0.00/0.01	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.01	% app-encoded or not : app
0.00/0.01	% Variant    : fo
0.00/0.01	% Ordering    : rpo6
0.00/0.01	% Command    : 
0.00/0.01	#!/bin/sh
0.00/0.01	
0.00/0.01	./zipperposition.native ${1:+"$1"} \
0.00/0.01	  -i tptp \
0.00/0.01	  -o tptp \
0.00/0.01	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.01	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.01	  --no-ho \
0.00/0.01	  --no-avatar \
0.00/0.01	  --no-induction \
0.00/0.01	  --no-unif-pattern \
0.00/0.01	  --ord $2 \
0.00/0.01	  --simultaneous-sup false \
0.00/0.01	  --no-max-vars \
0.00/0.01	  --no-fool
0.00/0.20	% Computer   : n155.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 17:47:08 CST 2018
0.00/0.26	% done 40 iterations in 0.048s
0.00/0.26	% SZS status Theorem for 'stdin'
0.00/0.26	% SZS output start Refutation
0.00/0.26	tff(zf_stmt_3, conjecture,
0.00/0.26	  (![R:app_encode_fun(a,app_encode_fun(a,$o)),
0.00/0.26	     S:app_encode_fun(a,app_encode_fun(a,$o)),Xx:a,Xy:a]:
0.00/0.26	     ((![Xq1:app_encode_fun(a,app_encode_fun(a,$o))]:
0.00/0.26	         (((![Xs:a,Xt:a]:
0.00/0.26	              ((app_encode_app(a,$o,
0.00/0.26	                               app_encode_app(a,app_encode_fun(a,$o),R,Xs),Xt) | 
0.00/0.26	                app_encode_app(a,$o,
0.00/0.26	                               app_encode_app(a,app_encode_fun(a,$o),S,Xs),Xt)) =>
0.00/0.26	               app_encode_app(a,$o,
0.00/0.26	                              app_encode_app(a,app_encode_fun(a,$o),Xq1,Xs),
0.00/0.26	                              Xt))) & 
0.00/0.26	           (![Xx0:a,Xy0:a,Xz:a]:
0.00/0.26	              ((app_encode_app(a,$o,
0.00/0.26	                               app_encode_app(a,app_encode_fun(a,$o),Xq1,Xx0),
0.00/0.26	                               Xy0) & 
0.00/0.26	                app_encode_app(a,$o,
0.00/0.26	                               app_encode_app(a,app_encode_fun(a,$o),Xq1,Xy0),
0.00/0.26	                               Xz)) =>
0.00/0.26	               app_encode_app(a,$o,
0.00/0.26	                              app_encode_app(a,app_encode_fun(a,$o),Xq1,Xx0),
0.00/0.26	                              Xz)))) =>
0.00/0.26	          app_encode_app(a,$o,app_encode_app(a,app_encode_fun(a,$o),Xq1,Xx),
0.00/0.26	                         Xy))) =>
0.00/0.26	      (![Xp1:app_encode_fun(a,app_encode_fun(a,$o))]:
0.00/0.26	         (((![Xss:a,Xtt:a]:
0.00/0.26	              (((![Xq2:app_encode_fun(a,app_encode_fun(a,$o))]:
0.00/0.26	                   (((![Xsss:a,Xttt:a]:
0.00/0.26	                        (app_encode_app(a,$o,
0.00/0.26	                                        app_encode_app(a,
0.00/0.26	                                                       app_encode_fun(a,$o),
0.00/0.26	                                                       R,Xsss),
0.00/0.26	                                        Xttt) =>
0.00/0.26	                         app_encode_app(a,$o,
0.00/0.26	                                        app_encode_app(a,
0.00/0.26	                                                       app_encode_fun(a,$o),
0.00/0.26	                                                       Xq2,Xsss),
0.00/0.26	                                        Xttt))) & 
0.00/0.26	                     (![Xx0:a,Xy0:a,Xz:a]:
0.00/0.26	                        ((app_encode_app(a,$o,
0.00/0.26	                                         app_encode_app(a,
0.00/0.26	                                                        app_encode_fun(a,$o),
0.00/0.26	                                                        Xq2,Xx0),
0.00/0.26	                                         Xy0) & 
0.00/0.26	                          app_encode_app(a,$o,
0.00/0.26	                                         app_encode_app(a,
0.00/0.26	                                                        app_encode_fun(a,$o),
