), y)
5.43/5.66	     | sk_Xb1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	     | sk_Xb1(sk_R) = c0
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             sk_Xa1(sk_R)), sk_Xb1(sk_R)), sk_Xc1(sk_R))),
5.43/5.66	    inference('simplify', [status(thm)], ['74'])).
5.43/5.66	tff('76', plain,
5.43/5.66	    (sk_Xb1(sk_R) = c0
5.43/5.66	     | sk_Xb1(sk_R) = sk_Xc1(sk_R)
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)),
5.43/5.66	    inference('clc', [status(thm)], ['75', '16'])).
5.43/5.66	tff('77', plain,
5.43/5.66	    (~ app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             sk_Xa1(sk_R)), sk_Xb1(sk_R)), sk_Xb1(sk_R))
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)
5.43/5.66	     | sk_Xb1(sk_R) = c0
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)),
5.43/5.66	    inference('sup-', [status(thm)], ['76', '16'])).
5.43/5.66	tff('78', plain,
5.43/5.66	    (sk_Xb1(sk_R) = c0
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)
5.43/5.66	     | ~ app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	               sk_R, sk_Xa1(sk_R)), sk_Xb1(sk_R)), sk_Xb1(sk_R))),
5.43/5.66	    inference('simplify', [status(thm)], ['77'])).
5.43/5.66	tff('79', plain,
5.43/5.66	    (~ app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             c0), sk_Xb1(sk_R)), sk_Xb1(sk_R))
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)
5.43/5.66	     | sk_Xb1(sk_R) = c0),
5.43/5.66	    inference('sup-', [status(thm)], ['54', '78'])).
5.43/5.66	tff('80', plain,
5.43/5.66	    (~ $true
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)
5.43/5.66	     | sk_Xb1(sk_R) = c0),
5.43/5.66	    inference('demod', [status(thm)], ['79', '59'])).
5.43/5.66	tff('81', plain,
5.43/5.66	    (sk_Xb1(sk_R) = c0
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)),
5.43/5.66	    inference('simplify', [status(thm)], ['80'])).
5.43/5.66	tff('82', plain,
5.43/5.66	    (~ app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             sk_Xa1(sk_R)), c0), sk_Xc1(sk_R))
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)),
5.43/5.66	    inference('sup-', [status(thm)], ['81', '16'])).
5.43/5.66	tff('83', plain,
5.43/5.66	    (app_encode_app(a, $o, 
5.43/5.66	       app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, x), 
5.43/5.66	         y), y)
5.43/5.66	     | ~ app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	               sk_R, sk_Xa1(sk_R)), c0), sk_Xc1(sk_R))),
5.43/5.66	    inference('simplify', [status(thm)], ['82'])).
5.43/5.66	tff('84', plain,
5.43/5.66	    (~ app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             sk_Xa1(sk_R)), c0), sk_Xa1(sk_R))
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)),
5.43/5.66	    inference('sup-', [status(thm)], ['61', '83'])).
5.43/5.66	tff('85', plain,
5.43/5.66	    (~ $true
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             x), y), y)),
5.43/5.66	    inference('demod', [status(thm)], ['84', '52'])).
5.43/5.66	tff('86', plain,
5.43/5.66	    app_encode_app(a, $o, 
5.43/5.66	      app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	        app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, x), 
5.43/5.66	        y), y),
5.43/5.66	    inference('simplify', [status(thm)], ['85'])).
5.43/5.66	tff('87', plain,
5.43/5.66	    ~ app_encode_app(a, $o, 
5.43/5.66	        app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	          app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	            app_encode_app(a, a, 
5.43/5.66	              app_encode_app(a, app_encode_fun(a, a), cP, x), w)), 
5.43/5.66	          app_encode_app(a, a, 
5.43/5.66	            app_encode_app(a, app_encode_fun(a, a), cP, y), z)), 
5.43/5.66	        app_encode_app(a, a, app_encode_app(a, app_encode_fun(a, a), cP, y), 
5.43/5.66	          z)),
5.43/5.66	    inference('cnf', [status(esa)], [zf_stmt_0])).
5.43/5.66	tff('88', plain,
5.43/5.66	    (~ $true
5.43/5.66	     | ~ app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	               sk_R, x), y), y)
5.43/5.66	     | ~ app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	               sk_R, w), z), z)),
5.43/5.66	    inference('sup-', [status(thm)], ['6', '87'])).
5.43/5.66	tff('89', plain,
5.43/5.66	    (~ app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             w), z), z)
5.43/5.66	     | ~ app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	               sk_R, x), y), y)),
5.43/5.66	    inference('simplify', [status(thm)], ['88'])).
5.43/5.66	tff('90', plain,
5.43/5.66	    (~ $true
5.43/5.66	     | ~ app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	               sk_R, w), z), z)),
5.43/5.66	    inference('sup-', [status(thm)], ['86', '89'])).
5.43/5.66	tff('91', plain,
5.43/5.66	    ![X1 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X1, w), 
5.43/5.66	           z), z)
5.43/5.66	       | sk_Xb(X1) = sk_Xc(X1)
5.43/5.66	       | sk_Xa(X1) = sk_Xc(X1)
5.43/5.66	       | sk_Xc(X1)
5.43/5.66	          = app_encode_app(a, a, 
5.43/5.66	              app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz1(X1)), 
5.43/5.66	              sk_Xz2(X1))),
5.43/5.66	    inference('cnf', [status(esa)], [zf_stmt_0])).
5.43/5.66	tff('92', plain,
5.43/5.66	    ![X1 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X1, w), 
5.43/5.66	           z), z)
5.43/5.66	       | sk_Xb(X1) = sk_Xc(X1)
5.43/5.66	       | sk_Xa(X1) = sk_Xc(X1)
5.43/5.66	       | sk_Xb(X1)
5.43/5.66	          = app_encode_app(a, a, 
5.43/5.66	              app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy1(X1)), 
5.43/5.66	              sk_Xy2(X1))),
5.43/5.66	    inference('cnf', [status(esa)], [zf_stmt_0])).
5.43/5.66	tff('93', plain,
5.43/5.66	    ![X1 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X1, w), 
5.43/5.66	           z), z)
5.43/5.66	       | sk_Xb(X1) = sk_Xc(X1)
5.43/5.66	       | sk_Xa(X1) = sk_Xc(X1)
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X1, 
5.43/5.66	               sk_Xx2(X1)), sk_Xy2(X1)), sk_Xz2(X1))),
5.43/5.66	    inference('cnf', [status(esa)], [zf_stmt_0])).
5.43/5.66	tff('94', plain,
5.43/5.66	    ![X1 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X1, w), 
5.43/5.66	           z), z)
5.43/5.66	       | sk_Xb(X1) = sk_Xc(X1)
5.43/5.66	       | sk_Xa(X1) = sk_Xc(X1)
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X1, 
5.43/5.66	               sk_Xx1(X1)), sk_Xy1(X1)), sk_Xz1(X1))),
5.43/5.66	    inference('cnf', [status(esa)], [zf_stmt_0])).
