0.00/0.00	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : app
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : kbo
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.20	% Computer   : n048.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 17:52:38 CST 2018
0.45/0.63	% done 193 iterations in 0.425s
0.45/0.63	% SZS status Theorem for 'stdin'
0.45/0.63	% SZS output start Refutation
0.45/0.63	tff(zf_stmt_3, conjecture,
0.45/0.63	  (![R:app_encode_fun(a,app_encode_fun(a,$o)),
0.45/0.63	     S:app_encode_fun(a,app_encode_fun(a,$o)),Xx:a,Xy:a]:
0.45/0.63	     ((![Xq:app_encode_fun(a,$o)]:
0.45/0.63	         (((![Xw:a]:
0.45/0.63	              ((app_encode_app(a,$o,
0.45/0.63	                               app_encode_app(a,app_encode_fun(a,$o),R,Xx),Xw) | 
0.45/0.63	                app_encode_app(a,$o,
0.45/0.63	                               app_encode_app(a,app_encode_fun(a,$o),S,Xx),Xw)) =>
0.45/0.63	               app_encode_app(a,$o,Xq,Xw))) & 
0.45/0.63	           (![Xu:a,Xv:a]:
0.45/0.63	              ((app_encode_app(a,$o,Xq,Xu) & 
0.45/0.63	                (app_encode_app(a,$o,
0.45/0.63	                                app_encode_app(a,app_encode_fun(a,$o),R,Xu),
0.45/0.63	                                Xv) | 
0.45/0.63	                 app_encode_app(a,$o,
0.45/0.63	                                app_encode_app(a,app_encode_fun(a,$o),S,Xu),
0.45/0.63	                                Xv))) =>
0.45/0.63	               app_encode_app(a,$o,Xq,Xv)))) =>
0.45/0.63	          app_encode_app(a,$o,Xq,Xy))) =>
0.45/0.63	      (![Xq:app_encode_fun(a,$o)]:
0.45/0.63	         (((![Xw:a]:
0.45/0.63	              (((![Xq0:app_encode_fun(a,$o)]:
0.45/0.63	                   (((![Xw0:a]:
0.45/0.63	                        (app_encode_app(a,$o,
0.45/0.63	                                        app_encode_app(a,
0.45/0.63	                                                       app_encode_fun(a,$o),
0.45/0.63	                                                       R,Xx),
0.45/0.63	                                        Xw0) =>
0.45/0.63	                         app_encode_app(a,$o,Xq0,Xw0))) & 
0.45/0.63	                     (![Xu:a,Xv:a]:
0.45/0.63	                        ((app_encode_app(a,$o,Xq0,Xu) & 
0.45/0.63	                          app_encode_app(a,$o,
0.45/0.63	                                         app_encode_app(a,
0.45/0.63	                                                        app_encode_fun(a,$o),
0.45/0.63	                                                        R,Xu),
0.45/0.63	                                         Xv)) =>
0.45/0.63	                         app_encode_app(a,$o,Xq0,Xv)))) =>
0.45/0.63	                    app_encode_app(a,$o,Xq0,Xw))) | 
0.45/0.63	                (![Xq0:app_encode_fun(a,$o)]:
0.45/0.63	                   (((![Xw0:a]:
0.45/0.63	                        (app_encode_app(a,$o,
0.45/0.63	                                        app_encode_app(a,
0.45/0.63	                                                       app_encode_fun(a,$o),
0.45/0.63	                                                       S,Xx),
0.45/0.63	                                        Xw0) =>
0.45/0.63	                         app_encode_app(a,$o,Xq0,Xw0))) & 
0.45/0.63	                     (![Xu:a,Xv:a]:
0.45/0.63	                        ((app_encode_app(a,$o,Xq0,Xu) & 
0.45/0.63	                          app_encode_app(a,$o,
0.45/0.63	                                         app_encode_app(a,
0.45/0.63	                                                        app_encode_fun(a,$o),
0.45/0.63	                                                        S,Xu),
0.45/0.63	                                         Xv)) =>
0.45/0.63	                         app_encode_app(a,$o,Xq0,Xv)))) =>
0.45/0.63	                    app_encode_app(a,$o,Xq0,Xw)))) =>
0.45/0.63	               app_encode_app(a,$o,Xq,Xw))) & 
0.45/0.63	           (![Xu:a,Xv:a]:
0.45/0.63	              ((app_encode_app(a,$o,Xq,Xu) & 
0.45/0.63	                ((![Xq0:app_encode_fun(a,$o)]:
0.45/0.63	                    (((![Xw:a]:
0.45/0.63	                         (app_encode_app(a,$o,
0.45/0.63	                                         app_encode_app(a,
0.45/0.63	                                                        app_encode_fun(a,$o),
0.45/0.63	                                                        R,Xu),
0.45/0.63	                                         Xw) =>
0.45/0.63	                          app_encode_app(a,$o,Xq0,Xw))) & 
0.45/0.63	                      (![Xu0:a,Xv0:a]:
0.45/0.63	                         ((app_encode_app(a,$o,Xq0,Xu0) & 
0.45/0.63	                           app_encode_app(a,$o,
0.45/0.63	                                          app_encode_app(a,
0.45/0.63	                                                         app_encode_fun(a,$o),
0.45/0.63	                                                         R,Xu0),
0.45/0.63	                                          Xv0)) =>
0.45/0.63	                          app_encode_app(a,$o,Xq0,Xv0)))) =>
0.45/0.63	                     app_encode_app(a,$o,Xq0,Xv))) | 
0.45/0.63	                 (![Xq0:app_encode_fun(a,$o)]:
0.45/0.63	                    (((![Xw:a]:
0.45/0.63	                         (app_encode_app(a,$o,
0.45/0.63	                                         app_encode_app(a,
0.45/0.63	                                                        app_encode_fun(a,$o),
0.45/0.63	                                                        S,Xu),
0.45/0.63	                                         Xw) =>
0.45/0.63	                          app_encode_app(a,$o,Xq0,Xw))) & 
0.45/0.63	                      (![Xu0:a,Xv0:a]:
0.45/0.63	                         ((app_encode_app(a,$o,Xq0,Xu0) & 
0.45/0.63	                           app_encode_app(a,$o,
0.45/0.63	                                          app_encode_app(a,
0.45/0.63	                                                         app_encode_fun(a,$o),
0.45/0.63	                                                         S,Xu0),
0.45/0.63	                                          Xv0)) =>
0.45/0.63	                          app_encode_app(a,$o,Xq0,Xv0)))) =>
0.45/0.63	                     app_encode_app(a,$o,Xq0,Xv))))) =>
0.45/0.63	               app_encode_app(a,$o,Xq,Xv)))) =>
0.45/0.63	          app_encode_app(a,$o,Xq,Xy)))))).
