0.00/0.00	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : app
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : kbo
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n159.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 17:38:54 CST 2018
4.73/4.97	% done 2186 iterations in 4.773s
4.73/4.97	% SZS status Theorem for 'stdin'
4.73/4.97	% SZS output start Refutation
4.73/4.97	tff(zf_stmt_4, conjecture,
4.73/4.97	  (![Xp:app_encode_fun(a,app_encode_fun(a,$o)),
4.73/4.97	     Xp2:app_encode_fun(a,app_encode_fun(b,app_encode_fun(b,$o)))]:
4.73/4.97	     (((![Xx:a,Xy:a]:
4.73/4.97	          (app_encode_app(a,$o,app_encode_app(a,app_encode_fun(a,$o),Xp,Xx),
4.73/4.97	                          Xy) =>
4.73/4.97	           app_encode_app(a,$o,app_encode_app(a,app_encode_fun(a,$o),Xp,Xy),
4.73/4.97	                          Xx))) & 
4.73/4.97	       (![Xx:a,Xy:a,Xz:a]:
4.73/4.97	          ((app_encode_app(a,$o,app_encode_app(a,app_encode_fun(a,$o),Xp,Xx),
4.73/4.97	                           Xy) & 
4.73/4.97	            app_encode_app(a,$o,app_encode_app(a,app_encode_fun(a,$o),Xp,Xy),
4.73/4.97	                           Xz)) =>
4.73/4.97	           app_encode_app(a,$o,app_encode_app(a,app_encode_fun(a,$o),Xp,Xx),
4.73/4.97	                          Xz))) & 
4.73/4.97	       (![Xx:a]:
4.73/4.97	          (app_encode_app(a,$o,app_encode_app(a,app_encode_fun(a,$o),Xp,Xx),
4.73/4.97	                          Xx) =>
4.73/4.97	           ((![Xx0:b,Xy:b]:
4.73/4.97	               (app_encode_app(b,$o,
4.73/4.97	                               app_encode_app(b,app_encode_fun(b,$o),
4.73/4.97	                                              app_encode_app(a,
4.73/4.97	                                                             app_encode_fun(
4.73/4.97	                                                             b,
4.73/4.97	                                                             app_encode_fun(
4.73/4.97	                                                             b,$o)),Xp2,Xx),
4.73/4.97	                                              Xx0),
4.73/4.97	                               Xy) =>
4.73/4.97	                app_encode_app(b,$o,
4.73/4.97	                               app_encode_app(b,app_encode_fun(b,$o),
4.73/4.97	                                              app_encode_app(a,
4.73/4.97	                                                             app_encode_fun(
4.73/4.97	                                                             b,
4.73/4.97	                                                             app_encode_fun(
4.73/4.97	                                                             b,$o)),Xp2,Xx),
4.73/4.97	                                              Xy),
4.73/4.97	                               Xx0))) & 
4.73/4.97	            (![Xx0:b,Xy:b,Xz:b]:
4.73/4.97	               ((app_encode_app(b,$o,
4.73/4.97	                                app_encode_app(b,app_encode_fun(b,$o),
4.73/4.97	                                               app_encode_app(a,
4.73/4.97	                                                              app_encode_fun(
4.73/4.97	                                                              b,
4.73/4.97	                                                              app_encode_fun(
4.73/4.97	                                                              b,$o)),Xp2,Xx),
4.73/4.97	                                               Xx0),
4.73/4.97	                                Xy) & 
4.73/4.97	                 app_encode_app(b,$o,
4.73/4.97	                                app_encode_app(b,app_encode_fun(b,$o),
4.73/4.97	                                               app_encode_app(a,
4.73/4.97	                                                              app_encode_fun(
4.73/4.97	                                                              b,
4.73/4.97	                                                              app_encode_fun(
4.73/4.97	                                                              b,$o)),Xp2,Xx),
4.73/4.97	                                               Xy),
4.73/4.97	                                Xz)) =>
4.73/4.97	                app_encode_app(b,$o,
4.73/4.97	                               app_encode_app(b,app_encode_fun(b,$o),
4.73/4.97	                                              app_encode_app(a,
4.73/4.97	                                                             app_encode_fun(
4.73/4.97	                                                             b,
4.73/4.97	                                                             app_encode_fun(
4.73/4.97	                                                             b,$o)),Xp2,Xx),
4.73/4.97	                                              Xx0),
4.73/4.97	                               Xz)))))) & 
4.73/4.97	       (![Xx:a,Xy:a]:
4.73/4.97	          (app_encode_app(a,$o,app_encode_app(a,app_encode_fun(a,$o),Xp,Xx),
4.73/4.97	                          Xy) =>
4.73/4.97	           (app_encode_app(a,app_encode_fun(b,app_encode_fun(b,$o)),Xp2,Xx) =
4.73/4.97	            app_encode_app(a,app_encode_fun(b,app_encode_fun(b,$o)),Xp2,Xy))))) =>
4.73/4.97	      ((![Xx:app_encode_fun(a,b),Xy:app_encode_fun(a,b)]:
4.73/4.97	          ((![Xx0:a,Xy0:a]:
4.73/4.97	              (app_encode_app(a,$o,
4.73/4.97	                              app_encode_app(a,app_encode_fun(a,$o),Xp,Xx0),
4.73/4.97	                              Xy0) =>
4.73/4.97	               app_encode_app(b,$o,
4.73/4.97	                              app_encode_app(b,app_encode_fun(b,$o),
4.73/4.97	                                             app_encode_app(a,
4.73/4.97	                                                            app_encode_fun(
4.73/4.97	                                                            b,
4.73/4.97	                                                            app_encode_fun(
4.73/4.97	                                                            b,$o)),Xp2,Xx0),
4.73/4.97	                                             app_encode_app(a,b,Xx,Xx0)),
4.73/4.97	                              app_encode_app(a,b,Xy,Xy0)))) =>
4.73/4.97	           (![Xx0:a,Xy0:a]:
4.73/4.97	              (app_encode_app(a,$o,
4.73/4.97	                              app_encode_app(a,app_encode_fun(a,$o),Xp,Xx0),
4.73/4.97	                              Xy0) =>
4.73/4.97	               app_encode_app(b,$o,
4.73/4.97	                              app_encode_app(b,app_encode_fun(b,$o),
4.73/4.97	                                             app_encode_app(a,
4.73/4.97	                                                            app_encode_fun(
4.73/4.97	                                                            b,
4.73/4.97	                                                            app_encode_fun(
4.73/4.97	                                                            b,$o)),Xp2,Xx0),
4.73/4.97	                                             app_encode_app(a,b,Xy,Xx0)),
4.73/4.97	                              app_encode_app(a,b,Xx,Xy0)))))) & 
4.73/4.97	       (![Xx:app_encode_fun(a,b),Xy:app_encode_fun(a,b),
4.73/4.97	          Xz:app_encode_fun(a,b)]:
4.73/4.97	          (((![Xx0:a,Xy0:a]:
4.73/4.97	               (app_encode_app(a,$o,
4.73/4.97	                               app_encode_app(a,app_encode_fun(a,$o),Xp,Xx0),
4.73/4.97	                               Xy0) =>
4.73/4.97	                app_encode_app(b,$o,
4.73/4.97	                               app_encode_app(b,app_encode_fun(b,$o),
4.73/4.97	                                              app_encode_app(a,
4.73/4.97	                                                             app_encode_fun(
4.73/4.97	                                                             b,
4.73/4.97	                                                             app_encode_fun(
4.73/4.97	                                                             b,$o)),Xp2,Xx0),
4.73/4.97	                                              app_encode_app(a,b,Xx,Xx0)),
4.73/4.97	                               app_encode_app(a,b,Xy,Xy0)))) & 
4.73/4.97	            (![Xx0:a,Xy0:a]:
4.73/4.97	               (app_encode_app(a,$o,
4.73/4.97	                               app_encode_app(a,app_encode_fun(a,$o),Xp,Xx0),
4.73/4.97	                               Xy0) =>
4.73/4.97	                app_encode_app(b,$o,
4.73/4.97	                               app_encode_app(b,app_encode_fun(b,$o),
4.73/4.97	                                              app_encode_app(a,
4.73/4.97	                                                             app_encode_fun(
4.73/4.97	                                                             b,
4.73/4.97	                                                             app_encode_fun(
4.73/4.97	                                                             b,$o)),Xp2,Xx0),
4.73/4.97	                                              app_encode_app(a,b,Xy,Xx0)),
4.73/4.97	                               app_encode_app(a,b,Xz,Xy0))))) =>
4.73/4.97	           (![Xx0:a,Xy0:a]:
4.73/4.97	              (app_encode_app(a,$o,
4.73/4.97	                              app_encode_app(a,app_encode_fun(a,$o),Xp,Xx0),
4.73/4.97	                              Xy0) =>
4.73/4.97	               app_encode_app(b,$o,
4.73/4.97	                              app_encode_app(b,app_encode_fun(b,$o),
4.73/4.97	                                             app_encode_app(a,
4.73/4.97	                                                            app_encode_fun(
4.73/4.97	                                                            b,
4.73/4.97	                                                            app_encode_fun(
4.73/4.97	                                                            b,$o)),Xp2,Xx0),
4.73/4.97	                                             app_encode_app(a,b,Xx,Xx0)),
4.73/4.97	                              app_encode_app(a,b,Xz,Xy0)))))))))).
