0.00/0.00	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : appext
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : rpo6
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n142.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 17:59:54 CST 2018
3.76/3.97	% done 2540 iterations in 3.773s
3.76/3.97	% SZS status Theorem for 'stdin'
3.76/3.97	% SZS output start Refutation
3.76/3.97	tff(zf_stmt_6, conjecture,
3.76/3.97	  (((![Xx:iS,Xy:iS]:
3.76/3.97	       (app_encode_app(iS,iS,app_encode_app(iS,app_encode_fun(iS,iS),cP,Xx),
3.76/3.97	                       Xy) !=
3.76/3.97	        c0)) & 
3.76/3.97	    (![Xx:iS,Xy:iS,Xu:iS,Xv:iS]:
3.76/3.97	       ((app_encode_app(iS,iS,app_encode_app(iS,app_encode_fun(iS,iS),cP,Xx),
3.76/3.97	                        Xu) =
3.76/3.97	         app_encode_app(iS,iS,app_encode_app(iS,app_encode_fun(iS,iS),cP,Xy),
3.76/3.97	                        Xv)) =>
3.76/3.97	        ((Xx = Xy) & (Xu = Xv)))) & 
3.76/3.97	    (![X:app_encode_fun(iS,$o)]:
3.76/3.97	       ((app_encode_app(iS,$o,X,c0) & 
3.76/3.97	         (![Xx:iS,Xy:iS]:
3.76/3.97	            ((app_encode_app(iS,$o,X,Xx) & app_encode_app(iS,$o,X,Xy)) =>
3.76/3.97	             app_encode_app(iS,$o,X,
3.76/3.97	                            app_encode_app(iS,iS,
3.76/3.97	                                           app_encode_app(iS,
3.76/3.97	                                                          app_encode_fun(
3.76/3.97	                                                          iS,iS),cP,Xx),
3.76/3.97	                                           Xy))))) =>
3.76/3.97	        (![Xx:iS]: app_encode_app(iS,$o,X,Xx))))) =>
3.76/3.97	   (![Xx:iS,Xy:iS,Xu:iS,Xv:iS]:
3.76/3.97	      (((![R:app_encode_fun(iS,app_encode_fun(iS,app_encode_fun(iS,$o)))]:
3.76/3.97	           ((![Xa:iS,Xb:iS,Xc:iS]:
3.76/3.97	               ((((Xa = c0) & (Xb = Xc)) | ((Xb = c0) & (Xa = Xc)) | 
3.76/3.97	                 (?[Xx1:iS,Xx2:iS,Xy1:iS,Xy2:iS,Xz1:iS,Xz2:iS]:
3.76/3.97	                    ((Xa =
3.76/3.97	                      app_encode_app(iS,iS,
3.76/3.97	                                     app_encode_app(iS,app_encode_fun(iS,iS),
3.76/3.97	                                                    cP,Xx1),
3.76/3.97	                                     Xx2)) & 
3.76/3.97	                     (Xb =
3.76/3.97	                      app_encode_app(iS,iS,
3.76/3.97	                                     app_encode_app(iS,app_encode_fun(iS,iS),
3.76/3.97	                                                    cP,Xy1),
3.76/3.97	                                     Xy2)) & 
3.76/3.97	                     (Xc =
3.76/3.97	                      app_encode_app(iS,iS,
3.76/3.97	                                     app_encode_app(iS,app_encode_fun(iS,iS),
3.76/3.97	                                                    cP,Xz1),
3.76/3.97	                                     Xz2)) & 
3.76/3.97	                     app_encode_app(iS,$o,
3.76/3.97	                                    app_encode_app(iS,app_encode_fun(iS,$o),
3.76/3.97	                                                   app_encode_app(iS,
3.76/3.97	                                                                  app_encode_fun(
3.76/3.97	                                                                  iS,
3.76/3.97	                                                                  app_encode_fun(
3.76/3.97	                                                                  iS,$o)),R,
3.76/3.97	                                                                  Xx1),
3.76/3.97	                                                   Xy1),
3.76/3.97	                                    Xz1) & 
3.76/3.97	                     app_encode_app(iS,$o,
3.76/3.97	                                    app_encode_app(iS,app_encode_fun(iS,$o),
3.76/3.97	                                                   app_encode_app(iS,
3.76/3.97	                                                                  app_encode_fun(
3.76/3.97	                                                                  iS,
3.76/3.97	                                                                  app_encode_fun(
3.76/3.97	                                                                  iS,$o)),R,
3.76/3.97	                                                                  Xx2),
3.76/3.97	                                                   Xy2),
3.76/3.97	                                    Xz2)))) =>
3.76/3.97	                app_encode_app(iS,$o,
3.76/3.97	                               app_encode_app(iS,app_encode_fun(iS,$o),
3.76/3.97	                                              app_encode_app(iS,
3.76/3.97	                                                             app_encode_fun(
3.76/3.97	                                                             iS,
3.76/3.97	                                                             app_encode_fun(
3.76/3.97	                                                             iS,$o)),R,Xa),
3.76/3.97	                                              Xb),
3.76/3.97	                               Xc))) =>
3.76/3.97	            app_encode_app(iS,$o,
3.76/3.97	                           app_encode_app(iS,app_encode_fun(iS,$o),
3.76/3.97	                                          app_encode_app(iS,
3.76/3.97	                                                         app_encode_fun(
3.76/3.97	                                                         iS,
3.76/3.97	                                                         app_encode_fun(
3.76/3.97	                                                         iS,$o)),R,Xx),
3.76/3.97	                                          Xy),
3.76/3.97	                           Xy))) & 
3.76/3.97	        (![R:app_encode_fun(iS,app_encode_fun(iS,app_encode_fun(iS,$o)))]:
3.76/3.97	           ((![Xa:iS,Xb:iS,Xc:iS]:
3.76/3.97	               ((((Xa = c0) & (Xb = Xc)) | ((Xb = c0) & (Xa = Xc)) | 
3.76/3.97	                 (?[Xx1:iS,Xx2:iS,Xy1:iS,Xy2:iS,Xz1:iS,Xz2:iS]:
3.76/3.97	                    ((Xa =
3.76/3.97	                      app_encode_app(iS,iS,
3.76/3.97	                                     app_encode_app(iS,app_encode_fun(iS,iS),
3.76/3.97	                                                    cP,Xx1),
3.76/3.97	                                     Xx2)) & 
3.76/3.97	                     (Xb =
3.76/3.97	                      app_encode_app(iS,iS,
3.76/3.97	                                     app_encode_app(iS,app_encode_fun(iS,iS),
3.76/3.97	                                                    cP,Xy1),
3.76/3.97	                                     Xy2)) & 
3.76/3.97	                     (Xc =
3.76/3.97	                      app_encode_app(iS,iS,
3.76/3.97	                                     app_encode_app(iS,app_encode_fun(iS,iS),
3.76/3.97	                                                    cP,Xz1),
3.76/3.97	                                     Xz2)) & 
3.76/3.97	                     app_encode_app(iS,$o,
3.76/3.97	                                    app_encode_app(iS,app_encode_fun(iS,$o),
3.76/3.97	                                                   app_encode_app(iS,
3.76/3.97	                                                                  app_encode_fun(
3.76/3.97	                                                                  iS,
3.76/3.97	                                                                  app_encode_fun(
3.76/3.97	                                                                  iS,$o)),R,
3.76/3.97	                                                                  Xx1),
3.76/3.97	                                                   Xy1),
3.76/3.97	                                    Xz1) & 
3.76/3.97	                     app_encode_app(iS,$o,
3.76/3.97	                                    app_encode_app(iS,app_encode_fun(iS,$o),
3.76/3.97	                                                   app_encode_app(iS,
3.76/3.97	                                                                  app_encode_fun(
3.76/3.97	                                                                  iS,
3.76/3.97	                                                                  app_encode_fun(
3.76/3.97	                                                                  iS,$o)),R,
3.76/3.97	                                                                  Xx2),
3.76/3.97	                                                   Xy2),
3.76/3.97	                                    Xz2)))) =>
3.76/3.97	                app_encode_app(iS,$o,
3.76/3.97	                               app_encode_app(iS,app_encode_fun(iS,$o),
3.76/3.97	                                              app_encode_app(iS,
3.76/3.97	                                                             app_encode_fun(
3.76/3.97	                                                             iS,
3.76/3.97	                                                             app_encode_fun(
3.76/3.97	                                                             iS,$o)),R,Xa),
3.76/3.97	                                              Xb),
3.76/3.97	                               Xc))) =>
3.76/3.97	            app_encode_app(iS,$o,
3.76/3.97	                           app_encode_app(iS,app_encode_fun(iS,$o),
3.76/3.97	                                          app_encode_app(iS,
3.76/3.97	                                                         app_encode_fun(
3.76/3.97	                                                         iS,
3.76/3.97	                                                         app_encode_fun(
3.76/3.97	                                                         iS,$o)),R,Xu),
3.76/3.97	                                          Xv),
3.76/3.97	                           Xv)))) =>
3.76/3.97	       (![R:app_encode_fun(iS,app_encode_fun(iS,app_encode_fun(iS,$o)))]:
3.76/3.97	          ((![Xa:iS,Xb:iS,Xc:iS]:
3.76/3.97	              ((((Xa = c0) & (Xb = Xc)) | ((Xb = c0) & (Xa = Xc)) | 
3.76/3.97	                (?[Xx1:iS,Xx2:iS,Xy1:iS,Xy2:iS,Xz1:iS,Xz2:iS]:
3.76/3.97	                   ((Xa =
3.76/3.97	                     app_encode_app(iS,iS,
3.76/3.97	                                    app_encode_app(iS,app_encode_fun(iS,iS),
3.76/3.97	                                                   cP,Xx1),
3.76/3.97	                                    Xx2)) & 
3.76/3.97	                    (Xb =
3.76/3.97	                     app_encode_app(iS,iS,
3.76/3.97	                                    app_encode_app(iS,app_encode_fun(iS,iS),
3.76/3.97	                                                   cP,Xy1),
3.76/3.97	                                    Xy2)) & 
3.76/3.97	                    (Xc =
3.76/3.97	                     app_encode_app(iS,iS,
3.76/3.97	                                    app_encode_app(iS,app_encode_fun(iS,iS),
3.76/3.97	                                                   cP,Xz1),
3.76/3.97	                                    Xz2)) & 
3.76/3.97	                    app_encode_app(iS,$o,
3.76/3.97	                                   app_encode_app(iS,app_encode_fun(iS,$o),
3.76/3.97	                                                  app_encode_app(iS,
3.76/3.97	                                                                 app_encode_fun(
3.76/3.97	                                                                 iS,
3.76/3.97	                                                                 app_encode_fun(
3.76/3.97	                                                                 iS,$o)),R,
3.76/3.97	                                                                 Xx1),
3.76/3.97	                                                  Xy1),
3.76/3.97	                                   Xz1) & 
3.76/3.97	                    app_encode_app(iS,$o,
3.76/3.97	                                   app_encode_app(iS,app_encode_fun(iS,$o),
3.76/3.97	                                                  app_encode_app(iS,
3.76/3.97	                                                                 app_encode_fun(
3.76/3.97	                                                                 iS,
3.76/3.97	                                                                 app_encode_fun(
3.76/3.97	                                                                 iS,$o)),R,
3.76/3.97	                                                                 Xx2),
3.76/3.97	                                                  Xy2),
3.76/3.97	                                   Xz2)))) =>
3.76/3.97	               app_encode_app(iS,$o,
3.76/3.97	                              app_encode_app(iS,app_encode_fun(iS,$o),
3.76/3.97	                                             app_encode_app(iS,
3.76/3.97	                                                            app_encode_fun(
3.76/3.97	                                                            iS,
3.76/3.97	                                                            app_encode_fun(
3.76/3.97	                                                            iS,$o)),R,Xa),
3.76/3.97	                                             Xb),
3.76/3.97	                              Xc))) =>
3.76/3.97	           app_encode_app(iS,$o,
3.76/3.97	                          app_encode_app(iS,app_encode_fun(iS,$o),
3.76/3.97	                                         app_encode_app(iS,
3.76/3.97	                                                        app_encode_fun(
3.76/3.97	                                                        iS,
3.76/3.97	                                                        app_encode_fun(iS,$o)),
3.76/3.97	                                                        R,
3.76/3.97	                                                        app_encode_app(
3.76/3.97	                                                        iS,iS,
3.76/3.97	                                                        app_encode_app(
3.76/3.97	                                                        iS,
3.76/3.97	                                                        app_encode_fun(iS,iS),
3.76/3.97	                                                        cP,Xx),Xu)),
3.76/3.97	                                         app_encode_app(iS,iS,
3.76/3.97	                                                        app_encode_app(
3.76/3.97	                                                        iS,
3.76/3.97	                                                        app_encode_fun(iS,iS),
3.76/3.97	                                                        cP,Xy),Xv)),
3.76/3.97	                          app_encode_app(iS,iS,
3.76/3.97	                                         app_encode_app(iS,
3.76/3.97	                                                        app_encode_fun(iS,iS),
3.76/3.97	                                                        cP,Xy),
3.76/3.97	                                         Xv)))))))).