0.45/0.63	tff(zf_stmt_0, negated_conjecture,
0.45/0.63	  (~
0.45/0.63	    (![R:app_encode_fun(a,app_encode_fun(a,$o)),
0.45/0.63	       S:app_encode_fun(a,app_encode_fun(a,$o)),Xx:a,Xy:a]:
0.45/0.63	       ((![Xq:app_encode_fun(a,$o)]:
0.45/0.63	           (((![Xw:a]:
0.45/0.63	                ((app_encode_app(a,$o,
0.45/0.63	                                 app_encode_app(a,app_encode_fun(a,$o),R,Xx),
0.45/0.63	                                 Xw) | 
0.45/0.63	                  app_encode_app(a,$o,
0.45/0.63	                                 app_encode_app(a,app_encode_fun(a,$o),S,Xx),
0.45/0.63	                                 Xw)) =>
0.45/0.63	                 app_encode_app(a,$o,Xq,Xw))) & 
0.45/0.63	             (![Xu:a,Xv:a]:
0.45/0.63	                ((app_encode_app(a,$o,Xq,Xu) & 
0.45/0.63	                  (app_encode_app(a,$o,
0.45/0.63	                                  app_encode_app(a,app_encode_fun(a,$o),R,Xu),
0.45/0.63	                                  Xv) | 
0.45/0.63	                   app_encode_app(a,$o,
0.45/0.63	                                  app_encode_app(a,app_encode_fun(a,$o),S,Xu),
0.45/0.63	                                  Xv))) =>
0.45/0.63	                 app_encode_app(a,$o,Xq,Xv)))) =>
0.45/0.63	            app_encode_app(a,$o,Xq,Xy))) =>
0.45/0.63	        (![Xq:app_encode_fun(a,$o)]:
0.45/0.63	           (((![Xw:a]:
0.45/0.63	                (((![Xq0:app_encode_fun(a,$o)]:
0.45/0.63	                     (((![Xw0:a]:
0.45/0.63	                          (app_encode_app(a,$o,
0.45/0.63	                                          app_encode_app(a,
0.45/0.63	                                                         app_encode_fun(a,$o),
0.45/0.63	                                                         R,Xx),
0.45/0.63	                                          Xw0) =>
0.45/0.63	                           app_encode_app(a,$o,Xq0,Xw0))) & 
0.45/0.63	                       (![Xu:a,Xv:a]:
0.45/0.63	                          ((app_encode_app(a,$o,Xq0,Xu) & 
0.45/0.63	                            app_encode_app(a,$o,
0.45/0.63	                                           app_encode_app(a,
0.45/0.63	                                                          app_encode_fun(
0.45/0.63	                                                          a,$o),R,Xu),
0.45/0.63	                                           Xv)) =>
0.45/0.63	                           app_encode_app(a,$o,Xq0,Xv)))) =>
0.45/0.63	                      app_encode_app(a,$o,Xq0,Xw))) | 
0.45/0.63	                  (![Xq0:app_encode_fun(a,$o)]:
0.45/0.63	                     (((![Xw0:a]:
0.45/0.63	                          (app_encode_app(a,$o,
0.45/0.63	                                          app_encode_app(a,
0.45/0.63	                                                         app_encode_fun(a,$o),
0.45/0.63	                                                         S,Xx),
0.45/0.63	                                          Xw0) =>
0.45/0.63	                           app_encode_app(a,$o,Xq0,Xw0))) & 
0.45/0.63	                       (![Xu:a,Xv:a]:
0.45/0.63	                          ((app_encode_app(a,$o,Xq0,Xu) & 
0.45/0.63	                            app_encode_app(a,$o,
0.45/0.63	                                           app_encode_app(a,
0.45/0.63	                                                          app_encode_fun(
0.45/0.63	                                                          a,$o),S,Xu),
0.45/0.63	                                           Xv)) =>
0.45/0.63	                           app_encode_app(a,$o,Xq0,Xv)))) =>
0.45/0.63	                      app_encode_app(a,$o,Xq0,Xw)))) =>
0.45/0.63	                 app_encode_app(a,$o,Xq,Xw))) & 
0.45/0.63	             (![Xu:a,Xv:a]:
0.45/0.63	                ((app_encode_app(a,$o,Xq,Xu) & 
0.45/0.63	                  ((![Xq0:app_encode_fun(a,$o)]:
0.45/0.63	                      (((![Xw:a]:
0.45/0.63	                           (app_encode_app(a,$o,
0.45/0.63	                                           app_encode_app(a,
0.45/0.63	                                                          app_encode_fun(
0.45/0.63	                                                          a,$o),R,Xu),
0.45/0.63	                                           Xw) =>
0.45/0.63	                            app_encode_app(a,$o,Xq0,Xw))) & 
0.45/0.63	                        (![Xu0:a,Xv0:a]:
0.45/0.63	                           ((app_encode_app(a,$o,Xq0,Xu0) & 
0.45/0.63	                             app_encode_app(a,$o,
0.45/0.63	                                            app_encode_app(a,
0.45/0.63	                                                           app_encode_fun(
0.45/0.63	                                                           a,$o),R,Xu0),
0.45/0.63	                                            Xv0)) =>
0.45/0.63	                            app_encode_app(a,$o,Xq0,Xv0)))) =>
0.45/0.63	                       app_encode_app(a,$o,Xq0,Xv))) | 
0.45/0.63	                   (![Xq0:app_encode_fun(a,$o)]:
0.45/0.63	                      (((![Xw:a]:
0.45/0.63	                           (app_encode_app(a,$o,
0.45/0.63	                                           app_encode_app(a,
0.45/0.63	                                                          app_encode_fun(
0.45/0.63	                                                          a,$o),S,Xu),
0.45/0.63	                                           Xw) =>
0.45/0.63	                            app_encode_app(a,$o,Xq0,Xw))) & 
0.45/0.63	                        (![Xu0:a,Xv0:a]:
0.45/0.63	                           ((app_encode_app(a,$o,Xq0,Xu0) & 
0.45/0.63	                             app_encode_app(a,$o,
0.45/0.63	                                            app_encode_app(a,
0.45/0.63	                                                           app_encode_fun(
0.45/0.63	                                                           a,$o),S,Xu0),
0.45/0.63	                                            Xv0)) =>
0.45/0.63	                            app_encode_app(a,$o,Xq0,Xv0)))) =>
0.45/0.63	                       app_encode_app(a,$o,Xq0,Xv))))) =>
0.45/0.63	                 app_encode_app(a,$o,Xq,Xv)))) =>
0.45/0.63	            app_encode_app(a,$o,Xq,Xy))))))).