5.43/5.66	tff('95', plain,
5.43/5.66	    ![X1 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X1, w), 
5.43/5.66	           z), z)
5.43/5.66	       | sk_Xb(X1) = sk_Xc(X1)
5.43/5.66	       | sk_Xa(X1) = sk_Xc(X1)
5.43/5.66	       | sk_Xa(X1)
5.43/5.66	          = app_encode_app(a, a, 
5.43/5.66	              app_encode_app(a, app_encode_fun(a, a), cP, sk_Xx1(X1)), 
5.43/5.66	              sk_Xx2(X1))),
5.43/5.66	    inference('cnf', [status(esa)], [zf_stmt_0])).
5.43/5.66	tff('96', plain,
5.43/5.66	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o))), 
5.43/5.66	      X1 : a, X2 : a, X3 : a, X4 : a]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             sk_Xa(X0)), 
5.43/5.66	           app_encode_app(a, a, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, a), cP, X4), X3)), 
5.43/5.66	         app_encode_app(a, a, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, a), cP, X2), X1))
5.43/5.66	       | sk_Xa(X0) = sk_Xc(X0)
5.43/5.66	       | sk_Xb(X0) = sk_Xc(X0)
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
5.43/5.66	               w), z), z)
5.43/5.66	       | ~ app_encode_app(a, $o, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	                 sk_R, sk_Xx1(X0)), X4), X2)
5.43/5.66	       | ~ app_encode_app(a, $o, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	                 sk_R, sk_Xx2(X0)), X3), X1)),
5.43/5.66	    inference('sup+', [status(thm)], ['95', '6'])).
5.43/5.66	tff('97', plain,
5.43/5.66	    ![X0 : a, X1 : a]:
5.43/5.66	      (~ $true
5.43/5.66	       | sk_Xa(sk_R) = sk_Xc(sk_R)
5.43/5.66	       | sk_Xb(sk_R) = sk_Xc(sk_R)
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	               sk_R, w), z), z)
5.43/5.66	       | ~ app_encode_app(a, $o, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	                 sk_R, sk_Xx2(sk_R)), X1), X0)
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	               sk_R, w), z), z)
5.43/5.66	       | sk_Xb(sk_R) = sk_Xc(sk_R)
5.43/5.66	       | sk_Xa(sk_R) = sk_Xc(sk_R)
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	               sk_R, sk_Xa(sk_R)), 
5.43/5.66	             app_encode_app(a, a, 
5.43/5.66	               app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy1(sk_R)), X1)), 
5.43/5.66	           app_encode_app(a, a, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz1(sk_R)), X0))),
5.43/5.66	    inference('sup-', [status(thm)], ['94', '96'])).
5.43/5.66	tff('98', plain,
5.43/5.66	    ![X0 : a, X1 : a]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             sk_Xa(sk_R)), 
5.43/5.66	           app_encode_app(a, a, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy1(sk_R)), X1)), 
5.43/5.66	         app_encode_app(a, a, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz1(sk_R)), X0))
5.43/5.66	       | ~ app_encode_app(a, $o, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	                 sk_R, sk_Xx2(sk_R)), X1), X0)
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	               sk_R, w), z), z)
5.43/5.66	       | sk_Xb(sk_R) = sk_Xc(sk_R)
5.43/5.66	       | sk_Xa(sk_R) = sk_Xc(sk_R)),
5.43/5.66	    inference('simplify', [status(thm)], ['97'])).
5.43/5.66	tff('99', plain,
5.43/5.66	    (~ $true
5.43/5.66	     | sk_Xa(sk_R) = sk_Xc(sk_R)
5.43/5.66	     | sk_Xb(sk_R) = sk_Xc(sk_R)
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             w), z), z)
5.43/5.66	     | sk_Xa(sk_R) = sk_Xc(sk_R)
5.43/5.66	     | sk_Xb(sk_R) = sk_Xc(sk_R)
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             w), z), z)
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             sk_Xa(sk_R)), 
5.43/5.66	           app_encode_app(a, a, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy1(sk_R)), 
5.43/5.66	             sk_Xy2(sk_R))), 
5.43/5.66	         app_encode_app(a, a, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz1(sk_R)), 
5.43/5.66	           sk_Xz2(sk_R)))),
5.43/5.66	    inference('sup-', [status(thm)], ['93', '98'])).
5.43/5.66	tff('100', plain,
5.43/5.66	    (app_encode_app(a, $o, 
5.43/5.66	       app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	           sk_Xa(sk_R)), 
5.43/5.66	         app_encode_app(a, a, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy1(sk_R)), 
5.43/5.66	           sk_Xy2(sk_R))), 
5.43/5.66	       app_encode_app(a, a, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz1(sk_R)), 
5.43/5.66	         sk_Xz2(sk_R)))
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             w), z), z)
5.43/5.66	     | sk_Xb(sk_R) = sk_Xc(sk_R)
5.43/5.66	     | sk_Xa(sk_R) = sk_Xc(sk_R)),
5.43/5.66	    inference('simplify', [status(thm)], ['99'])).
5.43/5.66	tff('101', plain,
5.43/5.66	    (app_encode_app(a, $o, 
5.43/5.66	       app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	           sk_Xa(sk_R)), sk_Xb(sk_R)), 
5.43/5.66	       app_encode_app(a, a, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz1(sk_R)), 
5.43/5.66	         sk_Xz2(sk_R)))
5.43/5.66	     | sk_Xa(sk_R) = sk_Xc(sk_R)
5.43/5.66	     | sk_Xb(sk_R) = sk_Xc(sk_R)
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             w), z), z)
5.43/5.66	     | sk_Xa(sk_R) = sk_Xc(sk_R)
5.43/5.66	     | sk_Xb(sk_R) = sk_Xc(sk_R)
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             w), z), z)),
5.43/5.66	    inference('sup+', [status(thm)], ['92', '100'])).
5.43/5.66	tff('102', plain,
5.43/5.66	    (app_encode_app(a, $o, 
5.43/5.66	       app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, w), 
5.43/5.66	         z), z)
5.43/5.66	     | sk_Xb(sk_R) = sk_Xc(sk_R)
5.43/5.66	     | sk_Xa(sk_R) = sk_Xc(sk_R)
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             sk_Xa(sk_R)), sk_Xb(sk_R)), 
5.43/5.66	         app_encode_app(a, a, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz1(sk_R)), 
5.43/5.66	           sk_Xz2(sk_R)))),
5.43/5.66	    inference('simplify', [status(thm)], ['101'])).
5.43/5.66	tff('103', plain,
5.43/5.66	    (app_encode_app(a, $o, 
5.43/5.66	       app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	           sk_Xa(sk_R)), sk_Xb(sk_R)), sk_Xc(sk_R))
5.43/5.66	     | sk_Xa(sk_R) = sk_Xc(sk_R)
5.43/5.66	     | sk_Xb(sk_R) = sk_Xc(sk_R)
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             w), z), z)
5.43/5.66	     | sk_Xa(sk_R) = sk_Xc(sk_R)
5.43/5.66	     | sk_Xb(sk_R) = sk_Xc(sk_R)
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             w), z), z)),
5.43/5.66	    inference('sup+', [status(thm)], ['91', '102'])).