3.76/3.97	tff(zf_stmt_0, negated_conjecture,
3.76/3.97	  (~
3.76/3.97	    (((![Xx:iS,Xy:iS]:
3.76/3.97	         (app_encode_app(iS,iS,
3.76/3.97	                         app_encode_app(iS,app_encode_fun(iS,iS),cP,Xx),Xy) !=
3.76/3.97	          c0)) & 
3.76/3.97	      (![Xx:iS,Xy:iS,Xu:iS,Xv:iS]:
3.76/3.97	         ((app_encode_app(iS,iS,
3.76/3.97	                          app_encode_app(iS,app_encode_fun(iS,iS),cP,Xx),Xu) =
3.76/3.97	           app_encode_app(iS,iS,
3.76/3.97	                          app_encode_app(iS,app_encode_fun(iS,iS),cP,Xy),Xv)) =>
3.76/3.97	          ((Xx = Xy) & (Xu = Xv)))) & 
3.76/3.97	      (![X:app_encode_fun(iS,$o)]:
3.76/3.97	         ((app_encode_app(iS,$o,X,c0) & 
3.76/3.97	           (![Xx:iS,Xy:iS]:
3.76/3.97	              ((app_encode_app(iS,$o,X,Xx) & app_encode_app(iS,$o,X,Xy)) =>
3.76/3.97	               app_encode_app(iS,$o,X,
3.76/3.97	                              app_encode_app(iS,iS,
3.76/3.97	                                             app_encode_app(iS,
3.76/3.97	                                                            app_encode_fun(
3.76/3.97	                                                            iS,iS),cP,Xx),
3.76/3.97	                                             Xy))))) =>
3.76/3.97	          (![Xx:iS]: app_encode_app(iS,$o,X,Xx))))) =>
3.76/3.97	     (![Xx:iS,Xy:iS,Xu:iS,Xv:iS]:
3.76/3.97	        (((![R:app_encode_fun(iS,app_encode_fun(iS,app_encode_fun(iS,$o)))]:
3.76/3.97	             ((![Xa:iS,Xb:iS,Xc:iS]:
3.76/3.97	                 ((((Xa = c0) & (Xb = Xc)) | ((Xb = c0) & (Xa = Xc)) | 
3.76/3.97	                   (?[Xx1:iS,Xx2:iS,Xy1:iS,Xy2:iS,Xz1:iS,Xz2:iS]:
3.76/3.97	                      ((Xa =
3.76/3.97	                        app_encode_app(iS,iS,
3.76/3.97	                                       app_encode_app(iS,
3.76/3.97	                                                      app_encode_fun(iS,iS),
3.76/3.97	                                                      cP,Xx1),
3.76/3.97	                                       Xx2)) & 
3.76/3.97	                       (Xb =
3.76/3.97	                        app_encode_app(iS,iS,
3.76/3.97	                                       app_encode_app(iS,
3.76/3.97	                                                      app_encode_fun(iS,iS),
3.76/3.97	                                                      cP,Xy1),
3.76/3.97	                                       Xy2)) & 
3.76/3.97	                       (Xc =
3.76/3.97	                        app_encode_app(iS,iS,
3.76/3.97	                                       app_encode_app(iS,
3.76/3.97	                                                      app_encode_fun(iS,iS),
3.76/3.97	                                                      cP,Xz1),
3.76/3.97	                                       Xz2)) & 
3.76/3.97	                       app_encode_app(iS,$o,
3.76/3.97	                                      app_encode_app(iS,
3.76/3.97	                                                     app_encode_fun(iS,$o),
3.76/3.97	                                                     app_encode_app(iS,
3.76/3.97	                                                                    app_encode_fun(
3.76/3.97	                                                                    iS,
3.76/3.97	                                                                    app_encode_fun(
3.76/3.97	                                                                    iS,$o)),
3.76/3.97	                                                                    R,Xx1),
3.76/3.97	                                                     Xy1),
3.76/3.98	                                      Xz1) & 
3.76/3.98	                       app_encode_app(iS,$o,
3.76/3.98	                                      app_encode_app(iS,
3.76/3.98	                                                     app_encode_fun(iS,$o),
3.76/3.98	                                                     app_encode_app(iS,
3.76/3.98	                                                                    app_encode_fun(
3.76/3.98	                                                                    iS,
3.76/3.98	                                                                    app_encode_fun(
3.76/3.98	                                                                    iS,$o)),
3.76/3.98	                                                                    R,Xx2),
3.76/3.98	                                                     Xy2),
3.76/3.98	                                      Xz2)))) =>
3.76/3.98	                  app_encode_app(iS,$o,
3.76/3.98	                                 app_encode_app(iS,app_encode_fun(iS,$o),
3.76/3.98	                                                app_encode_app(iS,
3.76/3.98	                                                               app_encode_fun(
3.76/3.98	                                                               iS,
3.76/3.98	                                                               app_encode_fun(
3.76/3.98	                                                               iS,$o)),R,Xa),
3.76/3.98	                                                Xb),
3.76/3.98	                                 Xc))) =>
3.76/3.98	              app_encode_app(iS,$o,
3.76/3.98	                             app_encode_app(iS,app_encode_fun(iS,$o),
3.76/3.98	                                            app_encode_app(iS,
3.76/3.98	                                                           app_encode_fun(
3.76/3.98	                                                           iS,
3.76/3.98	                                                           app_encode_fun(
3.76/3.98	                                                           iS,$o)),R,Xx),
3.76/3.98	                                            Xy),
3.76/3.98	                             Xy))) & 
3.76/3.98	          (![R:app_encode_fun(iS,app_encode_fun(iS,app_encode_fun(iS,$o)))]:
3.76/3.98	             ((![Xa:iS,Xb:iS,Xc:iS]:
3.76/3.98	                 ((((Xa = c0) & (Xb = Xc)) | ((Xb = c0) & (Xa = Xc)) | 
3.76/3.98	                   (?[Xx1:iS,Xx2:iS,Xy1:iS,Xy2:iS,Xz1:iS,Xz2:iS]:
3.76/3.98	                      ((Xa =
3.76/3.98	                        app_encode_app(iS,iS,
3.76/3.98	                                       app_encode_app(iS,
3.76/3.98	                                                      app_encode_fun(iS,iS),
3.76/3.98	                                                      cP,Xx1),
3.76/3.98	                                       Xx2)) & 
3.76/3.98	                       (Xb =
3.76/3.98	                        app_encode_app(iS,iS,
3.76/3.98	                                       app_encode_app(iS,
3.76/3.98	                                                      app_encode_fun(iS,iS),
3.76/3.98	                                                      cP,Xy1),
3.76/3.98	                                       Xy2)) & 
3.76/3.98	                       (Xc =
3.76/3.98	                        app_encode_app(iS,iS,
3.76/3.98	                                       app_encode_app(iS,
3.76/3.98	                                                      app_encode_fun(iS,iS),
3.76/3.98	                                                      cP,Xz1),
3.76/3.98	                                       Xz2)) & 
3.76/3.98	                       app_encode_app(iS,$o,
3.76/3.98	                                      app_encode_app(iS,
3.76/3.98	                                                     app_encode_fun(iS,$o),
3.76/3.98	                                                     app_encode_app(iS,
3.76/3.98	                                                                    app_encode_fun(
3.76/3.98	                                                                    iS,
3.76/3.98	                                                                    app_encode_fun(
3.76/3.98	                                                                    iS,$o)),
3.76/3.98	                                                                    R,Xx1),
3.76/3.98	                                                     Xy1),
3.76/3.98	                                      Xz1) & 
3.76/3.98	                       app_encode_app(iS,$o,
3.76/3.98	                                      app_encode_app(iS,
3.76/3.98	                                                     app_encode_fun(iS,$o),
3.76/3.98	                                                     app_encode_app(iS,
3.76/3.98	                                                                    app_encode_fun(
3.76/3.98	                                                                    iS,
3.76/3.98	                                                                    app_encode_fun(
3.76/3.98	                                                                    iS,$o)),
3.76/3.98	                                                                    R,Xx2),
3.76/3.98	                                                     Xy2),
3.76/3.98	                                      Xz2)))) =>
3.76/3.98	                  app_encode_app(iS,$o,
3.76/3.98	                                 app_encode_app(iS,app_encode_fun(iS,$o),
3.76/3.98	                                                app_encode_app(iS,
3.76/3.98	                                                               app_encode_fun(
3.76/3.98	                                                               iS,
3.76/3.98	                                                               app_encode_fun(
3.76/3.98	                                                               iS,$o)),R,Xa),
3.76/3.98	                                                Xb),
3.76/3.98	                                 Xc))) =>
3.76/3.98	              app_encode_app(iS,$o,
3.76/3.98	                             app_encode_app(iS,app_encode_fun(iS,$o),
3.76/3.98	                                            app_encode_app(iS,
3.76/3.98	                                                           app_encode_fun(
3.76/3.98	                                                           iS,
3.76/3.98	                                                           app_encode_fun(
3.76/3.98	                                                           iS,$o)),R,Xu),
3.76/3.98	                                            Xv),
3.76/3.98	                             Xv)))) =>
3.76/3.98	         (![R:app_encode_fun(iS,app_encode_fun(iS,app_encode_fun(iS,$o)))]:
3.76/3.98	            ((![Xa:iS,Xb:iS,Xc:iS]:
3.76/3.98	                ((((Xa = c0) & (Xb = Xc)) | ((Xb = c0) & (Xa = Xc)) | 
3.76/3.98	                  (?[Xx1:iS,Xx2:iS,Xy1:iS,Xy2:iS,Xz1:iS,Xz2:iS]:
3.76/3.98	                     ((Xa =
3.76/3.98	                       app_encode_app(iS,iS,
3.76/3.98	                                      app_encode_app(iS,
3.76/3.98	                                                     app_encode_fun(iS,iS),
3.76/3.98	                                                     cP,Xx1),
3.76/3.98	                                      Xx2)) & 
3.76/3.98	                      (Xb =
