0.00/0.01	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.01	% app-encoded or not : appext
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 $2 \
0.00/0.01	  --simultaneous-sup false \
0.00/0.01	  --no-max-vars \
0.00/0.01	  --no-fool
0.00/0.20	% Computer   : n109.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 18:00:09 CST 2018
3.78/4.06	% done 2540 iterations in 3.846s
3.78/4.06	% SZS status Theorem for 'stdin'
3.78/4.06	% SZS output start Refutation
3.78/4.06	tff(zf_stmt_10, conjecture,
3.78/4.06	  (((![Xx0:a,Xy0:a]:
3.78/4.06	       (app_encode_app(a,a,app_encode_app(a,app_encode_fun(a,a),cP,Xx0),Xy0) !=
3.78/4.06	        cZ)) & 
3.78/4.06	    (![Xx0:a,Xy0:a,Xu0:a,Xv0:a]:
3.78/4.06	       ((app_encode_app(a,a,app_encode_app(a,app_encode_fun(a,a),cP,Xx0),Xu0) =
3.78/4.06	         app_encode_app(a,a,app_encode_app(a,app_encode_fun(a,a),cP,Xy0),Xv0)) =>
3.78/4.06	        ((Xx0 = Xy0) & (Xu0 = Xv0)))) & 
3.78/4.06	    (![X:app_encode_fun(a,$o)]:
3.78/4.06	       ((app_encode_app(a,$o,X,cZ) & 
3.78/4.06	         (![Xx0:a,Xy0:a]:
3.78/4.06	            ((app_encode_app(a,$o,X,Xx0) & app_encode_app(a,$o,X,Xy0)) =>
3.78/4.06	             app_encode_app(a,$o,X,
3.78/4.06	                            app_encode_app(a,a,
3.78/4.06	                                           app_encode_app(a,
3.78/4.06	                                                          app_encode_fun(a,a),
3.78/4.06	                                                          cP,Xx0),
3.78/4.06	                                           Xy0))))) =>
3.78/4.06	        (![Xx0:a]: app_encode_app(a,$o,X,Xx0))))) =>
3.78/4.06	   ((![R:app_encode_fun(a,app_encode_fun(a,app_encode_fun(a,$o)))]:
3.78/4.06	       ((![Xa:a,Xb:a,Xc:a]:
3.78/4.06	           ((((Xa = cZ) & (Xb = Xc)) | ((Xb = cZ) & (Xa = Xc)) | 
3.78/4.06	             (?[Xx1:a,Xx2:a,Xy1:a,Xy2:a,Xz1:a,Xz2:a]:
3.78/4.06	                ((Xa =
3.78/4.06	                  app_encode_app(a,a,
3.78/4.06	                                 app_encode_app(a,app_encode_fun(a,a),cP,Xx1),
3.78/4.06	                                 Xx2)) & 
3.78/4.06	                 (Xb =
3.78/4.06	                  app_encode_app(a,a,
3.78/4.06	                                 app_encode_app(a,app_encode_fun(a,a),cP,Xy1),
3.78/4.06	                                 Xy2)) & 
3.78/4.06	                 (Xc =
3.78/4.06	                  app_encode_app(a,a,
3.78/4.06	                                 app_encode_app(a,app_encode_fun(a,a),cP,Xz1),
3.78/4.06	                                 Xz2)) & 
3.78/4.06	                 app_encode_app(a,$o,
3.78/4.06	                                app_encode_app(a,app_encode_fun(a,$o),
3.78/4.06	                                               app_encode_app(a,
3.78/4.06	                                                              app_encode_fun(
3.78/4.06	                                                              a,
3.78/4.06	                                                              app_encode_fun(
3.78/4.06	                                                              a,$o)),R,Xx1),
3.78/4.06	                                               Xy1),
3.78/4.06	                                Xz1) & 
3.78/4.06	                 app_encode_app(a,$o,
3.78/4.06	                                app_encode_app(a,app_encode_fun(a,$o),
3.78/4.06	                                               app_encode_app(a,
3.78/4.06	                                                              app_encode_fun(
3.78/4.06	                                                              a,
3.78/4.06	                                                              app_encode_fun(
3.78/4.06	                                                              a,$o)),R,Xx2),
3.78/4.06	                                               Xy2),
3.78/4.06	                                Xz2)))) =>
3.78/4.06	            app_encode_app(a,$o,
3.78/4.06	                           app_encode_app(a,app_encode_fun(a,$o),
3.78/4.06	                                          app_encode_app(a,
3.78/4.06	                                                         app_encode_fun(
3.78/4.06	                                                         a,
3.78/4.06	                                                         app_encode_fun(a,$o)),
3.78/4.06	                                                         R,Xa),
3.78/4.06	                                          Xb),
3.78/4.06	                           Xc))) =>
3.78/4.06	        app_encode_app(a,$o,
3.78/4.06	                       app_encode_app(a,app_encode_fun(a,$o),
3.78/4.06	                                      app_encode_app(a,
3.78/4.06	                                                     app_encode_fun(a,
3.78/4.06	                                                                    app_encode_fun(
3.78/4.06	                                                                    a,$o)),
3.78/4.06	                                                     R,x),
3.78/4.06	                                      u),
3.78/4.06	                       u))) =>
3.78/4.06	    ((![R:app_encode_fun(a,app_encode_fun(a,app_encode_fun(a,$o)))]:
3.78/4.06	        ((![Xa:a,Xb:a,Xc:a]:
3.78/4.06	            ((((Xa = cZ) & (Xb = Xc)) | ((Xb = cZ) & (Xa = Xc)) | 
3.78/4.06	              (?[Xx1:a,Xx2:a,Xy1:a,Xy2:a,Xz1:a,Xz2:a]:
3.78/4.06	                 ((Xa =
3.78/4.06	                   app_encode_app(a,a,
3.78/4.06	                                  app_encode_app(a,app_encode_fun(a,a),cP,Xx1),
3.78/4.06	                                  Xx2)) & 
3.78/4.06	                  (Xb =
3.78/4.06	                   app_encode_app(a,a,
3.78/4.06	                                  app_encode_app(a,app_encode_fun(a,a),cP,Xy1),
3.78/4.06	                                  Xy2)) & 
3.78/4.06	                  (Xc =
3.78/4.06	                   app_encode_app(a,a,
3.78/4.06	                                  app_encode_app(a,app_encode_fun(a,a),cP,Xz1),
3.78/4.06	                                  Xz2)) & 
3.78/4.06	                  app_encode_app(a,$o,
3.78/4.06	                                 app_encode_app(a,app_encode_fun(a,$o),
3.78/4.06	                                                app_encode_app(a,
3.78/4.06	                                                               app_encode_fun(
3.78/4.06	                                                               a,
3.78/4.06	                                                               app_encode_fun(
3.78/4.06	                                                               a,$o)),R,Xx1),
3.78/4.06	                                                Xy1),
3.78/4.06	                                 Xz1) & 
3.78/4.06	                  app_encode_app(a,$o,
3.78/4.06	                                 app_encode_app(a,app_encode_fun(a,$o),
3.78/4.06	                                                app_encode_app(a,
3.78/4.06	                                                               app_encode_fun(
3.78/4.06	                                                               a,
3.78/4.06	                                                               app_encode_fun(
3.78/4.06	                                                               a,$o)),R,Xx2),
3.78/4.06	                                                Xy2),
3.78/4.06	                                 Xz2)))) =>
3.78/4.06	             app_encode_app(a,$o,
3.78/4.06	                            app_encode_app(a,app_encode_fun(a,$o),
3.78/4.06	                                           app_encode_app(a,
3.78/4.06	                                                          app_encode_fun(
3.78/4.06	                                                          a,
3.78/4.06	                                                          app_encode_fun(
3.78/4.06	                                                          a,$o)),R,Xa),
3.78/4.06	                                           Xb),
3.78/4.06	                            Xc))) =>
3.78/4.06	         app_encode_app(a,$o,
3.78/4.06	                        app_encode_app(a,app_encode_fun(a,$o),
3.78/4.06	                                       app_encode_app(a,
3.78/4.06	                                                      app_encode_fun(
3.78/4.06	                                                      a,app_encode_fun(a,$o)),
3.78/4.06	                                                      R,y),
3.78/4.06	                                       v),
3.78/4.06	                        v))) =>
3.78/4.06	     (![R:app_encode_fun(a,app_encode_fun(a,app_encode_fun(a,$o)))]:
3.78/4.06	        ((![Xa:a,Xb:a,Xc:a]:
3.78/4.06	            ((((Xa = cZ) & (Xb = Xc)) | ((Xb = cZ) & (Xa = Xc)) | 
3.78/4.06	              (?[Xx1:a,Xx2:a,Xy1:a,Xy2:a,Xz1:a,Xz2:a]:
3.78/4.06	                 ((Xa =
3.78/4.06	                   app_encode_app(a,a,
3.78/4.06	                                  app_encode_app(a,app_encode_fun(a,a),cP,Xx1),
3.78/4.06	                                  Xx2)) & 
3.78/4.06	                  (Xb =
3.78/4.06	                   app_encode_app(a,a,
3.78/4.06	                                  app_encode_app(a,app_encode_fun(a,a),cP,Xy1),
3.78/4.06	                                  Xy2)) & 
3.78/4.06	                  (Xc =
3.78/4.06	                   app_encode_app(a,a,
3.78/4.06	                                  app_encode_app(a,app_encode_fun(a,a),cP,Xz1),
3.78/4.06	                                  Xz2)) & 
3.78/4.06	                  app_encode_app(a,$o,
3.78/4.06	                                 app_encode_app(a,app_encode_fun(a,$o),
3.78/4.06	                                                app_encode_app(a,
3.78/4.06	                                                               app_encode_fun(
3.78/4.06	                                                               a,
3.78/4.06	                                                               app_encode_fun(
3.78/4.06	                                                               a,$o)),R,Xx1),
3.78/4.06	                                                Xy1),
3.78/4.06	                                 Xz1) & 
3.78/4.06	                  app_encode_app(a,$o,
3.78/4.06	                                 app_encode_app(a,app_encode_fun(a,$o),
3.78/4.06	                                                app_encode_app(a,
3.78/4.06	                                                               app_encode_fun(
3.78/4.06	                                                               a,
3.78/4.06	                                                               app_encode_fun(
3.78/4.06	                                                               a,$o)),R,Xx2),
3.78/4.06	                                                Xy2),
3.78/4.06	                                 Xz2)))) =>
3.78/4.06	             app_encode_app(a,$o,
3.78/4.06	                            app_encode_app(a,app_encode_fun(a,$o),
3.78/4.06	                                           app_encode_app(a,
3.78/4.06	                                                          app_encode_fun(
3.78/4.06	                                                          a,
3.78/4.06	                                                          app_encode_fun(
3.78/4.06	                                                          a,$o)),R,Xa),
3.78/4.06	                                           Xb),
3.78/4.06	                            Xc))) =>
3.78/4.06	         app_encode_app(a,$o,
3.78/4.06	                        app_encode_app(a,app_encode_fun(a,$o),
3.78/4.06	                                       app_encode_app(a,
3.78/4.06	                                                      app_encode_fun(
3.78/4.06	                                                      a,app_encode_fun(a,$o)),
3.78/4.06	                                                      R,
3.78/4.06	                                                      app_encode_app(
3.78/4.06	                                                      a,a,
3.78/4.06	                                                      app_encode_app(
3.78/4.06	                                                      a,app_encode_fun(a,a),
3.78/4.06	                                                      cP,x),y)),
3.78/4.06	                                       app_encode_app(a,a,
3.78/4.06	                                                      app_encode_app(
3.78/4.06	                                                      a,app_encode_fun(a,a),
3.78/4.06	                                                      cP,u),v)),
3.78/4.06	                        app_encode_app(a,a,
3.78/4.06	                                       app_encode_app(a,app_encode_fun(a,a),
3.78/4.06	                                                      cP,u),
3.78/4.06	                                       v)))))))).