4.73/4.97	tff(zf_stmt_0, negated_conjecture,
4.73/4.97	  (~
4.73/4.97	    (![Xp:app_encode_fun(a,app_encode_fun(a,$o)),
4.73/4.97	       Xp2:app_encode_fun(a,app_encode_fun(b,app_encode_fun(b,$o)))]:
4.73/4.97	       (((![Xx:a,Xy:a]:
4.73/4.97	            (app_encode_app(a,$o,
4.73/4.97	                            app_encode_app(a,app_encode_fun(a,$o),Xp,Xx),Xy) =>
4.73/4.97	             app_encode_app(a,$o,
4.73/4.97	                            app_encode_app(a,app_encode_fun(a,$o),Xp,Xy),Xx))) & 
4.73/4.97	         (![Xx:a,Xy:a,Xz:a]:
4.73/4.97	            ((app_encode_app(a,$o,
4.73/4.97	                             app_encode_app(a,app_encode_fun(a,$o),Xp,Xx),Xy) & 
4.73/4.97	              app_encode_app(a,$o,
4.73/4.97	                             app_encode_app(a,app_encode_fun(a,$o),Xp,Xy),Xz)) =>
4.73/4.97	             app_encode_app(a,$o,
4.73/4.97	                            app_encode_app(a,app_encode_fun(a,$o),Xp,Xx),Xz))) & 
4.73/4.97	         (![Xx:a]:
4.73/4.97	            (app_encode_app(a,$o,
4.73/4.97	                            app_encode_app(a,app_encode_fun(a,$o),Xp,Xx),Xx) =>
4.73/4.97	             ((![Xx0:b,Xy:b]:
4.73/4.97	                 (app_encode_app(b,$o,
4.73/4.97	                                 app_encode_app(b,app_encode_fun(b,$o),
4.73/4.97	                                                app_encode_app(a,
4.73/4.97	                                                               app_encode_fun(
4.73/4.97	                                                               b,
4.73/4.97	                                                               app_encode_fun(
4.73/4.97	                                                               b,$o)),Xp2,Xx),
4.73/4.97	                                                Xx0),
4.73/4.97	                                 Xy) =>
4.73/4.97	                  app_encode_app(b,$o,
4.73/4.97	                                 app_encode_app(b,app_encode_fun(b,$o),
4.73/4.97	                                                app_encode_app(a,
4.73/4.97	                                                               app_encode_fun(
4.73/4.97	                                                               b,
4.73/4.97	                                                               app_encode_fun(
4.73/4.97	                                                               b,$o)),Xp2,Xx),
4.73/4.97	                                                Xy),
4.73/4.97	                                 Xx0))) & 
4.73/4.97	              (![Xx0:b,Xy:b,Xz:b]:
4.73/4.97	                 ((app_encode_app(b,$o,
4.73/4.97	                                  app_encode_app(b,app_encode_fun(b,$o),
4.73/4.97	                                                 app_encode_app(a,
4.73/4.97	                                                                app_encode_fun(
4.73/4.97	                                                                b,
4.73/4.97	                                                                app_encode_fun(
4.73/4.97	                                                                b,$o)),Xp2,Xx),
4.73/4.97	                                                 Xx0),
4.73/4.97	                                  Xy) & 
4.73/4.97	                   app_encode_app(b,$o,
4.73/4.97	                                  app_encode_app(b,app_encode_fun(b,$o),
4.73/4.97	                                                 app_encode_app(a,
4.73/4.97	                                                                app_encode_fun(
4.73/4.97	                                                                b,
4.73/4.97	                                                                app_encode_fun(
4.73/4.97	                                                                b,$o)),Xp2,Xx),
4.73/4.97	                                                 Xy),
4.73/4.97	                                  Xz)) =>
4.73/4.97	                  app_encode_app(b,$o,
4.73/4.97	                                 app_encode_app(b,app_encode_fun(b,$o),
4.73/4.97	                                                app_encode_app(a,
4.73/4.97	                                                               app_encode_fun(
4.73/4.97	                                                               b,
4.73/4.97	                                                               app_encode_fun(
4.73/4.97	                                                               b,$o)),Xp2,Xx),
4.73/4.97	                                                Xx0),
4.73/4.97	                                 Xz)))))) & 
4.73/4.97	         (![Xx:a,Xy:a]:
4.73/4.97	            (app_encode_app(a,$o,
4.73/4.97	                            app_encode_app(a,app_encode_fun(a,$o),Xp,Xx),Xy) =>
4.73/4.97	             (app_encode_app(a,app_encode_fun(b,app_encode_fun(b,$o)),Xp2,Xx) =
4.73/4.97	              app_encode_app(a,app_encode_fun(b,app_encode_fun(b,$o)),Xp2,Xy))))) =>
4.73/4.97	        ((![Xx:app_encode_fun(a,b),Xy:app_encode_fun(a,b)]:
4.73/4.97	            ((![Xx0:a,Xy0:a]:
4.73/4.97	                (app_encode_app(a,$o,
4.73/4.97	                                app_encode_app(a,app_encode_fun(a,$o),Xp,Xx0),
4.73/4.97	                                Xy0) =>
4.73/4.97	                 app_encode_app(b,$o,
4.73/4.97	                                app_encode_app(b,app_encode_fun(b,$o),
4.73/4.97	                                               app_encode_app(a,
4.73/4.97	                                                              app_encode_fun(
4.73/4.97	                                                              b,
4.73/4.97	                                                              app_encode_fun(
4.73/4.97	                                                              b,$o)),Xp2,Xx0),
4.73/4.97	                                               app_encode_app(a,b,Xx,Xx0)),
4.73/4.97	                                app_encode_app(a,b,Xy,Xy0)))) =>
4.73/4.97	             (![Xx0:a,Xy0:a]:
4.73/4.97	                (app_encode_app(a,$o,
4.73/4.97	                                app_encode_app(a,app_encode_fun(a,$o),Xp,Xx0),
4.73/4.97	                                Xy0) =>
4.73/4.97	                 app_encode_app(b,$o,
4.73/4.97	                                app_encode_app(b,app_encode_fun(b,$o),
4.73/4.97	                                               app_encode_app(a,
4.73/4.97	                                                              app_encode_fun(
4.73/4.97	                                                              b,
4.73/4.97	                                                              app_encode_fun(
4.73/4.97	                                                              b,$o)),Xp2,Xx0),
4.73/4.97	                                               app_encode_app(a,b,Xy,Xx0)),
4.73/4.97	                                app_encode_app(a,b,Xx,Xy0)))))) & 
4.73/4.97	         (![Xx:app_encode_fun(a,b),Xy:app_encode_fun(a,b),
4.73/4.97	            Xz:app_encode_fun(a,b)]:
4.73/4.97	            (((![Xx0:a,Xy0:a]:
4.73/4.97	                 (app_encode_app(a,$o,
4.73/4.97	                                 app_encode_app(a,app_encode_fun(a,$o),Xp,Xx0),
4.73/4.97	                                 Xy0) =>
4.73/4.97	                  app_encode_app(b,$o,
4.73/4.97	                                 app_encode_app(b,app_encode_fun(b,$o),
4.73/4.97	                                                app_encode_app(a,
4.73/4.97	                                                               app_encode_fun(
4.73/4.97	                                                               b,
4.73/4.97	                                                               app_encode_fun(
4.73/4.97	                                                               b,$o)),Xp2,Xx0),
4.73/4.97	                                                app_encode_app(a,b,Xx,Xx0)),
4.73/4.97	                                 app_encode_app(a,b,Xy,Xy0)))) & 
4.73/4.97	              (![Xx0:a,Xy0:a]:
4.73/4.97	                 (app_encode_app(a,$o,
4.73/4.97	                                 app_encode_app(a,app_encode_fun(a,$o),Xp,Xx0),
4.73/4.97	                                 Xy0) =>
4.73/4.97	                  app_encode_app(b,$o,
4.73/4.97	                                 app_encode_app(b,app_encode_fun(b,$o),
4.73/4.97	                                                app_encode_app(a,
4.73/4.97	                                                               app_encode_fun(
4.73/4.97	                                                               b,
4.73/4.97	                                                               app_encode_fun(
4.73/4.97	                                                               b,$o)),Xp2,Xx0),
4.73/4.97	                                                app_encode_app(a,b,Xy,Xx0)),
4.73/4.97	                                 app_encode_app(a,b,Xz,Xy0))))) =>
4.73/4.97	             (![Xx0:a,Xy0:a]:
4.73/4.97	                (app_encode_app(a,$o,
4.73/4.97	                                app_encode_app(a,app_encode_fun(a,$o),Xp,Xx0),
4.73/4.97	                                Xy0) =>
4.73/4.97	                 app_encode_app(b,$o,
4.73/4.97	                                app_encode_app(b,app_encode_fun(b,$o),
4.73/4.97	                                               app_encode_app(a,
4.73/4.97	                                                              app_encode_fun(
4.73/4.97	                                                              b,
4.73/4.97	                                                              app_encode_fun(
4.73/4.97	                                                              b,$o)),Xp2,Xx0),
4.73/4.97	                                               app_encode_app(a,b,Xx,Xx0)),
4.73/4.97	                                app_encode_app(a,b,Xz,Xy0))))))))))).