0.00/0.26	                                                        Xq2,Xy0),
0.00/0.26	                                         Xz)) =>
0.00/0.26	                         app_encode_app(a,$o,
0.00/0.26	                                        app_encode_app(a,
0.00/0.26	                                                       app_encode_fun(a,$o),
0.00/0.26	                                                       Xq2,Xx0),
0.00/0.26	                                        Xz)))) =>
0.00/0.26	                    app_encode_app(a,$o,
0.00/0.26	                                   app_encode_app(a,app_encode_fun(a,$o),Xq2,
0.00/0.26	                                                  Xss),
0.00/0.26	                                   Xtt))) | 
0.00/0.26	                (![Xq3:app_encode_fun(a,app_encode_fun(a,$o))]:
0.00/0.26	                   (((![Xssss:a,Xtttt:a]:
0.00/0.26	                        (app_encode_app(a,$o,
0.00/0.26	                                        app_encode_app(a,
0.00/0.26	                                                       app_encode_fun(a,$o),
0.00/0.26	                                                       S,Xssss),
0.00/0.26	                                        Xtttt) =>
0.00/0.26	                         app_encode_app(a,$o,
0.00/0.26	                                        app_encode_app(a,
0.00/0.26	                                                       app_encode_fun(a,$o),
0.00/0.26	                                                       Xq3,Xssss),
0.00/0.26	                                        Xtttt))) & 
0.00/0.26	                     (![Xx0:a,Xy0:a,Xz:a]:
0.00/0.26	                        ((app_encode_app(a,$o,
0.00/0.26	                                         app_encode_app(a,
0.00/0.26	                                                        app_encode_fun(a,$o),
0.00/0.26	                                                        Xq3,Xx0),
0.00/0.26	                                         Xy0) & 
0.00/0.26	                          app_encode_app(a,$o,
0.00/0.26	                                         app_encode_app(a,
0.00/0.26	                                                        app_encode_fun(a,$o),
0.00/0.26	                                                        Xq3,Xy0),
0.00/0.26	                                         Xz)) =>
0.00/0.26	                         app_encode_app(a,$o,
0.00/0.26	                                        app_encode_app(a,
0.00/0.26	                                                       app_encode_fun(a,$o),
0.00/0.26	                                                       Xq3,Xx0),
0.00/0.26	                                        Xz)))) =>
0.00/0.26	                    app_encode_app(a,$o,
0.00/0.26	                                   app_encode_app(a,app_encode_fun(a,$o),Xq3,
0.00/0.26	                                                  Xss),
0.00/0.26	                                   Xtt)))) =>
0.00/0.26	               app_encode_app(a,$o,
0.00/0.26	                              app_encode_app(a,app_encode_fun(a,$o),Xp1,Xss),
0.00/0.26	                              Xtt))) & 
0.00/0.26	           (![Xx0:a,Xy0:a,Xz:a]:
0.00/0.26	              ((app_encode_app(a,$o,
0.00/0.26	                               app_encode_app(a,app_encode_fun(a,$o),Xp1,Xx0),
0.00/0.26	                               Xy0) & 
0.00/0.26	                app_encode_app(a,$o,
0.00/0.26	                               app_encode_app(a,app_encode_fun(a,$o),Xp1,Xy0),
0.00/0.26	                               Xz)) =>
0.00/0.26	               app_encode_app(a,$o,
0.00/0.26	                              app_encode_app(a,app_encode_fun(a,$o),Xp1,Xx0),
0.00/0.26	                              Xz)))) =>
0.00/0.26	          app_encode_app(a,$o,app_encode_app(a,app_encode_fun(a,$o),Xp1,Xx),
0.00/0.26	                         Xy)))))).