3.78/4.06	tff(zf_stmt_0, negated_conjecture,
3.78/4.06	  (~
3.78/4.06	    (((![Xx0:a,Xy0:a]:
3.78/4.06	         (app_encode_app(a,a,app_encode_app(a,app_encode_fun(a,a),cP,Xx0),Xy0) !=
3.78/4.06	          cZ)) & 
3.78/4.06	      (![Xx0:a,Xy0:a,Xu0:a,Xv0:a]:
3.78/4.06	         ((app_encode_app(a,a,app_encode_app(a,app_encode_fun(a,a),cP,Xx0),
3.78/4.06	                          Xu0) =
3.78/4.06	           app_encode_app(a,a,app_encode_app(a,app_encode_fun(a,a),cP,Xy0),
3.78/4.06	                          Xv0)) =>
3.78/4.06	          ((Xx0 = Xy0) & (Xu0 = Xv0)))) & 
3.78/4.06	      (![X:app_encode_fun(a,$o)]:
3.78/4.06	         ((app_encode_app(a,$o,X,cZ) & 
3.78/4.06	           (![Xx0:a,Xy0:a]:
3.78/4.06	              ((app_encode_app(a,$o,X,Xx0) & app_encode_app(a,$o,X,Xy0)) =>
3.78/4.06	               app_encode_app(a,$o,X,
3.78/4.06	                              app_encode_app(a,a,
3.78/4.06	                                             app_encode_app(a,
3.78/4.06	                                                            app_encode_fun(
3.78/4.06	                                                            a,a),cP,Xx0),
3.78/4.06	                                             Xy0))))) =>
3.78/4.06	          (![Xx0:a]: app_encode_app(a,$o,X,Xx0))))) =>
3.78/4.06	     ((![R:app_encode_fun(a,app_encode_fun(a,app_encode_fun(a,$o)))]:
3.78/4.06	         ((![Xa:a,Xb:a,Xc:a]:
3.78/4.06	             ((((Xa = cZ) & (Xb = Xc)) | ((Xb = cZ) & (Xa = Xc)) | 
3.78/4.06	               (?[Xx1:a,Xx2:a,Xy1:a,Xy2:a,Xz1:a,Xz2:a]:
3.78/4.06	                  ((Xa =
3.78/4.06	                    app_encode_app(a,a,
3.78/4.06	                                   app_encode_app(a,app_encode_fun(a,a),cP,
3.78/4.06	                                                  Xx1),
3.78/4.06	                                   Xx2)) & 
3.78/4.06	                   (Xb =
3.78/4.06	                    app_encode_app(a,a,
3.78/4.06	                                   app_encode_app(a,app_encode_fun(a,a),cP,
3.78/4.06	                                                  Xy1),
3.78/4.06	                                   Xy2)) & 
3.78/4.06	                   (Xc =
3.78/4.06	                    app_encode_app(a,a,
3.78/4.06	                                   app_encode_app(a,app_encode_fun(a,a),cP,
3.78/4.06	                                                  Xz1),
3.78/4.06	                                   Xz2)) & 
3.78/4.06	                   app_encode_app(a,$o,
3.78/4.06	                                  app_encode_app(a,app_encode_fun(a,$o),
3.78/4.06	                                                 app_encode_app(a,
3.78/4.06	                                                                app_encode_fun(
3.78/4.06	                                                                a,
3.78/4.06	                                                                app_encode_fun(
3.78/4.06	                                                                a,$o)),R,Xx1),
3.78/4.06	                                                 Xy1),
3.78/4.06	                                  Xz1) & 
3.78/4.06	                   app_encode_app(a,$o,
3.78/4.06	                                  app_encode_app(a,app_encode_fun(a,$o),
3.78/4.06	                                                 app_encode_app(a,
3.78/4.06	                                                                app_encode_fun(
3.78/4.06	                                                                a,
3.78/4.06	                                                                app_encode_fun(
3.78/4.06	                                                                a,$o)),R,Xx2),
3.78/4.06	                                                 Xy2),
3.78/4.06	                                  Xz2)))) =>
3.78/4.06	              app_encode_app(a,$o,
3.78/4.06	                             app_encode_app(a,app_encode_fun(a,$o),
3.78/4.06	                                            app_encode_app(a,
3.78/4.06	                                                           app_encode_fun(
3.78/4.06	                                                           a,
3.78/4.06	                                                           app_encode_fun(
3.78/4.06	                                                           a,$o)),R,Xa),
3.78/4.06	                                            Xb),
3.78/4.06	                             Xc))) =>
3.78/4.06	          app_encode_app(a,$o,
3.78/4.06	                         app_encode_app(a,app_encode_fun(a,$o),
3.78/4.06	                                        app_encode_app(a,
3.78/4.06	                                                       app_encode_fun(
3.78/4.06	                                                       a,app_encode_fun(a,$o)),
3.78/4.06	                                                       R,x),
3.78/4.06	                                        u),
3.78/4.06	                         u))) =>
3.78/4.06	      ((![R:app_encode_fun(a,app_encode_fun(a,app_encode_fun(a,$o)))]:
3.78/4.06	          ((![Xa:a,Xb:a,Xc:a]:
3.78/4.06	              ((((Xa = cZ) & (Xb = Xc)) | ((Xb = cZ) & (Xa = Xc)) | 
3.78/4.06	                (?[Xx1:a,Xx2:a,Xy1:a,Xy2:a,Xz1:a,Xz2:a]:
3.78/4.06	                   ((Xa =
3.78/4.06	                     app_encode_app(a,a,
3.78/4.06	                                    app_encode_app(a,app_encode_fun(a,a),cP,
3.78/4.06	                                                   Xx1),
3.78/4.06	                                    Xx2)) & 
3.78/4.06	                    (Xb =
3.78/4.06	                     app_encode_app(a,a,
3.78/4.06	                                    app_encode_app(a,app_encode_fun(a,a),cP,
3.78/4.06	                                                   Xy1),
3.78/4.06	                                    Xy2)) & 
3.78/4.06	                    (Xc =
3.78/4.06	                     app_encode_app(a,a,
3.78/4.06	                                    app_encode_app(a,app_encode_fun(a,a),cP,
3.78/4.06	                                                   Xz1),
3.78/4.06	                                    Xz2)) & 
3.78/4.06	                    app_encode_app(a,$o,
3.78/4.06	                                   app_encode_app(a,app_encode_fun(a,$o),
3.78/4.06	                                                  app_encode_app(a,
3.78/4.06	                                                                 app_encode_fun(
3.78/4.06	                                                                 a,
3.78/4.06	                                                                 app_encode_fun(
3.78/4.06	                                                                 a,$o)),R,Xx1),
3.78/4.06	                                                  Xy1),
3.78/4.06	                                   Xz1) & 
3.78/4.06	                    app_encode_app(a,$o,
3.78/4.06	                                   app_encode_app(a,app_encode_fun(a,$o),
3.78/4.06	                                                  app_encode_app(a,
3.78/4.06	                                                                 app_encode_fun(
3.78/4.06	                                                                 a,
3.78/4.06	                                                                 app_encode_fun(
3.78/4.06	                                                                 a,$o)),R,Xx2),
3.78/4.06	                                                  Xy2),
3.78/4.06	                                   Xz2)))) =>
3.78/4.06	               app_encode_app(a,$o,
3.78/4.06	                              app_encode_app(a,app_encode_fun(a,$o),
3.78/4.06	                                             app_encode_app(a,
3.78/4.06	                                                            app_encode_fun(
3.78/4.06	                                                            a,
3.78/4.06	                                                            app_encode_fun(
3.78/4.06	                                                            a,$o)),R,Xa),
3.78/4.06	                                             Xb),
3.78/4.06	                              Xc))) =>
3.78/4.06	           app_encode_app(a,$o,
3.78/4.06	                          app_encode_app(a,app_encode_fun(a,$o),
3.78/4.06	                                         app_encode_app(a,
3.78/4.06	                                                        app_encode_fun(
3.78/4.06	                                                        a,
3.78/4.06	                                                        app_encode_fun(a,$o)),
3.78/4.06	                                                        R,y),
3.78/4.06	                                         v),