4.73/4.97	tff('0', plain,
4.73/4.97	    ![X0 : a, X1 : a]:
4.73/4.97	      (app_encode_app(a, $o, 
4.73/4.97	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)
4.73/4.97	       | app_encode_app(b, $o, 
4.73/4.97	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.97	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.97	               sk_Xp2, X0), app_encode_app(a, b, sk_Xx1, X0)), 
4.73/4.97	           app_encode_app(a, b, sk_Xy1, X1))
4.73/4.97	       | ~ app_encode_app(a, $o, 
4.73/4.97	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X0), X1)),
4.73/4.97	    inference('cnf', [status(esa)], [zf_stmt_0])).
4.73/4.97	tff('1', plain,
4.73/4.97	    ![X2 : a, X3 : a]:
4.73/4.97	      (app_encode_app(a, $o, 
4.73/4.97	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)
4.73/4.97	       | app_encode_app(b, $o, 
4.73/4.97	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.97	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.97	               sk_Xp2, X2), app_encode_app(a, b, sk_Xy1, X2)), 
4.73/4.97	           app_encode_app(a, b, sk_Xz, X3))
4.73/4.97	       | ~ app_encode_app(a, $o, 
4.73/4.97	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X2), X3)),
4.73/4.97	    inference('cnf', [status(esa)], [zf_stmt_0])).
4.73/4.97	tff('2', plain,
4.73/4.97	    ![X8 : a, X11 : b, X12 : b, X13 : b]:
4.73/4.97	      (app_encode_app(b, $o, 
4.73/4.97	         app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.97	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.97	             sk_Xp2, X8), X11), X12)
4.73/4.97	       | ~ app_encode_app(b, $o, 
4.73/4.97	             app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.97	               app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.97	                 sk_Xp2, X8), X13), X12)
4.73/4.97	       | ~ app_encode_app(b, $o, 
4.73/4.97	             app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.97	               app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.97	                 sk_Xp2, X8), X11), X13)
4.73/4.97	       | ~ app_encode_app(a, $o, 
4.73/4.97	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X8), X8)),
4.73/4.97	    inference('cnf', [status(esa)], [zf_stmt_0])).
4.73/4.97	tff('3', plain,
4.73/4.97	    ![X0 : a, X1 : a, X2 : b]:
4.73/4.97	      (~ $true
4.73/4.97	       | ~ app_encode_app(a, $o, 
4.73/4.97	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X1), X0)
4.73/4.97	       | app_encode_app(a, $o, 
4.73/4.97	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)
4.73/4.97	       | ~ app_encode_app(a, $o, 
4.73/4.97	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X1), X1)
4.73/4.97	       | ~ app_encode_app(b, $o, 
4.73/4.97	             app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.97	               app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.97	                 sk_Xp2, X1), X2), app_encode_app(a, b, sk_Xy1, X1))
4.73/4.97	       | app_encode_app(b, $o, 
4.73/4.97	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.97	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.97	               sk_Xp2, X1), X2), app_encode_app(a, b, sk_Xz, X0))),
4.73/4.97	    inference('sup-', [status(thm)], ['1', '2'])).
4.73/4.97	tff('4', plain,
4.73/4.97	    ![X0 : a, X1 : a, X2 : b]:
4.73/4.97	      (app_encode_app(b, $o, 
4.73/4.97	         app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.97	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.97	             sk_Xp2, X1), X2), app_encode_app(a, b, sk_Xz, X0))
4.73/4.97	       | ~ app_encode_app(b, $o, 
4.73/4.97	             app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.97	               app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.97	                 sk_Xp2, X1), X2), app_encode_app(a, b, sk_Xy1, X1))
4.73/4.97	       | ~ app_encode_app(a, $o, 
4.73/4.97	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X1), X1)
4.73/4.97	       | app_encode_app(a, $o, 
4.73/4.97	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)
4.73/4.97	       | ~ app_encode_app(a, $o, 
4.73/4.97	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X1), X0)),
4.73/4.97	    inference('simplify', [status(thm)], ['3'])).
4.73/4.97	tff('5', plain,
4.73/4.97	    ![X0 : a, X1 : a]:
4.73/4.97	      (~ $true
4.73/4.97	       | ~ app_encode_app(a, $o, 
4.73/4.97	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X0), X0)
4.73/4.97	       | app_encode_app(a, $o, 
4.73/4.97	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)
4.73/4.97	       | ~ app_encode_app(a, $o, 
4.73/4.97	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X0), X1)
4.73/4.97	       | app_encode_app(a, $o, 
4.73/4.97	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)
4.73/4.97	       | ~ app_encode_app(a, $o, 
4.73/4.97	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X0), X0)
4.73/4.97	       | app_encode_app(b, $o, 
4.73/4.97	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.97	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.97	               sk_Xp2, X0), app_encode_app(a, b, sk_Xx1, X0)), 
4.73/4.97	           app_encode_app(a, b, sk_Xz, X1))),
4.73/4.97	    inference('sup-', [status(thm)], ['0', '4'])).
4.73/4.97	tff('6', plain,
4.73/4.97	    ![X0 : a, X1 : a]:
4.73/4.97	      (app_encode_app(b, $o, 
4.73/4.97	         app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.97	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.97	             sk_Xp2, X0), app_encode_app(a, b, sk_Xx1, X0)), 
4.73/4.97	         app_encode_app(a, b, sk_Xz, X1))
4.73/4.97	       | ~ app_encode_app(a, $o, 
4.73/4.97	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X0), X1)
4.73/4.97	       | app_encode_app(a, $o, 
4.73/4.97	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)
4.73/4.97	       | ~ app_encode_app(a, $o, 
4.73/4.97	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X0), X0)),
4.73/4.97	    inference('simplify', [status(thm)], ['5'])).
4.73/4.97	tff('7', plain,
4.73/4.97	    (app_encode_app(a, $o, 
4.73/4.97	       app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)
4.73/4.97	     | ~ app_encode_app(b, $o, 
4.73/4.97	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.97	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.97	               sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xx1, sk_Xx01)), 
4.73/4.97	           app_encode_app(a, b, sk_Xz, sk_Xy01))),
4.73/4.97	    inference('cnf', [status(esa)], [zf_stmt_0])).
4.73/4.97	tff('8', plain,
4.73/4.97	    (~ $true
4.73/4.97	     | ~ app_encode_app(a, $o, 
4.73/4.97	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01)
4.73/4.97	     | app_encode_app(a, $o, 
4.73/4.97	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)
4.73/4.97	     | ~ app_encode_app(a, $o, 
4.73/4.97	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xy01)
4.73/4.97	     | app_encode_app(a, $o, 
4.73/4.97	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)),
4.73/4.97	    inference('sup-', [status(thm)], ['6', '7'])).
4.73/4.97	tff('9', plain,
4.73/4.97	    (~ app_encode_app(a, $o, 
4.73/4.97	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xy01)
4.73/4.97	     | app_encode_app(a, $o, 
4.73/4.97	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)
4.73/4.97	     | ~ app_encode_app(a, $o, 
4.73/4.97	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01)),
4.73/4.97	    inference('simplify', [status(thm)], ['8'])).
4.73/4.97	tff('10', plain,
4.73/4.97	    (app_encode_app(a, $o, 
4.73/4.97	       app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)
4.73/4.97	     | app_encode_app(a, $o, 
4.73/4.97	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xy01)),
4.73/4.97	    inference('cnf', [status(esa)], [zf_stmt_0])).
4.73/4.97	tff('11', plain,
4.73/4.97	    (~ app_encode_app(a, $o, 
4.73/4.97	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01)
4.73/4.97	     | app_encode_app(a, $o, 
4.73/4.97	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)),
4.73/4.97	    inference('clc', [status(thm)], ['9', '10'])).
4.73/4.97	tff('12', plain,
4.73/4.97	    ![X14 : a, X15 : a]:
4.73/4.97	      (app_encode_app(a, $o, 
4.73/4.97	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X14), X15)
4.73/4.97	       | ~ app_encode_app(a, $o, 
4.73/4.97	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X15), X14)),
4.73/4.97	    inference('cnf', [status(esa)], [zf_stmt_0])).