0.00/0.26	tff(zf_stmt_0, negated_conjecture,
0.00/0.26	  (~
0.00/0.26	    (![R:app_encode_fun(a,app_encode_fun(a,$o)),
0.00/0.26	       S:app_encode_fun(a,app_encode_fun(a,$o)),Xx:a,Xy:a]:
0.00/0.26	       ((![Xq1:app_encode_fun(a,app_encode_fun(a,$o))]:
0.00/0.26	           (((![Xs:a,Xt:a]:
0.00/0.26	                ((app_encode_app(a,$o,
0.00/0.26	                                 app_encode_app(a,app_encode_fun(a,$o),R,Xs),
0.00/0.26	                                 Xt) | 
0.00/0.26	                  app_encode_app(a,$o,
0.00/0.26	                                 app_encode_app(a,app_encode_fun(a,$o),S,Xs),
0.00/0.26	                                 Xt)) =>
0.00/0.26	                 app_encode_app(a,$o,
0.00/0.26	                                app_encode_app(a,app_encode_fun(a,$o),Xq1,Xs),
0.00/0.26	                                Xt))) & 
0.00/0.26	             (![Xx0:a,Xy0:a,Xz:a]:
0.00/0.26	                ((app_encode_app(a,$o,
0.00/0.26	                                 app_encode_app(a,app_encode_fun(a,$o),Xq1,
0.00/0.26	                                                Xx0),
0.00/0.26	                                 Xy0) & 
0.00/0.26	                  app_encode_app(a,$o,
0.00/0.26	                                 app_encode_app(a,app_encode_fun(a,$o),Xq1,
0.00/0.26	                                                Xy0),
0.00/0.26	                                 Xz)) =>
0.00/0.26	                 app_encode_app(a,$o,
0.00/0.26	                                app_encode_app(a,app_encode_fun(a,$o),Xq1,Xx0),
0.00/0.26	                                Xz)))) =>
0.00/0.26	            app_encode_app(a,$o,
0.00/0.26	                           app_encode_app(a,app_encode_fun(a,$o),Xq1,Xx),Xy))) =>
0.00/0.26	        (![Xp1:app_encode_fun(a,app_encode_fun(a,$o))]:
0.00/0.26	           (((![Xss:a,Xtt:a]:
0.00/0.26	                (((![Xq2:app_encode_fun(a,app_encode_fun(a,$o))]:
0.00/0.26	                     (((![Xsss:a,Xttt:a]:
0.00/0.26	                          (app_encode_app(a,$o,
0.00/0.26	                                          app_encode_app(a,
0.00/0.26	                                                         app_encode_fun(a,$o),
0.00/0.26	                                                         R,Xsss),
0.00/0.26	                                          Xttt) =>
0.00/0.26	                           app_encode_app(a,$o,
0.00/0.26	                                          app_encode_app(a,
0.00/0.26	                                                         app_encode_fun(a,$o),
0.00/0.26	                                                         Xq2,Xsss),
0.00/0.26	                                          Xttt))) & 
0.00/0.26	                       (![Xx0:a,Xy0:a,Xz:a]:
0.00/0.26	                          ((app_encode_app(a,$o,
0.00/0.26	                                           app_encode_app(a,
0.00/0.26	                                                          app_encode_fun(
0.00/0.26	                                                          a,$o),Xq2,Xx0),
0.00/0.26	                                           Xy0) & 
0.00/0.26	                            app_encode_app(a,$o,
0.00/0.26	                                           app_encode_app(a,
0.00/0.26	                                                          app_encode_fun(
0.00/0.26	                                                          a,$o),Xq2,Xy0),
0.00/0.26	                                           Xz)) =>
0.00/0.26	                           app_encode_app(a,$o,
0.00/0.26	                                          app_encode_app(a,
0.00/0.26	                                                         app_encode_fun(a,$o),
0.00/0.26	                                                         Xq2,Xx0),
0.00/0.26	                                          Xz)))) =>
0.00/0.26	                      app_encode_app(a,$o,
0.00/0.26	                                     app_encode_app(a,app_encode_fun(a,$o),
0.00/0.26	                                                    Xq2,Xss),
0.00/0.26	                                     Xtt))) | 
0.00/0.26	                  (![Xq3:app_encode_fun(a,app_encode_fun(a,$o))]:
0.00/0.26	                     (((![Xssss:a,Xtttt:a]:
0.00/0.26	                          (app_encode_app(a,$o,
0.00/0.26	                                          app_encode_app(a,
0.00/0.26	                                                         app_encode_fun(a,$o),
0.00/0.26	                                                         S,Xssss),
0.00/0.26	                                          Xtttt) =>
0.00/0.26	                           app_encode_app(a,$o,
0.00/0.26	                                          app_encode_app(a,
0.00/0.26	                                                         app_encode_fun(a,$o),
0.00/0.26	                                                         Xq3,Xssss),
0.00/0.26	                                          Xtttt))) & 