3.78/4.06	                          v))) =>
3.78/4.06	       (![R:app_encode_fun(a,app_encode_fun(a,app_encode_fun(a,$o)))]:
3.78/4.06	          ((![Xa:a,Xb:a,Xc:a]:
3.78/4.06	              ((((Xa = cZ) & (Xb = Xc)) | ((Xb = cZ) & (Xa = Xc)) | 
3.78/4.06	                (?[Xx1:a,Xx2:a,Xy1:a,Xy2:a,Xz1:a,Xz2:a]:
3.78/4.06	                   ((Xa =
3.78/4.06	                     app_encode_app(a,a,
3.78/4.06	                                    app_encode_app(a,app_encode_fun(a,a),cP,
3.78/4.06	                                                   Xx1),
3.78/4.06	                                    Xx2)) & 
3.78/4.06	                    (Xb =
3.78/4.06	                     app_encode_app(a,a,
3.78/4.06	                                    app_encode_app(a,app_encode_fun(a,a),cP,
3.78/4.06	                                                   Xy1),
3.78/4.06	                                    Xy2)) & 
3.78/4.06	                    (Xc =
3.78/4.06	                     app_encode_app(a,a,
3.78/4.06	                                    app_encode_app(a,app_encode_fun(a,a),cP,
3.78/4.06	                                                   Xz1),
3.78/4.06	                                    Xz2)) & 
3.78/4.06	                    app_encode_app(a,$o,
3.78/4.06	                                   app_encode_app(a,app_encode_fun(a,$o),
3.78/4.06	                                                  app_encode_app(a,
3.78/4.06	                                                                 app_encode_fun(
3.78/4.06	                                                                 a,
3.78/4.06	                                                                 app_encode_fun(
3.78/4.06	                                                                 a,$o)),R,Xx1),
3.78/4.06	                                                  Xy1),
3.78/4.06	                                   Xz1) & 
3.78/4.06	                    app_encode_app(a,$o,
3.78/4.06	                                   app_encode_app(a,app_encode_fun(a,$o),
3.78/4.06	                                                  app_encode_app(a,
3.78/4.06	                                                                 app_encode_fun(
3.78/4.06	                                                                 a,
3.78/4.06	                                                                 app_encode_fun(
3.78/4.06	                                                                 a,$o)),R,Xx2),
3.78/4.06	                                                  Xy2),
3.78/4.06	                                   Xz2)))) =>
3.78/4.06	               app_encode_app(a,$o,
3.78/4.06	                              app_encode_app(a,app_encode_fun(a,$o),
3.78/4.06	                                             app_encode_app(a,
3.78/4.06	                                                            app_encode_fun(
3.78/4.06	                                                            a,
3.78/4.06	                                                            app_encode_fun(
3.78/4.06	                                                            a,$o)),R,Xa),
3.78/4.06	                                             Xb),
3.78/4.06	                              Xc))) =>
3.78/4.06	           app_encode_app(a,$o,
3.78/4.07	                          app_encode_app(a,app_encode_fun(a,$o),
3.78/4.07	                                         app_encode_app(a,
3.78/4.07	                                                        app_encode_fun(
3.78/4.07	                                                        a,
3.78/4.07	                                                        app_encode_fun(a,$o)),
3.78/4.07	                                                        R,
3.78/4.07	                                                        app_encode_app(
3.78/4.07	                                                        a,a,
3.78/4.07	                                                        app_encode_app(
3.78/4.07	                                                        a,
3.78/4.07	                                                        app_encode_fun(a,a),
3.78/4.07	                                                        cP,x),y)),
3.78/4.07	                                         app_encode_app(a,a,
3.78/4.07	                                                        app_encode_app(
3.78/4.07	                                                        a,
3.78/4.07	                                                        app_encode_fun(a,a),
3.78/4.07	                                                        cP,u),v)),
3.78/4.07	                          app_encode_app(a,a,
3.78/4.07	                                         app_encode_app(a,
3.78/4.07	                                                        app_encode_fun(a,a),
3.78/4.07	                                                        cP,u),
3.78/4.07	                                         v))))))))).
3.78/4.07	tff('0', plain,
3.78/4.07	    ![X12 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
3.78/4.07	      (app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X12, 
3.78/4.07	             y), v), v)
3.78/4.07	       | sk_Xa1(X12) = cZ
3.78/4.07	       | sk_Xb1(X12) = cZ
3.78/4.07	       | sk_Xc1(X12)
3.78/4.07	          = app_encode_app(a, a, 
3.78/4.07	              app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz11(X12)), 
3.78/4.07	              sk_Xz21(X12))),
3.78/4.07	    inference('cnf', [status(esa)], [zf_stmt_0])).
3.78/4.07	tff('1', plain,
3.78/4.07	    ![X12 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
3.78/4.07	      (app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X12, 
3.78/4.07	             y), v), v)
3.78/4.07	       | sk_Xa1(X12) = cZ
3.78/4.07	       | sk_Xb1(X12) = cZ
3.78/4.07	       | sk_Xb1(X12)
3.78/4.07	          = app_encode_app(a, a, 
3.78/4.07	              app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy11(X12)), 
3.78/4.07	              sk_Xy21(X12))),
3.78/4.07	    inference('cnf', [status(esa)], [zf_stmt_0])).
3.78/4.07	tff('2', plain,
3.78/4.07	    ![X12 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
3.78/4.07	      (app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X12, 
3.78/4.07	             y), v), v)
3.78/4.07	       | sk_Xa1(X12) = cZ
3.78/4.07	       | sk_Xb1(X12) = cZ
3.78/4.07	       | app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
3.78/4.07	               X12, sk_Xx21(X12)), sk_Xy21(X12)), sk_Xz21(X12))),
3.78/4.07	    inference('cnf', [status(esa)], [zf_stmt_0])).
3.78/4.07	tff('3', plain,
3.78/4.07	    ![X12 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
3.78/4.07	      (app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X12, 
3.78/4.07	             y), v), v)
3.78/4.07	       | sk_Xa1(X12) = cZ
3.78/4.07	       | sk_Xb1(X12) = cZ
3.78/4.07	       | app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
3.78/4.07	               X12, sk_Xx11(X12)), sk_Xy11(X12)), sk_Xz11(X12))),
3.78/4.07	    inference('cnf', [status(esa)], [zf_stmt_0])).
3.78/4.07	tff('4', plain,
3.78/4.07	    ![X12 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
3.78/4.07	      (app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X12, 
3.78/4.07	             y), v), v)
3.78/4.07	       | sk_Xa1(X12) = cZ
3.78/4.07	       | sk_Xb1(X12) = cZ
3.78/4.07	       | sk_Xa1(X12)
3.78/4.07	          = app_encode_app(a, a, 
3.78/4.07	              app_encode_app(a, app_encode_fun(a, a), cP, sk_Xx11(X12)), 
3.78/4.07	              sk_Xx21(X12))),
3.78/4.07	    inference('cnf', [status(esa)], [zf_stmt_0])).
3.78/4.07	tff('5', plain,
3.78/4.07	    ![X13 : a, X14 : a, X15 : a, X16 : a, X17 : a, X18 : a, X19 : a, 
3.78/4.07	      X20 : a, X21 : a]:
3.78/4.07	      (app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             X13), X14), X15)
3.78/4.07	       | X13
3.78/4.07	          != app_encode_app(a, a, 
3.78/4.07	               app_encode_app(a, app_encode_fun(a, a), cP, X16), X17)
3.78/4.07	       | X14
3.78/4.07	          != app_encode_app(a, a, 
3.78/4.07	               app_encode_app(a, app_encode_fun(a, a), cP, X18), X19)
3.78/4.07	       | ~ app_encode_app(a, $o, 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
3.78/4.07	                 sk_R, X16), X18), X20)
3.78/4.07	       | ~ app_encode_app(a, $o, 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
3.78/4.07	                 sk_R, X17), X19), X21)
3.78/4.07	       | X15
3.78/4.07	          != app_encode_app(a, a, 
3.78/4.07	               app_encode_app(a, app_encode_fun(a, a), cP, X20), X21)),
3.78/4.07	    inference('cnf', [status(esa)], [zf_stmt_0])).