3.76/3.98	                       app_encode_app(iS,iS,
3.76/3.98	                                      app_encode_app(iS,
3.76/3.98	                                                     app_encode_fun(iS,iS),
3.76/3.98	                                                     cP,Xy1),
3.76/3.98	                                      Xy2)) & 
3.76/3.98	                      (Xc =
3.76/3.98	                       app_encode_app(iS,iS,
3.76/3.98	                                      app_encode_app(iS,
3.76/3.98	                                                     app_encode_fun(iS,iS),
3.76/3.98	                                                     cP,Xz1),
3.76/3.98	                                      Xz2)) & 
3.76/3.98	                      app_encode_app(iS,$o,
3.76/3.98	                                     app_encode_app(iS,app_encode_fun(iS,$o),
3.76/3.98	                                                    app_encode_app(iS,
3.76/3.98	                                                                   app_encode_fun(
3.76/3.98	                                                                   iS,
3.76/3.98	                                                                   app_encode_fun(
3.76/3.98	                                                                   iS,$o)),R,
3.76/3.98	                                                                   Xx1),
3.76/3.98	                                                    Xy1),
3.76/3.98	                                     Xz1) & 
3.76/3.98	                      app_encode_app(iS,$o,
3.76/3.98	                                     app_encode_app(iS,app_encode_fun(iS,$o),
3.76/3.98	                                                    app_encode_app(iS,
3.76/3.98	                                                                   app_encode_fun(
3.76/3.98	                                                                   iS,
3.76/3.98	                                                                   app_encode_fun(
3.76/3.98	                                                                   iS,$o)),R,
3.76/3.98	                                                                   Xx2),
3.76/3.98	                                                    Xy2),
3.76/3.98	                                     Xz2)))) =>
3.76/3.98	                 app_encode_app(iS,$o,
3.76/3.98	                                app_encode_app(iS,app_encode_fun(iS,$o),
3.76/3.98	                                               app_encode_app(iS,
3.76/3.98	                                                              app_encode_fun(
3.76/3.98	                                                              iS,
3.76/3.98	                                                              app_encode_fun(
3.76/3.98	                                                              iS,$o)),R,Xa),
3.76/3.98	                                               Xb),
3.76/3.98	                                Xc))) =>
3.76/3.98	             app_encode_app(iS,$o,
3.76/3.98	                            app_encode_app(iS,app_encode_fun(iS,$o),
3.76/3.98	                                           app_encode_app(iS,
3.76/3.98	                                                          app_encode_fun(
3.76/3.98	                                                          iS,
3.76/3.98	                                                          app_encode_fun(
3.76/3.98	                                                          iS,$o)),R,
3.76/3.98	                                                          app_encode_app(
3.76/3.98	                                                          iS,iS,
3.76/3.98	                                                          app_encode_app(
3.76/3.98	                                                          iS,
3.76/3.98	                                                          app_encode_fun(
3.76/3.98	                                                          iS,iS),cP,Xx),Xu)),
3.76/3.98	                                           app_encode_app(iS,iS,
3.76/3.98	                                                          app_encode_app(
3.76/3.98	                                                          iS,
3.76/3.98	                                                          app_encode_fun(
3.76/3.98	                                                          iS,iS),cP,Xy),Xv)),
3.76/3.98	                            app_encode_app(iS,iS,
3.76/3.98	                                           app_encode_app(iS,
3.76/3.98	                                                          app_encode_fun(
3.76/3.98	                                                          iS,iS),cP,Xy),
3.76/3.98	                                           Xv))))))))).
3.76/3.98	tff('0', plain,
3.76/3.98	    ![X13 : app_encode_fun(iS, app_encode_fun(iS, app_encode_fun(iS, $o)))]:
3.76/3.98	      (app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             X13, sk_Xu), sk_Xv), sk_Xv)
3.76/3.98	       | sk_Xa1(X13) = c0
3.76/3.98	       | sk_Xb1(X13) = c0
3.76/3.98	       | sk_Xc1(X13)
3.76/3.98	          = app_encode_app(iS, iS, 
3.76/3.98	              app_encode_app(iS, app_encode_fun(iS, iS), cP, sk_Xz11(X13)), 
3.76/3.98	              sk_Xz21(X13))),
3.76/3.98	    inference('cnf', [status(esa)], [zf_stmt_0])).
3.76/3.98	tff('1', plain,
3.76/3.98	    ![X13 : app_encode_fun(iS, app_encode_fun(iS, app_encode_fun(iS, $o)))]:
3.76/3.98	      (app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             X13, sk_Xu), sk_Xv), sk_Xv)
3.76/3.98	       | sk_Xa1(X13) = c0
3.76/3.98	       | sk_Xb1(X13) = c0
3.76/3.98	       | sk_Xb1(X13)
3.76/3.98	          = app_encode_app(iS, iS, 
3.76/3.98	              app_encode_app(iS, app_encode_fun(iS, iS), cP, sk_Xy11(X13)), 
3.76/3.98	              sk_Xy21(X13))),
3.76/3.98	    inference('cnf', [status(esa)], [zf_stmt_0])).
3.76/3.98	tff('2', plain,
3.76/3.98	    ![X13 : app_encode_fun(iS, app_encode_fun(iS, app_encode_fun(iS, $o)))]:
3.76/3.98	      (app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             X13, sk_Xu), sk_Xv), sk_Xv)
3.76/3.98	       | sk_Xa1(X13) = c0
3.76/3.98	       | sk_Xb1(X13) = c0
3.76/3.98	       | app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               X13, sk_Xx21(X13)), sk_Xy21(X13)), sk_Xz21(X13))),
3.76/3.98	    inference('cnf', [status(esa)], [zf_stmt_0])).
3.76/3.98	tff('3', plain,
3.76/3.98	    ![X13 : app_encode_fun(iS, app_encode_fun(iS, app_encode_fun(iS, $o)))]:
3.76/3.98	      (app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             X13, sk_Xu), sk_Xv), sk_Xv)
3.76/3.98	       | sk_Xa1(X13) = c0
3.76/3.98	       | sk_Xb1(X13) = c0
3.76/3.98	       | app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               X13, sk_Xx11(X13)), sk_Xy11(X13)), sk_Xz11(X13))),
3.76/3.98	    inference('cnf', [status(esa)], [zf_stmt_0])).
3.76/3.98	tff('4', plain,
3.76/3.98	    ![X13 : app_encode_fun(iS, app_encode_fun(iS, app_encode_fun(iS, $o)))]:
3.76/3.98	      (app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             X13, sk_Xu), sk_Xv), sk_Xv)
3.76/3.98	       | sk_Xa1(X13) = c0
3.76/3.98	       | sk_Xb1(X13) = c0
3.76/3.98	       | sk_Xa1(X13)
3.76/3.98	          = app_encode_app(iS, iS, 
3.76/3.98	              app_encode_app(iS, app_encode_fun(iS, iS), cP, sk_Xx11(X13)), 
3.76/3.98	              sk_Xx21(X13))),
3.76/3.98	    inference('cnf', [status(esa)], [zf_stmt_0])).
3.76/3.98	tff('5', plain,
3.76/3.98	    ![X14 : iS, X15 : iS, X16 : iS, X17 : iS, X18 : iS, X19 : iS, X20 : iS, 
3.76/3.98	      X21 : iS, X22 : iS]:
3.76/3.98	      (app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, X14), X15), X16)
3.76/3.98	       | X14
3.76/3.98	          != app_encode_app(iS, iS, 
3.76/3.98	               app_encode_app(iS, app_encode_fun(iS, iS), cP, X17), X18)
3.76/3.98	       | X15
3.76/3.98	          != app_encode_app(iS, iS, 
3.76/3.98	               app_encode_app(iS, app_encode_fun(iS, iS), cP, X19), X20)
3.76/3.98	       | ~ app_encode_app(iS, $o, 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	               app_encode_app(iS, 
3.76/3.98	                 app_encode_fun(iS, app_encode_fun(iS, $o)), sk_R, X17), X19), 
3.76/3.98	             X21)
3.76/3.98	       | ~ app_encode_app(iS, $o, 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	               app_encode_app(iS, 
3.76/3.98	                 app_encode_fun(iS, app_encode_fun(iS, $o)), sk_R, X18), X20), 
3.76/3.98	             X22)
3.76/3.98	       | X16
3.76/3.98	          != app_encode_app(iS, iS, 
3.76/3.98	               app_encode_app(iS, app_encode_fun(iS, iS), cP, X21), X22)),
3.76/3.98	    inference('cnf', [status(esa)], [zf_stmt_0])).
3.76/3.98	tff('6', plain,
3.76/3.98	    ![X17 : iS, X18 : iS, X19 : iS, X20 : iS, X21 : iS, X22 : iS]:
3.76/3.98	      (~ app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               sk_R, X18), X20), X22)
3.76/3.98	       | ~ app_encode_app(iS, $o, 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	               app_encode_app(iS, 
3.76/3.98	                 app_encode_fun(iS, app_encode_fun(iS, $o)), sk_R, X17), X19), 
3.76/3.98	             X21)
3.76/3.98	       | app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               sk_R, 
3.76/3.98	               app_encode_app(iS, iS, 
3.76/3.98	                 app_encode_app(iS, app_encode_fun(iS, iS), cP, X17), X18)), 
3.76/3.98	             app_encode_app(iS, iS, 
3.76/3.98	               app_encode_app(iS, app_encode_fun(iS, iS), cP, X19), X20)), 
3.76/3.98	           app_encode_app(iS, iS, 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, iS), cP, X21), X22))),
3.76/3.98	    inference('simplify', [status(thm)], ['5'])).
3.76/3.98	tff('7', plain,
3.76/3.98	    ![X0 : app_encode_fun(iS, app_encode_fun(iS, app_encode_fun(iS, $o))), 
3.76/3.98	      X1 : iS, X2 : iS, X3 : iS, X4 : iS]:
3.76/3.98	      (app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xa1(X0)), 
3.76/3.98	           app_encode_app(iS, iS, 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, iS), cP, X4), X3)), 
3.76/3.98	         app_encode_app(iS, iS, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, iS), cP, X2), X1))
3.76/3.98	       | sk_Xb1(X0) = c0
3.76/3.98	       | sk_Xa1(X0) = c0
3.76/3.98	       | app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               X0, sk_Xu), sk_Xv), sk_Xv)
3.76/3.98	       | ~ app_encode_app(iS, $o, 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	               app_encode_app(iS, 
3.76/3.98	                 app_encode_fun(iS, app_encode_fun(iS, $o)), sk_R, 
3.76/3.98	                 sk_Xx11(X0)), X4), X2)
3.76/3.98	       | ~ app_encode_app(iS, $o, 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	               app_encode_app(iS, 
3.76/3.98	                 app_encode_fun(iS, app_encode_fun(iS, $o)), sk_R, 
3.76/3.98	                 sk_Xx21(X0)), X3), X1)),
3.76/3.98	    inference('sup+', [status(thm)], ['4', '6'])).