0.00/0.26	                       (![Xx0:a,Xy0:a,Xz:a]:
0.00/0.26	                          ((app_encode_app(a,$o,
0.00/0.26	                                           app_encode_app(a,
0.00/0.26	                                                          app_encode_fun(
0.00/0.26	                                                          a,$o),Xq3,Xx0),
0.00/0.26	                                           Xy0) & 
0.00/0.26	                            app_encode_app(a,$o,
0.00/0.26	                                           app_encode_app(a,
0.00/0.26	                                                          app_encode_fun(
0.00/0.26	                                                          a,$o),Xq3,Xy0),
0.00/0.26	                                           Xz)) =>
0.00/0.26	                           app_encode_app(a,$o,
0.00/0.26	                                          app_encode_app(a,
0.00/0.26	                                                         app_encode_fun(a,$o),
0.00/0.26	                                                         Xq3,Xx0),
0.00/0.26	                                          Xz)))) =>
0.00/0.26	                      app_encode_app(a,$o,
0.00/0.26	                                     app_encode_app(a,app_encode_fun(a,$o),
0.00/0.26	                                                    Xq3,Xss),
0.00/0.26	                                     Xtt)))) =>
0.00/0.26	                 app_encode_app(a,$o,
0.00/0.26	                                app_encode_app(a,app_encode_fun(a,$o),Xp1,Xss),
0.00/0.26	                                Xtt))) & 
0.00/0.26	             (![Xx0:a,Xy0:a,Xz:a]:
0.00/0.26	                ((app_encode_app(a,$o,
0.00/0.26	                                 app_encode_app(a,app_encode_fun(a,$o),Xp1,
0.00/0.26	                                                Xx0),
0.00/0.26	                                 Xy0) & 
0.00/0.26	                  app_encode_app(a,$o,
0.00/0.26	                                 app_encode_app(a,app_encode_fun(a,$o),Xp1,
0.00/0.26	                                                Xy0),
0.00/0.26	                                 Xz)) =>
0.00/0.26	                 app_encode_app(a,$o,
0.00/0.26	                                app_encode_app(a,app_encode_fun(a,$o),Xp1,Xx0),
0.00/0.26	                                Xz)))) =>
0.00/0.26	            app_encode_app(a,$o,
0.00/0.26	                           app_encode_app(a,app_encode_fun(a,$o),Xp1,Xx),Xy))))))).
0.00/0.26	tff('0', plain,
0.00/0.26	    ![X0 : app_encode_fun(a, app_encode_fun(a, $o))]:
0.00/0.26	      (app_encode_app(a, $o, 
0.00/0.26	         app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xx), sk_Xy)
0.00/0.26	       | app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xy0(X0)), 
0.00/0.26	           sk_Xz(X0))
0.00/0.26	       | app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xs(X0)), 
0.00/0.26	           sk_Xt(X0))
0.00/0.26	       | app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xs(X0)), 
0.00/0.26	           sk_Xt(X0))),
0.00/0.26	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.26	tff('1', plain,
0.00/0.26	    ![X0 : app_encode_fun(a, app_encode_fun(a, $o))]:
0.00/0.26	      (app_encode_app(a, $o, 
0.00/0.26	         app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xx), sk_Xy)
0.00/0.26	       | app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xx0(X0)), 
0.00/0.26	           sk_Xy0(X0))
0.00/0.26	       | app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xs(X0)), 
0.00/0.26	           sk_Xt(X0))
0.00/0.26	       | app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xs(X0)), 
0.00/0.26	           sk_Xt(X0))),
0.00/0.26	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.26	tff('2', plain,
0.00/0.26	    ![X1 : a, X2 : a, X3 : a]:
0.00/0.26	      (~ app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, X1), X2)
0.00/0.26	       | ~ app_encode_app(a, $o, 
0.00/0.26	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, X2), X3)
0.00/0.26	       | app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, X1), X3)),
0.00/0.26	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.26	tff('3', plain,
0.00/0.26	    ![X0 : a]:
0.00/0.26	      (~ $true
0.00/0.26	       | app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xs(sk_Xp1)), 
0.00/0.26	           sk_Xt(sk_Xp1))
0.00/0.26	       | app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xs(sk_Xp1)), 
0.00/0.26	           sk_Xt(sk_Xp1))
0.00/0.26	       | app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, sk_Xx), sk_Xy)
0.00/0.26	       | app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, sk_Xx0(sk_Xp1)), 
0.00/0.26	           X0)
0.00/0.26	       | ~ app_encode_app(a, $o, 
0.00/0.26	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, sk_Xy0(sk_Xp1)), 
0.00/0.26	             X0)),
0.00/0.26	    inference('sup-', [status(thm)], ['1', '2'])).