3.78/4.07	tff('6', plain,
3.78/4.07	    ![X16 : a, X17 : a, X18 : a, X19 : a, X20 : a, X21 : a]:
3.78/4.07	      (~ app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
3.78/4.07	               sk_R, X17), X19), X21)
3.78/4.07	       | ~ app_encode_app(a, $o, 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
3.78/4.07	                 sk_R, X16), X18), X20)
3.78/4.07	       | app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
3.78/4.07	               sk_R, 
3.78/4.07	               app_encode_app(a, a, 
3.78/4.07	                 app_encode_app(a, app_encode_fun(a, a), cP, X16), X17)), 
3.78/4.07	             app_encode_app(a, a, 
3.78/4.07	               app_encode_app(a, app_encode_fun(a, a), cP, X18), X19)), 
3.78/4.07	           app_encode_app(a, a, 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, a), cP, X20), X21))),
3.78/4.07	    inference('simplify', [status(thm)], ['5'])).
3.78/4.07	tff('7', plain,
3.78/4.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o))), 
3.78/4.07	      X1 : a, X2 : a, X3 : a, X4 : a]:
3.78/4.07	      (app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             sk_Xa1(X0)), 
3.78/4.07	           app_encode_app(a, a, 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, a), cP, X4), X3)), 
3.78/4.07	         app_encode_app(a, a, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, a), cP, X2), X1))
3.78/4.07	       | sk_Xb1(X0) = cZ
3.78/4.07	       | sk_Xa1(X0) = cZ
3.78/4.07	       | app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
3.78/4.07	               y), v), v)
3.78/4.07	       | ~ app_encode_app(a, $o, 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
3.78/4.07	                 sk_R, sk_Xx11(X0)), X4), X2)
3.78/4.07	       | ~ app_encode_app(a, $o, 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
3.78/4.07	                 sk_R, sk_Xx21(X0)), X3), X1)),
3.78/4.07	    inference('sup+', [status(thm)], ['4', '6'])).
3.78/4.07	tff('8', plain,
3.78/4.07	    ![X0 : a, X1 : a]:
3.78/4.07	      (~ $true
3.78/4.07	       | sk_Xb1(sk_R) = cZ
3.78/4.07	       | sk_Xa1(sk_R) = cZ
3.78/4.07	       | app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
3.78/4.07	               sk_R, y), v), v)
3.78/4.07	       | ~ app_encode_app(a, $o, 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
3.78/4.07	                 sk_R, sk_Xx21(sk_R)), X1), X0)
3.78/4.07	       | app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
3.78/4.07	               sk_R, y), v), v)
3.78/4.07	       | sk_Xa1(sk_R) = cZ
3.78/4.07	       | sk_Xb1(sk_R) = cZ
3.78/4.07	       | app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
3.78/4.07	               sk_R, sk_Xa1(sk_R)), 
3.78/4.07	             app_encode_app(a, a, 
3.78/4.07	               app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy11(sk_R)), 
3.78/4.07	               X1)), 
3.78/4.07	           app_encode_app(a, a, 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz11(sk_R)), X0))),
3.78/4.07	    inference('sup-', [status(thm)], ['3', '7'])).
3.78/4.07	tff('9', plain,
3.78/4.07	    ![X0 : a, X1 : a]:
3.78/4.07	      (app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             sk_Xa1(sk_R)), 
3.78/4.07	           app_encode_app(a, a, 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy11(sk_R)), X1)), 
3.78/4.07	         app_encode_app(a, a, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz11(sk_R)), X0))
3.78/4.07	       | ~ app_encode_app(a, $o, 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
3.78/4.07	                 sk_R, sk_Xx21(sk_R)), X1), X0)
3.78/4.07	       | app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
3.78/4.07	               sk_R, y), v), v)
3.78/4.07	       | sk_Xa1(sk_R) = cZ
3.78/4.07	       | sk_Xb1(sk_R) = cZ),
3.78/4.07	    inference('simplify', [status(thm)], ['8'])).
3.78/4.07	tff('10', plain,
3.78/4.07	    (~ $true
3.78/4.07	     | sk_Xb1(sk_R) = cZ
3.78/4.07	     | sk_Xa1(sk_R) = cZ
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             y), v), v)
3.78/4.07	     | sk_Xb1(sk_R) = cZ
3.78/4.07	     | sk_Xa1(sk_R) = cZ
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             y), v), v)
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             sk_Xa1(sk_R)), 
3.78/4.07	           app_encode_app(a, a, 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy11(sk_R)), 
3.78/4.07	             sk_Xy21(sk_R))), 
3.78/4.07	         app_encode_app(a, a, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz11(sk_R)), 
3.78/4.07	           sk_Xz21(sk_R)))),
3.78/4.07	    inference('sup-', [status(thm)], ['2', '9'])).
3.78/4.07	tff('11', plain,
3.78/4.07	    (app_encode_app(a, $o, 
3.78/4.07	       app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	           sk_Xa1(sk_R)), 
3.78/4.07	         app_encode_app(a, a, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy11(sk_R)), 
3.78/4.07	           sk_Xy21(sk_R))), 
3.78/4.07	       app_encode_app(a, a, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz11(sk_R)), 
3.78/4.07	         sk_Xz21(sk_R)))
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             y), v), v)
3.78/4.07	     | sk_Xa1(sk_R) = cZ
3.78/4.07	     | sk_Xb1(sk_R) = cZ),
3.78/4.07	    inference('simplify', [status(thm)], ['10'])).
3.78/4.07	tff('12', plain,
3.78/4.07	    (app_encode_app(a, $o, 
3.78/4.07	       app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	           sk_Xa1(sk_R)), sk_Xb1(sk_R)), 
3.78/4.07	       app_encode_app(a, a, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz11(sk_R)), 
3.78/4.07	         sk_Xz21(sk_R)))
3.78/4.07	     | sk_Xb1(sk_R) = cZ
3.78/4.07	     | sk_Xa1(sk_R) = cZ
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             y), v), v)
3.78/4.07	     | sk_Xb1(sk_R) = cZ
3.78/4.07	     | sk_Xa1(sk_R) = cZ
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             y), v), v)),
3.78/4.07	    inference('sup+', [status(thm)], ['1', '11'])).
3.78/4.07	tff('13', plain,
3.78/4.07	    (app_encode_app(a, $o, 
3.78/4.07	       app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, y), 
3.78/4.07	         v), v)
3.78/4.07	     | sk_Xa1(sk_R) = cZ
3.78/4.07	     | sk_Xb1(sk_R) = cZ
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             sk_Xa1(sk_R)), sk_Xb1(sk_R)), 
3.78/4.07	         app_encode_app(a, a, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz11(sk_R)), 
3.78/4.07	           sk_Xz21(sk_R)))),
3.78/4.07	    inference('simplify', [status(thm)], ['12'])).
3.78/4.07	tff('14', plain,
3.78/4.07	    (app_encode_app(a, $o, 
3.78/4.07	       app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	           sk_Xa1(sk_R)), sk_Xb1(sk_R)), sk_Xc1(sk_R))
3.78/4.07	     | sk_Xb1(sk_R) = cZ
3.78/4.07	     | sk_Xa1(sk_R) = cZ
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             y), v), v)
3.78/4.07	     | sk_Xb1(sk_R) = cZ
3.78/4.07	     | sk_Xa1(sk_R) = cZ
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             y), v), v)),
3.78/4.07	    inference('sup+', [status(thm)], ['0', '13'])).
3.78/4.07	tff('15', plain,
3.78/4.07	    (app_encode_app(a, $o, 
3.78/4.07	       app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, y), 
3.78/4.07	         v), v)
3.78/4.07	     | sk_Xa1(sk_R) = cZ
3.78/4.07	     | sk_Xb1(sk_R) = cZ
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             sk_Xa1(sk_R)), sk_Xb1(sk_R)), sk_Xc1(sk_R))),
3.78/4.07	    inference('simplify', [status(thm)], ['14'])).
3.78/4.07	tff('16', plain,
3.78/4.07	    ![X12 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
3.78/4.07	      (app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X12, 
3.78/4.07	             y), v), v)
3.78/4.07	       | ~ app_encode_app(a, $o, 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
3.78/4.07	                 X12, sk_Xa1(X12)), sk_Xb1(X12)), sk_Xc1(X12))),
3.78/4.07	    inference('cnf', [status(esa)], [zf_stmt_0])).
3.78/4.07	tff('17', plain,
3.78/4.07	    (sk_Xb1(sk_R) = cZ
3.78/4.07	     | sk_Xa1(sk_R) = cZ
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             y), v), v)),
3.78/4.07	    inference('clc', [status(thm)], ['15', '16'])).
3.78/4.07	tff('18', plain,
3.78/4.07	    ![X12 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
3.78/4.07	      (app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X12, 
3.78/4.07	             y), v), v)
3.78/4.07	       | sk_Xa1(X12) = cZ
3.78/4.07	       | sk_Xa1(X12) = sk_Xc1(X12)
3.78/4.07	       | sk_Xb1(X12)
3.78/4.07	          = app_encode_app(a, a, 
3.78/4.07	              app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy11(X12)), 
3.78/4.07	              sk_Xy21(X12))),
3.78/4.07	    inference('cnf', [status(esa)], [zf_stmt_0])).
3.78/4.07	tff('19', plain,
3.78/4.07	    ![X4 : a, X5 : a]:
3.78/4.07	      app_encode_app(a, a, app_encode_app(a, app_encode_fun(a, a), cP, X4), 
3.78/4.07	        X5)
3.78/4.07	       != cZ,
3.78/4.07	    inference('cnf', [status(esa)], [zf_stmt_0])).