5.43/5.66	tff('104', plain,
5.43/5.66	    (app_encode_app(a, $o, 
5.43/5.66	       app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, w), 
5.43/5.66	         z), z)
5.43/5.66	     | sk_Xb(sk_R) = sk_Xc(sk_R)
5.43/5.66	     | sk_Xa(sk_R) = sk_Xc(sk_R)
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             sk_Xa(sk_R)), sk_Xb(sk_R)), sk_Xc(sk_R))),
5.43/5.66	    inference('simplify', [status(thm)], ['103'])).
5.43/5.66	tff('105', plain,
5.43/5.66	    ![X1 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X1, w), 
5.43/5.66	           z), z)
5.43/5.66	       | ~ app_encode_app(a, $o, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	                 X1, sk_Xa(X1)), sk_Xb(X1)), sk_Xc(X1))),
5.43/5.66	    inference('cnf', [status(esa)], [zf_stmt_0])).
5.43/5.66	tff('106', plain,
5.43/5.66	    (sk_Xa(sk_R) = sk_Xc(sk_R)
5.43/5.66	     | sk_Xb(sk_R) = sk_Xc(sk_R)
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             w), z), z)),
5.43/5.66	    inference('clc', [status(thm)], ['104', '105'])).
5.43/5.66	tff('107', plain,
5.43/5.66	    ![X1 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X1, w), 
5.43/5.66	           z), z)
5.43/5.66	       | sk_Xa(X1) = c0
5.43/5.66	       | sk_Xa(X1) = sk_Xc(X1)
5.43/5.66	       | sk_Xc(X1)
5.43/5.66	          = app_encode_app(a, a, 
5.43/5.66	              app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz1(X1)), 
5.43/5.66	              sk_Xz2(X1))),
5.43/5.66	    inference('cnf', [status(esa)], [zf_stmt_0])).
5.43/5.66	tff('108', plain,
5.43/5.66	    ![X1 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X1, w), 
5.43/5.66	           z), z)
5.43/5.66	       | sk_Xa(X1) = c0
5.43/5.66	       | sk_Xa(X1) = sk_Xc(X1)
5.43/5.66	       | sk_Xb(X1)
5.43/5.66	          = app_encode_app(a, a, 
5.43/5.66	              app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy1(X1)), 
5.43/5.66	              sk_Xy2(X1))),
5.43/5.66	    inference('cnf', [status(esa)], [zf_stmt_0])).
5.43/5.66	tff('109', plain,
5.43/5.66	    ![X1 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X1, w), 
5.43/5.66	           z), z)
5.43/5.66	       | sk_Xa(X1) = c0
5.43/5.66	       | sk_Xa(X1) = sk_Xc(X1)
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X1, 
5.43/5.66	               sk_Xx2(X1)), sk_Xy2(X1)), sk_Xz2(X1))),
5.43/5.66	    inference('cnf', [status(esa)], [zf_stmt_0])).
5.43/5.66	tff('110', plain,
5.43/5.66	    ![X1 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X1, w), 
5.43/5.66	           z), z)
5.43/5.66	       | sk_Xa(X1) = c0
5.43/5.66	       | sk_Xa(X1) = sk_Xc(X1)
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X1, 
5.43/5.66	               sk_Xx1(X1)), sk_Xy1(X1)), sk_Xz1(X1))),
5.43/5.66	    inference('cnf', [status(esa)], [zf_stmt_0])).
5.43/5.66	tff('111', plain,
5.43/5.66	    ![X1 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X1, w), 
5.43/5.66	           z), z)
5.43/5.66	       | sk_Xa(X1) = c0
5.43/5.66	       | sk_Xa(X1) = sk_Xc(X1)
5.43/5.66	       | sk_Xa(X1)
5.43/5.66	          = app_encode_app(a, a, 
5.43/5.66	              app_encode_app(a, app_encode_fun(a, a), cP, sk_Xx1(X1)), 
5.43/5.66	              sk_Xx2(X1))),
5.43/5.66	    inference('cnf', [status(esa)], [zf_stmt_0])).
5.43/5.66	tff('112', plain,
5.43/5.66	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o))), 
5.43/5.66	      X1 : a, X2 : a, X3 : a, X4 : a]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             sk_Xa(X0)), 
5.43/5.66	           app_encode_app(a, a, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, a), cP, X4), X3)), 
5.43/5.66	         app_encode_app(a, a, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, a), cP, X2), X1))
5.43/5.66	       | sk_Xa(X0) = sk_Xc(X0)
5.43/5.66	       | sk_Xa(X0) = c0
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
5.43/5.66	               w), z), z)
5.43/5.66	       | ~ app_encode_app(a, $o, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	                 sk_R, sk_Xx1(X0)), X4), X2)
5.43/5.66	       | ~ app_encode_app(a, $o, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	                 sk_R, sk_Xx2(X0)), X3), X1)),
5.43/5.66	    inference('sup+', [status(thm)], ['111', '6'])).
5.43/5.66	tff('113', plain,
5.43/5.66	    ![X0 : a, X1 : a]:
5.43/5.66	      (~ $true
5.43/5.66	       | sk_Xa(sk_R) = sk_Xc(sk_R)
5.43/5.66	       | sk_Xa(sk_R) = c0
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	               sk_R, w), z), z)
5.43/5.66	       | ~ app_encode_app(a, $o, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	                 sk_R, sk_Xx2(sk_R)), X1), X0)
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	               sk_R, w), z), z)
5.43/5.66	       | sk_Xa(sk_R) = c0
5.43/5.66	       | sk_Xa(sk_R) = sk_Xc(sk_R)
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	               sk_R, sk_Xa(sk_R)), 
5.43/5.66	             app_encode_app(a, a, 
5.43/5.66	               app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy1(sk_R)), X1)), 
5.43/5.66	           app_encode_app(a, a, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz1(sk_R)), X0))),
5.43/5.66	    inference('sup-', [status(thm)], ['110', '112'])).
5.43/5.66	tff('114', plain,
5.43/5.66	    ![X0 : a, X1 : a]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             sk_Xa(sk_R)), 
5.43/5.66	           app_encode_app(a, a, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy1(sk_R)), X1)), 
5.43/5.66	         app_encode_app(a, a, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz1(sk_R)), X0))
5.43/5.66	       | ~ app_encode_app(a, $o, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	                 sk_R, sk_Xx2(sk_R)), X1), X0)
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	               sk_R, w), z), z)
5.43/5.66	       | sk_Xa(sk_R) = c0
5.43/5.66	       | sk_Xa(sk_R) = sk_Xc(sk_R)),
5.43/5.66	    inference('simplify', [status(thm)], ['113'])).