0.00/0.26	tff('4', plain,
0.00/0.26	    ![X0 : a]:
0.00/0.26	      (~ app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, sk_Xy0(sk_Xp1)), 
0.00/0.26	           X0)
0.00/0.26	       | app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, sk_Xx0(sk_Xp1)), 
0.00/0.26	           X0)
0.00/0.26	       | app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, sk_Xx), sk_Xy)
0.00/0.26	       | app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xs(sk_Xp1)), 
0.00/0.26	           sk_Xt(sk_Xp1))
0.00/0.26	       | app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xs(sk_Xp1)), 
0.00/0.26	           sk_Xt(sk_Xp1))),
0.00/0.26	    inference('simplify', [status(thm)], ['3'])).
0.00/0.26	tff('5', plain,
0.00/0.26	    ~ app_encode_app(a, $o, 
0.00/0.26	        app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, sk_Xx), sk_Xy),
0.00/0.26	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.26	tff('6', plain,
0.00/0.26	    ![X0 : a]:
0.00/0.26	      (app_encode_app(a, $o, 
0.00/0.26	         app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xs(sk_Xp1)), 
0.00/0.26	         sk_Xt(sk_Xp1))
0.00/0.26	       | app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xs(sk_Xp1)), 
0.00/0.26	           sk_Xt(sk_Xp1))
0.00/0.26	       | app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, sk_Xx0(sk_Xp1)), 
0.00/0.26	           X0)
0.00/0.26	       | ~ app_encode_app(a, $o, 
0.00/0.26	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, sk_Xy0(sk_Xp1)), 
0.00/0.26	             X0)),
0.00/0.26	    inference('clc', [status(thm)], ['4', '5'])).
0.00/0.26	tff('7', plain,
0.00/0.26	    (~ $true
0.00/0.26	     | app_encode_app(a, $o, 
0.00/0.26	         app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xs(sk_Xp1)), 
0.00/0.26	         sk_Xt(sk_Xp1))
0.00/0.26	     | app_encode_app(a, $o, 
0.00/0.26	         app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xs(sk_Xp1)), 
0.00/0.26	         sk_Xt(sk_Xp1))
0.00/0.26	     | app_encode_app(a, $o, 
0.00/0.26	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, sk_Xx), sk_Xy)
0.00/0.26	     | app_encode_app(a, $o, 
0.00/0.26	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, sk_Xx0(sk_Xp1)), 
0.00/0.26	         sk_Xz(sk_Xp1))
0.00/0.26	     | app_encode_app(a, $o, 
0.00/0.26	         app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xs(sk_Xp1)), 
0.00/0.26	         sk_Xt(sk_Xp1))
0.00/0.26	     | app_encode_app(a, $o, 
0.00/0.26	         app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xs(sk_Xp1)), 
0.00/0.26	         sk_Xt(sk_Xp1))),
0.00/0.26	    inference('sup-', [status(thm)], ['0', '6'])).