3.78/4.07	tff('20', plain,
3.78/4.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
3.78/4.07	      (sk_Xb1(X0) != cZ
3.78/4.07	       | sk_Xa1(X0) = sk_Xc1(X0)
3.78/4.07	       | sk_Xa1(X0) = cZ
3.78/4.07	       | app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
3.78/4.07	               y), v), v)),
3.78/4.07	    inference('sup-', [status(thm)], ['18', '19'])).
3.78/4.07	tff('21', plain,
3.78/4.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
3.78/4.07	      (~ app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
3.78/4.07	               sk_Xa1(X0)), sk_Xb1(X0)), sk_Xa1(X0))
3.78/4.07	       | app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
3.78/4.07	               y), v), v)
3.78/4.07	       | sk_Xa1(X0) = cZ
3.78/4.07	       | sk_Xb1(X0) != cZ
3.78/4.07	       | app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
3.78/4.07	               y), v), v)),
3.78/4.07	    inference('sup-', [status(thm)], ['20', '16'])).
3.78/4.07	tff('22', plain,
3.78/4.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
3.78/4.07	      (sk_Xb1(X0) != cZ
3.78/4.07	       | sk_Xa1(X0) = cZ
3.78/4.07	       | app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
3.78/4.07	               y), v), v)
3.78/4.07	       | ~ app_encode_app(a, $o, 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
3.78/4.07	                 X0, sk_Xa1(X0)), sk_Xb1(X0)), sk_Xa1(X0))),
3.78/4.07	    inference('simplify', [status(thm)], ['21'])).
3.78/4.07	tff('23', plain,
3.78/4.07	    (~ app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             sk_Xa1(sk_R)), cZ), sk_Xa1(sk_R))
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             y), v), v)
3.78/4.07	     | sk_Xa1(sk_R) = cZ
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             y), v), v)
3.78/4.07	     | sk_Xa1(sk_R) = cZ
3.78/4.07	     | sk_Xb1(sk_R) != cZ),
3.78/4.07	    inference('sup-', [status(thm)], ['17', '22'])).
3.78/4.07	tff('24', plain,
3.78/4.07	    ![X13 : a, X14 : a, X15 : a]:
3.78/4.07	      (app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             X13), X14), X15)
3.78/4.07	       | X14 != cZ
3.78/4.07	       | X13 != X15),
3.78/4.07	    inference('cnf', [status(esa)], [zf_stmt_0])).
3.78/4.07	tff('25', plain,
3.78/4.07	    ![X15 : a]:
3.78/4.07	      app_encode_app(a, $o, 
3.78/4.07	        app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	          app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	            X15), cZ), X15),
3.78/4.07	    inference('simplify', [status(thm)], ['24'])).
3.78/4.07	tff('26', plain,
3.78/4.07	    (~ $true
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             y), v), v)
3.78/4.07	     | sk_Xa1(sk_R) = cZ
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             y), v), v)
3.78/4.07	     | sk_Xa1(sk_R) = cZ
3.78/4.07	     | sk_Xb1(sk_R) != cZ),
3.78/4.07	    inference('demod', [status(thm)], ['23', '25'])).
3.78/4.07	tff('27', plain,
3.78/4.07	    (sk_Xb1(sk_R) != cZ
3.78/4.07	     | sk_Xa1(sk_R) = cZ
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             y), v), v)),
3.78/4.07	    inference('simplify', [status(thm)], ['26'])).
3.78/4.07	tff('28', plain,
3.78/4.07	    (app_encode_app(a, $o, 
3.78/4.07	       app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, y), 
3.78/4.07	         v), v)
3.78/4.07	     | sk_Xa1(sk_R) = cZ),
3.78/4.07	    inference('clc', [status(thm)], ['27', '17'])).
3.78/4.07	tff('29', plain,
3.78/4.07	    ![X12 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
3.78/4.07	      (app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X12, 
3.78/4.07	             y), v), v)
3.78/4.07	       | sk_Xb1(X12) = sk_Xc1(X12)
3.78/4.07	       | sk_Xb1(X12) = cZ
3.78/4.07	       | sk_Xa1(X12)
3.78/4.07	          = app_encode_app(a, a, 
3.78/4.07	              app_encode_app(a, app_encode_fun(a, a), cP, sk_Xx11(X12)), 
3.78/4.07	              sk_Xx21(X12))),
3.78/4.07	    inference('cnf', [status(esa)], [zf_stmt_0])).
3.78/4.07	tff('30', plain,
3.78/4.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
3.78/4.07	      (sk_Xa1(X0) != cZ
3.78/4.07	       | sk_Xb1(X0) = cZ
3.78/4.07	       | sk_Xb1(X0) = sk_Xc1(X0)
3.78/4.07	       | app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
3.78/4.07	               y), v), v)),
3.78/4.07	    inference('sup-', [status(thm)], ['29', '19'])).
3.78/4.07	tff('31', plain,
3.78/4.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
3.78/4.07	      (~ app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
3.78/4.07	               sk_Xa1(X0)), sk_Xb1(X0)), sk_Xb1(X0))
3.78/4.07	       | app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
3.78/4.07	               y), v), v)
3.78/4.07	       | sk_Xb1(X0) = cZ
3.78/4.07	       | sk_Xa1(X0) != cZ
3.78/4.07	       | app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
3.78/4.07	               y), v), v)),
3.78/4.07	    inference('sup-', [status(thm)], ['30', '16'])).
3.78/4.07	tff('32', plain,
3.78/4.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
3.78/4.07	      (sk_Xa1(X0) != cZ
3.78/4.07	       | sk_Xb1(X0) = cZ
3.78/4.07	       | app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
3.78/4.07	               y), v), v)
3.78/4.07	       | ~ app_encode_app(a, $o, 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
3.78/4.07	                 X0, sk_Xa1(X0)), sk_Xb1(X0)), sk_Xb1(X0))),
3.78/4.07	    inference('simplify', [status(thm)], ['31'])).
3.78/4.07	tff('33', plain,
3.78/4.07	    (~ app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             cZ), sk_Xb1(sk_R)), sk_Xb1(sk_R))
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             y), v), v)
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             y), v), v)
3.78/4.07	     | sk_Xb1(sk_R) = cZ
3.78/4.07	     | sk_Xa1(sk_R) != cZ),
3.78/4.07	    inference('sup-', [status(thm)], ['28', '32'])).
3.78/4.07	tff('34', plain,
3.78/4.07	    ![X13 : a, X14 : a, X15 : a]:
3.78/4.07	      (app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             X13), X14), X15)
3.78/4.07	       | X13 != cZ
3.78/4.07	       | X14 != X15),
3.78/4.07	    inference('cnf', [status(esa)], [zf_stmt_0])).
3.78/4.07	tff('35', plain,
3.78/4.07	    ![X15 : a]:
3.78/4.07	      app_encode_app(a, $o, 
3.78/4.07	        app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	          app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	            cZ), X15), X15),
3.78/4.07	    inference('simplify', [status(thm)], ['34'])).
3.78/4.07	tff('36', plain,
3.78/4.07	    (~ $true
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             y), v), v)
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             y), v), v)
3.78/4.07	     | sk_Xb1(sk_R) = cZ
3.78/4.07	     | sk_Xa1(sk_R) != cZ),
3.78/4.07	    inference('demod', [status(thm)], ['33', '35'])).
3.78/4.07	tff('37', plain,
3.78/4.07	    (sk_Xa1(sk_R) != cZ
3.78/4.07	     | sk_Xb1(sk_R) = cZ
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             y), v), v)),
3.78/4.07	    inference('simplify', [status(thm)], ['36'])).
3.78/4.07	tff('38', plain,
3.78/4.07	    (app_encode_app(a, $o, 
3.78/4.07	       app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, y), 
3.78/4.07	         v), v)
3.78/4.07	     | sk_Xb1(sk_R) = cZ),
3.78/4.07	    inference('clc', [status(thm)], ['37', '28'])).
3.78/4.07	tff('39', plain,
3.78/4.07	    ![X12 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
3.78/4.07	      (app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X12, 
3.78/4.07	             y), v), v)
3.78/4.07	       | sk_Xb1(X12) = sk_Xc1(X12)
3.78/4.07	       | sk_Xa1(X12) = sk_Xc1(X12)
3.78/4.07	       | sk_Xa1(X12)
3.78/4.07	          = app_encode_app(a, a, 
3.78/4.07	              app_encode_app(a, app_encode_fun(a, a), cP, sk_Xx11(X12)), 
3.78/4.07	              sk_Xx21(X12))),
3.78/4.07	    inference('cnf', [status(esa)], [zf_stmt_0])).
3.78/4.07	tff('40', plain,
3.78/4.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
3.78/4.07	      (sk_Xa1(X0) != cZ
3.78/4.07	       | sk_Xa1(X0) = sk_Xc1(X0)
3.78/4.07	       | sk_Xb1(X0) = sk_Xc1(X0)
3.78/4.07	       | app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
3.78/4.07	               y), v), v)),
3.78/4.07	    inference('sup-', [status(thm)], ['39', '19'])).
3.78/4.07	tff('41', plain,
3.78/4.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
3.78/4.07	      (sk_Xb1(X0) != sk_Xa1(X0)
3.78/4.07	       | app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
3.78/4.07	               y), v), v)
3.78/4.07	       | sk_Xa1(X0) = sk_Xc1(X0)
3.78/4.07	       | sk_Xa1(X0) != cZ),
3.78/4.07	    inference('eq_fact', [status(thm)], ['40'])).