0.45/0.63	tff('0', plain,
0.45/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.45/0.63	      (app_encode_app(a, $o, X0, sk_Xy)
0.45/0.63	       | app_encode_app(a, $o, X0, sk_Xu(X0))
0.45/0.63	       | ~ app_encode_app(a, $o, X0, sk_Xw(X0))),
0.45/0.63	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.45/0.63	tff('1', plain,
0.45/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.45/0.63	      (app_encode_app(a, $o, X0, sk_Xy)
0.45/0.63	       | app_encode_app(a, $o, 
0.45/0.63	           app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xu(X0)), 
0.45/0.63	           sk_Xv(X0))
0.45/0.63	       | app_encode_app(a, $o, 
0.45/0.63	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xu(X0)), 
0.45/0.63	           sk_Xv(X0))
0.45/0.63	       | app_encode_app(a, $o, 
0.45/0.63	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xx), sk_Xw(X0))
0.45/0.63	       | app_encode_app(a, $o, 
0.45/0.63	           app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xx), sk_Xw(X0))),
0.45/0.63	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.45/0.63	tff('2', plain,
0.45/0.63	    ![X1 : a, X2 : a, X5 : a]:
0.45/0.63	      (~ app_encode_app(a, $o, sk_Xq, X1)
0.45/0.63	       | ~ app_encode_app(a, $o, 
0.45/0.63	             app_encode_app(a, app_encode_fun(a, $o), sk_S, X1), X5)
0.45/0.63	       | app_encode_app(a, $o, sk_Xq01(X2, X1), X5)
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, X2)),
0.45/0.63	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.45/0.63	tff('3', plain,
0.45/0.63	    ![X0 : app_encode_fun(a, $o), X1 : a]:
0.45/0.63	      (~ $true
0.45/0.63	       | app_encode_app(a, $o, 
0.45/0.63	           app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xx), sk_Xw(X0))
0.45/0.63	       | app_encode_app(a, $o, 
0.45/0.63	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xx), sk_Xw(X0))
0.45/0.63	       | app_encode_app(a, $o, 
0.45/0.63	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xu(X0)), 
0.45/0.63	           sk_Xv(X0))
0.45/0.63	       | app_encode_app(a, $o, X0, sk_Xy)
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, X1)
0.45/0.63	       | app_encode_app(a, $o, sk_Xq01(X1, sk_Xu(X0)), sk_Xv(X0))
0.45/0.63	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xu(X0))),
0.45/0.63	    inference('sup-', [status(thm)], ['1', '2'])).
0.45/0.63	tff('4', plain,
0.45/0.63	    ![X0 : app_encode_fun(a, $o), X1 : a]:
0.45/0.63	      (~ app_encode_app(a, $o, sk_Xq, sk_Xu(X0))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq01(X1, sk_Xu(X0)), sk_Xv(X0))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, X1)
0.45/0.63	       | app_encode_app(a, $o, X0, sk_Xy)
0.45/0.63	       | app_encode_app(a, $o, 
0.45/0.63	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xu(X0)), 
0.45/0.63	           sk_Xv(X0))
0.45/0.63	       | app_encode_app(a, $o, 
0.45/0.63	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xx), sk_Xw(X0))
0.45/0.63	       | app_encode_app(a, $o, 
0.45/0.63	           app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xx), sk_Xw(X0))),
0.45/0.63	    inference('simplify', [status(thm)], ['3'])).
0.45/0.63	tff('5', plain,
0.45/0.63	    ![X1 : a, X2 : a]:
0.45/0.63	      (~ app_encode_app(a, $o, sk_Xq, X1)
0.45/0.63	       | ~ app_encode_app(a, $o, sk_Xq01(X2, X1), X2)
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, X2)),
0.45/0.63	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.45/0.63	tff('6', plain,
0.45/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.45/0.63	      (~ $true
0.45/0.63	       | app_encode_app(a, $o, 
0.45/0.63	           app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xx), sk_Xw(X0))
0.45/0.63	       | app_encode_app(a, $o, 
0.45/0.63	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xx), sk_Xw(X0))
0.45/0.63	       | app_encode_app(a, $o, 
0.45/0.63	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xu(X0)), 
0.45/0.63	           sk_Xv(X0))
0.45/0.63	       | app_encode_app(a, $o, X0, sk_Xy)
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, sk_Xv(X0))
0.45/0.63	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xu(X0))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, sk_Xv(X0))
0.45/0.63	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xu(X0))),
0.45/0.63	    inference('sup-', [status(thm)], ['4', '5'])).
0.45/0.63	tff('7', plain,
0.45/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.45/0.63	      (~ app_encode_app(a, $o, sk_Xq, sk_Xu(X0))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, sk_Xv(X0))
0.45/0.63	       | app_encode_app(a, $o, X0, sk_Xy)
0.45/0.63	       | app_encode_app(a, $o, 
0.45/0.63	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xu(X0)), 
0.45/0.63	           sk_Xv(X0))
0.45/0.63	       | app_encode_app(a, $o, 
0.45/0.63	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xx), sk_Xw(X0))
0.45/0.63	       | app_encode_app(a, $o, 
0.45/0.63	           app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xx), sk_Xw(X0))),
0.45/0.63	    inference('simplify', [status(thm)], ['6'])).