0.00/0.26	tff('8', plain,
0.00/0.26	    (app_encode_app(a, $o, 
0.00/0.26	       app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, sk_Xx0(sk_Xp1)), 
0.00/0.26	       sk_Xz(sk_Xp1))
0.00/0.26	     | app_encode_app(a, $o, 
0.00/0.26	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, sk_Xx), sk_Xy)
0.00/0.26	     | app_encode_app(a, $o, 
0.00/0.26	         app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xs(sk_Xp1)), 
0.00/0.26	         sk_Xt(sk_Xp1))
0.00/0.26	     | app_encode_app(a, $o, 
0.00/0.26	         app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xs(sk_Xp1)), 
0.00/0.26	         sk_Xt(sk_Xp1))),
0.00/0.26	    inference('simplify', [status(thm)], ['7'])).
0.00/0.26	tff('9', plain,
0.00/0.26	    ![X0 : app_encode_fun(a, app_encode_fun(a, $o))]:
0.00/0.26	      (app_encode_app(a, $o, 
0.00/0.26	         app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xx), sk_Xy)
0.00/0.26	       | ~ app_encode_app(a, $o, 
0.00/0.26	             app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xx0(X0)), 
0.00/0.26	             sk_Xz(X0))
0.00/0.26	       | app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xs(X0)), 
0.00/0.26	           sk_Xt(X0))
0.00/0.26	       | app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xs(X0)), 
0.00/0.26	           sk_Xt(X0))),
0.00/0.26	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.26	tff('10', plain,
0.00/0.26	    (app_encode_app(a, $o, 
0.00/0.26	       app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xs(sk_Xp1)), 
0.00/0.26	       sk_Xt(sk_Xp1))
0.00/0.26	     | app_encode_app(a, $o, 
0.00/0.26	         app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xs(sk_Xp1)), 
0.00/0.26	         sk_Xt(sk_Xp1))
0.00/0.26	     | app_encode_app(a, $o, 
0.00/0.26	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, sk_Xx), sk_Xy)),
0.00/0.26	    inference('clc', [status(thm)], ['8', '9'])).
0.00/0.26	tff('11', plain,
0.00/0.26	    (app_encode_app(a, $o, 
0.00/0.26	       app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xs(sk_Xp1)), 
0.00/0.26	       sk_Xt(sk_Xp1))
0.00/0.26	     | app_encode_app(a, $o, 
0.00/0.26	         app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xs(sk_Xp1)), 
0.00/0.26	         sk_Xt(sk_Xp1))),
0.00/0.26	    inference('clc', [status(thm)], ['10', '5'])).
0.00/0.26	tff('12', plain,
0.00/0.26	    ![X4 : a, X5 : a, X11 : a, X12 : a]:
0.00/0.26	      (app_encode_app(a, $o, 
0.00/0.26	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, X4), X5)
0.00/0.26	       | app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_Xq3(X5, X4), X11), 
0.00/0.26	           X12)
0.00/0.26	       | ~ app_encode_app(a, $o, 
0.00/0.26	             app_encode_app(a, app_encode_fun(a, $o), sk_S, X11), X12)),
0.00/0.26	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.26	tff('13', plain,
0.00/0.26	    ![X0 : a, X1 : a]:
0.00/0.26	      (~ $true
0.00/0.26	       | app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xs(sk_Xp1)), 
0.00/0.26	           sk_Xt(sk_Xp1))
0.00/0.26	       | app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_Xq3(X1, X0), 
0.00/0.26	             sk_Xs(sk_Xp1)), sk_Xt(sk_Xp1))
0.00/0.26	       | app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, X0), X1)),
0.00/0.26	    inference('sup-', [status(thm)], ['11', '12'])).
0.00/0.26	tff('14', plain,
0.00/0.26	    ![X0 : a, X1 : a]:
0.00/0.26	      (app_encode_app(a, $o, 
0.00/0.26	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, X0), X1)
0.00/0.26	       | app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_Xq3(X1, X0), 
0.00/0.26	             sk_Xs(sk_Xp1)), sk_Xt(sk_Xp1))
0.00/0.26	       | app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xs(sk_Xp1)), 
0.00/0.26	           sk_Xt(sk_Xp1))),
0.00/0.26	    inference('simplify', [status(thm)], ['13'])).