3.78/4.07	tff('42', plain,
3.78/4.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
3.78/4.07	      (~ app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
3.78/4.07	               sk_Xa1(X0)), sk_Xb1(X0)), sk_Xa1(X0))
3.78/4.07	       | sk_Xa1(X0) != cZ
3.78/4.07	       | app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
3.78/4.07	               y), v), v)
3.78/4.07	       | sk_Xb1(X0) != sk_Xa1(X0)
3.78/4.07	       | app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
3.78/4.07	               y), v), v)),
3.78/4.07	    inference('sup-', [status(thm)], ['41', '16'])).
3.78/4.07	tff('43', plain,
3.78/4.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
3.78/4.07	      (sk_Xb1(X0) != sk_Xa1(X0)
3.78/4.07	       | app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
3.78/4.07	               y), v), v)
3.78/4.07	       | sk_Xa1(X0) != cZ
3.78/4.07	       | ~ app_encode_app(a, $o, 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
3.78/4.07	                 X0, sk_Xa1(X0)), sk_Xb1(X0)), sk_Xa1(X0))),
3.78/4.07	    inference('simplify', [status(thm)], ['42'])).
3.78/4.07	tff('44', plain,
3.78/4.07	    (~ app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             sk_Xa1(sk_R)), cZ), sk_Xa1(sk_R))
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             y), v), v)
3.78/4.07	     | sk_Xa1(sk_R) != cZ
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             y), v), v)
3.78/4.07	     | sk_Xb1(sk_R) != sk_Xa1(sk_R)),
3.78/4.07	    inference('sup-', [status(thm)], ['38', '43'])).
3.78/4.07	tff('45', plain,
3.78/4.07	    (~ $true
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             y), v), v)
3.78/4.07	     | sk_Xa1(sk_R) != cZ
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             y), v), v)
3.78/4.07	     | sk_Xb1(sk_R) != sk_Xa1(sk_R)),
3.78/4.07	    inference('demod', [status(thm)], ['44', '25'])).
3.78/4.07	tff('46', plain,
3.78/4.07	    (sk_Xb1(sk_R) != sk_Xa1(sk_R)
3.78/4.07	     | sk_Xa1(sk_R) != cZ
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             y), v), v)),
3.78/4.07	    inference('simplify', [status(thm)], ['45'])).
3.78/4.07	tff('47', plain,
3.78/4.07	    (app_encode_app(a, $o, 
3.78/4.07	       app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, y), 
3.78/4.07	         v), v)
3.78/4.07	     | sk_Xb1(sk_R) != sk_Xa1(sk_R)),
3.78/4.07	    inference('clc', [status(thm)], ['46', '28'])).
3.78/4.07	tff('48', plain,
3.78/4.07	    (cZ != sk_Xa1(sk_R)
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             y), v), v)
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             y), v), v)),
3.78/4.07	    inference('sup-', [status(thm)], ['38', '47'])).
3.78/4.07	tff('49', plain,
3.78/4.07	    (app_encode_app(a, $o, 
3.78/4.07	       app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, y), 
3.78/4.07	         v), v)
3.78/4.07	     | cZ != sk_Xa1(sk_R)),
3.78/4.07	    inference('simplify', [status(thm)], ['48'])).
3.78/4.07	tff('50', plain,
3.78/4.07	    app_encode_app(a, $o, 
3.78/4.07	      app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	        app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, y), 
3.78/4.07	        v), v),
3.78/4.07	    inference('clc', [status(thm)], ['49', '28'])).
3.78/4.07	tff('51', plain,
3.78/4.07	    ~ app_encode_app(a, $o, 
3.78/4.07	        app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	          app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	            app_encode_app(a, a, 
3.78/4.07	              app_encode_app(a, app_encode_fun(a, a), cP, x), y)), 
3.78/4.07	          app_encode_app(a, a, 
3.78/4.07	            app_encode_app(a, app_encode_fun(a, a), cP, u), v)), 
3.78/4.07	        app_encode_app(a, a, app_encode_app(a, app_encode_fun(a, a), cP, u), 
3.78/4.07	          v)),
3.78/4.07	    inference('cnf', [status(esa)], [zf_stmt_0])).
3.78/4.07	tff('52', plain,
3.78/4.07	    (~ $true
3.78/4.07	     | ~ app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
3.78/4.07	               sk_R, x), u), u)
3.78/4.07	     | ~ app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
3.78/4.07	               sk_R, y), v), v)),
3.78/4.07	    inference('sup-', [status(thm)], ['6', '51'])).
3.78/4.07	tff('53', plain,
3.78/4.07	    (~ app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             y), v), v)
3.78/4.07	     | ~ app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
3.78/4.07	               sk_R, x), u), u)),
3.78/4.07	    inference('simplify', [status(thm)], ['52'])).
3.78/4.07	tff('54', plain,
3.78/4.07	    (~ $true
3.78/4.07	     | ~ app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
3.78/4.07	               sk_R, x), u), u)),
3.78/4.07	    inference('sup-', [status(thm)], ['50', '53'])).
3.78/4.07	tff('55', plain,
3.78/4.07	    ![X22 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
3.78/4.07	      (app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X22, 
3.78/4.07	             x), u), u)
3.78/4.07	       | sk_Xa(X22) = cZ
3.78/4.07	       | sk_Xb(X22) = cZ
3.78/4.07	       | sk_Xc(X22)
3.78/4.07	          = app_encode_app(a, a, 
3.78/4.07	              app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz1(X22)), 
3.78/4.07	              sk_Xz2(X22))),
3.78/4.07	    inference('cnf', [status(esa)], [zf_stmt_0])).
3.78/4.07	tff('56', plain,
3.78/4.07	    ![X22 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
3.78/4.07	      (app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X22, 
3.78/4.07	             x), u), u)
3.78/4.07	       | sk_Xa(X22) = cZ
3.78/4.07	       | sk_Xb(X22) = cZ
3.78/4.07	       | sk_Xb(X22)
3.78/4.07	          = app_encode_app(a, a, 
3.78/4.07	              app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy1(X22)), 
3.78/4.07	              sk_Xy2(X22))),
3.78/4.07	    inference('cnf', [status(esa)], [zf_stmt_0])).
3.78/4.07	tff('57', plain,
3.78/4.07	    ![X22 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
3.78/4.07	      (app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X22, 
3.78/4.07	             x), u), u)
3.78/4.07	       | sk_Xa(X22) = cZ
3.78/4.07	       | sk_Xb(X22) = cZ
3.78/4.07	       | app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
3.78/4.07	               X22, sk_Xx2(X22)), sk_Xy2(X22)), sk_Xz2(X22))),
3.78/4.07	    inference('cnf', [status(esa)], [zf_stmt_0])).
3.78/4.07	tff('58', plain,
3.78/4.07	    ![X22 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
3.78/4.07	      (app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X22, 
3.78/4.07	             x), u), u)
3.78/4.07	       | sk_Xa(X22) = cZ
3.78/4.07	       | sk_Xb(X22) = cZ
3.78/4.07	       | app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
3.78/4.07	               X22, sk_Xx1(X22)), sk_Xy1(X22)), sk_Xz1(X22))),
3.78/4.07	    inference('cnf', [status(esa)], [zf_stmt_0])).
3.78/4.07	tff('59', plain,
3.78/4.07	    ![X22 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
3.78/4.07	      (app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X22, 
3.78/4.07	             x), u), u)
3.78/4.07	       | sk_Xa(X22) = cZ
3.78/4.07	       | sk_Xb(X22) = cZ
3.78/4.07	       | sk_Xa(X22)
3.78/4.07	          = app_encode_app(a, a, 
3.78/4.07	              app_encode_app(a, app_encode_fun(a, a), cP, sk_Xx1(X22)), 
3.78/4.07	              sk_Xx2(X22))),
3.78/4.07	    inference('cnf', [status(esa)], [zf_stmt_0])).
3.78/4.07	tff('60', plain,
3.78/4.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o))), 
3.78/4.07	      X1 : a, X2 : a, X3 : a, X4 : a]:
3.78/4.07	      (app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             sk_Xa(X0)), 
3.78/4.07	           app_encode_app(a, a, 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, a), cP, X4), X3)), 
3.78/4.07	         app_encode_app(a, a, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, a), cP, X2), X1))
3.78/4.07	       | sk_Xb(X0) = cZ
3.78/4.07	       | sk_Xa(X0) = cZ
3.78/4.07	       | app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
3.78/4.07	               x), u), u)
3.78/4.07	       | ~ app_encode_app(a, $o, 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
3.78/4.07	                 sk_R, sk_Xx1(X0)), X4), X2)
3.78/4.07	       | ~ app_encode_app(a, $o, 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
3.78/4.07	                 sk_R, sk_Xx2(X0)), X3), X1)),
3.78/4.07	    inference('sup+', [status(thm)], ['59', '6'])).