0.45/0.63	tff('8', plain,
0.45/0.63	    ![X1 : a, X2 : a, X8 : a]:
0.45/0.63	      (~ app_encode_app(a, $o, sk_Xq, X1)
0.45/0.63	       | ~ app_encode_app(a, $o, 
0.45/0.63	             app_encode_app(a, app_encode_fun(a, $o), sk_R, X1), X8)
0.45/0.63	       | app_encode_app(a, $o, sk_Xq0(X2, X1), X8)
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, X2)),
0.45/0.63	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.45/0.63	tff('9', plain,
0.45/0.63	    ![X0 : app_encode_fun(a, $o), X1 : a]:
0.45/0.63	      (~ $true
0.45/0.63	       | app_encode_app(a, $o, 
0.45/0.63	           app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xx), sk_Xw(X0))
0.45/0.63	       | app_encode_app(a, $o, 
0.45/0.63	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xx), sk_Xw(X0))
0.45/0.63	       | app_encode_app(a, $o, X0, sk_Xy)
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, sk_Xv(X0))
0.45/0.63	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xu(X0))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, X1)
0.45/0.63	       | app_encode_app(a, $o, sk_Xq0(X1, sk_Xu(X0)), sk_Xv(X0))
0.45/0.63	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xu(X0))),
0.45/0.63	    inference('sup-', [status(thm)], ['7', '8'])).
0.45/0.63	tff('10', plain,
0.45/0.63	    ![X0 : app_encode_fun(a, $o), X1 : a]:
0.45/0.63	      (app_encode_app(a, $o, sk_Xq0(X1, sk_Xu(X0)), sk_Xv(X0))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, X1)
0.45/0.63	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xu(X0))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, sk_Xv(X0))
0.45/0.63	       | app_encode_app(a, $o, X0, sk_Xy)
0.45/0.63	       | app_encode_app(a, $o, 
0.45/0.63	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xx), sk_Xw(X0))
0.45/0.63	       | app_encode_app(a, $o, 
0.45/0.63	           app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xx), sk_Xw(X0))),
0.45/0.63	    inference('simplify', [status(thm)], ['9'])).
0.45/0.63	tff('11', plain,
0.45/0.63	    ![X1 : a, X2 : a]:
0.45/0.63	      (~ app_encode_app(a, $o, sk_Xq, X1)
0.45/0.63	       | ~ app_encode_app(a, $o, sk_Xq0(X2, X1), X2)
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, X2)),
0.45/0.63	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.45/0.63	tff('12', plain,
0.45/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.45/0.63	      (~ $true
0.45/0.63	       | app_encode_app(a, $o, 
0.45/0.63	           app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xx), sk_Xw(X0))
0.45/0.63	       | app_encode_app(a, $o, 
0.45/0.63	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xx), sk_Xw(X0))
0.45/0.63	       | app_encode_app(a, $o, X0, sk_Xy)
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, sk_Xv(X0))
0.45/0.63	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xu(X0))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, sk_Xv(X0))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, sk_Xv(X0))
0.45/0.63	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xu(X0))),
0.45/0.63	    inference('sup-', [status(thm)], ['10', '11'])).
0.45/0.63	tff('13', plain,
0.45/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.45/0.63	      (~ app_encode_app(a, $o, sk_Xq, sk_Xu(X0))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, sk_Xv(X0))
0.45/0.63	       | app_encode_app(a, $o, X0, sk_Xy)
0.45/0.63	       | app_encode_app(a, $o, 
0.45/0.63	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xx), sk_Xw(X0))
0.45/0.63	       | app_encode_app(a, $o, 
0.45/0.63	           app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xx), sk_Xw(X0))),
0.45/0.63	    inference('simplify', [status(thm)], ['12'])).
0.45/0.63	tff('14', plain,
0.45/0.63	    ![X9 : a, X13 : a]:
0.45/0.63	      (app_encode_app(a, $o, sk_Xq, X9)
0.45/0.63	       | app_encode_app(a, $o, sk_Xq03(X9), X13)
0.45/0.63	       | ~ app_encode_app(a, $o, 
0.45/0.63	             app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xx), X13)),
0.45/0.63	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.45/0.63	tff('15', plain,
0.45/0.63	    ![X0 : app_encode_fun(a, $o), X1 : a]:
0.45/0.63	      (~ $true
0.45/0.63	       | app_encode_app(a, $o, 
0.45/0.63	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xx), sk_Xw(X0))
0.45/0.63	       | app_encode_app(a, $o, X0, sk_Xy)
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, sk_Xv(X0))
0.45/0.63	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xu(X0))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq03(X1), sk_Xw(X0))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, X1)),
0.45/0.63	    inference('sup-', [status(thm)], ['13', '14'])).
0.45/0.63	tff('16', plain,
0.45/0.63	    ![X0 : app_encode_fun(a, $o), X1 : a]:
0.45/0.63	      (app_encode_app(a, $o, sk_Xq, X1)
0.45/0.63	       | app_encode_app(a, $o, sk_Xq03(X1), sk_Xw(X0))
0.45/0.63	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xu(X0))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, sk_Xv(X0))
0.45/0.63	       | app_encode_app(a, $o, X0, sk_Xy)
0.45/0.63	       | app_encode_app(a, $o, 
0.45/0.63	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xx), sk_Xw(X0))),
0.45/0.63	    inference('simplify', [status(thm)], ['15'])).