5.43/5.66	tff('115', plain,
5.43/5.66	    (~ $true
5.43/5.66	     | sk_Xa(sk_R) = sk_Xc(sk_R)
5.43/5.66	     | sk_Xa(sk_R) = c0
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             w), z), z)
5.43/5.66	     | sk_Xa(sk_R) = sk_Xc(sk_R)
5.43/5.66	     | sk_Xa(sk_R) = c0
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             w), z), z)
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             sk_Xa(sk_R)), 
5.43/5.66	           app_encode_app(a, a, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy1(sk_R)), 
5.43/5.66	             sk_Xy2(sk_R))), 
5.43/5.66	         app_encode_app(a, a, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz1(sk_R)), 
5.43/5.66	           sk_Xz2(sk_R)))),
5.43/5.66	    inference('sup-', [status(thm)], ['109', '114'])).
5.43/5.66	tff('116', plain,
5.43/5.66	    (app_encode_app(a, $o, 
5.43/5.66	       app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	           sk_Xa(sk_R)), 
5.43/5.66	         app_encode_app(a, a, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy1(sk_R)), 
5.43/5.66	           sk_Xy2(sk_R))), 
5.43/5.66	       app_encode_app(a, a, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz1(sk_R)), 
5.43/5.66	         sk_Xz2(sk_R)))
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             w), z), z)
5.43/5.66	     | sk_Xa(sk_R) = c0
5.43/5.66	     | sk_Xa(sk_R) = sk_Xc(sk_R)),
5.43/5.66	    inference('simplify', [status(thm)], ['115'])).
5.43/5.66	tff('117', plain,
5.43/5.66	    (app_encode_app(a, $o, 
5.43/5.66	       app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	           sk_Xa(sk_R)), sk_Xb(sk_R)), 
5.43/5.66	       app_encode_app(a, a, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz1(sk_R)), 
5.43/5.66	         sk_Xz2(sk_R)))
5.43/5.66	     | sk_Xa(sk_R) = sk_Xc(sk_R)
5.43/5.66	     | sk_Xa(sk_R) = c0
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             w), z), z)
5.43/5.66	     | sk_Xa(sk_R) = sk_Xc(sk_R)
5.43/5.66	     | sk_Xa(sk_R) = c0
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             w), z), z)),
5.43/5.66	    inference('sup+', [status(thm)], ['108', '116'])).
5.43/5.66	tff('118', plain,
5.43/5.66	    (app_encode_app(a, $o, 
5.43/5.66	       app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, w), 
5.43/5.66	         z), z)
5.43/5.66	     | sk_Xa(sk_R) = c0
5.43/5.66	     | sk_Xa(sk_R) = sk_Xc(sk_R)
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             sk_Xa(sk_R)), sk_Xb(sk_R)), 
5.43/5.66	         app_encode_app(a, a, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz1(sk_R)), 
5.43/5.66	           sk_Xz2(sk_R)))),
5.43/5.66	    inference('simplify', [status(thm)], ['117'])).
5.43/5.66	tff('119', plain,
5.43/5.66	    (app_encode_app(a, $o, 
5.43/5.66	       app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	           sk_Xa(sk_R)), sk_Xb(sk_R)), sk_Xc(sk_R))
5.43/5.66	     | sk_Xa(sk_R) = sk_Xc(sk_R)
5.43/5.66	     | sk_Xa(sk_R) = c0
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             w), z), z)
5.43/5.66	     | sk_Xa(sk_R) = sk_Xc(sk_R)
5.43/5.66	     | sk_Xa(sk_R) = c0
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             w), z), z)),
5.43/5.66	    inference('sup+', [status(thm)], ['107', '118'])).
5.43/5.66	tff('120', plain,
5.43/5.66	    (app_encode_app(a, $o, 
5.43/5.66	       app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, w), 
5.43/5.66	         z), z)
5.43/5.66	     | sk_Xa(sk_R) = c0
5.43/5.66	     | sk_Xa(sk_R) = sk_Xc(sk_R)
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             sk_Xa(sk_R)), sk_Xb(sk_R)), sk_Xc(sk_R))),
5.43/5.66	    inference('simplify', [status(thm)], ['119'])).
5.43/5.66	tff('121', plain,
5.43/5.66	    (sk_Xa(sk_R) = sk_Xc(sk_R)
5.43/5.66	     | sk_Xa(sk_R) = c0
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             w), z), z)),
5.43/5.66	    inference('clc', [status(thm)], ['120', '105'])).
5.43/5.66	tff('122', plain,
5.43/5.66	    ![X1 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X1, w), 
5.43/5.66	           z), z)
5.43/5.66	       | sk_Xa(X1) = c0
5.43/5.66	       | sk_Xb(X1) = c0
5.43/5.66	       | sk_Xc(X1)
5.43/5.66	          = app_encode_app(a, a, 
5.43/5.66	              app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz1(X1)), 
5.43/5.66	              sk_Xz2(X1))),
5.43/5.66	    inference('cnf', [status(esa)], [zf_stmt_0])).
5.43/5.66	tff('123', plain,
5.43/5.66	    ![X1 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X1, w), 
5.43/5.66	           z), z)
5.43/5.66	       | sk_Xa(X1) = c0
5.43/5.66	       | sk_Xb(X1) = c0
5.43/5.66	       | sk_Xb(X1)
5.43/5.66	          = app_encode_app(a, a, 
5.43/5.66	              app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy1(X1)), 
5.43/5.66	              sk_Xy2(X1))),
5.43/5.66	    inference('cnf', [status(esa)], [zf_stmt_0])).
5.43/5.66	tff('124', plain,
5.43/5.66	    ![X1 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X1, w), 
5.43/5.66	           z), z)
5.43/5.66	       | sk_Xa(X1) = c0
5.43/5.66	       | sk_Xb(X1) = c0
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X1, 
5.43/5.66	               sk_Xx2(X1)), sk_Xy2(X1)), sk_Xz2(X1))),
5.43/5.66	    inference('cnf', [status(esa)], [zf_stmt_0])).
5.43/5.66	tff('125', plain,
5.43/5.66	    ![X1 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X1, w), 
5.43/5.66	           z), z)
5.43/5.66	       | sk_Xa(X1) = c0
5.43/5.66	       | sk_Xb(X1) = c0
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X1, 
5.43/5.66	               sk_Xx1(X1)), sk_Xy1(X1)), sk_Xz1(X1))),
5.43/5.66	    inference('cnf', [status(esa)], [zf_stmt_0])).
5.43/5.66	tff('126', plain,
5.43/5.66	    ![X1 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X1, w), 
5.43/5.66	           z), z)
5.43/5.66	       | sk_Xa(X1) = c0
5.43/5.66	       | sk_Xb(X1) = c0
5.43/5.66	       | sk_Xa(X1)
5.43/5.66	          = app_encode_app(a, a, 
5.43/5.66	              app_encode_app(a, app_encode_fun(a, a), cP, sk_Xx1(X1)), 
5.43/5.66	              sk_Xx2(X1))),
5.43/5.66	    inference('cnf', [status(esa)], [zf_stmt_0])).