3.78/4.07	tff('61', plain,
3.78/4.07	    ![X0 : a, X1 : a]:
3.78/4.07	      (~ $true
3.78/4.07	       | sk_Xb(sk_R) = cZ
3.78/4.07	       | sk_Xa(sk_R) = cZ
3.78/4.07	       | app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
3.78/4.07	               sk_R, x), u), u)
3.78/4.07	       | ~ app_encode_app(a, $o, 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
3.78/4.07	                 sk_R, sk_Xx2(sk_R)), X1), X0)
3.78/4.07	       | app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
3.78/4.07	               sk_R, x), u), u)
3.78/4.07	       | sk_Xa(sk_R) = cZ
3.78/4.07	       | sk_Xb(sk_R) = cZ
3.78/4.07	       | app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
3.78/4.07	               sk_R, sk_Xa(sk_R)), 
3.78/4.07	             app_encode_app(a, a, 
3.78/4.07	               app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy1(sk_R)), X1)), 
3.78/4.07	           app_encode_app(a, a, 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz1(sk_R)), X0))),
3.78/4.07	    inference('sup-', [status(thm)], ['58', '60'])).
3.78/4.07	tff('62', plain,
3.78/4.07	    ![X0 : a, X1 : a]:
3.78/4.07	      (app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             sk_Xa(sk_R)), 
3.78/4.07	           app_encode_app(a, a, 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy1(sk_R)), X1)), 
3.78/4.07	         app_encode_app(a, a, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz1(sk_R)), X0))
3.78/4.07	       | ~ app_encode_app(a, $o, 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
3.78/4.07	                 sk_R, sk_Xx2(sk_R)), X1), X0)
3.78/4.07	       | app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
3.78/4.07	               sk_R, x), u), u)
3.78/4.07	       | sk_Xa(sk_R) = cZ
3.78/4.07	       | sk_Xb(sk_R) = cZ),
3.78/4.07	    inference('simplify', [status(thm)], ['61'])).
3.78/4.07	tff('63', plain,
3.78/4.07	    (~ $true
3.78/4.07	     | sk_Xb(sk_R) = cZ
3.78/4.07	     | sk_Xa(sk_R) = cZ
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             x), u), u)
3.78/4.07	     | sk_Xb(sk_R) = cZ
3.78/4.07	     | sk_Xa(sk_R) = cZ
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             x), u), u)
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             sk_Xa(sk_R)), 
3.78/4.07	           app_encode_app(a, a, 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy1(sk_R)), 
3.78/4.07	             sk_Xy2(sk_R))), 
3.78/4.07	         app_encode_app(a, a, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz1(sk_R)), 
3.78/4.07	           sk_Xz2(sk_R)))),
3.78/4.07	    inference('sup-', [status(thm)], ['57', '62'])).
3.78/4.07	tff('64', plain,
3.78/4.07	    (app_encode_app(a, $o, 
3.78/4.07	       app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	           sk_Xa(sk_R)), 
3.78/4.07	         app_encode_app(a, a, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy1(sk_R)), 
3.78/4.07	           sk_Xy2(sk_R))), 
3.78/4.07	       app_encode_app(a, a, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz1(sk_R)), 
3.78/4.07	         sk_Xz2(sk_R)))
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             x), u), u)
3.78/4.07	     | sk_Xa(sk_R) = cZ
3.78/4.07	     | sk_Xb(sk_R) = cZ),
3.78/4.07	    inference('simplify', [status(thm)], ['63'])).
3.78/4.07	tff('65', plain,
3.78/4.07	    (app_encode_app(a, $o, 
3.78/4.07	       app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	           sk_Xa(sk_R)), sk_Xb(sk_R)), 
3.78/4.07	       app_encode_app(a, a, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz1(sk_R)), 
3.78/4.07	         sk_Xz2(sk_R)))
3.78/4.07	     | sk_Xb(sk_R) = cZ
3.78/4.07	     | sk_Xa(sk_R) = cZ
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             x), u), u)
3.78/4.07	     | sk_Xb(sk_R) = cZ
3.78/4.07	     | sk_Xa(sk_R) = cZ
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             x), u), u)),
3.78/4.07	    inference('sup+', [status(thm)], ['56', '64'])).
3.78/4.07	tff('66', plain,
3.78/4.07	    (app_encode_app(a, $o, 
3.78/4.07	       app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, x), 
3.78/4.07	         u), u)
3.78/4.07	     | sk_Xa(sk_R) = cZ
3.78/4.07	     | sk_Xb(sk_R) = cZ
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             sk_Xa(sk_R)), sk_Xb(sk_R)), 
3.78/4.07	         app_encode_app(a, a, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, a), cP, sk_Xz1(sk_R)), 
3.78/4.07	           sk_Xz2(sk_R)))),
3.78/4.07	    inference('simplify', [status(thm)], ['65'])).
3.78/4.07	tff('67', plain,
3.78/4.07	    (app_encode_app(a, $o, 
3.78/4.07	       app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	           sk_Xa(sk_R)), sk_Xb(sk_R)), sk_Xc(sk_R))
3.78/4.07	     | sk_Xb(sk_R) = cZ
3.78/4.07	     | sk_Xa(sk_R) = cZ
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             x), u), u)
3.78/4.07	     | sk_Xb(sk_R) = cZ
3.78/4.07	     | sk_Xa(sk_R) = cZ
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             x), u), u)),
3.78/4.07	    inference('sup+', [status(thm)], ['55', '66'])).
3.78/4.07	tff('68', plain,
3.78/4.07	    (app_encode_app(a, $o, 
3.78/4.07	       app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, x), 
3.78/4.07	         u), u)
3.78/4.07	     | sk_Xa(sk_R) = cZ
3.78/4.07	     | sk_Xb(sk_R) = cZ
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             sk_Xa(sk_R)), sk_Xb(sk_R)), sk_Xc(sk_R))),
3.78/4.07	    inference('simplify', [status(thm)], ['67'])).
3.78/4.07	tff('69', plain,
3.78/4.07	    ![X22 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
3.78/4.07	      (app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X22, 
3.78/4.07	             x), u), u)
3.78/4.07	       | ~ app_encode_app(a, $o, 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
3.78/4.07	                 X22, sk_Xa(X22)), sk_Xb(X22)), sk_Xc(X22))),
3.78/4.07	    inference('cnf', [status(esa)], [zf_stmt_0])).
3.78/4.07	tff('70', plain,
3.78/4.07	    (sk_Xb(sk_R) = cZ
3.78/4.07	     | sk_Xa(sk_R) = cZ
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             x), u), u)),
3.78/4.07	    inference('clc', [status(thm)], ['68', '69'])).
3.78/4.07	tff('71', plain,
3.78/4.07	    ![X22 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
3.78/4.07	      (app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X22, 
3.78/4.07	             x), u), u)
3.78/4.07	       | sk_Xa(X22) = cZ
3.78/4.07	       | sk_Xa(X22) = sk_Xc(X22)
3.78/4.07	       | sk_Xb(X22)
3.78/4.07	          = app_encode_app(a, a, 
3.78/4.07	              app_encode_app(a, app_encode_fun(a, a), cP, sk_Xy1(X22)), 
3.78/4.07	              sk_Xy2(X22))),
3.78/4.07	    inference('cnf', [status(esa)], [zf_stmt_0])).
3.78/4.07	tff('72', plain,
3.78/4.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
3.78/4.07	      (sk_Xb(X0) != cZ
3.78/4.07	       | sk_Xa(X0) = sk_Xc(X0)
3.78/4.07	       | sk_Xa(X0) = cZ
3.78/4.07	       | app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
3.78/4.07	               x), u), u)),
3.78/4.07	    inference('sup-', [status(thm)], ['71', '19'])).
3.78/4.07	tff('73', plain,
3.78/4.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
3.78/4.07	      (~ app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
3.78/4.07	               sk_Xa(X0)), sk_Xb(X0)), sk_Xa(X0))
3.78/4.07	       | app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
3.78/4.07	               x), u), u)
3.78/4.07	       | sk_Xa(X0) = cZ
3.78/4.07	       | sk_Xb(X0) != cZ
3.78/4.07	       | app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
3.78/4.07	               x), u), u)),
3.78/4.07	    inference('sup-', [status(thm)], ['72', '69'])).
3.78/4.07	tff('74', plain,
3.78/4.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
3.78/4.07	      (sk_Xb(X0) != cZ
3.78/4.07	       | sk_Xa(X0) = cZ
3.78/4.07	       | app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
3.78/4.07	               x), u), u)
3.78/4.07	       | ~ app_encode_app(a, $o, 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
3.78/4.07	                 X0, sk_Xa(X0)), sk_Xb(X0)), sk_Xa(X0))),
3.78/4.07	    inference('simplify', [status(thm)], ['73'])).
3.78/4.07	tff('75', plain,
3.78/4.07	    (~ app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             sk_Xa(sk_R)), cZ), sk_Xa(sk_R))
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             x), u), u)
3.78/4.07	     | sk_Xa(sk_R) = cZ
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             x), u), u)
3.78/4.07	     | sk_Xa(sk_R) = cZ
3.78/4.07	     | sk_Xb(sk_R) != cZ),
3.78/4.07	    inference('sup-', [status(thm)], ['70', '74'])).
3.78/4.07	tff('76', plain,
3.78/4.07	    (~ $true
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             x), u), u)
3.78/4.07	     | sk_Xa(sk_R) = cZ
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             x), u), u)
3.78/4.07	     | sk_Xa(sk_R) = cZ
3.78/4.07	     | sk_Xb(sk_R) != cZ),
3.78/4.07	    inference('demod', [status(thm)], ['75', '25'])).
3.78/4.07	tff('77', plain,
3.78/4.07	    (sk_Xb(sk_R) != cZ
3.78/4.07	     | sk_Xa(sk_R) = cZ
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             x), u), u)),
3.78/4.07	    inference('simplify', [status(thm)], ['76'])).