4.73/4.97	tff('13', plain,
4.73/4.97	    (~ $true
4.73/4.97	     | app_encode_app(a, $o, 
4.73/4.97	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)
4.73/4.97	     | app_encode_app(a, $o, 
4.73/4.97	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy01), sk_Xx01)),
4.73/4.97	    inference('sup-', [status(thm)], ['10', '12'])).
4.73/4.97	tff('14', plain,
4.73/4.97	    (app_encode_app(a, $o, 
4.73/4.97	       app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy01), sk_Xx01)
4.73/4.97	     | app_encode_app(a, $o, 
4.73/4.97	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)),
4.73/4.97	    inference('simplify', [status(thm)], ['13'])).
4.73/4.97	tff('15', plain,
4.73/4.97	    ![X16 : a, X17 : a, X18 : a]:
4.73/4.97	      (~ app_encode_app(a, $o, 
4.73/4.97	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X16), X17)
4.73/4.97	       | ~ app_encode_app(a, $o, 
4.73/4.97	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X17), X18)
4.73/4.97	       | app_encode_app(a, $o, 
4.73/4.97	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X16), X18)),
4.73/4.97	    inference('cnf', [status(esa)], [zf_stmt_0])).
4.73/4.97	tff('16', plain,
4.73/4.97	    ![X0 : a]:
4.73/4.97	      (~ $true
4.73/4.97	       | app_encode_app(a, $o, 
4.73/4.97	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)
4.73/4.97	       | app_encode_app(a, $o, 
4.73/4.97	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), X0)
4.73/4.97	       | ~ app_encode_app(a, $o, 
4.73/4.97	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy01), X0)),
4.73/4.97	    inference('sup-', [status(thm)], ['10', '15'])).
4.73/4.97	tff('17', plain,
4.73/4.97	    ![X0 : a]:
4.73/4.97	      (~ app_encode_app(a, $o, 
4.73/4.97	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy01), X0)
4.73/4.97	       | app_encode_app(a, $o, 
4.73/4.97	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), X0)
4.73/4.97	       | app_encode_app(a, $o, 
4.73/4.97	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)),
4.73/4.97	    inference('simplify', [status(thm)], ['16'])).
4.73/4.97	tff('18', plain,
4.73/4.97	    (~ $true
4.73/4.97	     | app_encode_app(a, $o, 
4.73/4.97	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)
4.73/4.97	     | app_encode_app(a, $o, 
4.73/4.97	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)
4.73/4.97	     | app_encode_app(a, $o, 
4.73/4.97	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01)),
4.73/4.97	    inference('sup-', [status(thm)], ['14', '17'])).
4.73/4.97	tff('19', plain,
4.73/4.97	    (app_encode_app(a, $o, 
4.73/4.97	       app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01)
4.73/4.97	     | app_encode_app(a, $o, 
4.73/4.97	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)),
4.73/4.97	    inference('simplify', [status(thm)], ['18'])).
4.73/4.97	tff('20', plain,
4.73/4.97	    app_encode_app(a, $o, 
4.73/4.97	      app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0),
4.73/4.97	    inference('clc', [status(thm)], ['11', '19'])).
4.73/4.97	tff('21', plain,
4.73/4.97	    ![X6 : a, X7 : a]:
4.73/4.97	      (app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), sk_Xp2, 
4.73/4.97	         X7)
4.73/4.97	        = app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.97	            sk_Xp2, X6)
4.73/4.97	       | ~ app_encode_app(a, $o, 
4.73/4.97	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X7), X6)),
4.73/4.97	    inference('cnf', [status(esa)], [zf_stmt_0])).
4.73/4.97	tff('22', plain,
4.73/4.97	    (~ $true
4.73/4.97	     | app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), sk_Xp2, 
4.73/4.97	         sk_Xx0)
4.73/4.97	        = app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.97	            sk_Xp2, sk_Xy0)),
4.73/4.97	    inference('sup-', [status(thm)], ['20', '21'])).
4.73/4.97	tff('23', plain,
4.73/4.97	    app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), sk_Xp2, 
4.73/4.97	      sk_Xx0)
4.73/4.97	     = app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), sk_Xp2, 
4.73/4.97	         sk_Xy0),
4.73/4.97	    inference('simplify', [status(thm)], ['22'])).
4.73/4.97	tff('24', plain,
4.73/4.97	    ![X2 : a, X3 : a, X4 : a, X5 : a]:
4.73/4.97	      (~ app_encode_app(a, $o, 
4.73/4.97	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X4), X5)
4.73/4.97	       | app_encode_app(b, $o, 
4.73/4.97	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.97	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.97	               sk_Xp2, X4), app_encode_app(a, b, sk_Xx, X4)), 
4.73/4.97	           app_encode_app(a, b, sk_Xy, X5))
4.73/4.97	       | app_encode_app(b, $o, 
4.73/4.97	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.97	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.97	               sk_Xp2, X2), app_encode_app(a, b, sk_Xy1, X2)), 
4.73/4.97	           app_encode_app(a, b, sk_Xz, X3))
4.73/4.97	       | ~ app_encode_app(a, $o, 
4.73/4.97	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X2), X3)),
4.73/4.97	    inference('cnf', [status(esa)], [zf_stmt_0])).
4.73/4.97	tff('25', plain,
4.73/4.97	    ![X0 : a, X1 : a, X2 : a]:
4.73/4.97	      (app_encode_app(b, $o, 
4.73/4.97	         app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.97	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.97	             sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.73/4.97	         app_encode_app(a, b, sk_Xy, X0))
4.73/4.97	       | ~ app_encode_app(a, $o, 
4.73/4.97	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X2), X1)
4.73/4.97	       | app_encode_app(b, $o, 
4.73/4.97	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.97	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.97	               sk_Xp2, X2), app_encode_app(a, b, sk_Xy1, X2)), 
4.73/4.97	           app_encode_app(a, b, sk_Xz, X1))
4.73/4.97	       | ~ app_encode_app(a, $o, 
4.73/4.97	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy0), X0)),
4.73/4.97	    inference('sup+', [status(thm)], ['23', '24'])).
4.73/4.97	tff('26', plain,
4.73/4.97	    ![X4 : a, X5 : a]:
4.73/4.97	      (~ app_encode_app(a, $o, 
4.73/4.97	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X4), X5)
4.73/4.97	       | app_encode_app(b, $o, 
4.73/4.97	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.97	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.97	               sk_Xp2, X4), app_encode_app(a, b, sk_Xx, X4)), 
4.73/4.97	           app_encode_app(a, b, sk_Xy, X5))
4.73/4.97	       | app_encode_app(a, $o, 
4.73/4.97	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xy01)),
4.73/4.97	    inference('cnf', [status(esa)], [zf_stmt_0])).
4.73/4.97	tff('27', plain,
4.73/4.97	    ![X0 : a]:
4.73/4.97	      (app_encode_app(b, $o, 
4.73/4.97	         app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.97	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.97	             sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.73/4.97	         app_encode_app(a, b, sk_Xy, X0))
4.73/4.97	       | app_encode_app(a, $o, 
4.73/4.97	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xy01)
4.73/4.97	       | ~ app_encode_app(a, $o, 
4.73/4.97	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy0), X0)),
4.73/4.97	    inference('sup+', [status(thm)], ['23', '26'])).
4.73/4.97	tff('28', plain,
4.73/4.97	    ![X8 : a, X9 : b, X10 : b]:
4.73/4.97	      (~ app_encode_app(b, $o, 
4.73/4.97	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.97	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.97	               sk_Xp2, X8), X9), X10)
4.73/4.97	       | app_encode_app(b, $o, 
4.73/4.97	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.97	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.97	               sk_Xp2, X8), X10), X9)
4.73/4.97	       | ~ app_encode_app(a, $o, 
4.73/4.97	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X8), X8)),
4.73/4.97	    inference('cnf', [status(esa)], [zf_stmt_0])).
4.73/4.97	tff('29', plain,
4.73/4.97	    ![X0 : a]:
4.73/4.97	      (~ $true
4.73/4.97	       | ~ app_encode_app(a, $o, 
4.73/4.97	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy0), X0)
4.73/4.97	       | app_encode_app(a, $o, 
4.73/4.97	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xy01)
4.73/4.97	       | ~ app_encode_app(a, $o, 
4.73/4.97	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xx0)
4.73/4.97	       | app_encode_app(b, $o, 
4.73/4.97	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.97	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.97	               sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xy, X0)), 
4.73/4.97	           app_encode_app(a, b, sk_Xx, sk_Xy0))),
4.73/4.97	    inference('sup-', [status(thm)], ['27', '28'])).
4.73/4.97	tff('30', plain,
4.73/4.97	    (~ $true
4.73/4.97	     | app_encode_app(a, $o, 
4.73/4.97	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy0), sk_Xx0)),
4.73/4.97	    inference('sup-', [status(thm)], ['20', '12'])).
4.73/4.97	tff('31', plain,
4.73/4.97	    app_encode_app(a, $o, 
4.73/4.97	      app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy0), sk_Xx0),
4.73/4.97	    inference('simplify', [status(thm)], ['30'])).