3.76/3.98	tff('8', plain,
3.76/3.98	    ![X0 : iS, X1 : iS]:
3.76/3.98	      (~ $true
3.76/3.98	       | sk_Xb1(sk_R) = c0
3.76/3.98	       | sk_Xa1(sk_R) = c0
3.76/3.98	       | app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               sk_R, sk_Xu), sk_Xv), sk_Xv)
3.76/3.98	       | ~ app_encode_app(iS, $o, 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	               app_encode_app(iS, 
3.76/3.98	                 app_encode_fun(iS, app_encode_fun(iS, $o)), sk_R, 
3.76/3.98	                 sk_Xx21(sk_R)), X1), X0)
3.76/3.98	       | app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               sk_R, sk_Xu), sk_Xv), sk_Xv)
3.76/3.98	       | sk_Xa1(sk_R) = c0
3.76/3.98	       | sk_Xb1(sk_R) = c0
3.76/3.98	       | app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               sk_R, sk_Xa1(sk_R)), 
3.76/3.98	             app_encode_app(iS, iS, 
3.76/3.98	               app_encode_app(iS, app_encode_fun(iS, iS), cP, sk_Xy11(sk_R)), 
3.76/3.98	               X1)), 
3.76/3.98	           app_encode_app(iS, iS, 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, iS), cP, sk_Xz11(sk_R)), 
3.76/3.98	             X0))),
3.76/3.98	    inference('sup-', [status(thm)], ['3', '7'])).
3.76/3.98	tff('9', plain,
3.76/3.98	    ![X0 : iS, X1 : iS]:
3.76/3.98	      (app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xa1(sk_R)), 
3.76/3.98	           app_encode_app(iS, iS, 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, iS), cP, sk_Xy11(sk_R)), 
3.76/3.98	             X1)), 
3.76/3.98	         app_encode_app(iS, iS, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, iS), cP, sk_Xz11(sk_R)), X0))
3.76/3.98	       | ~ app_encode_app(iS, $o, 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	               app_encode_app(iS, 
3.76/3.98	                 app_encode_fun(iS, app_encode_fun(iS, $o)), sk_R, 
3.76/3.98	                 sk_Xx21(sk_R)), X1), X0)
3.76/3.98	       | app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               sk_R, sk_Xu), sk_Xv), sk_Xv)
3.76/3.98	       | sk_Xa1(sk_R) = c0
3.76/3.98	       | sk_Xb1(sk_R) = c0),
3.76/3.98	    inference('simplify', [status(thm)], ['8'])).
3.76/3.98	tff('10', plain,
3.76/3.98	    ![X12 : app_encode_fun(iS, app_encode_fun(iS, app_encode_fun(iS, $o)))]:
3.76/3.98	      (app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             X12, sk_Xx), sk_Xy), sk_Xy)
3.76/3.98	       | sk_Xa(X12) = c0
3.76/3.98	       | sk_Xb(X12) = c0
3.76/3.98	       | sk_Xc(X12)
3.76/3.98	          = app_encode_app(iS, iS, 
3.76/3.98	              app_encode_app(iS, app_encode_fun(iS, iS), cP, sk_Xz1(X12)), 
3.76/3.98	              sk_Xz2(X12))),
3.76/3.98	    inference('cnf', [status(esa)], [zf_stmt_0])).
3.76/3.98	tff('11', plain,
3.76/3.98	    ![X12 : app_encode_fun(iS, app_encode_fun(iS, app_encode_fun(iS, $o)))]:
3.76/3.98	      (app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             X12, sk_Xx), sk_Xy), sk_Xy)
3.76/3.98	       | sk_Xa(X12) = c0
3.76/3.98	       | sk_Xb(X12) = c0
3.76/3.98	       | sk_Xb(X12)
3.76/3.98	          = app_encode_app(iS, iS, 
3.76/3.98	              app_encode_app(iS, app_encode_fun(iS, iS), cP, sk_Xy1(X12)), 
3.76/3.98	              sk_Xy2(X12))),
3.76/3.98	    inference('cnf', [status(esa)], [zf_stmt_0])).
3.76/3.98	tff('12', plain,
3.76/3.98	    ![X12 : app_encode_fun(iS, app_encode_fun(iS, app_encode_fun(iS, $o)))]:
3.76/3.98	      (app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             X12, sk_Xx), sk_Xy), sk_Xy)
3.76/3.98	       | sk_Xa(X12) = c0
3.76/3.98	       | sk_Xb(X12) = c0
3.76/3.98	       | app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               X12, sk_Xx2(X12)), sk_Xy2(X12)), sk_Xz2(X12))),
3.76/3.98	    inference('cnf', [status(esa)], [zf_stmt_0])).
3.76/3.98	tff('13', plain,
3.76/3.98	    ![X12 : app_encode_fun(iS, app_encode_fun(iS, app_encode_fun(iS, $o)))]:
3.76/3.98	      (app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             X12, sk_Xx), sk_Xy), sk_Xy)
3.76/3.98	       | sk_Xa(X12) = c0
3.76/3.98	       | sk_Xb(X12) = c0
3.76/3.98	       | app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               X12, sk_Xx1(X12)), sk_Xy1(X12)), sk_Xz1(X12))),
3.76/3.98	    inference('cnf', [status(esa)], [zf_stmt_0])).
3.76/3.98	tff('14', plain,
3.76/3.98	    ![X12 : app_encode_fun(iS, app_encode_fun(iS, app_encode_fun(iS, $o)))]:
3.76/3.98	      (app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             X12, sk_Xx), sk_Xy), sk_Xy)
3.76/3.98	       | sk_Xa(X12) = c0
3.76/3.98	       | sk_Xb(X12) = c0
3.76/3.98	       | sk_Xa(X12)
3.76/3.98	          = app_encode_app(iS, iS, 
3.76/3.98	              app_encode_app(iS, app_encode_fun(iS, iS), cP, sk_Xx1(X12)), 
3.76/3.98	              sk_Xx2(X12))),
3.76/3.98	    inference('cnf', [status(esa)], [zf_stmt_0])).
3.76/3.98	tff('15', plain,
3.76/3.98	    ![X0 : app_encode_fun(iS, app_encode_fun(iS, app_encode_fun(iS, $o))), 
3.76/3.98	      X1 : iS, X2 : iS, X3 : iS, X4 : iS]:
3.76/3.98	      (app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xa(X0)), 
3.76/3.98	           app_encode_app(iS, iS, 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, iS), cP, X4), X3)), 
3.76/3.98	         app_encode_app(iS, iS, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, iS), cP, X2), X1))
3.76/3.98	       | sk_Xb(X0) = c0
3.76/3.98	       | sk_Xa(X0) = c0
3.76/3.98	       | app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               X0, sk_Xx), sk_Xy), sk_Xy)
3.76/3.98	       | ~ app_encode_app(iS, $o, 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	               app_encode_app(iS, 
3.76/3.98	                 app_encode_fun(iS, app_encode_fun(iS, $o)), sk_R, 
3.76/3.98	                 sk_Xx1(X0)), X4), X2)
3.76/3.98	       | ~ app_encode_app(iS, $o, 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	               app_encode_app(iS, 
3.76/3.98	                 app_encode_fun(iS, app_encode_fun(iS, $o)), sk_R, 
3.76/3.98	                 sk_Xx2(X0)), X3), X1)),
3.76/3.98	    inference('sup+', [status(thm)], ['14', '6'])).
3.76/3.98	tff('16', plain,
3.76/3.98	    ![X0 : iS, X1 : iS]:
3.76/3.98	      (~ $true
3.76/3.98	       | sk_Xb(sk_R) = c0
3.76/3.98	       | sk_Xa(sk_R) = c0
3.76/3.98	       | app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               sk_R, sk_Xx), sk_Xy), sk_Xy)
3.76/3.98	       | ~ app_encode_app(iS, $o, 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	               app_encode_app(iS, 
3.76/3.98	                 app_encode_fun(iS, app_encode_fun(iS, $o)), sk_R, 
3.76/3.98	                 sk_Xx2(sk_R)), X1), X0)
3.76/3.98	       | app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               sk_R, sk_Xx), sk_Xy), sk_Xy)
3.76/3.98	       | sk_Xa(sk_R) = c0
3.76/3.98	       | sk_Xb(sk_R) = c0
3.76/3.98	       | app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               sk_R, sk_Xa(sk_R)), 
3.76/3.98	             app_encode_app(iS, iS, 
3.76/3.98	               app_encode_app(iS, app_encode_fun(iS, iS), cP, sk_Xy1(sk_R)), 
3.76/3.98	               X1)), 
3.76/3.98	           app_encode_app(iS, iS, 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, iS), cP, sk_Xz1(sk_R)), 
3.76/3.98	             X0))),
3.76/3.98	    inference('sup-', [status(thm)], ['13', '15'])).
3.76/3.98	tff('17', plain,
3.76/3.98	    ![X0 : iS, X1 : iS]:
3.76/3.98	      (app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xa(sk_R)), 
3.76/3.98	           app_encode_app(iS, iS, 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, iS), cP, sk_Xy1(sk_R)), 
3.76/3.98	             X1)), 
3.76/3.98	         app_encode_app(iS, iS, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, iS), cP, sk_Xz1(sk_R)), X0))
3.76/3.98	       | ~ app_encode_app(iS, $o, 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	               app_encode_app(iS, 
3.76/3.98	                 app_encode_fun(iS, app_encode_fun(iS, $o)), sk_R, 
3.76/3.98	                 sk_Xx2(sk_R)), X1), X0)
3.76/3.98	       | app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               sk_R, sk_Xx), sk_Xy), sk_Xy)
3.76/3.98	       | sk_Xa(sk_R) = c0
3.76/3.98	       | sk_Xb(sk_R) = c0),
3.76/3.98	    inference('simplify', [status(thm)], ['16'])).
3.76/3.98	tff('18', plain,
3.76/3.98	    (~ $true
3.76/3.98	     | sk_Xb(sk_R) = c0
3.76/3.98	     | sk_Xa(sk_R) = c0
3.76/3.98	     | app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xx), sk_Xy), sk_Xy)
3.76/3.98	     | sk_Xb(sk_R) = c0
3.76/3.98	     | sk_Xa(sk_R) = c0
3.76/3.98	     | app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xx), sk_Xy), sk_Xy)
3.76/3.98	     | app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xa(sk_R)), 
3.76/3.98	           app_encode_app(iS, iS, 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, iS), cP, sk_Xy1(sk_R)), 
3.76/3.98	             sk_Xy2(sk_R))), 
3.76/3.98	         app_encode_app(iS, iS, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, iS), cP, sk_Xz1(sk_R)), 
3.76/3.98	           sk_Xz2(sk_R)))),
3.76/3.98	    inference('sup-', [status(thm)], ['12', '17'])).
3.76/3.98	tff('19', plain,
3.76/3.98	    (app_encode_app(iS, $o, 
3.76/3.98	       app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	           sk_R, sk_Xa(sk_R)), 
3.76/3.98	         app_encode_app(iS, iS, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, iS), cP, sk_Xy1(sk_R)), 
3.76/3.98	           sk_Xy2(sk_R))), 
3.76/3.98	       app_encode_app(iS, iS, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, iS), cP, sk_Xz1(sk_R)), 
3.76/3.98	         sk_Xz2(sk_R)))
3.76/3.98	     | app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xx), sk_Xy), sk_Xy)
3.76/3.98	     | sk_Xa(sk_R) = c0
3.76/3.98	     | sk_Xb(sk_R) = c0),
3.76/3.98	    inference('simplify', [status(thm)], ['18'])).