5.43/5.66	tff('127', plain,
5.43/5.66	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o))), 
5.43/5.66	      X1 : a, X2 : a, X3 : a, X4 : a]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             sk_Xa(X0)), 
5.43/5.66	           app_encode_app(a, a, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, a), cP, X4), X3)), 
5.43/5.66	         app_encode_app(a, a, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, a), cP, X2), X1))
5.43/5.66	       | sk_Xb(X0) = c0
5.43/5.66	       | sk_Xa(X0) = c0
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
5.43/5.66	               w), z), z)
5.43/5.66	       | ~ app_encode_app(a, $o, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	                 sk_R, sk_Xx1(X0)), X4), X2)
5.43/5.66	       | ~ app_encode_app(a, $o, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	                 sk_R, sk_Xx2(X0)), X3), X1)),
5.43/5.66	    inference('sup+', [status(thm)], ['126', '6'])).
5.43/5.66	tff('128', plain,
5.43/5.66	    ![X0 : a, X1 : a]:
5.43/5.66	      (~ $true
5.43/5.66	       | sk_Xb(sk_R) = c0
5.43/5.66	       | sk_Xa(sk_R) = c0
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	               sk_R, w), z), z)
5.43/5.66	       | ~ app_encode_app(a, $o, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	                 sk_R, sk_Xx2(sk_R)), X1), X0)
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	               sk_R, w), z), z)
5.43/5.66	       | sk_Xa(sk_R) = c0
5.43/5.66	       | sk_Xb(sk_R) = c0
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	               sk_R, sk_Xa(sk_R)), 
5.43/5.66	             app_encode_app(a, a, 
5.43/5.66	               app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy1(sk_R)), X1)), 
5.43/5.66	           app_encode_app(a, a, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz1(sk_R)), X0))),
5.43/5.66	    inference('sup-', [status(thm)], ['125', '127'])).
5.43/5.66	tff('129', plain,
5.43/5.66	    ![X0 : a, X1 : a]:
5.43/5.66	      (app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             sk_Xa(sk_R)), 
5.43/5.66	           app_encode_app(a, a, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy1(sk_R)), X1)), 
5.43/5.66	         app_encode_app(a, a, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz1(sk_R)), X0))
5.43/5.66	       | ~ app_encode_app(a, $o, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	                 sk_R, sk_Xx2(sk_R)), X1), X0)
5.43/5.66	       | app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	               sk_R, w), z), z)
5.43/5.66	       | sk_Xa(sk_R) = c0
5.43/5.66	       | sk_Xb(sk_R) = c0),
5.43/5.66	    inference('simplify', [status(thm)], ['128'])).
5.43/5.66	tff('130', plain,
5.43/5.66	    (~ $true
5.43/5.66	     | sk_Xb(sk_R) = c0
5.43/5.66	     | sk_Xa(sk_R) = c0
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             w), z), z)
5.43/5.66	     | sk_Xb(sk_R) = c0
5.43/5.66	     | sk_Xa(sk_R) = c0
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             w), z), z)
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             sk_Xa(sk_R)), 
5.43/5.66	           app_encode_app(a, a, 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy1(sk_R)), 
5.43/5.66	             sk_Xy2(sk_R))), 
5.43/5.66	         app_encode_app(a, a, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz1(sk_R)), 
5.43/5.66	           sk_Xz2(sk_R)))),
5.43/5.66	    inference('sup-', [status(thm)], ['124', '129'])).
5.43/5.66	tff('131', plain,
5.43/5.66	    (app_encode_app(a, $o, 
5.43/5.66	       app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	           sk_Xa(sk_R)), 
5.43/5.66	         app_encode_app(a, a, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy1(sk_R)), 
5.43/5.66	           sk_Xy2(sk_R))), 
5.43/5.66	       app_encode_app(a, a, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz1(sk_R)), 
5.43/5.66	         sk_Xz2(sk_R)))
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             w), z), z)
5.43/5.66	     | sk_Xa(sk_R) = c0
5.43/5.66	     | sk_Xb(sk_R) = c0),
5.43/5.66	    inference('simplify', [status(thm)], ['130'])).
5.43/5.66	tff('132', plain,
5.43/5.66	    (app_encode_app(a, $o, 
5.43/5.66	       app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	           sk_Xa(sk_R)), sk_Xb(sk_R)), 
5.43/5.66	       app_encode_app(a, a, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz1(sk_R)), 
5.43/5.66	         sk_Xz2(sk_R)))
5.43/5.66	     | sk_Xb(sk_R) = c0
5.43/5.66	     | sk_Xa(sk_R) = c0
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             w), z), z)
5.43/5.66	     | sk_Xb(sk_R) = c0
5.43/5.66	     | sk_Xa(sk_R) = c0
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             w), z), z)),
5.43/5.66	    inference('sup+', [status(thm)], ['123', '131'])).
5.43/5.66	tff('133', plain,
5.43/5.66	    (app_encode_app(a, $o, 
5.43/5.66	       app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, w), 
5.43/5.66	         z), z)
5.43/5.66	     | sk_Xa(sk_R) = c0
5.43/5.66	     | sk_Xb(sk_R) = c0
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             sk_Xa(sk_R)), sk_Xb(sk_R)), 
5.43/5.66	         app_encode_app(a, a, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz1(sk_R)), 
5.43/5.66	           sk_Xz2(sk_R)))),
5.43/5.66	    inference('simplify', [status(thm)], ['132'])).
5.43/5.66	tff('134', plain,
5.43/5.66	    (app_encode_app(a, $o, 
5.43/5.66	       app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	           sk_Xa(sk_R)), sk_Xb(sk_R)), sk_Xc(sk_R))
5.43/5.66	     | sk_Xb(sk_R) = c0
5.43/5.66	     | sk_Xa(sk_R) = c0
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             w), z), z)
5.43/5.66	     | sk_Xb(sk_R) = c0
5.43/5.66	     | sk_Xa(sk_R) = c0
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             w), z), z)),
5.43/5.66	    inference('sup+', [status(thm)], ['122', '133'])).
5.43/5.66	tff('135', plain,
5.43/5.66	    (app_encode_app(a, $o, 
5.43/5.66	       app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, w), 
5.43/5.66	         z), z)
5.43/5.66	     | sk_Xa(sk_R) = c0
5.43/5.66	     | sk_Xb(sk_R) = c0
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             sk_Xa(sk_R)), sk_Xb(sk_R)), sk_Xc(sk_R))),
5.43/5.66	    inference('simplify', [status(thm)], ['134'])).
5.43/5.66	tff('136', plain,
5.43/5.66	    (sk_Xb(sk_R) = c0
5.43/5.66	     | sk_Xa(sk_R) = c0
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             w), z), z)),
5.43/5.66	    inference('clc', [status(thm)], ['135', '105'])).