4.73/4.97	tff('32', plain,
4.73/4.97	    ![X0 : a]:
4.73/4.97	      (~ $true
4.73/4.97	       | app_encode_app(a, $o, 
4.73/4.97	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), X0)
4.73/4.97	       | ~ app_encode_app(a, $o, 
4.73/4.97	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy0), X0)),
4.73/4.97	    inference('sup-', [status(thm)], ['20', '15'])).
4.73/4.97	tff('33', plain,
4.73/4.97	    ![X0 : a]:
4.73/4.97	      (~ app_encode_app(a, $o, 
4.73/4.97	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy0), X0)
4.73/4.97	       | app_encode_app(a, $o, 
4.73/4.97	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), X0)),
4.73/4.97	    inference('simplify', [status(thm)], ['32'])).
4.73/4.97	tff('34', plain,
4.73/4.97	    (~ $true
4.73/4.97	     | app_encode_app(a, $o, 
4.73/4.97	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xx0)),
4.73/4.97	    inference('sup-', [status(thm)], ['31', '33'])).
4.73/4.97	tff('35', plain,
4.73/4.97	    app_encode_app(a, $o, 
4.73/4.97	      app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xx0),
4.73/4.97	    inference('simplify', [status(thm)], ['34'])).
4.73/4.97	tff('36', plain,
4.73/4.97	    ![X0 : a]:
4.73/4.97	      (~ $true
4.73/4.97	       | ~ app_encode_app(a, $o, 
4.73/4.97	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy0), X0)
4.73/4.97	       | app_encode_app(a, $o, 
4.73/4.97	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xy01)
4.73/4.97	       | ~ $true
4.73/4.97	       | app_encode_app(b, $o, 
4.73/4.97	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.97	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.97	               sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xy, X0)), 
4.73/4.97	           app_encode_app(a, b, sk_Xx, sk_Xy0))),
4.73/4.97	    inference('demod', [status(thm)], ['29', '35'])).
4.73/4.97	tff('37', plain,
4.73/4.97	    ![X0 : a]:
4.73/4.97	      (app_encode_app(b, $o, 
4.73/4.97	         app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.97	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.97	             sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xy, X0)), 
4.73/4.97	         app_encode_app(a, b, sk_Xx, sk_Xy0))
4.73/4.97	       | app_encode_app(a, $o, 
4.73/4.97	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xy01)
4.73/4.97	       | ~ app_encode_app(a, $o, 
4.73/4.97	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy0), X0)),
4.73/4.97	    inference('simplify', [status(thm)], ['36'])).
4.73/4.97	tff('38', plain,
4.73/4.97	    (~ app_encode_app(b, $o, 
4.73/4.97	         app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.97	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.97	             sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xy, sk_Xx0)), 
4.73/4.97	         app_encode_app(a, b, sk_Xx, sk_Xy0))
4.73/4.97	     | app_encode_app(a, $o, 
4.73/4.97	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xy01)),
4.73/4.97	    inference('cnf', [status(esa)], [zf_stmt_0])).
4.73/4.97	tff('39', plain,
4.73/4.97	    (~ $true
4.73/4.97	     | ~ app_encode_app(a, $o, 
4.73/4.97	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy0), sk_Xx0)
4.73/4.97	     | app_encode_app(a, $o, 
4.73/4.97	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xy01)
4.73/4.97	     | app_encode_app(a, $o, 
4.73/4.97	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xy01)),
4.73/4.97	    inference('sup-', [status(thm)], ['37', '38'])).
4.73/4.97	tff('40', plain,
4.73/4.97	    (~ $true
4.73/4.97	     | ~ $true
4.73/4.97	     | app_encode_app(a, $o, 
4.73/4.97	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xy01)
4.73/4.97	     | app_encode_app(a, $o, 
4.73/4.97	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xy01)),
4.73/4.97	    inference('demod', [status(thm)], ['39', '31'])).
4.73/4.97	tff('41', plain,
4.73/4.97	    app_encode_app(a, $o, 
4.73/4.97	      app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xy01),
4.73/4.97	    inference('simplify', [status(thm)], ['40'])).
4.73/4.97	tff('42', plain,
4.73/4.97	    (~ $true
4.73/4.97	     | app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), sk_Xp2, 
4.73/4.97	         sk_Xx01)
4.73/4.97	        = app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.97	            sk_Xp2, sk_Xy01)),
4.73/4.97	    inference('sup-', [status(thm)], ['41', '21'])).
4.73/4.97	tff('43', plain,
4.73/4.97	    app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), sk_Xp2, 
4.73/4.98	      sk_Xx01)
4.73/4.98	     = app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), sk_Xp2, 
4.73/4.98	         sk_Xy01),
4.73/4.98	    inference('simplify', [status(thm)], ['42'])).
4.73/4.98	tff('44', plain,
4.73/4.98	    ![X0 : b, X1 : b]:
4.73/4.98	      (~ app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xx01), X1), X0)
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy01), 
4.73/4.98	             sk_Xy01)
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xy01), X0), X1)),
4.73/4.98	    inference('sup-', [status(thm)], ['43', '28'])).
4.73/4.98	tff('45', plain,
4.73/4.98	    ![X0 : b, X1 : b]:
4.73/4.98	      (~ app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xx01), X1), X0)
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy01), 
4.73/4.98	             sk_Xy01)
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xx01), X0), X1)),
4.73/4.98	    inference('demod', [status(thm)], ['44', '43'])).
4.73/4.98	tff('46', plain,
4.73/4.98	    (~ $true
4.73/4.98	     | app_encode_app(a, $o, 
4.73/4.98	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy01), sk_Xx01)),
4.73/4.98	    inference('sup-', [status(thm)], ['41', '12'])).
4.73/4.98	tff('47', plain,
4.73/4.98	    app_encode_app(a, $o, 
4.73/4.98	      app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy01), sk_Xx01),
4.73/4.98	    inference('simplify', [status(thm)], ['46'])).
4.73/4.98	tff('48', plain,
4.73/4.98	    ![X0 : a]:
4.73/4.98	      (~ $true
4.73/4.98	       | app_encode_app(a, $o, 
4.73/4.98	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy01), X0)
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), X0)),
4.73/4.98	    inference('sup-', [status(thm)], ['47', '15'])).
4.73/4.98	tff('49', plain,
4.73/4.98	    ![X0 : a]:
4.73/4.98	      (~ app_encode_app(a, $o, 
4.73/4.98	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), X0)
4.73/4.98	       | app_encode_app(a, $o, 
4.73/4.98	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy01), X0)),
4.73/4.98	    inference('simplify', [status(thm)], ['48'])).
4.73/4.98	tff('50', plain,
4.73/4.98	    ![X0 : a]:
4.73/4.98	      (~ $true
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), X0)
4.73/4.98	       | app_encode_app(a, $o, 
4.73/4.98	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X0), sk_Xy01)),
4.73/4.98	    inference('sup-', [status(thm)], ['49', '12'])).
4.73/4.98	tff('51', plain,
4.73/4.98	    ![X0 : a]:
4.73/4.98	      (app_encode_app(a, $o, 
4.73/4.98	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X0), sk_Xy01)
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), X0)),
4.73/4.98	    inference('simplify', [status(thm)], ['50'])).
4.73/4.98	tff('52', plain,
4.73/4.98	    (~ $true
4.73/4.98	     | app_encode_app(a, $o, 
4.73/4.98	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy01), sk_Xy01)),
4.73/4.98	    inference('sup-', [status(thm)], ['41', '51'])).
4.73/4.98	tff('53', plain,
4.73/4.98	    app_encode_app(a, $o, 
4.73/4.98	      app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy01), sk_Xy01),
4.73/4.98	    inference('simplify', [status(thm)], ['52'])).
4.73/4.98	tff('54', plain,
4.73/4.98	    ![X0 : b, X1 : b]:
4.73/4.98	      (~ app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xx01), X1), X0)
4.73/4.98	       | ~ $true
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xx01), X0), X1)),
4.73/4.98	    inference('demod', [status(thm)], ['45', '53'])).
4.73/4.98	tff('55', plain,
4.73/4.98	    ![X0 : b, X1 : b]:
4.73/4.98	      (app_encode_app(b, $o, 
4.73/4.98	         app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	             sk_Xp2, sk_Xx01), X0), X1)
4.73/4.98	       | ~ app_encode_app(b, $o, 
4.73/4.98	             app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	               app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	                 sk_Xp2, sk_Xx01), X1), X0)),
4.73/4.98	    inference('simplify', [status(thm)], ['54'])).
4.73/4.98	tff('56', plain,
4.73/4.98	    ![X0 : a, X1 : a]:
4.73/4.98	      (~ $true
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy0), X1)
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), X0)
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.73/4.98	           app_encode_app(a, b, sk_Xy, X1))
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xz, X0)), 
4.73/4.98	           app_encode_app(a, b, sk_Xy1, sk_Xx01))),
4.73/4.98	    inference('sup-', [status(thm)], ['25', '55'])).