3.76/3.98	tff('20', plain,
3.76/3.98	    (app_encode_app(iS, $o, 
3.76/3.98	       app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	           sk_R, sk_Xa(sk_R)), sk_Xb(sk_R)), 
3.76/3.98	       app_encode_app(iS, iS, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, iS), cP, sk_Xz1(sk_R)), 
3.76/3.98	         sk_Xz2(sk_R)))
3.76/3.98	     | sk_Xb(sk_R) = c0
3.76/3.98	     | sk_Xa(sk_R) = c0
3.76/3.98	     | app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xx), sk_Xy), sk_Xy)
3.76/3.98	     | sk_Xb(sk_R) = c0
3.76/3.98	     | sk_Xa(sk_R) = c0
3.76/3.98	     | app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xx), sk_Xy), sk_Xy)),
3.76/3.98	    inference('sup+', [status(thm)], ['11', '19'])).
3.76/3.98	tff('21', plain,
3.76/3.98	    (app_encode_app(iS, $o, 
3.76/3.98	       app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	           sk_R, sk_Xx), sk_Xy), sk_Xy)
3.76/3.98	     | sk_Xa(sk_R) = c0
3.76/3.98	     | sk_Xb(sk_R) = c0
3.76/3.98	     | app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xa(sk_R)), sk_Xb(sk_R)), 
3.76/3.98	         app_encode_app(iS, iS, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, iS), cP, sk_Xz1(sk_R)), 
3.76/3.98	           sk_Xz2(sk_R)))),
3.76/3.98	    inference('simplify', [status(thm)], ['20'])).
3.76/3.98	tff('22', plain,
3.76/3.98	    (app_encode_app(iS, $o, 
3.76/3.98	       app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	           sk_R, sk_Xa(sk_R)), sk_Xb(sk_R)), sk_Xc(sk_R))
3.76/3.98	     | sk_Xb(sk_R) = c0
3.76/3.98	     | sk_Xa(sk_R) = c0
3.76/3.98	     | app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xx), sk_Xy), sk_Xy)
3.76/3.98	     | sk_Xb(sk_R) = c0
3.76/3.98	     | sk_Xa(sk_R) = c0
3.76/3.98	     | app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xx), sk_Xy), sk_Xy)),
3.76/3.98	    inference('sup+', [status(thm)], ['10', '21'])).
3.76/3.98	tff('23', plain,
3.76/3.98	    (app_encode_app(iS, $o, 
3.76/3.98	       app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	           sk_R, sk_Xx), sk_Xy), sk_Xy)
3.76/3.98	     | sk_Xa(sk_R) = c0
3.76/3.98	     | sk_Xb(sk_R) = c0
3.76/3.98	     | app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xa(sk_R)), sk_Xb(sk_R)), sk_Xc(sk_R))),
3.76/3.98	    inference('simplify', [status(thm)], ['22'])).
3.76/3.98	tff('24', plain,
3.76/3.98	    ![X12 : app_encode_fun(iS, app_encode_fun(iS, app_encode_fun(iS, $o)))]:
3.76/3.98	      (app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             X12, sk_Xx), sk_Xy), sk_Xy)
3.76/3.98	       | ~ app_encode_app(iS, $o, 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	               app_encode_app(iS, 
3.76/3.98	                 app_encode_fun(iS, app_encode_fun(iS, $o)), X12, sk_Xa(X12)), 
3.76/3.98	               sk_Xb(X12)), sk_Xc(X12))),
3.76/3.98	    inference('cnf', [status(esa)], [zf_stmt_0])).
3.76/3.98	tff('25', plain,
3.76/3.98	    (sk_Xb(sk_R) = c0
3.76/3.98	     | sk_Xa(sk_R) = c0
3.76/3.98	     | app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xx), sk_Xy), sk_Xy)),
3.76/3.98	    inference('clc', [status(thm)], ['23', '24'])).
3.76/3.98	tff('26', plain,
3.76/3.98	    ![X12 : app_encode_fun(iS, app_encode_fun(iS, app_encode_fun(iS, $o)))]:
3.76/3.98	      (app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             X12, sk_Xx), sk_Xy), sk_Xy)
3.76/3.98	       | sk_Xa(X12) = c0
3.76/3.98	       | sk_Xa(X12) = sk_Xc(X12)
3.76/3.98	       | sk_Xb(X12)
3.76/3.98	          = app_encode_app(iS, iS, 
3.76/3.98	              app_encode_app(iS, app_encode_fun(iS, iS), cP, sk_Xy1(X12)), 
3.76/3.98	              sk_Xy2(X12))),
3.76/3.98	    inference('cnf', [status(esa)], [zf_stmt_0])).
3.76/3.98	tff('27', plain,
3.76/3.98	    ![X4 : iS, X5 : iS]:
3.76/3.98	      app_encode_app(iS, iS, 
3.76/3.98	        app_encode_app(iS, app_encode_fun(iS, iS), cP, X4), X5)
3.76/3.98	       != c0,
3.76/3.98	    inference('cnf', [status(esa)], [zf_stmt_0])).
3.76/3.98	tff('28', plain,
3.76/3.98	    ![X0 : app_encode_fun(iS, app_encode_fun(iS, app_encode_fun(iS, $o)))]:
3.76/3.98	      (sk_Xb(X0) != c0
3.76/3.98	       | sk_Xa(X0) = sk_Xc(X0)
3.76/3.98	       | sk_Xa(X0) = c0
3.76/3.98	       | app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               X0, sk_Xx), sk_Xy), sk_Xy)),
3.76/3.98	    inference('sup-', [status(thm)], ['26', '27'])).
3.76/3.98	tff('29', plain,
3.76/3.98	    ![X0 : app_encode_fun(iS, app_encode_fun(iS, app_encode_fun(iS, $o)))]:
3.76/3.98	      (~ app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               X0, sk_Xa(X0)), sk_Xb(X0)), sk_Xa(X0))
3.76/3.98	       | app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               X0, sk_Xx), sk_Xy), sk_Xy)
3.76/3.98	       | sk_Xa(X0) = c0
3.76/3.98	       | sk_Xb(X0) != c0
3.76/3.98	       | app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               X0, sk_Xx), sk_Xy), sk_Xy)),
3.76/3.98	    inference('sup-', [status(thm)], ['28', '24'])).
3.76/3.98	tff('30', plain,
3.76/3.98	    ![X0 : app_encode_fun(iS, app_encode_fun(iS, app_encode_fun(iS, $o)))]:
3.76/3.98	      (sk_Xb(X0) != c0
3.76/3.98	       | sk_Xa(X0) = c0
3.76/3.98	       | app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               X0, sk_Xx), sk_Xy), sk_Xy)
3.76/3.98	       | ~ app_encode_app(iS, $o, 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	               app_encode_app(iS, 
3.76/3.98	                 app_encode_fun(iS, app_encode_fun(iS, $o)), X0, sk_Xa(X0)), 
3.76/3.98	               sk_Xb(X0)), sk_Xa(X0))),
3.76/3.98	    inference('simplify', [status(thm)], ['29'])).
3.76/3.98	tff('31', plain,
3.76/3.98	    (~ app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xa(sk_R)), c0), sk_Xa(sk_R))
3.76/3.98	     | app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xx), sk_Xy), sk_Xy)
3.76/3.98	     | sk_Xa(sk_R) = c0
3.76/3.98	     | app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xx), sk_Xy), sk_Xy)
3.76/3.98	     | sk_Xa(sk_R) = c0
3.76/3.98	     | sk_Xb(sk_R) != c0),
3.76/3.98	    inference('sup-', [status(thm)], ['25', '30'])).
3.76/3.98	tff('32', plain,
3.76/3.98	    ![X14 : iS, X15 : iS, X16 : iS]:
3.76/3.98	      (app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, X14), X15), X16)
3.76/3.98	       | X15 != c0
3.76/3.98	       | X14 != X16),
3.76/3.98	    inference('cnf', [status(esa)], [zf_stmt_0])).
3.76/3.98	tff('33', plain,
3.76/3.98	    ![X16 : iS]:
3.76/3.98	      app_encode_app(iS, $o, 
3.76/3.98	        app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	          app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	            sk_R, X16), c0), X16),
3.76/3.98	    inference('simplify', [status(thm)], ['32'])).
3.76/3.98	tff('34', plain,
3.76/3.98	    (~ $true
3.76/3.98	     | app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xx), sk_Xy), sk_Xy)
3.76/3.98	     | sk_Xa(sk_R) = c0
3.76/3.98	     | app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xx), sk_Xy), sk_Xy)
3.76/3.98	     | sk_Xa(sk_R) = c0
3.76/3.98	     | sk_Xb(sk_R) != c0),
3.76/3.98	    inference('demod', [status(thm)], ['31', '33'])).
3.76/3.98	tff('35', plain,
3.76/3.98	    (sk_Xb(sk_R) != c0
3.76/3.98	     | sk_Xa(sk_R) = c0
3.76/3.98	     | app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xx), sk_Xy), sk_Xy)),
3.76/3.98	    inference('simplify', [status(thm)], ['34'])).
3.76/3.98	tff('36', plain,
3.76/3.98	    (app_encode_app(iS, $o, 
3.76/3.98	       app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	           sk_R, sk_Xx), sk_Xy), sk_Xy)
3.76/3.98	     | sk_Xa(sk_R) = c0),
3.76/3.98	    inference('clc', [status(thm)], ['35', '25'])).
3.76/3.98	tff('37', plain,
3.76/3.98	    ![X12 : app_encode_fun(iS, app_encode_fun(iS, app_encode_fun(iS, $o)))]:
3.76/3.98	      (app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             X12, sk_Xx), sk_Xy), sk_Xy)
3.76/3.98	       | sk_Xb(X12) = sk_Xc(X12)
3.76/3.98	       | sk_Xb(X12) = c0
3.76/3.98	       | sk_Xa(X12)
3.76/3.98	          = app_encode_app(iS, iS, 
3.76/3.98	              app_encode_app(iS, app_encode_fun(iS, iS), cP, sk_Xx1(X12)), 
3.76/3.98	              sk_Xx2(X12))),
3.76/3.98	    inference('cnf', [status(esa)], [zf_stmt_0])).
3.76/3.98	tff('38', plain,
3.76/3.98	    ![X0 : app_encode_fun(iS, app_encode_fun(iS, app_encode_fun(iS, $o)))]:
3.76/3.98	      (sk_Xa(X0) != c0
3.76/3.98	       | sk_Xb(X0) = c0
3.76/3.98	       | sk_Xb(X0) = sk_Xc(X0)
3.76/3.98	       | app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               X0, sk_Xx), sk_Xy), sk_Xy)),
3.76/3.98	    inference('sup-', [status(thm)], ['37', '27'])).
3.76/3.98	tff('39', plain,
3.76/3.98	    ![X0 : app_encode_fun(iS, app_encode_fun(iS, app_encode_fun(iS, $o)))]:
3.76/3.98	      (~ app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               X0, sk_Xa(X0)), sk_Xb(X0)), sk_Xb(X0))
3.76/3.98	       | app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               X0, sk_Xx), sk_Xy), sk_Xy)
3.76/3.98	       | sk_Xb(X0) = c0
3.76/3.98	       | sk_Xa(X0) != c0
3.76/3.98	       | app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               X0, sk_Xx), sk_Xy), sk_Xy)),
3.76/3.98	    inference('sup-', [status(thm)], ['38', '24'])).