0.45/0.63	tff('17', plain,
0.45/0.63	    ![X9 : a]:
0.45/0.63	      (app_encode_app(a, $o, sk_Xq, X9)
0.45/0.63	       | ~ app_encode_app(a, $o, sk_Xq03(X9), X9)),
0.45/0.63	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.45/0.63	tff('18', plain,
0.45/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.45/0.63	      (~ $true
0.45/0.63	       | app_encode_app(a, $o, 
0.45/0.63	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xx), sk_Xw(X0))
0.45/0.63	       | app_encode_app(a, $o, X0, sk_Xy)
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, sk_Xv(X0))
0.45/0.63	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xu(X0))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, sk_Xw(X0))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, sk_Xw(X0))),
0.45/0.63	    inference('sup-', [status(thm)], ['16', '17'])).
0.45/0.63	tff('19', plain,
0.45/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.45/0.63	      (app_encode_app(a, $o, sk_Xq, sk_Xw(X0))
0.45/0.63	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xu(X0))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, sk_Xv(X0))
0.45/0.63	       | app_encode_app(a, $o, X0, sk_Xy)
0.45/0.63	       | app_encode_app(a, $o, 
0.45/0.63	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xx), sk_Xw(X0))),
0.45/0.63	    inference('simplify', [status(thm)], ['18'])).
0.45/0.63	tff('20', plain,
0.45/0.63	    ![X9 : a, X10 : a]:
0.45/0.63	      (app_encode_app(a, $o, sk_Xq, X9)
0.45/0.63	       | app_encode_app(a, $o, sk_Xq02(X9), X10)
0.45/0.63	       | ~ app_encode_app(a, $o, 
0.45/0.63	             app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xx), X10)),
0.45/0.63	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.45/0.63	tff('21', plain,
0.45/0.63	    ![X0 : app_encode_fun(a, $o), X1 : a]:
0.45/0.63	      (~ $true
0.45/0.63	       | app_encode_app(a, $o, X0, sk_Xy)
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, sk_Xv(X0))
0.45/0.63	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xu(X0))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, sk_Xw(X0))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq02(X1), sk_Xw(X0))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, X1)),
0.45/0.63	    inference('sup-', [status(thm)], ['19', '20'])).
0.45/0.63	tff('22', plain,
0.45/0.63	    ![X0 : app_encode_fun(a, $o), X1 : a]:
0.45/0.63	      (app_encode_app(a, $o, sk_Xq, X1)
0.45/0.63	       | app_encode_app(a, $o, sk_Xq02(X1), sk_Xw(X0))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, sk_Xw(X0))
0.45/0.63	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xu(X0))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, sk_Xv(X0))
0.45/0.63	       | app_encode_app(a, $o, X0, sk_Xy)),
0.45/0.63	    inference('simplify', [status(thm)], ['21'])).
0.45/0.63	tff('23', plain,
0.45/0.63	    ![X9 : a]:
0.45/0.63	      (app_encode_app(a, $o, sk_Xq, X9)
0.45/0.63	       | ~ app_encode_app(a, $o, sk_Xq02(X9), X9)),
0.45/0.63	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.45/0.63	tff('24', plain,
0.45/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.45/0.63	      (~ $true
0.45/0.63	       | app_encode_app(a, $o, X0, sk_Xy)
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, sk_Xv(X0))
0.45/0.63	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xu(X0))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, sk_Xw(X0))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, sk_Xw(X0))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, sk_Xw(X0))),
0.45/0.63	    inference('sup-', [status(thm)], ['22', '23'])).
0.45/0.63	tff('25', plain,
0.45/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.45/0.63	      (app_encode_app(a, $o, sk_Xq, sk_Xw(X0))
0.45/0.63	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xu(X0))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, sk_Xv(X0))
0.45/0.63	       | app_encode_app(a, $o, X0, sk_Xy)),
0.45/0.63	    inference('simplify', [status(thm)], ['24'])).
0.45/0.63	tff('26', plain,
0.45/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.45/0.63	      (app_encode_app(a, $o, X0, sk_Xy)
0.45/0.63	       | ~ app_encode_app(a, $o, X0, sk_Xv(X0))
0.45/0.63	       | app_encode_app(a, $o, 
0.45/0.63	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xx), sk_Xw(X0))
0.45/0.63	       | app_encode_app(a, $o, 
0.45/0.63	           app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xx), sk_Xw(X0))),
0.45/0.63	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.45/0.63	tff('27', plain,
0.45/0.63	    (~ $true
0.45/0.63	     | app_encode_app(a, $o, sk_Xq, sk_Xy)
0.45/0.63	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xu(sk_Xq))
0.45/0.63	     | app_encode_app(a, $o, sk_Xq, sk_Xw(sk_Xq))
0.45/0.63	     | app_encode_app(a, $o, 
0.45/0.63	         app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xx), sk_Xw(sk_Xq))
0.45/0.63	     | app_encode_app(a, $o, 
0.45/0.63	         app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xx), sk_Xw(sk_Xq))
0.45/0.63	     | app_encode_app(a, $o, sk_Xq, sk_Xy)),
0.45/0.63	    inference('sup-', [status(thm)], ['25', '26'])).
0.45/0.63	tff('28', plain,
0.45/0.63	    (app_encode_app(a, $o, 
0.45/0.63	       app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xx), sk_Xw(sk_Xq))
0.45/0.63	     | app_encode_app(a, $o, 
0.45/0.63	         app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xx), sk_Xw(sk_Xq))
0.45/0.63	     | app_encode_app(a, $o, sk_Xq, sk_Xw(sk_Xq))
0.45/0.63	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xu(sk_Xq))
0.45/0.63	     | app_encode_app(a, $o, sk_Xq, sk_Xy)),
0.45/0.63	    inference('simplify', [status(thm)], ['27'])).
0.45/0.63	tff('29', plain,
0.45/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.45/0.63	      (app_encode_app(a, $o, X0, sk_Xy)
0.45/0.63	       | app_encode_app(a, $o, X0, sk_Xu(X0))
0.45/0.63	       | app_encode_app(a, $o, 
0.45/0.63	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xx), sk_Xw(X0))
0.45/0.63	       | app_encode_app(a, $o, 
0.45/0.63	           app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xx), sk_Xw(X0))),
0.45/0.63	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.45/0.63	tff('30', plain,
0.45/0.63	    ![X0 : app_encode_fun(a, $o), X1 : a]:
0.45/0.63	      (~ $true
0.45/0.63	       | app_encode_app(a, $o, 
0.45/0.63	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xx), sk_Xw(X0))
0.45/0.63	       | app_encode_app(a, $o, X0, sk_Xu(X0))
0.45/0.63	       | app_encode_app(a, $o, X0, sk_Xy)
0.45/0.63	       | app_encode_app(a, $o, sk_Xq03(X1), sk_Xw(X0))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, X1)),
0.45/0.63	    inference('sup-', [status(thm)], ['29', '14'])).