4.73/4.98	tff('57', plain,
4.73/4.98	    ![X0 : a, X1 : a]:
4.73/4.98	      (app_encode_app(b, $o, 
4.73/4.98	         app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	             sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xz, X0)), 
4.73/4.98	         app_encode_app(a, b, sk_Xy1, sk_Xx01))
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.73/4.98	           app_encode_app(a, b, sk_Xy, X1))
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), X0)
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy0), X1)),
4.73/4.98	    inference('simplify', [status(thm)], ['56'])).
4.73/4.98	tff('58', plain,
4.73/4.98	    ![X0 : a, X1 : a]:
4.73/4.98	      (~ $true
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy0), X0)
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), X1)
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xz, X1)), 
4.73/4.98	           app_encode_app(a, b, sk_Xy1, sk_Xx01))
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xx0)
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xy, X0)), 
4.73/4.98	           app_encode_app(a, b, sk_Xx, sk_Xy0))),
4.73/4.98	    inference('sup-', [status(thm)], ['57', '28'])).
4.73/4.98	tff('59', plain,
4.73/4.98	    ![X0 : a, X1 : a]:
4.73/4.98	      (~ $true
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy0), X0)
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), X1)
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xz, X1)), 
4.73/4.98	           app_encode_app(a, b, sk_Xy1, sk_Xx01))
4.73/4.98	       | ~ $true
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xy, X0)), 
4.73/4.98	           app_encode_app(a, b, sk_Xx, sk_Xy0))),
4.73/4.98	    inference('demod', [status(thm)], ['58', '35'])).
4.73/4.98	tff('60', plain,
4.73/4.98	    ![X0 : a, X1 : a]:
4.73/4.98	      (app_encode_app(b, $o, 
4.73/4.98	         app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	             sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xy, X0)), 
4.73/4.98	         app_encode_app(a, b, sk_Xx, sk_Xy0))
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xz, X1)), 
4.73/4.98	           app_encode_app(a, b, sk_Xy1, sk_Xx01))
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), X1)
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy0), X0)),
4.73/4.98	    inference('simplify', [status(thm)], ['59'])).
4.73/4.98	tff('61', plain,
4.73/4.98	    ![X2 : a, X3 : a]:
4.73/4.98	      (~ app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xy, sk_Xx0)), 
4.73/4.98	           app_encode_app(a, b, sk_Xx, sk_Xy0))
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, X2), app_encode_app(a, b, sk_Xy1, X2)), 
4.73/4.98	           app_encode_app(a, b, sk_Xz, X3))
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X2), X3)),
4.73/4.98	    inference('cnf', [status(esa)], [zf_stmt_0])).
4.73/4.98	tff('62', plain,
4.73/4.98	    ![X0 : a, X1 : a, X2 : a]:
4.73/4.98	      (~ $true
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy0), sk_Xx0)
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), X2)
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xz, X2)), 
4.73/4.98	           app_encode_app(a, b, sk_Xy1, sk_Xx01))
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X1), X0)
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, X1), app_encode_app(a, b, sk_Xy1, X1)), 
4.73/4.98	           app_encode_app(a, b, sk_Xz, X0))),
4.73/4.98	    inference('sup-', [status(thm)], ['60', '61'])).
4.73/4.98	tff('63', plain,
4.73/4.98	    ![X0 : a, X1 : a, X2 : a]:
4.73/4.98	      (~ $true
4.73/4.98	       | ~ $true
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), X2)
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xz, X2)), 
4.73/4.98	           app_encode_app(a, b, sk_Xy1, sk_Xx01))
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X1), X0)
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, X1), app_encode_app(a, b, sk_Xy1, X1)), 
4.73/4.98	           app_encode_app(a, b, sk_Xz, X0))),
4.73/4.98	    inference('demod', [status(thm)], ['62', '31'])).
4.73/4.98	tff('64', plain,
4.73/4.98	    ![X0 : a, X1 : a, X2 : a]:
4.73/4.98	      (app_encode_app(b, $o, 
4.73/4.98	         app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	             sk_Xp2, X1), app_encode_app(a, b, sk_Xy1, X1)), 
4.73/4.98	         app_encode_app(a, b, sk_Xz, X0))
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X1), X0)
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xz, X2)), 
4.73/4.98	           app_encode_app(a, b, sk_Xy1, sk_Xx01))
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), X2)),
4.73/4.98	    inference('simplify', [status(thm)], ['63'])).
4.73/4.98	tff('65', plain,
4.73/4.98	    ![X0 : a, X1 : a, X2 : a]:
4.73/4.98	      (~ $true
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), X0)
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X2), X1)
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, X2), app_encode_app(a, b, sk_Xy1, X2)), 
4.73/4.98	           app_encode_app(a, b, sk_Xz, X1))
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), 
4.73/4.98	             sk_Xx01)
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xy1, sk_Xx01)), 
4.73/4.98	           app_encode_app(a, b, sk_Xz, X0))),
4.73/4.98	    inference('sup-', [status(thm)], ['64', '28'])).
4.73/4.98	tff('66', plain,
4.73/4.98	    ![X0 : a]:
4.73/4.98	      (~ $true
4.73/4.98	       | app_encode_app(a, $o, 
4.73/4.98	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), X0)
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy01), X0)),
4.73/4.98	    inference('sup-', [status(thm)], ['41', '15'])).
4.73/4.98	tff('67', plain,
4.73/4.98	    ![X0 : a]:
4.73/4.98	      (~ app_encode_app(a, $o, 
4.73/4.98	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy01), X0)
4.73/4.98	       | app_encode_app(a, $o, 
4.73/4.98	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), X0)),
4.73/4.98	    inference('simplify', [status(thm)], ['66'])).
4.73/4.98	tff('68', plain,
4.73/4.98	    (~ $true
4.73/4.98	     | app_encode_app(a, $o, 
4.73/4.98	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01)),
4.73/4.98	    inference('sup-', [status(thm)], ['47', '67'])).
4.73/4.98	tff('69', plain,
4.73/4.98	    app_encode_app(a, $o, 
4.73/4.98	      app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01),
4.73/4.98	    inference('simplify', [status(thm)], ['68'])).
4.73/4.98	tff('70', plain,
4.73/4.98	    ![X0 : a, X1 : a, X2 : a]:
4.73/4.98	      (~ $true
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), X0)
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X2), X1)
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, X2), app_encode_app(a, b, sk_Xy1, X2)), 
4.73/4.98	           app_encode_app(a, b, sk_Xz, X1))
4.73/4.98	       | ~ $true
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xy1, sk_Xx01)), 
4.73/4.98	           app_encode_app(a, b, sk_Xz, X0))),
4.73/4.98	    inference('demod', [status(thm)], ['65', '69'])).
4.73/4.98	tff('71', plain,
4.73/4.98	    ![X0 : a, X1 : a, X2 : a]:
4.73/4.98	      (app_encode_app(b, $o, 
4.73/4.98	         app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	             sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xy1, sk_Xx01)), 
4.73/4.98	         app_encode_app(a, b, sk_Xz, X0))
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, X2), app_encode_app(a, b, sk_Xy1, X2)), 
4.73/4.98	           app_encode_app(a, b, sk_Xz, X1))
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X2), X1)
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), X0)),
4.73/4.98	    inference('simplify', [status(thm)], ['70'])).
4.73/4.98	tff('72', plain,
4.73/4.98	    ![X0 : a]:
4.73/4.98	      (~ $true
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), X0)
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), X0)
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xy1, sk_Xx01)), 
4.73/4.98	           app_encode_app(a, b, sk_Xz, X0))),
4.73/4.98	    inference('eq_fact', [status(thm)], ['71'])).
4.73/4.98	tff('73', plain,
4.73/4.98	    ![X0 : a]:
4.73/4.98	      (app_encode_app(b, $o, 
4.73/4.98	         app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	             sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xy1, sk_Xx01)), 
4.73/4.98	         app_encode_app(a, b, sk_Xz, X0))
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), X0)),
4.73/4.98	    inference('simplify', [status(thm)], ['72'])).
4.73/4.98	tff('74', plain,
4.73/4.98	    ![X0 : a, X1 : a, X4 : a, X5 : a]:
4.73/4.98	      (~ app_encode_app(a, $o, 
4.73/4.98	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X4), X5)
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, X4), app_encode_app(a, b, sk_Xx, X4)), 
4.73/4.98	           app_encode_app(a, b, sk_Xy, X5))
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, X0), app_encode_app(a, b, sk_Xx1, X0)), 
4.73/4.98	           app_encode_app(a, b, sk_Xy1, X1))
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X0), X1)),
4.73/4.98	    inference('cnf', [status(esa)], [zf_stmt_0])).
4.73/4.98	tff('75', plain,
4.73/4.98	    ![X0 : a, X1 : a, X2 : a]:
4.73/4.98	      (app_encode_app(b, $o, 
4.73/4.98	         app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	             sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.73/4.98	         app_encode_app(a, b, sk_Xy, X0))
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X2), X1)
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, X2), app_encode_app(a, b, sk_Xx1, X2)), 
4.73/4.98	           app_encode_app(a, b, sk_Xy1, X1))
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy0), X0)),
4.73/4.98	    inference('sup+', [status(thm)], ['23', '74'])).