5.43/5.66	tff('137', plain,
5.43/5.66	    (~ app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             sk_Xa(sk_R)), c0), sk_Xc(sk_R))
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             w), z), z)
5.43/5.66	     | sk_Xa(sk_R) = c0
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             w), z), z)),
5.43/5.66	    inference('sup-', [status(thm)], ['136', '105'])).
5.43/5.66	tff('138', plain,
5.43/5.66	    (sk_Xa(sk_R) = c0
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             w), z), z)
5.43/5.66	     | ~ app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	               sk_R, sk_Xa(sk_R)), c0), sk_Xc(sk_R))),
5.43/5.66	    inference('simplify', [status(thm)], ['137'])).
5.43/5.66	tff('139', plain,
5.43/5.66	    (~ app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             sk_Xa(sk_R)), c0), sk_Xa(sk_R))
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             w), z), z)
5.43/5.66	     | sk_Xa(sk_R) = c0
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             w), z), z)
5.43/5.66	     | sk_Xa(sk_R) = c0),
5.43/5.66	    inference('sup-', [status(thm)], ['121', '138'])).
5.43/5.66	tff('140', plain,
5.43/5.66	    (~ $true
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             w), z), z)
5.43/5.66	     | sk_Xa(sk_R) = c0
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             w), z), z)
5.43/5.66	     | sk_Xa(sk_R) = c0),
5.43/5.66	    inference('demod', [status(thm)], ['139', '52'])).
5.43/5.66	tff('141', plain,
5.43/5.66	    (sk_Xa(sk_R) = c0
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             w), z), z)),
5.43/5.66	    inference('simplify', [status(thm)], ['140'])).
5.43/5.66	tff('142', plain,
5.43/5.66	    (~ app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             c0), sk_Xb(sk_R)), sk_Xc(sk_R))
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             w), z), z)
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             w), z), z)),
5.43/5.66	    inference('sup-', [status(thm)], ['141', '105'])).
5.43/5.66	tff('143', plain,
5.43/5.66	    (app_encode_app(a, $o, 
5.43/5.66	       app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, w), 
5.43/5.66	         z), z)
5.43/5.66	     | ~ app_encode_app(a, $o, 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.66	               sk_R, c0), sk_Xb(sk_R)), sk_Xc(sk_R))),
5.43/5.66	    inference('simplify', [status(thm)], ['142'])).
5.43/5.66	tff('144', plain,
5.43/5.66	    (~ app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.66	             c0), sk_Xb(sk_R)), sk_Xb(sk_R))
5.43/5.66	     | app_encode_app(a, $o, 
5.43/5.66	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.66	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.67	             w), z), z)
5.43/5.67	     | sk_Xa(sk_R) = sk_Xc(sk_R)
5.43/5.67	     | app_encode_app(a, $o, 
5.43/5.67	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.67	             w), z), z)),
5.43/5.67	    inference('sup-', [status(thm)], ['106', '143'])).
5.43/5.67	tff('145', plain,
5.43/5.67	    (~ $true
5.43/5.67	     | app_encode_app(a, $o, 
5.43/5.67	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.67	             w), z), z)
5.43/5.67	     | sk_Xa(sk_R) = sk_Xc(sk_R)
5.43/5.67	     | app_encode_app(a, $o, 
5.43/5.67	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.67	             w), z), z)),
5.43/5.67	    inference('demod', [status(thm)], ['144', '59'])).
5.43/5.67	tff('146', plain,
5.43/5.67	    (sk_Xa(sk_R) = sk_Xc(sk_R)
5.43/5.67	     | app_encode_app(a, $o, 
5.43/5.67	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.67	             w), z), z)),
5.43/5.67	    inference('simplify', [status(thm)], ['145'])).
5.43/5.67	tff('147', plain,
5.43/5.67	    ![X1 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
5.43/5.67	      (app_encode_app(a, $o, 
5.43/5.67	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X1, w), 
5.43/5.67	           z), z)
5.43/5.67	       | sk_Xb(X1) = sk_Xc(X1)
5.43/5.67	       | sk_Xb(X1) = c0
5.43/5.67	       | sk_Xc(X1)
5.43/5.67	          = app_encode_app(a, a, 
5.43/5.67	              app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz1(X1)), 
5.43/5.67	              sk_Xz2(X1))),
5.43/5.67	    inference('cnf', [status(esa)], [zf_stmt_0])).
5.43/5.67	tff('148', plain,
5.43/5.67	    ![X1 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
5.43/5.67	      (app_encode_app(a, $o, 
5.43/5.67	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X1, w), 
5.43/5.67	           z), z)
5.43/5.67	       | sk_Xb(X1) = sk_Xc(X1)
5.43/5.67	       | sk_Xb(X1) = c0
5.43/5.67	       | sk_Xb(X1)
5.43/5.67	          = app_encode_app(a, a, 
5.43/5.67	              app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy1(X1)), 
5.43/5.67	              sk_Xy2(X1))),
5.43/5.67	    inference('cnf', [status(esa)], [zf_stmt_0])).
5.43/5.67	tff('149', plain,
5.43/5.67	    ![X1 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
5.43/5.67	      (app_encode_app(a, $o, 
5.43/5.67	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X1, w), 
5.43/5.67	           z), z)
5.43/5.67	       | sk_Xb(X1) = sk_Xc(X1)
5.43/5.67	       | sk_Xb(X1) = c0
5.43/5.67	       | app_encode_app(a, $o, 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X1, 
5.43/5.67	               sk_Xx2(X1)), sk_Xy2(X1)), sk_Xz2(X1))),
5.43/5.67	    inference('cnf', [status(esa)], [zf_stmt_0])).
5.43/5.67	tff('150', plain,
5.43/5.67	    ![X1 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
5.43/5.67	      (app_encode_app(a, $o, 
5.43/5.67	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X1, w), 
5.43/5.67	           z), z)
5.43/5.67	       | sk_Xb(X1) = sk_Xc(X1)
5.43/5.67	       | sk_Xb(X1) = c0
5.43/5.67	       | app_encode_app(a, $o, 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X1, 
5.43/5.67	               sk_Xx1(X1)), sk_Xy1(X1)), sk_Xz1(X1))),
5.43/5.67	    inference('cnf', [status(esa)], [zf_stmt_0])).
5.43/5.67	tff('151', plain,
5.43/5.67	    ![X1 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
5.43/5.67	      (app_encode_app(a, $o, 
5.43/5.67	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X1, w), 
5.43/5.67	           z), z)
5.43/5.67	       | sk_Xb(X1) = sk_Xc(X1)
5.43/5.67	       | sk_Xb(X1) = c0
5.43/5.67	       | sk_Xa(X1)
5.43/5.67	          = app_encode_app(a, a, 
5.43/5.67	              app_encode_app(a, app_encode_fun(a, a), cP, sk_Xx1(X1)), 
5.43/5.67	              sk_Xx2(X1))),
5.43/5.67	    inference('cnf', [status(esa)], [zf_stmt_0])).