3.76/3.98	tff('40', plain,
3.76/3.98	    ![X0 : app_encode_fun(iS, app_encode_fun(iS, app_encode_fun(iS, $o)))]:
3.76/3.98	      (sk_Xa(X0) != c0
3.76/3.98	       | sk_Xb(X0) = c0
3.76/3.98	       | app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               X0, sk_Xx), sk_Xy), sk_Xy)
3.76/3.98	       | ~ app_encode_app(iS, $o, 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	               app_encode_app(iS, 
3.76/3.98	                 app_encode_fun(iS, app_encode_fun(iS, $o)), X0, sk_Xa(X0)), 
3.76/3.98	               sk_Xb(X0)), sk_Xb(X0))),
3.76/3.98	    inference('simplify', [status(thm)], ['39'])).
3.76/3.98	tff('41', plain,
3.76/3.98	    (~ app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, c0), sk_Xb(sk_R)), sk_Xb(sk_R))
3.76/3.98	     | app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xx), sk_Xy), sk_Xy)
3.76/3.98	     | app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xx), sk_Xy), sk_Xy)
3.76/3.98	     | sk_Xb(sk_R) = c0
3.76/3.98	     | sk_Xa(sk_R) != c0),
3.76/3.98	    inference('sup-', [status(thm)], ['36', '40'])).
3.76/3.98	tff('42', plain,
3.76/3.98	    ![X14 : iS, X15 : iS, X16 : iS]:
3.76/3.98	      (app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, X14), X15), X16)
3.76/3.98	       | X14 != c0
3.76/3.98	       | X15 != X16),
3.76/3.98	    inference('cnf', [status(esa)], [zf_stmt_0])).
3.76/3.98	tff('43', plain,
3.76/3.98	    ![X16 : iS]:
3.76/3.98	      app_encode_app(iS, $o, 
3.76/3.98	        app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	          app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	            sk_R, c0), X16), X16),
3.76/3.98	    inference('simplify', [status(thm)], ['42'])).
3.76/3.98	tff('44', plain,
3.76/3.98	    (~ $true
3.76/3.98	     | app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xx), sk_Xy), sk_Xy)
3.76/3.98	     | app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xx), sk_Xy), sk_Xy)
3.76/3.98	     | sk_Xb(sk_R) = c0
3.76/3.98	     | sk_Xa(sk_R) != c0),
3.76/3.98	    inference('demod', [status(thm)], ['41', '43'])).
3.76/3.98	tff('45', plain,
3.76/3.98	    (sk_Xa(sk_R) != c0
3.76/3.98	     | sk_Xb(sk_R) = c0
3.76/3.98	     | app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xx), sk_Xy), sk_Xy)),
3.76/3.98	    inference('simplify', [status(thm)], ['44'])).
3.76/3.98	tff('46', plain,
3.76/3.98	    (app_encode_app(iS, $o, 
3.76/3.98	       app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	           sk_R, sk_Xx), sk_Xy), sk_Xy)
3.76/3.98	     | sk_Xb(sk_R) = c0),
3.76/3.98	    inference('clc', [status(thm)], ['45', '36'])).
3.76/3.98	tff('47', plain,
3.76/3.98	    ![X12 : app_encode_fun(iS, app_encode_fun(iS, app_encode_fun(iS, $o)))]:
3.76/3.98	      (app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             X12, sk_Xx), sk_Xy), sk_Xy)
3.76/3.98	       | sk_Xb(X12) = sk_Xc(X12)
3.76/3.98	       | sk_Xa(X12) = sk_Xc(X12)
3.76/3.98	       | sk_Xa(X12)
3.76/3.98	          = app_encode_app(iS, iS, 
3.76/3.98	              app_encode_app(iS, app_encode_fun(iS, iS), cP, sk_Xx1(X12)), 
3.76/3.98	              sk_Xx2(X12))),
3.76/3.98	    inference('cnf', [status(esa)], [zf_stmt_0])).
3.76/3.98	tff('48', plain,
3.76/3.98	    ![X0 : app_encode_fun(iS, app_encode_fun(iS, app_encode_fun(iS, $o)))]:
3.76/3.98	      (sk_Xa(X0) != c0
3.76/3.98	       | sk_Xa(X0) = sk_Xc(X0)
3.76/3.98	       | sk_Xb(X0) = sk_Xc(X0)
3.76/3.98	       | app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               X0, sk_Xx), sk_Xy), sk_Xy)),
3.76/3.98	    inference('sup-', [status(thm)], ['47', '27'])).
3.76/3.98	tff('49', plain,
3.76/3.98	    ![X0 : app_encode_fun(iS, app_encode_fun(iS, app_encode_fun(iS, $o)))]:
3.76/3.98	      (sk_Xb(X0) != sk_Xa(X0)
3.76/3.98	       | app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               X0, sk_Xx), sk_Xy), sk_Xy)
3.76/3.98	       | sk_Xa(X0) = sk_Xc(X0)
3.76/3.98	       | sk_Xa(X0) != c0),
3.76/3.98	    inference('eq_fact', [status(thm)], ['48'])).
3.76/3.98	tff('50', plain,
3.76/3.98	    ![X0 : app_encode_fun(iS, app_encode_fun(iS, app_encode_fun(iS, $o)))]:
3.76/3.98	      (~ app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               X0, sk_Xa(X0)), sk_Xb(X0)), sk_Xa(X0))
3.76/3.98	       | sk_Xa(X0) != c0
3.76/3.98	       | app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               X0, sk_Xx), sk_Xy), sk_Xy)
3.76/3.98	       | sk_Xb(X0) != sk_Xa(X0)
3.76/3.98	       | app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               X0, sk_Xx), sk_Xy), sk_Xy)),
3.76/3.98	    inference('sup-', [status(thm)], ['49', '24'])).
3.76/3.98	tff('51', plain,
3.76/3.98	    ![X0 : app_encode_fun(iS, app_encode_fun(iS, app_encode_fun(iS, $o)))]:
3.76/3.98	      (sk_Xb(X0) != sk_Xa(X0)
3.76/3.98	       | app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               X0, sk_Xx), sk_Xy), sk_Xy)
3.76/3.98	       | sk_Xa(X0) != c0
3.76/3.98	       | ~ app_encode_app(iS, $o, 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	               app_encode_app(iS, 
3.76/3.98	                 app_encode_fun(iS, app_encode_fun(iS, $o)), X0, sk_Xa(X0)), 
3.76/3.98	               sk_Xb(X0)), sk_Xa(X0))),
3.76/3.98	    inference('simplify', [status(thm)], ['50'])).
3.76/3.98	tff('52', plain,
3.76/3.98	    (~ app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xa(sk_R)), c0), sk_Xa(sk_R))
3.76/3.98	     | app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xx), sk_Xy), sk_Xy)
3.76/3.98	     | sk_Xa(sk_R) != c0
3.76/3.98	     | app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xx), sk_Xy), sk_Xy)
3.76/3.98	     | sk_Xb(sk_R) != sk_Xa(sk_R)),
3.76/3.98	    inference('sup-', [status(thm)], ['46', '51'])).
3.76/3.98	tff('53', plain,
3.76/3.98	    (~ $true
3.76/3.98	     | app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xx), sk_Xy), sk_Xy)
3.76/3.98	     | sk_Xa(sk_R) != c0
3.76/3.98	     | app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xx), sk_Xy), sk_Xy)
3.76/3.98	     | sk_Xb(sk_R) != sk_Xa(sk_R)),
3.76/3.98	    inference('demod', [status(thm)], ['52', '33'])).
3.76/3.98	tff('54', plain,
3.76/3.98	    (sk_Xb(sk_R) != sk_Xa(sk_R)
3.76/3.98	     | sk_Xa(sk_R) != c0
3.76/3.98	     | app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xx), sk_Xy), sk_Xy)),
3.76/3.98	    inference('simplify', [status(thm)], ['53'])).
3.76/3.98	tff('55', plain,
3.76/3.98	    (app_encode_app(iS, $o, 
3.76/3.98	       app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	           sk_R, sk_Xx), sk_Xy), sk_Xy)
3.76/3.98	     | sk_Xb(sk_R) != sk_Xa(sk_R)),
3.76/3.98	    inference('clc', [status(thm)], ['54', '36'])).
3.76/3.98	tff('56', plain,
3.76/3.98	    (c0 != sk_Xa(sk_R)
3.76/3.98	     | app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xx), sk_Xy), sk_Xy)
3.76/3.98	     | app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xx), sk_Xy), sk_Xy)),
3.76/3.98	    inference('sup-', [status(thm)], ['46', '55'])).
3.76/3.98	tff('57', plain,
3.76/3.98	    (app_encode_app(iS, $o, 
3.76/3.98	       app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	           sk_R, sk_Xx), sk_Xy), sk_Xy)
3.76/3.98	     | c0 != sk_Xa(sk_R)),
3.76/3.98	    inference('simplify', [status(thm)], ['56'])).
3.76/3.98	tff('58', plain,
3.76/3.98	    app_encode_app(iS, $o, 
3.76/3.98	      app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	        app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), sk_R, 
3.76/3.98	          sk_Xx), sk_Xy), sk_Xy),
3.76/3.98	    inference('clc', [status(thm)], ['57', '36'])).
3.76/3.98	tff('59', plain,
3.76/3.98	    ~ app_encode_app(iS, $o, 
3.76/3.98	        app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	          app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	            sk_R, 
3.76/3.98	            app_encode_app(iS, iS, 
3.76/3.98	              app_encode_app(iS, app_encode_fun(iS, iS), cP, sk_Xx), sk_Xu)), 
3.76/3.98	          app_encode_app(iS, iS, 
3.76/3.98	            app_encode_app(iS, app_encode_fun(iS, iS), cP, sk_Xy), sk_Xv)), 
3.76/3.98	        app_encode_app(iS, iS, 
3.76/3.98	          app_encode_app(iS, app_encode_fun(iS, iS), cP, sk_Xy), sk_Xv)),
3.76/3.98	    inference('cnf', [status(esa)], [zf_stmt_0])).
3.76/3.98	tff('60', plain,
3.76/3.98	    (~ $true
3.76/3.98	     | ~ app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               sk_R, sk_Xx), sk_Xy), sk_Xy)
3.76/3.98	     | ~ app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               sk_R, sk_Xu), sk_Xv), sk_Xv)),
3.76/3.98	    inference('sup-', [status(thm)], ['6', '59'])).
3.76/3.98	tff('61', plain,
3.76/3.98	    (~ app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xu), sk_Xv), sk_Xv)
3.76/3.98	     | ~ app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               sk_R, sk_Xx), sk_Xy), sk_Xy)),
3.76/3.98	    inference('simplify', [status(thm)], ['60'])).
3.76/3.98	tff('62', plain,
3.76/3.98	    (~ $true
3.76/3.98	     | ~ app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               sk_R, sk_Xu), sk_Xv), sk_Xv)),
3.76/3.98	    inference('sup-', [status(thm)], ['58', '61'])).
3.76/3.98	tff('63', plain,
3.76/3.98	    ~ app_encode_app(iS, $o, 
3.76/3.98	        app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	          app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	            sk_R, sk_Xu), sk_Xv), sk_Xv),
3.76/3.98	    inference('simplify', [status(thm)], ['62'])).