0.45/0.63	tff('31', plain,
0.45/0.63	    ![X0 : app_encode_fun(a, $o), X1 : a]:
0.45/0.63	      (app_encode_app(a, $o, sk_Xq, X1)
0.45/0.63	       | app_encode_app(a, $o, sk_Xq03(X1), sk_Xw(X0))
0.45/0.63	       | app_encode_app(a, $o, X0, sk_Xy)
0.45/0.63	       | app_encode_app(a, $o, X0, sk_Xu(X0))
0.45/0.63	       | app_encode_app(a, $o, 
0.45/0.63	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xx), sk_Xw(X0))),
0.45/0.63	    inference('simplify', [status(thm)], ['30'])).
0.45/0.63	tff('32', plain,
0.45/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.45/0.63	      (~ $true
0.45/0.63	       | app_encode_app(a, $o, 
0.45/0.63	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xx), sk_Xw(X0))
0.45/0.63	       | app_encode_app(a, $o, X0, sk_Xu(X0))
0.45/0.63	       | app_encode_app(a, $o, X0, sk_Xy)
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, sk_Xw(X0))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, sk_Xw(X0))),
0.45/0.63	    inference('sup-', [status(thm)], ['31', '17'])).
0.45/0.63	tff('33', plain,
0.45/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.45/0.63	      (app_encode_app(a, $o, sk_Xq, sk_Xw(X0))
0.45/0.63	       | app_encode_app(a, $o, X0, sk_Xy)
0.45/0.63	       | app_encode_app(a, $o, X0, sk_Xu(X0))
0.45/0.63	       | app_encode_app(a, $o, 
0.45/0.63	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xx), sk_Xw(X0))),
0.45/0.63	    inference('simplify', [status(thm)], ['32'])).
0.45/0.63	tff('34', plain,
0.45/0.63	    ![X0 : app_encode_fun(a, $o), X1 : a]:
0.45/0.63	      (~ $true
0.45/0.63	       | app_encode_app(a, $o, X0, sk_Xu(X0))
0.45/0.63	       | app_encode_app(a, $o, X0, sk_Xy)
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, sk_Xw(X0))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq02(X1), sk_Xw(X0))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, X1)),
0.45/0.63	    inference('sup-', [status(thm)], ['33', '20'])).
0.45/0.63	tff('35', plain,
0.45/0.63	    ![X0 : app_encode_fun(a, $o), X1 : a]:
0.45/0.63	      (app_encode_app(a, $o, sk_Xq, X1)
0.45/0.63	       | app_encode_app(a, $o, sk_Xq02(X1), sk_Xw(X0))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, sk_Xw(X0))
0.45/0.63	       | app_encode_app(a, $o, X0, sk_Xy)
0.45/0.63	       | app_encode_app(a, $o, X0, sk_Xu(X0))),
0.45/0.63	    inference('simplify', [status(thm)], ['34'])).
0.45/0.63	tff('36', plain,
0.45/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.45/0.63	      (~ $true
0.45/0.63	       | app_encode_app(a, $o, X0, sk_Xu(X0))
0.45/0.63	       | app_encode_app(a, $o, X0, sk_Xy)
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, sk_Xw(X0))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, sk_Xw(X0))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, sk_Xw(X0))),
0.45/0.63	    inference('sup-', [status(thm)], ['35', '23'])).
0.45/0.63	tff('37', plain,
0.45/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.45/0.63	      (app_encode_app(a, $o, sk_Xq, sk_Xw(X0))
0.45/0.63	       | app_encode_app(a, $o, X0, sk_Xy)
0.45/0.63	       | app_encode_app(a, $o, X0, sk_Xu(X0))),
0.45/0.63	    inference('simplify', [status(thm)], ['36'])).
0.45/0.63	tff('38', plain,
0.45/0.63	    (app_encode_app(a, $o, sk_Xq, sk_Xy)
0.45/0.63	     | app_encode_app(a, $o, sk_Xq, sk_Xw(sk_Xq))
0.45/0.63	     | app_encode_app(a, $o, 
0.45/0.63	         app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xx), sk_Xw(sk_Xq))
0.45/0.63	     | app_encode_app(a, $o, 
0.45/0.63	         app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xx), sk_Xw(sk_Xq))),
0.45/0.63	    inference('clc', [status(thm)], ['28', '37'])).
0.45/0.63	tff('39', plain, ~ app_encode_app(a, $o, sk_Xq, sk_Xy),
0.45/0.63	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.45/0.63	tff('40', plain,
0.45/0.63	    (app_encode_app(a, $o, 
0.45/0.63	       app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xx), sk_Xw(sk_Xq))
0.45/0.63	     | app_encode_app(a, $o, 
0.45/0.63	         app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xx), sk_Xw(sk_Xq))
0.45/0.63	     | app_encode_app(a, $o, sk_Xq, sk_Xw(sk_Xq))),
0.45/0.63	    inference('clc', [status(thm)], ['38', '39'])).
0.45/0.63	tff('41', plain,
0.45/0.63	    ![X0 : a]:
0.45/0.63	      (~ $true
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, sk_Xw(sk_Xq))
0.45/0.63	       | app_encode_app(a, $o, 
0.45/0.63	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xx), 
0.45/0.63	           sk_Xw(sk_Xq))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq03(X0), sk_Xw(sk_Xq))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, X0)),
0.45/0.63	    inference('sup-', [status(thm)], ['40', '14'])).