5.43/5.67	tff('152', plain,
5.43/5.67	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o))), 
5.43/5.67	      X1 : a, X2 : a, X3 : a, X4 : a]:
5.43/5.67	      (app_encode_app(a, $o, 
5.43/5.67	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.67	             sk_Xa(X0)), 
5.43/5.67	           app_encode_app(a, a, 
5.43/5.67	             app_encode_app(a, app_encode_fun(a, a), cP, X4), X3)), 
5.43/5.67	         app_encode_app(a, a, 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, a), cP, X2), X1))
5.43/5.67	       | sk_Xb(X0) = c0
5.43/5.67	       | sk_Xb(X0) = sk_Xc(X0)
5.43/5.67	       | app_encode_app(a, $o, 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
5.43/5.67	               w), z), z)
5.43/5.67	       | ~ app_encode_app(a, $o, 
5.43/5.67	             app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.67	                 sk_R, sk_Xx1(X0)), X4), X2)
5.43/5.67	       | ~ app_encode_app(a, $o, 
5.43/5.67	             app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.67	                 sk_R, sk_Xx2(X0)), X3), X1)),
5.43/5.67	    inference('sup+', [status(thm)], ['151', '6'])).
5.43/5.67	tff('153', plain,
5.43/5.67	    ![X0 : a, X1 : a]:
5.43/5.67	      (~ $true
5.43/5.67	       | sk_Xb(sk_R) = c0
5.43/5.67	       | sk_Xb(sk_R) = sk_Xc(sk_R)
5.43/5.67	       | app_encode_app(a, $o, 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.67	               sk_R, w), z), z)
5.43/5.67	       | ~ app_encode_app(a, $o, 
5.43/5.67	             app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.67	                 sk_R, sk_Xx2(sk_R)), X1), X0)
5.43/5.67	       | app_encode_app(a, $o, 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.67	               sk_R, w), z), z)
5.43/5.67	       | sk_Xb(sk_R) = sk_Xc(sk_R)
5.43/5.67	       | sk_Xb(sk_R) = c0
5.43/5.67	       | app_encode_app(a, $o, 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.67	               sk_R, sk_Xa(sk_R)), 
5.43/5.67	             app_encode_app(a, a, 
5.43/5.67	               app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy1(sk_R)), X1)), 
5.43/5.67	           app_encode_app(a, a, 
5.43/5.67	             app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz1(sk_R)), X0))),
5.43/5.67	    inference('sup-', [status(thm)], ['150', '152'])).
5.43/5.67	tff('154', plain,
5.43/5.67	    ![X0 : a, X1 : a]:
5.43/5.67	      (app_encode_app(a, $o, 
5.43/5.67	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.67	             sk_Xa(sk_R)), 
5.43/5.67	           app_encode_app(a, a, 
5.43/5.67	             app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy1(sk_R)), X1)), 
5.43/5.67	         app_encode_app(a, a, 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz1(sk_R)), X0))
5.43/5.67	       | ~ app_encode_app(a, $o, 
5.43/5.67	             app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.67	                 sk_R, sk_Xx2(sk_R)), X1), X0)
5.43/5.67	       | app_encode_app(a, $o, 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.67	               sk_R, w), z), z)
5.43/5.67	       | sk_Xb(sk_R) = sk_Xc(sk_R)
5.43/5.67	       | sk_Xb(sk_R) = c0),
5.43/5.67	    inference('simplify', [status(thm)], ['153'])).
5.43/5.67	tff('155', plain,
5.43/5.67	    (~ $true
5.43/5.67	     | sk_Xb(sk_R) = c0
5.43/5.67	     | sk_Xb(sk_R) = sk_Xc(sk_R)
5.43/5.67	     | app_encode_app(a, $o, 
5.43/5.67	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.67	             w), z), z)
5.43/5.67	     | sk_Xb(sk_R) = c0
5.43/5.67	     | sk_Xb(sk_R) = sk_Xc(sk_R)
5.43/5.67	     | app_encode_app(a, $o, 
5.43/5.67	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.67	             w), z), z)
5.43/5.67	     | app_encode_app(a, $o, 
5.43/5.67	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.67	             sk_Xa(sk_R)), 
5.43/5.67	           app_encode_app(a, a, 
5.43/5.67	             app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy1(sk_R)), 
5.43/5.67	             sk_Xy2(sk_R))), 
5.43/5.67	         app_encode_app(a, a, 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz1(sk_R)), 
5.43/5.67	           sk_Xz2(sk_R)))),
5.43/5.67	    inference('sup-', [status(thm)], ['149', '154'])).
5.43/5.67	tff('156', plain,
5.43/5.67	    (app_encode_app(a, $o, 
5.43/5.67	       app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.67	           sk_Xa(sk_R)), 
5.43/5.67	         app_encode_app(a, a, 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy1(sk_R)), 
5.43/5.67	           sk_Xy2(sk_R))), 
5.43/5.67	       app_encode_app(a, a, 
5.43/5.67	         app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz1(sk_R)), 
5.43/5.67	         sk_Xz2(sk_R)))
5.43/5.67	     | app_encode_app(a, $o, 
5.43/5.67	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.67	             w), z), z)
5.43/5.67	     | sk_Xb(sk_R) = sk_Xc(sk_R)
5.43/5.67	     | sk_Xb(sk_R) = c0),
5.43/5.67	    inference('simplify', [status(thm)], ['155'])).
5.43/5.67	tff('157', plain,
5.43/5.67	    (app_encode_app(a, $o, 
5.43/5.67	       app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.67	           sk_Xa(sk_R)), sk_Xb(sk_R)), 
5.43/5.67	       app_encode_app(a, a, 
5.43/5.67	         app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz1(sk_R)), 
5.43/5.67	         sk_Xz2(sk_R)))
5.43/5.67	     | sk_Xb(sk_R) = c0
5.43/5.67	     | sk_Xb(sk_R) = sk_Xc(sk_R)
5.43/5.67	     | app_encode_app(a, $o, 
5.43/5.67	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.67	             w), z), z)
5.43/5.67	     | sk_Xb(sk_R) = c0
5.43/5.67	     | sk_Xb(sk_R) = sk_Xc(sk_R)
5.43/5.67	     | app_encode_app(a, $o, 
5.43/5.67	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.67	             w), z), z)),
5.43/5.67	    inference('sup+', [status(thm)], ['148', '156'])).
5.43/5.67	tff('158', plain,
5.43/5.67	    (app_encode_app(a, $o, 
5.43/5.67	       app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, w), 
5.43/5.67	         z), z)
5.43/5.67	     | sk_Xb(sk_R) = sk_Xc(sk_R)
5.43/5.67	     | sk_Xb(sk_R) = c0
5.43/5.67	     | app_encode_app(a, $o, 
5.43/5.67	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.67	             sk_Xa(sk_R)), sk_Xb(sk_R)), 
5.43/5.67	         app_encode_app(a, a, 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz1(sk_R)), 
5.43/5.67	           sk_Xz2(sk_R)))),
5.43/5.67	    inference('simplify', [status(thm)], ['157'])).