0.00/0.26	tff('15', plain,
0.00/0.26	    ![X4 : a, X5 : a, X6 : a, X7 : a]:
0.00/0.26	      (app_encode_app(a, $o, 
0.00/0.26	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, X4), X5)
0.00/0.26	       | app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_Xq2(X5, X4), X6), X7)
0.00/0.26	       | ~ app_encode_app(a, $o, 
0.00/0.26	             app_encode_app(a, app_encode_fun(a, $o), sk_R, X6), X7)),
0.00/0.26	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.26	tff('16', plain,
0.00/0.26	    ![X0 : a, X1 : a, X2 : a, X3 : a]:
0.00/0.26	      (~ $true
0.00/0.26	       | app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_Xq3(X3, X2), 
0.00/0.26	             sk_Xs(sk_Xp1)), sk_Xt(sk_Xp1))
0.00/0.26	       | app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, X2), X3)
0.00/0.26	       | app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_Xq2(X1, X0), 
0.00/0.26	             sk_Xs(sk_Xp1)), sk_Xt(sk_Xp1))
0.00/0.26	       | app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, X0), X1)),
0.00/0.26	    inference('sup-', [status(thm)], ['14', '15'])).
0.00/0.26	tff('17', plain,
0.00/0.26	    ![X0 : a, X1 : a, X2 : a, X3 : a]:
0.00/0.26	      (app_encode_app(a, $o, 
0.00/0.26	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, X0), X1)
0.00/0.26	       | app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_Xq2(X1, X0), 
0.00/0.26	             sk_Xs(sk_Xp1)), sk_Xt(sk_Xp1))
0.00/0.26	       | app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, X2), X3)
0.00/0.26	       | app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_Xq3(X3, X2), 
0.00/0.26	             sk_Xs(sk_Xp1)), sk_Xt(sk_Xp1))),
0.00/0.26	    inference('simplify', [status(thm)], ['16'])).
0.00/0.26	tff('18', plain,
0.00/0.26	    ![X4 : a, X5 : a]:
0.00/0.26	      (app_encode_app(a, $o, 
0.00/0.26	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, X4), X5)
0.00/0.26	       | ~ app_encode_app(a, $o, 
0.00/0.26	             app_encode_app(a, app_encode_fun(a, $o), sk_Xq3(X5, X4), X4), 
0.00/0.26	             X5)),
0.00/0.26	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.26	tff('19', plain,
0.00/0.26	    ![X0 : a, X1 : a]:
0.00/0.26	      (~ $true
0.00/0.26	       | app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, sk_Xs(sk_Xp1)), 
0.00/0.26	           sk_Xt(sk_Xp1))
0.00/0.26	       | app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_Xq2(X1, X0), 
0.00/0.26	             sk_Xs(sk_Xp1)), sk_Xt(sk_Xp1))
0.00/0.26	       | app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, X0), X1)
0.00/0.26	       | app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, sk_Xs(sk_Xp1)), 
0.00/0.26	           sk_Xt(sk_Xp1))),
0.00/0.26	    inference('sup-', [status(thm)], ['17', '18'])).
0.00/0.26	tff('20', plain,
0.00/0.26	    ![X0 : a, X1 : a]:
0.00/0.26	      (app_encode_app(a, $o, 
0.00/0.26	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, X0), X1)
0.00/0.26	       | app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_Xq2(X1, X0), 
0.00/0.26	             sk_Xs(sk_Xp1)), sk_Xt(sk_Xp1))
0.00/0.26	       | app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, sk_Xs(sk_Xp1)), 
0.00/0.26	           sk_Xt(sk_Xp1))),
0.00/0.26	    inference('simplify', [status(thm)], ['19'])).