0.45/0.63	tff('42', plain,
0.45/0.63	    ![X0 : a]:
0.45/0.63	      (app_encode_app(a, $o, sk_Xq, X0)
0.45/0.63	       | app_encode_app(a, $o, sk_Xq03(X0), sk_Xw(sk_Xq))
0.45/0.63	       | app_encode_app(a, $o, 
0.45/0.63	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xx), 
0.45/0.63	           sk_Xw(sk_Xq))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, sk_Xw(sk_Xq))),
0.45/0.63	    inference('simplify', [status(thm)], ['41'])).
0.45/0.63	tff('43', plain,
0.45/0.63	    ![X0 : a, X1 : a]:
0.45/0.63	      (~ $true
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, sk_Xw(sk_Xq))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq03(X1), sk_Xw(sk_Xq))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, X1)
0.45/0.63	       | app_encode_app(a, $o, sk_Xq02(X0), sk_Xw(sk_Xq))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, X0)),
0.45/0.63	    inference('sup-', [status(thm)], ['42', '20'])).
0.45/0.63	tff('44', plain,
0.45/0.63	    ![X0 : a, X1 : a]:
0.45/0.63	      (app_encode_app(a, $o, sk_Xq, X0)
0.45/0.63	       | app_encode_app(a, $o, sk_Xq02(X0), sk_Xw(sk_Xq))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, X1)
0.45/0.63	       | app_encode_app(a, $o, sk_Xq03(X1), sk_Xw(sk_Xq))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, sk_Xw(sk_Xq))),
0.45/0.63	    inference('simplify', [status(thm)], ['43'])).
0.45/0.63	tff('45', plain,
0.45/0.63	    ![X0 : a]:
0.45/0.63	      (~ $true
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, sk_Xw(sk_Xq))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq03(X0), sk_Xw(sk_Xq))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, X0)
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, sk_Xw(sk_Xq))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, sk_Xw(sk_Xq))),
0.45/0.63	    inference('sup-', [status(thm)], ['44', '23'])).
0.45/0.63	tff('46', plain,
0.45/0.63	    ![X0 : a]:
0.45/0.63	      (app_encode_app(a, $o, sk_Xq, X0)
0.45/0.63	       | app_encode_app(a, $o, sk_Xq03(X0), sk_Xw(sk_Xq))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, sk_Xw(sk_Xq))),
0.45/0.63	    inference('simplify', [status(thm)], ['45'])).
0.45/0.63	tff('47', plain,
0.45/0.63	    (~ $true
0.45/0.63	     | app_encode_app(a, $o, sk_Xq, sk_Xw(sk_Xq))
0.45/0.63	     | app_encode_app(a, $o, sk_Xq, sk_Xw(sk_Xq))
0.45/0.63	     | app_encode_app(a, $o, sk_Xq, sk_Xw(sk_Xq))),
0.45/0.63	    inference('sup-', [status(thm)], ['46', '17'])).
0.45/0.63	tff('48', plain, app_encode_app(a, $o, sk_Xq, sk_Xw(sk_Xq)),
0.45/0.63	    inference('simplify', [status(thm)], ['47'])).
0.45/0.63	tff('49', plain,
0.45/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.45/0.63	      (app_encode_app(a, $o, X0, sk_Xy)
0.45/0.63	       | app_encode_app(a, $o, 
0.45/0.63	           app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xu(X0)), 
0.45/0.63	           sk_Xv(X0))
0.45/0.63	       | app_encode_app(a, $o, 
0.45/0.63	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xu(X0)), 
0.45/0.63	           sk_Xv(X0))
0.45/0.63	       | ~ app_encode_app(a, $o, X0, sk_Xw(X0))),
0.45/0.63	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.45/0.63	tff('50', plain,
0.45/0.63	    ![X0 : app_encode_fun(a, $o), X1 : a]:
0.45/0.63	      (~ $true
0.45/0.63	       | ~ app_encode_app(a, $o, X0, sk_Xw(X0))
0.45/0.63	       | app_encode_app(a, $o, 
0.45/0.63	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xu(X0)), 
0.45/0.63	           sk_Xv(X0))
0.45/0.63	       | app_encode_app(a, $o, X0, sk_Xy)
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, X1)
0.45/0.63	       | app_encode_app(a, $o, sk_Xq01(X1, sk_Xu(X0)), sk_Xv(X0))
0.45/0.63	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xu(X0))),
0.45/0.63	    inference('sup-', [status(thm)], ['49', '2'])).
0.45/0.63	tff('51', plain,
0.45/0.63	    ![X0 : app_encode_fun(a, $o), X1 : a]:
0.45/0.63	      (~ app_encode_app(a, $o, sk_Xq, sk_Xu(X0))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq01(X1, sk_Xu(X0)), sk_Xv(X0))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, X1)
0.45/0.63	       | app_encode_app(a, $o, X0, sk_Xy)
0.45/0.63	       | app_encode_app(a, $o, 
0.45/0.63	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xu(X0)), 
0.45/0.63	           sk_Xv(X0))
0.45/0.63	       | ~ app_encode_app(a, $o, X0, sk_Xw(X0))),
0.45/0.63	    inference('simplify', [status(thm)], ['50'])).
0.45/0.63	tff('52', plain,
0.45/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.45/0.63	      (~ $true
0.45/0.63	       | ~ app_encode_app(a, $o, X0, sk_Xw(X0))
0.45/0.63	       | app_encode_app(a, $o, 
0.45/0.63	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xu(X0)), 
0.45/0.63	           sk_Xv(X0))
0.45/0.63	       | app_encode_app(a, $o, X0, sk_Xy)
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, sk_Xv(X0))
0.45/0.63	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xu(X0))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, sk_Xv(X0))
0.45/0.63	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xu(X0))),
0.45/0.63	    inference('sup-', [status(thm)], ['51', '5'])).
0.45/0.63	tff('53', plain,
0.45/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.45/0.63	      (~ app_encode_app(a, $o, sk_Xq, sk_Xu(X0))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, sk_Xv(X0))
0.45/0.63	       | app_encode_app(a, $o, X0, sk_Xy)
0.45/0.63	       | app_encode_app(a, $o, 
0.45/0.63	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xu(X0)), 
0.45/0.63	           sk_Xv(X0))
0.45/0.63	       | ~ app_encode_app(a, $o, X0, sk_Xw(X0))),
0.45/0.63	    inference('simplify', [status(thm)], ['52'])).