5.43/5.67	tff('159', plain,
5.43/5.67	    (app_encode_app(a, $o, 
5.43/5.67	       app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.67	           sk_Xa(sk_R)), sk_Xb(sk_R)), sk_Xc(sk_R))
5.43/5.67	     | sk_Xb(sk_R) = c0
5.43/5.67	     | sk_Xb(sk_R) = sk_Xc(sk_R)
5.43/5.67	     | app_encode_app(a, $o, 
5.43/5.67	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.67	             w), z), z)
5.43/5.67	     | sk_Xb(sk_R) = c0
5.43/5.67	     | sk_Xb(sk_R) = sk_Xc(sk_R)
5.43/5.67	     | app_encode_app(a, $o, 
5.43/5.67	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.67	             w), z), z)),
5.43/5.67	    inference('sup+', [status(thm)], ['147', '158'])).
5.43/5.67	tff('160', plain,
5.43/5.67	    (app_encode_app(a, $o, 
5.43/5.67	       app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, w), 
5.43/5.67	         z), z)
5.43/5.67	     | sk_Xb(sk_R) = sk_Xc(sk_R)
5.43/5.67	     | sk_Xb(sk_R) = c0
5.43/5.67	     | app_encode_app(a, $o, 
5.43/5.67	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.67	             sk_Xa(sk_R)), sk_Xb(sk_R)), sk_Xc(sk_R))),
5.43/5.67	    inference('simplify', [status(thm)], ['159'])).
5.43/5.67	tff('161', plain,
5.43/5.67	    (sk_Xb(sk_R) = c0
5.43/5.67	     | sk_Xb(sk_R) = sk_Xc(sk_R)
5.43/5.67	     | app_encode_app(a, $o, 
5.43/5.67	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.67	             w), z), z)),
5.43/5.67	    inference('clc', [status(thm)], ['160', '105'])).
5.43/5.67	tff('162', plain,
5.43/5.67	    (~ app_encode_app(a, $o, 
5.43/5.67	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.67	             sk_Xa(sk_R)), sk_Xb(sk_R)), sk_Xb(sk_R))
5.43/5.67	     | app_encode_app(a, $o, 
5.43/5.67	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.67	             w), z), z)
5.43/5.67	     | sk_Xb(sk_R) = c0
5.43/5.67	     | app_encode_app(a, $o, 
5.43/5.67	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.67	             w), z), z)),
5.43/5.67	    inference('sup-', [status(thm)], ['161', '105'])).
5.43/5.67	tff('163', plain,
5.43/5.67	    (sk_Xb(sk_R) = c0
5.43/5.67	     | app_encode_app(a, $o, 
5.43/5.67	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.67	             w), z), z)
5.43/5.67	     | ~ app_encode_app(a, $o, 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.67	               sk_R, sk_Xa(sk_R)), sk_Xb(sk_R)), sk_Xb(sk_R))),
5.43/5.67	    inference('simplify', [status(thm)], ['162'])).
5.43/5.67	tff('164', plain,
5.43/5.67	    (~ app_encode_app(a, $o, 
5.43/5.67	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.67	             c0), sk_Xb(sk_R)), sk_Xb(sk_R))
5.43/5.67	     | app_encode_app(a, $o, 
5.43/5.67	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.67	             w), z), z)
5.43/5.67	     | app_encode_app(a, $o, 
5.43/5.67	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.67	             w), z), z)
5.43/5.67	     | sk_Xb(sk_R) = c0),
5.43/5.67	    inference('sup-', [status(thm)], ['141', '163'])).
5.43/5.67	tff('165', plain,
5.43/5.67	    (~ $true
5.43/5.67	     | app_encode_app(a, $o, 
5.43/5.67	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.67	             w), z), z)
5.43/5.67	     | app_encode_app(a, $o, 
5.43/5.67	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.67	             w), z), z)
5.43/5.67	     | sk_Xb(sk_R) = c0),
5.43/5.67	    inference('demod', [status(thm)], ['164', '59'])).
5.43/5.67	tff('166', plain,
5.43/5.67	    (sk_Xb(sk_R) = c0
5.43/5.67	     | app_encode_app(a, $o, 
5.43/5.67	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.67	             w), z), z)),
5.43/5.67	    inference('simplify', [status(thm)], ['165'])).
5.43/5.67	tff('167', plain,
5.43/5.67	    (~ app_encode_app(a, $o, 
5.43/5.67	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.67	             sk_Xa(sk_R)), c0), sk_Xc(sk_R))
5.43/5.67	     | app_encode_app(a, $o, 
5.43/5.67	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.67	             w), z), z)
5.43/5.67	     | app_encode_app(a, $o, 
5.43/5.67	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.67	             w), z), z)),
5.43/5.67	    inference('sup-', [status(thm)], ['166', '105'])).
5.43/5.67	tff('168', plain,
5.43/5.67	    (app_encode_app(a, $o, 
5.43/5.67	       app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, w), 
5.43/5.67	         z), z)
5.43/5.67	     | ~ app_encode_app(a, $o, 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
5.43/5.67	               sk_R, sk_Xa(sk_R)), c0), sk_Xc(sk_R))),
5.43/5.67	    inference('simplify', [status(thm)], ['167'])).
5.43/5.67	tff('169', plain,
5.43/5.67	    (~ app_encode_app(a, $o, 
5.43/5.67	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.67	             sk_Xa(sk_R)), c0), sk_Xa(sk_R))
5.43/5.67	     | app_encode_app(a, $o, 
5.43/5.67	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.67	             w), z), z)
5.43/5.67	     | app_encode_app(a, $o, 
5.43/5.67	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.67	             w), z), z)),
5.43/5.67	    inference('sup-', [status(thm)], ['146', '168'])).
5.43/5.67	tff('170', plain,
5.43/5.67	    (~ $true
5.43/5.67	     | app_encode_app(a, $o, 
5.43/5.67	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.67	             w), z), z)
5.43/5.67	     | app_encode_app(a, $o, 
5.43/5.67	         app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
5.43/5.67	             w), z), z)),
5.43/5.67	    inference('demod', [status(thm)], ['169', '52'])).
5.43/5.67	tff('171', plain,
5.43/5.67	    app_encode_app(a, $o, 
5.43/5.67	      app_encode_app(a, app_encode_fun(a, $o), 
5.43/5.67	        app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, w), 
5.43/5.67	        z), z),
5.43/5.67	    inference('simplify', [status(thm)], ['170'])).
5.43/5.67	tff('172', plain, (~ $true | ~ $true),
5.43/5.67	    inference('demod', [status(thm)], ['90', '171'])).
5.43/5.67	tff('173', plain, $false, inference('simplify', [status(thm)], ['172'])).
5.43/5.67	
5.43/5.67	% SZS output end Refutation
5.43/5.67	EOF