4.73/4.98	tff('76', plain,
4.73/4.98	    ![X0 : a, X1 : a]:
4.73/4.98	      (~ $true
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy0), X1)
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), X0)
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.73/4.98	           app_encode_app(a, b, sk_Xy, X1))
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xy1, X0)), 
4.73/4.98	           app_encode_app(a, b, sk_Xx1, sk_Xx01))),
4.73/4.98	    inference('sup-', [status(thm)], ['75', '55'])).
4.73/4.98	tff('77', plain,
4.73/4.98	    ![X0 : a, X1 : a]:
4.73/4.98	      (app_encode_app(b, $o, 
4.73/4.98	         app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	             sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xy1, X0)), 
4.73/4.98	         app_encode_app(a, b, sk_Xx1, sk_Xx01))
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.73/4.98	           app_encode_app(a, b, sk_Xy, X1))
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), X0)
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy0), X1)),
4.73/4.98	    inference('simplify', [status(thm)], ['76'])).
4.73/4.98	tff('78', plain,
4.73/4.98	    ![X0 : a, X1 : a]:
4.73/4.98	      (~ $true
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy0), X0)
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), X1)
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xy1, X1)), 
4.73/4.98	           app_encode_app(a, b, sk_Xx1, sk_Xx01))
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xx0)
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xy, X0)), 
4.73/4.98	           app_encode_app(a, b, sk_Xx, sk_Xy0))),
4.73/4.98	    inference('sup-', [status(thm)], ['77', '28'])).
4.73/4.98	tff('79', plain,
4.73/4.98	    ![X0 : a, X1 : a]:
4.73/4.98	      (~ $true
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy0), X0)
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), X1)
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xy1, X1)), 
4.73/4.98	           app_encode_app(a, b, sk_Xx1, sk_Xx01))
4.73/4.98	       | ~ $true
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xy, X0)), 
4.73/4.98	           app_encode_app(a, b, sk_Xx, sk_Xy0))),
4.73/4.98	    inference('demod', [status(thm)], ['78', '35'])).
4.73/4.98	tff('80', plain,
4.73/4.98	    ![X0 : a, X1 : a]:
4.73/4.98	      (app_encode_app(b, $o, 
4.73/4.98	         app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	             sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xy, X0)), 
4.73/4.98	         app_encode_app(a, b, sk_Xx, sk_Xy0))
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xy1, X1)), 
4.73/4.98	           app_encode_app(a, b, sk_Xx1, sk_Xx01))
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), X1)
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy0), X0)),
4.73/4.98	    inference('simplify', [status(thm)], ['79'])).
4.73/4.98	tff('81', plain,
4.73/4.98	    ![X0 : a, X1 : a]:
4.73/4.98	      (~ app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xy, sk_Xx0)), 
4.73/4.98	           app_encode_app(a, b, sk_Xx, sk_Xy0))
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, X0), app_encode_app(a, b, sk_Xx1, X0)), 
4.73/4.98	           app_encode_app(a, b, sk_Xy1, X1))
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X0), X1)),
4.73/4.98	    inference('cnf', [status(esa)], [zf_stmt_0])).
4.73/4.98	tff('82', plain,
4.73/4.98	    ![X0 : a, X1 : a, X2 : a]:
4.73/4.98	      (~ $true
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy0), sk_Xx0)
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), X2)
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xy1, X2)), 
4.73/4.98	           app_encode_app(a, b, sk_Xx1, sk_Xx01))
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X1), X0)
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, X1), app_encode_app(a, b, sk_Xx1, X1)), 
4.73/4.98	           app_encode_app(a, b, sk_Xy1, X0))),
4.73/4.98	    inference('sup-', [status(thm)], ['80', '81'])).
4.73/4.98	tff('83', plain,
4.73/4.98	    ![X0 : a, X1 : a, X2 : a]:
4.73/4.98	      (~ $true
4.73/4.98	       | ~ $true
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), X2)
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xy1, X2)), 
4.73/4.98	           app_encode_app(a, b, sk_Xx1, sk_Xx01))
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X1), X0)
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, X1), app_encode_app(a, b, sk_Xx1, X1)), 
4.73/4.98	           app_encode_app(a, b, sk_Xy1, X0))),
4.73/4.98	    inference('demod', [status(thm)], ['82', '31'])).
4.73/4.98	tff('84', plain,
4.73/4.98	    ![X0 : a, X1 : a, X2 : a]:
4.73/4.98	      (app_encode_app(b, $o, 
4.73/4.98	         app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	             sk_Xp2, X1), app_encode_app(a, b, sk_Xx1, X1)), 
4.73/4.98	         app_encode_app(a, b, sk_Xy1, X0))
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X1), X0)
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xy1, X2)), 
4.73/4.98	           app_encode_app(a, b, sk_Xx1, sk_Xx01))
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), X2)),
4.73/4.98	    inference('simplify', [status(thm)], ['83'])).
4.73/4.98	tff('85', plain,
4.73/4.98	    ![X0 : a, X1 : a, X2 : a]:
4.73/4.98	      (~ $true
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), X0)
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X2), X1)
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, X2), app_encode_app(a, b, sk_Xx1, X2)), 
4.73/4.98	           app_encode_app(a, b, sk_Xy1, X1))
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), 
4.73/4.98	             sk_Xx01)
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xx1, sk_Xx01)), 
4.73/4.98	           app_encode_app(a, b, sk_Xy1, X0))),
4.73/4.98	    inference('sup-', [status(thm)], ['84', '28'])).
4.73/4.98	tff('86', plain,
4.73/4.98	    ![X0 : a, X1 : a, X2 : a]:
4.73/4.98	      (~ $true
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), X0)
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X2), X1)
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, X2), app_encode_app(a, b, sk_Xx1, X2)), 
4.73/4.98	           app_encode_app(a, b, sk_Xy1, X1))
4.73/4.98	       | ~ $true
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xx1, sk_Xx01)), 
4.73/4.98	           app_encode_app(a, b, sk_Xy1, X0))),
4.73/4.98	    inference('demod', [status(thm)], ['85', '69'])).
4.73/4.98	tff('87', plain,
4.73/4.98	    ![X0 : a, X1 : a, X2 : a]:
4.73/4.98	      (app_encode_app(b, $o, 
4.73/4.98	         app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	             sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xx1, sk_Xx01)), 
4.73/4.98	         app_encode_app(a, b, sk_Xy1, X0))
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, X2), app_encode_app(a, b, sk_Xx1, X2)), 
4.73/4.98	           app_encode_app(a, b, sk_Xy1, X1))
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X2), X1)
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), X0)),
4.73/4.98	    inference('simplify', [status(thm)], ['86'])).
4.73/4.98	tff('88', plain,
4.73/4.98	    ![X0 : a]:
4.73/4.98	      (~ $true
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), X0)
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), X0)
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xx1, sk_Xx01)), 
4.73/4.98	           app_encode_app(a, b, sk_Xy1, X0))),
4.73/4.98	    inference('eq_fact', [status(thm)], ['87'])).
4.73/4.98	tff('89', plain,
4.73/4.98	    ![X0 : a]:
4.73/4.98	      (app_encode_app(b, $o, 
4.73/4.98	         app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	             sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xx1, sk_Xx01)), 
4.73/4.98	         app_encode_app(a, b, sk_Xy1, X0))
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), X0)),
4.73/4.98	    inference('simplify', [status(thm)], ['88'])).
4.73/4.98	tff('90', plain,
4.73/4.98	    ![X0 : b, X1 : b, X2 : b]:
4.73/4.98	      (~ app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xx01), X1), X0)
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy01), 
4.73/4.98	             sk_Xy01)
4.73/4.98	       | ~ app_encode_app(b, $o, 
4.73/4.98	             app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	               app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	                 sk_Xp2, sk_Xy01), X2), X1)
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xy01), X2), X0)),
4.73/4.98	    inference('sup-', [status(thm)], ['43', '2'])).
4.73/4.98	tff('91', plain,
4.73/4.98	    ![X0 : b, X1 : b, X2 : b]:
4.73/4.98	      (~ app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xx01), X1), X0)
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy01), 
4.73/4.98	             sk_Xy01)
4.73/4.98	       | ~ app_encode_app(b, $o, 
4.73/4.98	             app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	               app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	                 sk_Xp2, sk_Xx01), X2), X1)
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xx01), X2), X0)),
4.73/4.98	    inference('demod', [status(thm)], ['90', '43', '43'])).
4.73/4.98	tff('92', plain,
4.73/4.98	    ![X0 : b, X1 : b, X2 : b]:
4.73/4.98	      (~ app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xx01), X1), X0)
4.73/4.98	       | ~ $true
4.73/4.98	       | ~ app_encode_app(b, $o, 
4.73/4.98	             app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	               app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	                 sk_Xp2, sk_Xx01), X2), X1)
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xx01), X2), X0)),
4.73/4.98	    inference('demod', [status(thm)], ['91', '53'])).