0.45/0.63	tff('54', plain,
0.45/0.63	    ![X0 : app_encode_fun(a, $o), X1 : a]:
0.45/0.63	      (~ $true
0.45/0.63	       | ~ app_encode_app(a, $o, X0, sk_Xw(X0))
0.45/0.63	       | app_encode_app(a, $o, X0, sk_Xy)
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, sk_Xv(X0))
0.45/0.63	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xu(X0))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, X1)
0.45/0.63	       | app_encode_app(a, $o, sk_Xq0(X1, sk_Xu(X0)), sk_Xv(X0))
0.45/0.63	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xu(X0))),
0.45/0.63	    inference('sup-', [status(thm)], ['53', '8'])).
0.45/0.63	tff('55', plain,
0.45/0.63	    ![X0 : app_encode_fun(a, $o), X1 : a]:
0.45/0.63	      (app_encode_app(a, $o, sk_Xq0(X1, sk_Xu(X0)), sk_Xv(X0))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, X1)
0.45/0.63	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xu(X0))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, sk_Xv(X0))
0.45/0.63	       | app_encode_app(a, $o, X0, sk_Xy)
0.45/0.63	       | ~ app_encode_app(a, $o, X0, sk_Xw(X0))),
0.45/0.63	    inference('simplify', [status(thm)], ['54'])).
0.45/0.63	tff('56', plain,
0.45/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.45/0.63	      (~ $true
0.45/0.63	       | ~ app_encode_app(a, $o, X0, sk_Xw(X0))
0.45/0.63	       | app_encode_app(a, $o, X0, sk_Xy)
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, sk_Xv(X0))
0.45/0.63	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xu(X0))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, sk_Xv(X0))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, sk_Xv(X0))
0.45/0.63	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xu(X0))),
0.45/0.63	    inference('sup-', [status(thm)], ['55', '11'])).
0.45/0.63	tff('57', plain,
0.45/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.45/0.63	      (~ app_encode_app(a, $o, sk_Xq, sk_Xu(X0))
0.45/0.63	       | app_encode_app(a, $o, sk_Xq, sk_Xv(X0))
0.45/0.63	       | app_encode_app(a, $o, X0, sk_Xy)
0.45/0.63	       | ~ app_encode_app(a, $o, X0, sk_Xw(X0))),
0.45/0.63	    inference('simplify', [status(thm)], ['56'])).
0.45/0.63	tff('58', plain,
0.45/0.63	    (~ $true
0.45/0.63	     | app_encode_app(a, $o, sk_Xq, sk_Xy)
0.45/0.63	     | app_encode_app(a, $o, sk_Xq, sk_Xv(sk_Xq))
0.45/0.63	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xu(sk_Xq))),
0.45/0.63	    inference('sup-', [status(thm)], ['48', '57'])).
0.45/0.63	tff('59', plain,
0.45/0.63	    (~ app_encode_app(a, $o, sk_Xq, sk_Xu(sk_Xq))
0.45/0.63	     | app_encode_app(a, $o, sk_Xq, sk_Xv(sk_Xq))
0.45/0.63	     | app_encode_app(a, $o, sk_Xq, sk_Xy)),
0.45/0.63	    inference('simplify', [status(thm)], ['58'])).
0.45/0.63	tff('60', plain,
0.45/0.63	    (app_encode_app(a, $o, sk_Xq, sk_Xv(sk_Xq))
0.45/0.63	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xu(sk_Xq))),
0.45/0.63	    inference('clc', [status(thm)], ['59', '39'])).
0.45/0.63	tff('61', plain,
0.45/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.45/0.63	      (app_encode_app(a, $o, X0, sk_Xy)
0.45/0.63	       | ~ app_encode_app(a, $o, X0, sk_Xv(X0))
0.45/0.63	       | ~ app_encode_app(a, $o, X0, sk_Xw(X0))),
0.45/0.63	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.45/0.63	tff('62', plain,
0.45/0.63	    (~ $true
0.45/0.63	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xu(sk_Xq))
0.45/0.63	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xw(sk_Xq))
0.45/0.63	     | app_encode_app(a, $o, sk_Xq, sk_Xy)),
0.45/0.63	    inference('sup-', [status(thm)], ['60', '61'])).
0.45/0.63	tff('63', plain,
0.45/0.63	    (~ $true
0.45/0.63	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xu(sk_Xq))
0.45/0.63	     | ~ $true
0.45/0.63	     | app_encode_app(a, $o, sk_Xq, sk_Xy)),
0.45/0.63	    inference('demod', [status(thm)], ['62', '48'])).
0.45/0.63	tff('64', plain,
0.45/0.63	    (app_encode_app(a, $o, sk_Xq, sk_Xy)
0.45/0.63	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xu(sk_Xq))),
0.45/0.63	    inference('simplify', [status(thm)], ['63'])).
0.45/0.63	tff('65', plain, ~ app_encode_app(a, $o, sk_Xq, sk_Xu(sk_Xq)),
0.45/0.63	    inference('clc', [status(thm)], ['64', '39'])).
0.45/0.63	tff('66', plain,
0.45/0.63	    (~ $true
0.45/0.63	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xw(sk_Xq))
0.45/0.63	     | app_encode_app(a, $o, sk_Xq, sk_Xy)),
0.45/0.63	    inference('sup-', [status(thm)], ['0', '65'])).
0.45/0.63	tff('67', plain, (~ $true | ~ $true | app_encode_app(a, $o, sk_Xq, sk_Xy)),
0.45/0.63	    inference('demod', [status(thm)], ['66', '48'])).
0.45/0.63	tff('68', plain, app_encode_app(a, $o, sk_Xq, sk_Xy),
0.45/0.63	    inference('simplify', [status(thm)], ['67'])).
0.45/0.63	tff('69', plain, ~ $true, inference('sup-', [status(thm)], ['68', '39'])).
0.45/0.63	tff('70', plain, $false, inference('simplify', [status(thm)], ['69'])).
0.45/0.63	
0.45/0.63	% SZS output end Refutation
0.45/0.63	EOF