3.78/4.07	tff('78', plain,
3.78/4.07	    (app_encode_app(a, $o, 
3.78/4.07	       app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, x), 
3.78/4.07	         u), u)
3.78/4.07	     | sk_Xa(sk_R) = cZ),
3.78/4.07	    inference('clc', [status(thm)], ['77', '70'])).
3.78/4.07	tff('79', plain,
3.78/4.07	    ![X22 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
3.78/4.07	      (app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X22, 
3.78/4.07	             x), u), u)
3.78/4.07	       | sk_Xb(X22) = sk_Xc(X22)
3.78/4.07	       | sk_Xb(X22) = cZ
3.78/4.07	       | sk_Xa(X22)
3.78/4.07	          = app_encode_app(a, a, 
3.78/4.07	              app_encode_app(a, app_encode_fun(a, a), cP, sk_Xx1(X22)), 
3.78/4.07	              sk_Xx2(X22))),
3.78/4.07	    inference('cnf', [status(esa)], [zf_stmt_0])).
3.78/4.07	tff('80', plain,
3.78/4.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
3.78/4.07	      (sk_Xa(X0) != cZ
3.78/4.07	       | sk_Xb(X0) = cZ
3.78/4.07	       | sk_Xb(X0) = sk_Xc(X0)
3.78/4.07	       | app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
3.78/4.07	               x), u), u)),
3.78/4.07	    inference('sup-', [status(thm)], ['79', '19'])).
3.78/4.07	tff('81', plain,
3.78/4.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
3.78/4.07	      (~ app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
3.78/4.07	               sk_Xa(X0)), sk_Xb(X0)), sk_Xb(X0))
3.78/4.07	       | app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
3.78/4.07	               x), u), u)
3.78/4.07	       | sk_Xb(X0) = cZ
3.78/4.07	       | sk_Xa(X0) != cZ
3.78/4.07	       | app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
3.78/4.07	               x), u), u)),
3.78/4.07	    inference('sup-', [status(thm)], ['80', '69'])).
3.78/4.07	tff('82', plain,
3.78/4.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
3.78/4.07	      (sk_Xa(X0) != cZ
3.78/4.07	       | sk_Xb(X0) = cZ
3.78/4.07	       | app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
3.78/4.07	               x), u), u)
3.78/4.07	       | ~ app_encode_app(a, $o, 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
3.78/4.07	                 X0, sk_Xa(X0)), sk_Xb(X0)), sk_Xb(X0))),
3.78/4.07	    inference('simplify', [status(thm)], ['81'])).
3.78/4.07	tff('83', plain,
3.78/4.07	    (~ app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             cZ), sk_Xb(sk_R)), sk_Xb(sk_R))
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             x), u), u)
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             x), u), u)
3.78/4.07	     | sk_Xb(sk_R) = cZ
3.78/4.07	     | sk_Xa(sk_R) != cZ),
3.78/4.07	    inference('sup-', [status(thm)], ['78', '82'])).
3.78/4.07	tff('84', plain,
3.78/4.07	    (~ $true
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             x), u), u)
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             x), u), u)
3.78/4.07	     | sk_Xb(sk_R) = cZ
3.78/4.07	     | sk_Xa(sk_R) != cZ),
3.78/4.07	    inference('demod', [status(thm)], ['83', '35'])).
3.78/4.07	tff('85', plain,
3.78/4.07	    (sk_Xa(sk_R) != cZ
3.78/4.07	     | sk_Xb(sk_R) = cZ
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             x), u), u)),
3.78/4.07	    inference('simplify', [status(thm)], ['84'])).
3.78/4.07	tff('86', plain,
3.78/4.07	    (app_encode_app(a, $o, 
3.78/4.07	       app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, x), 
3.78/4.07	         u), u)
3.78/4.07	     | sk_Xb(sk_R) = cZ),
3.78/4.07	    inference('clc', [status(thm)], ['85', '78'])).
3.78/4.07	tff('87', plain,
3.78/4.07	    ![X22 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
3.78/4.07	      (app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X22, 
3.78/4.07	             x), u), u)
3.78/4.07	       | sk_Xb(X22) = sk_Xc(X22)
3.78/4.07	       | sk_Xa(X22) = sk_Xc(X22)
3.78/4.07	       | sk_Xa(X22)
3.78/4.07	          = app_encode_app(a, a, 
3.78/4.07	              app_encode_app(a, app_encode_fun(a, a), cP, sk_Xx1(X22)), 
3.78/4.07	              sk_Xx2(X22))),
3.78/4.07	    inference('cnf', [status(esa)], [zf_stmt_0])).
3.78/4.07	tff('88', plain,
3.78/4.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
3.78/4.07	      (sk_Xa(X0) != cZ
3.78/4.07	       | sk_Xa(X0) = sk_Xc(X0)
3.78/4.07	       | sk_Xb(X0) = sk_Xc(X0)
3.78/4.07	       | app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
3.78/4.07	               x), u), u)),
3.78/4.07	    inference('sup-', [status(thm)], ['87', '19'])).
3.78/4.07	tff('89', plain,
3.78/4.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
3.78/4.07	      (sk_Xb(X0) != sk_Xa(X0)
3.78/4.07	       | app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
3.78/4.07	               x), u), u)
3.78/4.07	       | sk_Xa(X0) = sk_Xc(X0)
3.78/4.07	       | sk_Xa(X0) != cZ),
3.78/4.07	    inference('eq_fact', [status(thm)], ['88'])).
3.78/4.07	tff('90', plain,
3.78/4.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
3.78/4.07	      (~ app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
3.78/4.07	               sk_Xa(X0)), sk_Xb(X0)), sk_Xa(X0))
3.78/4.07	       | sk_Xa(X0) != cZ
3.78/4.07	       | app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
3.78/4.07	               x), u), u)
3.78/4.07	       | sk_Xb(X0) != sk_Xa(X0)
3.78/4.07	       | app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
3.78/4.07	               x), u), u)),
3.78/4.07	    inference('sup-', [status(thm)], ['89', '69'])).
3.78/4.07	tff('91', plain,
3.78/4.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, app_encode_fun(a, $o)))]:
3.78/4.07	      (sk_Xb(X0) != sk_Xa(X0)
3.78/4.07	       | app_encode_app(a, $o, 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), X0, 
3.78/4.07	               x), u), u)
3.78/4.07	       | sk_Xa(X0) != cZ
3.78/4.07	       | ~ app_encode_app(a, $o, 
3.78/4.07	             app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	               app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), 
3.78/4.07	                 X0, sk_Xa(X0)), sk_Xb(X0)), sk_Xa(X0))),
3.78/4.07	    inference('simplify', [status(thm)], ['90'])).
3.78/4.07	tff('92', plain,
3.78/4.07	    (~ app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             sk_Xa(sk_R)), cZ), sk_Xa(sk_R))
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             x), u), u)
3.78/4.07	     | sk_Xa(sk_R) != cZ
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             x), u), u)
3.78/4.07	     | sk_Xb(sk_R) != sk_Xa(sk_R)),
3.78/4.07	    inference('sup-', [status(thm)], ['86', '91'])).
3.78/4.07	tff('93', plain,
3.78/4.07	    (~ $true
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             x), u), u)
3.78/4.07	     | sk_Xa(sk_R) != cZ
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             x), u), u)
3.78/4.07	     | sk_Xb(sk_R) != sk_Xa(sk_R)),
3.78/4.07	    inference('demod', [status(thm)], ['92', '25'])).
3.78/4.07	tff('94', plain,
3.78/4.07	    (sk_Xb(sk_R) != sk_Xa(sk_R)
3.78/4.07	     | sk_Xa(sk_R) != cZ
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             x), u), u)),
3.78/4.07	    inference('simplify', [status(thm)], ['93'])).
3.78/4.07	tff('95', plain,
3.78/4.07	    (app_encode_app(a, $o, 
3.78/4.07	       app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, x), 
3.78/4.07	         u), u)
3.78/4.07	     | sk_Xb(sk_R) != sk_Xa(sk_R)),
3.78/4.07	    inference('clc', [status(thm)], ['94', '78'])).
3.78/4.07	tff('96', plain,
3.78/4.07	    (cZ != sk_Xa(sk_R)
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             x), u), u)
3.78/4.07	     | app_encode_app(a, $o, 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	           app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, 
3.78/4.07	             x), u), u)),
3.78/4.07	    inference('sup-', [status(thm)], ['86', '95'])).
3.78/4.07	tff('97', plain,
3.78/4.07	    (app_encode_app(a, $o, 
3.78/4.07	       app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	         app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, x), 
3.78/4.07	         u), u)
3.78/4.07	     | cZ != sk_Xa(sk_R)),
3.78/4.07	    inference('simplify', [status(thm)], ['96'])).
3.78/4.07	tff('98', plain,
3.78/4.07	    app_encode_app(a, $o, 
3.78/4.07	      app_encode_app(a, app_encode_fun(a, $o), 
3.78/4.07	        app_encode_app(a, app_encode_fun(a, app_encode_fun(a, $o)), sk_R, x), 
3.78/4.07	        u), u),
3.78/4.07	    inference('clc', [status(thm)], ['97', '78'])).
3.78/4.07	tff('99', plain, (~ $true | ~ $true),
3.78/4.07	    inference('demod', [status(thm)], ['54', '98'])).
3.78/4.07	tff('100', plain, $false, inference('simplify', [status(thm)], ['99'])).
3.78/4.07	
3.78/4.07	% SZS output end Refutation
3.78/4.07	EOF