3.76/3.98	tff('64', plain,
3.76/3.98	    ![X0 : iS, X1 : iS]:
3.76/3.98	      (sk_Xb1(sk_R) = c0
3.76/3.98	       | sk_Xa1(sk_R) = c0
3.76/3.98	       | ~ app_encode_app(iS, $o, 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	               app_encode_app(iS, 
3.76/3.98	                 app_encode_fun(iS, app_encode_fun(iS, $o)), sk_R, 
3.76/3.98	                 sk_Xx21(sk_R)), X1), X0)
3.76/3.98	       | app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               sk_R, sk_Xa1(sk_R)), 
3.76/3.98	             app_encode_app(iS, iS, 
3.76/3.98	               app_encode_app(iS, app_encode_fun(iS, iS), cP, sk_Xy11(sk_R)), 
3.76/3.98	               X1)), 
3.76/3.98	           app_encode_app(iS, iS, 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, iS), cP, sk_Xz11(sk_R)), 
3.76/3.98	             X0))),
3.76/3.98	    inference('clc', [status(thm)], ['9', '63'])).
3.76/3.98	tff('65', plain,
3.76/3.98	    (~ $true
3.76/3.98	     | sk_Xb1(sk_R) = c0
3.76/3.98	     | sk_Xa1(sk_R) = c0
3.76/3.98	     | app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xu), sk_Xv), sk_Xv)
3.76/3.98	     | app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xa1(sk_R)), 
3.76/3.98	           app_encode_app(iS, iS, 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, iS), cP, sk_Xy11(sk_R)), 
3.76/3.98	             sk_Xy21(sk_R))), 
3.76/3.98	         app_encode_app(iS, iS, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, iS), cP, sk_Xz11(sk_R)), 
3.76/3.98	           sk_Xz21(sk_R)))
3.76/3.98	     | sk_Xa1(sk_R) = c0
3.76/3.98	     | sk_Xb1(sk_R) = c0),
3.76/3.98	    inference('sup-', [status(thm)], ['2', '64'])).
3.76/3.98	tff('66', plain,
3.76/3.98	    (app_encode_app(iS, $o, 
3.76/3.98	       app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	           sk_R, sk_Xa1(sk_R)), 
3.76/3.98	         app_encode_app(iS, iS, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, iS), cP, sk_Xy11(sk_R)), 
3.76/3.98	           sk_Xy21(sk_R))), 
3.76/3.98	       app_encode_app(iS, iS, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, iS), cP, sk_Xz11(sk_R)), 
3.76/3.98	         sk_Xz21(sk_R)))
3.76/3.98	     | app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xu), sk_Xv), sk_Xv)
3.76/3.98	     | sk_Xa1(sk_R) = c0
3.76/3.98	     | sk_Xb1(sk_R) = c0),
3.76/3.98	    inference('simplify', [status(thm)], ['65'])).
3.76/3.98	tff('67', plain,
3.76/3.98	    (sk_Xb1(sk_R) = c0
3.76/3.98	     | sk_Xa1(sk_R) = c0
3.76/3.98	     | app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xa1(sk_R)), 
3.76/3.98	           app_encode_app(iS, iS, 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, iS), cP, sk_Xy11(sk_R)), 
3.76/3.98	             sk_Xy21(sk_R))), 
3.76/3.98	         app_encode_app(iS, iS, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, iS), cP, sk_Xz11(sk_R)), 
3.76/3.98	           sk_Xz21(sk_R)))),
3.76/3.98	    inference('clc', [status(thm)], ['66', '63'])).
3.76/3.98	tff('68', plain,
3.76/3.98	    (app_encode_app(iS, $o, 
3.76/3.98	       app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	           sk_R, sk_Xa1(sk_R)), sk_Xb1(sk_R)), 
3.76/3.98	       app_encode_app(iS, iS, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, iS), cP, sk_Xz11(sk_R)), 
3.76/3.98	         sk_Xz21(sk_R)))
3.76/3.98	     | sk_Xb1(sk_R) = c0
3.76/3.98	     | sk_Xa1(sk_R) = c0
3.76/3.98	     | app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xu), sk_Xv), sk_Xv)
3.76/3.98	     | sk_Xa1(sk_R) = c0
3.76/3.98	     | sk_Xb1(sk_R) = c0),
3.76/3.98	    inference('sup+', [status(thm)], ['1', '67'])).
3.76/3.98	tff('69', plain,
3.76/3.98	    (app_encode_app(iS, $o, 
3.76/3.98	       app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	           sk_R, sk_Xu), sk_Xv), sk_Xv)
3.76/3.98	     | sk_Xa1(sk_R) = c0
3.76/3.98	     | sk_Xb1(sk_R) = c0
3.76/3.98	     | app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xa1(sk_R)), sk_Xb1(sk_R)), 
3.76/3.98	         app_encode_app(iS, iS, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, iS), cP, sk_Xz11(sk_R)), 
3.76/3.98	           sk_Xz21(sk_R)))),
3.76/3.98	    inference('simplify', [status(thm)], ['68'])).
3.76/3.98	tff('70', plain,
3.76/3.98	    (app_encode_app(iS, $o, 
3.76/3.98	       app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	           sk_R, sk_Xa1(sk_R)), sk_Xb1(sk_R)), 
3.76/3.98	       app_encode_app(iS, iS, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, iS), cP, sk_Xz11(sk_R)), 
3.76/3.98	         sk_Xz21(sk_R)))
3.76/3.98	     | sk_Xb1(sk_R) = c0
3.76/3.98	     | sk_Xa1(sk_R) = c0),
3.76/3.98	    inference('clc', [status(thm)], ['69', '63'])).
3.76/3.98	tff('71', plain,
3.76/3.98	    (app_encode_app(iS, $o, 
3.76/3.98	       app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	           sk_R, sk_Xa1(sk_R)), sk_Xb1(sk_R)), sk_Xc1(sk_R))
3.76/3.98	     | sk_Xb1(sk_R) = c0
3.76/3.98	     | sk_Xa1(sk_R) = c0
3.76/3.98	     | app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xu), sk_Xv), sk_Xv)
3.76/3.98	     | sk_Xa1(sk_R) = c0
3.76/3.98	     | sk_Xb1(sk_R) = c0),
3.76/3.98	    inference('sup+', [status(thm)], ['0', '70'])).
3.76/3.98	tff('72', plain,
3.76/3.98	    (app_encode_app(iS, $o, 
3.76/3.98	       app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	           sk_R, sk_Xu), sk_Xv), sk_Xv)
3.76/3.98	     | sk_Xa1(sk_R) = c0
3.76/3.98	     | sk_Xb1(sk_R) = c0
3.76/3.98	     | app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xa1(sk_R)), sk_Xb1(sk_R)), sk_Xc1(sk_R))),
3.76/3.98	    inference('simplify', [status(thm)], ['71'])).
3.76/3.98	tff('73', plain,
3.76/3.98	    (app_encode_app(iS, $o, 
3.76/3.98	       app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	           sk_R, sk_Xa1(sk_R)), sk_Xb1(sk_R)), sk_Xc1(sk_R))
3.76/3.98	     | sk_Xb1(sk_R) = c0
3.76/3.98	     | sk_Xa1(sk_R) = c0),
3.76/3.98	    inference('clc', [status(thm)], ['72', '63'])).
3.76/3.98	tff('74', plain,
3.76/3.98	    ![X13 : app_encode_fun(iS, app_encode_fun(iS, app_encode_fun(iS, $o)))]:
3.76/3.98	      (app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             X13, sk_Xu), sk_Xv), sk_Xv)
3.76/3.98	       | ~ app_encode_app(iS, $o, 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	               app_encode_app(iS, 
3.76/3.98	                 app_encode_fun(iS, app_encode_fun(iS, $o)), X13, 
3.76/3.98	                 sk_Xa1(X13)), sk_Xb1(X13)), sk_Xc1(X13))),
3.76/3.98	    inference('cnf', [status(esa)], [zf_stmt_0])).
3.76/3.98	tff('75', plain,
3.76/3.98	    (~ $true
3.76/3.98	     | sk_Xa1(sk_R) = c0
3.76/3.98	     | sk_Xb1(sk_R) = c0
3.76/3.98	     | app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xu), sk_Xv), sk_Xv)),
3.76/3.98	    inference('sup-', [status(thm)], ['73', '74'])).
3.76/3.98	tff('76', plain,
3.76/3.98	    (app_encode_app(iS, $o, 
3.76/3.98	       app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	           sk_R, sk_Xu), sk_Xv), sk_Xv)
3.76/3.98	     | sk_Xb1(sk_R) = c0
3.76/3.98	     | sk_Xa1(sk_R) = c0),
3.76/3.98	    inference('simplify', [status(thm)], ['75'])).
3.76/3.98	tff('77', plain, (sk_Xa1(sk_R) = c0 | sk_Xb1(sk_R) = c0),
3.76/3.98	    inference('clc', [status(thm)], ['76', '63'])).
3.76/3.98	tff('78', plain,
3.76/3.98	    ![X13 : app_encode_fun(iS, app_encode_fun(iS, app_encode_fun(iS, $o)))]:
3.76/3.98	      (app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             X13, sk_Xu), sk_Xv), sk_Xv)
3.76/3.98	       | sk_Xa1(X13) = c0
3.76/3.98	       | sk_Xa1(X13) = sk_Xc1(X13)
3.76/3.98	       | sk_Xb1(X13)
3.76/3.98	          = app_encode_app(iS, iS, 
3.76/3.98	              app_encode_app(iS, app_encode_fun(iS, iS), cP, sk_Xy11(X13)), 
3.76/3.98	              sk_Xy21(X13))),
3.76/3.98	    inference('cnf', [status(esa)], [zf_stmt_0])).
3.76/3.98	tff('79', plain,
3.76/3.98	    ![X0 : app_encode_fun(iS, app_encode_fun(iS, app_encode_fun(iS, $o)))]:
3.76/3.98	      (sk_Xb1(X0) != c0
3.76/3.98	       | sk_Xa1(X0) = sk_Xc1(X0)
3.76/3.98	       | sk_Xa1(X0) = c0
3.76/3.98	       | app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               X0, sk_Xu), sk_Xv), sk_Xv)),
3.76/3.98	    inference('sup-', [status(thm)], ['78', '27'])).
3.76/3.98	tff('80', plain,
3.76/3.98	    ![X0 : app_encode_fun(iS, app_encode_fun(iS, app_encode_fun(iS, $o)))]:
3.76/3.98	      (~ app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               X0, sk_Xa1(X0)), sk_Xb1(X0)), sk_Xa1(X0))
3.76/3.98	       | app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               X0, sk_Xu), sk_Xv), sk_Xv)
3.76/3.98	       | sk_Xa1(X0) = c0
3.76/3.98	       | sk_Xb1(X0) != c0
3.76/3.98	       | app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               X0, sk_Xu), sk_Xv), sk_Xv)),
3.76/3.98	    inference('sup-', [status(thm)], ['79', '74'])).
3.76/3.98	tff('81', plain,
3.76/3.98	    ![X0 : app_encode_fun(iS, app_encode_fun(iS, app_encode_fun(iS, $o)))]:
3.76/3.98	      (sk_Xb1(X0) != c0
3.76/3.98	       | sk_Xa1(X0) = c0
3.76/3.98	       | app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               X0, sk_Xu), sk_Xv), sk_Xv)
3.76/3.98	       | ~ app_encode_app(iS, $o, 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	               app_encode_app(iS, 
3.76/3.98	                 app_encode_fun(iS, app_encode_fun(iS, $o)), X0, sk_Xa1(X0)), 
3.76/3.98	               sk_Xb1(X0)), sk_Xa1(X0))),
3.76/3.98	    inference('simplify', [status(thm)], ['80'])).