4.73/4.98	tff('93', plain,
4.73/4.98	    ![X0 : b, X1 : b, X2 : b]:
4.73/4.98	      (app_encode_app(b, $o, 
4.73/4.98	         app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	             sk_Xp2, sk_Xx01), X2), X0)
4.73/4.98	       | ~ app_encode_app(b, $o, 
4.73/4.98	             app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	               app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	                 sk_Xp2, sk_Xx01), X2), X1)
4.73/4.98	       | ~ app_encode_app(b, $o, 
4.73/4.98	             app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	               app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	                 sk_Xp2, sk_Xx01), X1), X0)),
4.73/4.98	    inference('simplify', [status(thm)], ['92'])).
4.73/4.98	tff('94', plain,
4.73/4.98	    ![X0 : a, X1 : b]:
4.73/4.98	      (~ $true
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), X0)
4.73/4.98	       | ~ app_encode_app(b, $o, 
4.73/4.98	             app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	               app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	                 sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xy1, X0)), X1)
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xx1, sk_Xx01)), X1)),
4.73/4.98	    inference('sup-', [status(thm)], ['89', '93'])).
4.73/4.98	tff('95', plain,
4.73/4.98	    ![X0 : a, X1 : b]:
4.73/4.98	      (app_encode_app(b, $o, 
4.73/4.98	         app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	             sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xx1, sk_Xx01)), X1)
4.73/4.98	       | ~ app_encode_app(b, $o, 
4.73/4.98	             app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	               app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	                 sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xy1, X0)), X1)
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), X0)),
4.73/4.98	    inference('simplify', [status(thm)], ['94'])).
4.73/4.98	tff('96', plain,
4.73/4.98	    ![X0 : a]:
4.73/4.98	      (~ $true
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), X0)
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), 
4.73/4.98	             sk_Xx01)
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xx1, sk_Xx01)), 
4.73/4.98	           app_encode_app(a, b, sk_Xz, X0))),
4.73/4.98	    inference('sup-', [status(thm)], ['73', '95'])).
4.73/4.98	tff('97', plain,
4.73/4.98	    ![X0 : a]:
4.73/4.98	      (~ $true
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), X0)
4.73/4.98	       | ~ $true
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xx1, sk_Xx01)), 
4.73/4.98	           app_encode_app(a, b, sk_Xz, X0))),
4.73/4.98	    inference('demod', [status(thm)], ['96', '69'])).
4.73/4.98	tff('98', plain,
4.73/4.98	    ![X0 : a]:
4.73/4.98	      (app_encode_app(b, $o, 
4.73/4.98	         app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	             sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xx1, sk_Xx01)), 
4.73/4.98	         app_encode_app(a, b, sk_Xz, X0))
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), X0)),
4.73/4.98	    inference('simplify', [status(thm)], ['97'])).
4.73/4.98	tff('99', plain,
4.73/4.98	    ![X4 : a, X5 : a]:
4.73/4.98	      (~ app_encode_app(a, $o, 
4.73/4.98	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X4), X5)
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, X4), app_encode_app(a, b, sk_Xx, X4)), 
4.73/4.98	           app_encode_app(a, b, sk_Xy, X5))
4.73/4.98	       | ~ app_encode_app(b, $o, 
4.73/4.98	             app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	               app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	                 sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xx1, sk_Xx01)), 
4.73/4.98	             app_encode_app(a, b, sk_Xz, sk_Xy01))),
4.73/4.98	    inference('cnf', [status(esa)], [zf_stmt_0])).
4.73/4.98	tff('100', plain,
4.73/4.98	    ![X0 : a, X1 : a]:
4.73/4.98	      (~ $true
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), 
4.73/4.98	             sk_Xy01)
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, X1), app_encode_app(a, b, sk_Xx, X1)), 
4.73/4.98	           app_encode_app(a, b, sk_Xy, X0))
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X1), X0)),
4.73/4.98	    inference('sup-', [status(thm)], ['98', '99'])).
4.73/4.98	tff('101', plain,
4.73/4.98	    ![X0 : a, X1 : a]:
4.73/4.98	      (~ $true
4.73/4.98	       | ~ $true
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, X1), app_encode_app(a, b, sk_Xx, X1)), 
4.73/4.98	           app_encode_app(a, b, sk_Xy, X0))
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X1), X0)),
4.73/4.98	    inference('demod', [status(thm)], ['100', '41'])).
4.73/4.98	tff('102', plain,
4.73/4.98	    ![X0 : a, X1 : a]:
4.73/4.98	      (~ app_encode_app(a, $o, 
4.73/4.98	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X1), X0)
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, X1), app_encode_app(a, b, sk_Xx, X1)), 
4.73/4.98	           app_encode_app(a, b, sk_Xy, X0))),
4.73/4.98	    inference('simplify', [status(thm)], ['101'])).
4.73/4.98	tff('103', plain,
4.73/4.98	    ![X0 : a]:
4.73/4.98	      (app_encode_app(b, $o, 
4.73/4.98	         app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	             sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.73/4.98	         app_encode_app(a, b, sk_Xy, X0))
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy0), X0)),
4.73/4.98	    inference('sup+', [status(thm)], ['23', '102'])).
4.73/4.98	tff('104', plain,
4.73/4.98	    ![X0 : a]:
4.73/4.98	      (~ $true
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy0), X0)
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xx0)
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xy, X0)), 
4.73/4.98	           app_encode_app(a, b, sk_Xx, sk_Xy0))),
4.73/4.98	    inference('sup-', [status(thm)], ['103', '28'])).
4.73/4.98	tff('105', plain,
4.73/4.98	    ![X0 : a]:
4.73/4.98	      (~ $true
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy0), X0)
4.73/4.98	       | ~ $true
4.73/4.98	       | app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xy, X0)), 
4.73/4.98	           app_encode_app(a, b, sk_Xx, sk_Xy0))),
4.73/4.98	    inference('demod', [status(thm)], ['104', '35'])).
4.73/4.98	tff('106', plain,
4.73/4.98	    ![X0 : a]:
4.73/4.98	      (app_encode_app(b, $o, 
4.73/4.98	         app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	             sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xy, X0)), 
4.73/4.98	         app_encode_app(a, b, sk_Xx, sk_Xy0))
4.73/4.98	       | ~ app_encode_app(a, $o, 
4.73/4.98	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy0), X0)),
4.73/4.98	    inference('simplify', [status(thm)], ['105'])).
4.73/4.98	tff('107', plain,
4.73/4.98	    (~ app_encode_app(b, $o, 
4.73/4.98	         app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	             sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xy, sk_Xx0)), 
4.73/4.98	         app_encode_app(a, b, sk_Xx, sk_Xy0))
4.73/4.98	     | ~ app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xx1, sk_Xx01)), 
4.73/4.98	           app_encode_app(a, b, sk_Xz, sk_Xy01))),
4.73/4.98	    inference('cnf', [status(esa)], [zf_stmt_0])).
4.73/4.98	tff('108', plain,
4.73/4.98	    (~ $true
4.73/4.98	     | ~ app_encode_app(a, $o, 
4.73/4.98	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xy01)
4.73/4.98	     | ~ app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xy, sk_Xx0)), 
4.73/4.98	           app_encode_app(a, b, sk_Xx, sk_Xy0))),
4.73/4.98	    inference('sup-', [status(thm)], ['98', '107'])).
4.73/4.98	tff('109', plain,
4.73/4.98	    (~ $true
4.73/4.98	     | ~ $true
4.73/4.98	     | ~ app_encode_app(b, $o, 
4.73/4.98	           app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	               sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xy, sk_Xx0)), 
4.73/4.98	           app_encode_app(a, b, sk_Xx, sk_Xy0))),
4.73/4.98	    inference('demod', [status(thm)], ['108', '41'])).
4.73/4.98	tff('110', plain,
4.73/4.98	    ~ app_encode_app(b, $o, 
4.73/4.98	        app_encode_app(b, app_encode_fun(b, $o), 
4.73/4.98	          app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.73/4.98	            sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xy, sk_Xx0)), 
4.73/4.98	        app_encode_app(a, b, sk_Xx, sk_Xy0)),
4.73/4.98	    inference('simplify', [status(thm)], ['109'])).
4.73/4.98	tff('111', plain,
4.73/4.98	    (~ $true
4.73/4.98	     | ~ app_encode_app(a, $o, 
4.73/4.98	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy0), sk_Xx0)),
4.73/4.98	    inference('sup-', [status(thm)], ['106', '110'])).
4.73/4.98	tff('112', plain, (~ $true | ~ $true),
4.73/4.98	    inference('demod', [status(thm)], ['111', '31'])).
4.73/4.98	tff('113', plain, $false, inference('simplify', [status(thm)], ['112'])).
4.73/4.98	
4.73/4.98	% SZS output end Refutation
4.73/4.98	EOF