3.76/3.98	tff('82', plain,
3.76/3.98	    (~ app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xa1(sk_R)), c0), sk_Xa1(sk_R))
3.76/3.98	     | sk_Xa1(sk_R) = c0
3.76/3.98	     | app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xu), sk_Xv), sk_Xv)
3.76/3.98	     | sk_Xa1(sk_R) = c0
3.76/3.98	     | sk_Xb1(sk_R) != c0),
3.76/3.98	    inference('sup-', [status(thm)], ['77', '81'])).
3.76/3.98	tff('83', plain,
3.76/3.98	    (~ $true
3.76/3.98	     | sk_Xa1(sk_R) = c0
3.76/3.98	     | app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xu), sk_Xv), sk_Xv)
3.76/3.98	     | sk_Xa1(sk_R) = c0
3.76/3.98	     | sk_Xb1(sk_R) != c0),
3.76/3.98	    inference('demod', [status(thm)], ['82', '33'])).
3.76/3.98	tff('84', plain,
3.76/3.98	    (sk_Xb1(sk_R) != c0
3.76/3.98	     | app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xu), sk_Xv), sk_Xv)
3.76/3.98	     | sk_Xa1(sk_R) = c0),
3.76/3.98	    inference('simplify', [status(thm)], ['83'])).
3.76/3.98	tff('85', plain,
3.76/3.98	    (sk_Xa1(sk_R) = c0
3.76/3.98	     | app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xu), sk_Xv), sk_Xv)),
3.76/3.98	    inference('clc', [status(thm)], ['84', '77'])).
3.76/3.98	tff('86', plain, sk_Xa1(sk_R) = c0,
3.76/3.98	    inference('clc', [status(thm)], ['85', '63'])).
3.76/3.98	tff('87', plain,
3.76/3.98	    ![X13 : app_encode_fun(iS, app_encode_fun(iS, app_encode_fun(iS, $o)))]:
3.76/3.98	      (app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             X13, sk_Xu), sk_Xv), sk_Xv)
3.76/3.98	       | sk_Xb1(X13) = sk_Xc1(X13)
3.76/3.98	       | sk_Xb1(X13) = c0
3.76/3.98	       | sk_Xa1(X13)
3.76/3.98	          = app_encode_app(iS, iS, 
3.76/3.98	              app_encode_app(iS, app_encode_fun(iS, iS), cP, sk_Xx11(X13)), 
3.76/3.98	              sk_Xx21(X13))),
3.76/3.98	    inference('cnf', [status(esa)], [zf_stmt_0])).
3.76/3.98	tff('88', plain,
3.76/3.98	    ![X0 : app_encode_fun(iS, app_encode_fun(iS, app_encode_fun(iS, $o)))]:
3.76/3.98	      (sk_Xa1(X0) != c0
3.76/3.98	       | sk_Xb1(X0) = c0
3.76/3.98	       | sk_Xb1(X0) = sk_Xc1(X0)
3.76/3.98	       | app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               X0, sk_Xu), sk_Xv), sk_Xv)),
3.76/3.98	    inference('sup-', [status(thm)], ['87', '27'])).
3.76/3.98	tff('89', plain,
3.76/3.98	    ![X0 : app_encode_fun(iS, app_encode_fun(iS, app_encode_fun(iS, $o)))]:
3.76/3.98	      (~ app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               X0, sk_Xa1(X0)), sk_Xb1(X0)), sk_Xb1(X0))
3.76/3.98	       | app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               X0, sk_Xu), sk_Xv), sk_Xv)
3.76/3.98	       | sk_Xb1(X0) = c0
3.76/3.98	       | sk_Xa1(X0) != c0
3.76/3.98	       | app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               X0, sk_Xu), sk_Xv), sk_Xv)),
3.76/3.98	    inference('sup-', [status(thm)], ['88', '74'])).
3.76/3.98	tff('90', plain,
3.76/3.98	    ![X0 : app_encode_fun(iS, app_encode_fun(iS, app_encode_fun(iS, $o)))]:
3.76/3.98	      (sk_Xa1(X0) != c0
3.76/3.98	       | sk_Xb1(X0) = c0
3.76/3.98	       | app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               X0, sk_Xu), sk_Xv), sk_Xv)
3.76/3.98	       | ~ app_encode_app(iS, $o, 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	               app_encode_app(iS, 
3.76/3.98	                 app_encode_fun(iS, app_encode_fun(iS, $o)), X0, sk_Xa1(X0)), 
3.76/3.98	               sk_Xb1(X0)), sk_Xb1(X0))),
3.76/3.98	    inference('simplify', [status(thm)], ['89'])).
3.76/3.98	tff('91', plain,
3.76/3.98	    (~ app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, c0), sk_Xb1(sk_R)), sk_Xb1(sk_R))
3.76/3.98	     | app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xu), sk_Xv), sk_Xv)
3.76/3.98	     | sk_Xb1(sk_R) = c0
3.76/3.98	     | sk_Xa1(sk_R) != c0),
3.76/3.98	    inference('sup-', [status(thm)], ['86', '90'])).
3.76/3.98	tff('92', plain,
3.76/3.98	    (~ $true
3.76/3.98	     | app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xu), sk_Xv), sk_Xv)
3.76/3.98	     | sk_Xb1(sk_R) = c0
3.76/3.98	     | c0 != c0),
3.76/3.98	    inference('demod', [status(thm)], ['91', '43', '86'])).
3.76/3.98	tff('93', plain,
3.76/3.98	    (sk_Xb1(sk_R) = c0
3.76/3.98	     | app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xu), sk_Xv), sk_Xv)),
3.76/3.98	    inference('simplify', [status(thm)], ['92'])).
3.76/3.98	tff('94', plain, sk_Xb1(sk_R) = c0,
3.76/3.98	    inference('clc', [status(thm)], ['93', '63'])).
3.76/3.98	tff('95', plain,
3.76/3.98	    ![X13 : app_encode_fun(iS, app_encode_fun(iS, app_encode_fun(iS, $o)))]:
3.76/3.98	      (app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             X13, sk_Xu), sk_Xv), sk_Xv)
3.76/3.98	       | sk_Xb1(X13) = sk_Xc1(X13)
3.76/3.98	       | sk_Xa1(X13) = sk_Xc1(X13)
3.76/3.98	       | sk_Xa1(X13)
3.76/3.98	          = app_encode_app(iS, iS, 
3.76/3.98	              app_encode_app(iS, app_encode_fun(iS, iS), cP, sk_Xx11(X13)), 
3.76/3.98	              sk_Xx21(X13))),
3.76/3.98	    inference('cnf', [status(esa)], [zf_stmt_0])).
3.76/3.98	tff('96', plain,
3.76/3.98	    ![X0 : app_encode_fun(iS, app_encode_fun(iS, app_encode_fun(iS, $o)))]:
3.76/3.98	      (sk_Xa1(X0) != c0
3.76/3.98	       | sk_Xa1(X0) = sk_Xc1(X0)
3.76/3.98	       | sk_Xb1(X0) = sk_Xc1(X0)
3.76/3.98	       | app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               X0, sk_Xu), sk_Xv), sk_Xv)),
3.76/3.98	    inference('sup-', [status(thm)], ['95', '27'])).
3.76/3.98	tff('97', plain,
3.76/3.98	    ![X0 : app_encode_fun(iS, app_encode_fun(iS, app_encode_fun(iS, $o)))]:
3.76/3.98	      (sk_Xb1(X0) != sk_Xa1(X0)
3.76/3.98	       | app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               X0, sk_Xu), sk_Xv), sk_Xv)
3.76/3.98	       | sk_Xa1(X0) = sk_Xc1(X0)
3.76/3.98	       | sk_Xa1(X0) != c0),
3.76/3.98	    inference('eq_fact', [status(thm)], ['96'])).
3.76/3.98	tff('98', plain,
3.76/3.98	    ![X0 : app_encode_fun(iS, app_encode_fun(iS, app_encode_fun(iS, $o)))]:
3.76/3.98	      (~ app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               X0, sk_Xa1(X0)), sk_Xb1(X0)), sk_Xa1(X0))
3.76/3.98	       | sk_Xa1(X0) != c0
3.76/3.98	       | app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               X0, sk_Xu), sk_Xv), sk_Xv)
3.76/3.98	       | sk_Xb1(X0) != sk_Xa1(X0)
3.76/3.98	       | app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               X0, sk_Xu), sk_Xv), sk_Xv)),
3.76/3.98	    inference('sup-', [status(thm)], ['97', '74'])).
3.76/3.98	tff('99', plain,
3.76/3.98	    ![X0 : app_encode_fun(iS, app_encode_fun(iS, app_encode_fun(iS, $o)))]:
3.76/3.98	      (sk_Xb1(X0) != sk_Xa1(X0)
3.76/3.98	       | app_encode_app(iS, $o, 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	               X0, sk_Xu), sk_Xv), sk_Xv)
3.76/3.98	       | sk_Xa1(X0) != c0
3.76/3.98	       | ~ app_encode_app(iS, $o, 
3.76/3.98	             app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	               app_encode_app(iS, 
3.76/3.98	                 app_encode_fun(iS, app_encode_fun(iS, $o)), X0, sk_Xa1(X0)), 
3.76/3.98	               sk_Xb1(X0)), sk_Xa1(X0))),
3.76/3.98	    inference('simplify', [status(thm)], ['98'])).
3.76/3.98	tff('100', plain,
3.76/3.98	    (~ app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xa1(sk_R)), c0), sk_Xa1(sk_R))
3.76/3.98	     | sk_Xa1(sk_R) != c0
3.76/3.98	     | app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xu), sk_Xv), sk_Xv)
3.76/3.98	     | sk_Xb1(sk_R) != sk_Xa1(sk_R)),
3.76/3.98	    inference('sup-', [status(thm)], ['94', '99'])).
3.76/3.98	tff('101', plain,
3.76/3.98	    (~ $true
3.76/3.98	     | c0 != c0
3.76/3.98	     | app_encode_app(iS, $o, 
3.76/3.98	         app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	           app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), 
3.76/3.98	             sk_R, sk_Xu), sk_Xv), sk_Xv)
3.76/3.98	     | c0 != c0),
3.76/3.98	    inference('demod', [status(thm)],
3.76/3.98	              ['100', '86', '86', '43', '86', '94', '86'])).
3.76/3.98	tff('102', plain,
3.76/3.98	    app_encode_app(iS, $o, 
3.76/3.98	      app_encode_app(iS, app_encode_fun(iS, $o), 
3.76/3.98	        app_encode_app(iS, app_encode_fun(iS, app_encode_fun(iS, $o)), sk_R, 
3.76/3.98	          sk_Xu), sk_Xv), sk_Xv),
3.76/3.98	    inference('simplify', [status(thm)], ['101'])).
3.76/3.98	tff('103', plain, ~ $true, inference('sup-', [status(thm)], ['102', '63'])).
3.76/3.98	tff('104', plain, $false, inference('simplify', [status(thm)], ['103'])).
3.76/3.98	
3.76/3.98	% SZS output end Refutation
3.76/3.98	EOF