0.00/0.26	tff('21', plain,
0.00/0.26	    ![X0 : app_encode_fun(a, app_encode_fun(a, $o))]:
0.00/0.26	      (app_encode_app(a, $o, 
0.00/0.26	         app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xx), sk_Xy)
0.00/0.26	       | app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xy0(X0)), 
0.00/0.26	           sk_Xz(X0))
0.00/0.26	       | ~ app_encode_app(a, $o, 
0.00/0.26	             app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xs(X0)), 
0.00/0.26	             sk_Xt(X0))),
0.00/0.26	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.26	tff('22', plain,
0.00/0.26	    ![X0 : app_encode_fun(a, app_encode_fun(a, $o))]:
0.00/0.26	      (app_encode_app(a, $o, 
0.00/0.26	         app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xx), sk_Xy)
0.00/0.26	       | app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xx0(X0)), 
0.00/0.26	           sk_Xy0(X0))
0.00/0.26	       | ~ app_encode_app(a, $o, 
0.00/0.26	             app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xs(X0)), 
0.00/0.26	             sk_Xt(X0))),
0.00/0.26	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.26	tff('23', plain,
0.00/0.26	    ![X0 : a]:
0.00/0.26	      (~ $true
0.00/0.26	       | ~ app_encode_app(a, $o, 
0.00/0.26	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, sk_Xs(sk_Xp1)), 
0.00/0.26	             sk_Xt(sk_Xp1))
0.00/0.26	       | app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, sk_Xx), sk_Xy)
0.00/0.26	       | app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, sk_Xx0(sk_Xp1)), 
0.00/0.26	           X0)
0.00/0.26	       | ~ app_encode_app(a, $o, 
0.00/0.26	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, sk_Xy0(sk_Xp1)), 
0.00/0.26	             X0)),
0.00/0.26	    inference('sup-', [status(thm)], ['22', '2'])).
0.00/0.26	tff('24', plain,
0.00/0.26	    ![X0 : a]:
0.00/0.26	      (~ app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, sk_Xy0(sk_Xp1)), 
0.00/0.26	           X0)
0.00/0.26	       | app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, sk_Xx0(sk_Xp1)), 
0.00/0.26	           X0)
0.00/0.26	       | app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, sk_Xx), sk_Xy)
0.00/0.26	       | ~ app_encode_app(a, $o, 
0.00/0.26	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, sk_Xs(sk_Xp1)), 
0.00/0.26	             sk_Xt(sk_Xp1))),
0.00/0.26	    inference('simplify', [status(thm)], ['23'])).
0.00/0.26	tff('25', plain,
0.00/0.26	    ![X0 : a]:
0.00/0.26	      (~ app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, sk_Xs(sk_Xp1)), 
0.00/0.26	           sk_Xt(sk_Xp1))
0.00/0.26	       | app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, sk_Xx0(sk_Xp1)), 
0.00/0.26	           X0)
0.00/0.26	       | ~ app_encode_app(a, $o, 
0.00/0.26	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, sk_Xy0(sk_Xp1)), 
0.00/0.26	             X0)),
0.00/0.26	    inference('clc', [status(thm)], ['24', '5'])).
0.00/0.26	tff('26', plain,
0.00/0.26	    (~ $true
0.00/0.26	     | ~ app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, sk_Xs(sk_Xp1)), 
0.00/0.26	           sk_Xt(sk_Xp1))
0.00/0.26	     | app_encode_app(a, $o, 
0.00/0.26	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, sk_Xx), sk_Xy)
0.00/0.26	     | app_encode_app(a, $o, 
0.00/0.26	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, sk_Xx0(sk_Xp1)), 
0.00/0.26	         sk_Xz(sk_Xp1))
0.00/0.26	     | ~ app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, sk_Xs(sk_Xp1)), 
0.00/0.26	           sk_Xt(sk_Xp1))),
0.00/0.26	    inference('sup-', [status(thm)], ['21', '25'])).
0.00/0.26	tff('27', plain,
0.00/0.26	    (app_encode_app(a, $o, 
0.00/0.26	       app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, sk_Xx0(sk_Xp1)), 
0.00/0.26	       sk_Xz(sk_Xp1))
0.00/0.26	     | app_encode_app(a, $o, 
0.00/0.26	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, sk_Xx), sk_Xy)
0.00/0.26	     | ~ app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, sk_Xs(sk_Xp1)), 
0.00/0.26	           sk_Xt(sk_Xp1))),
0.00/0.26	    inference('simplify', [status(thm)], ['26'])).
0.00/0.26	tff('28', plain,
0.00/0.26	    ![X0 : app_encode_fun(a, app_encode_fun(a, $o))]:
0.00/0.26	      (app_encode_app(a, $o, 
0.00/0.26	         app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xx), sk_Xy)
0.00/0.26	       | ~ app_encode_app(a, $o, 
0.00/0.26	             app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xx0(X0)), 
0.00/0.26	             sk_Xz(X0))
0.00/0.26	       | ~ app_encode_app(a, $o, 
0.00/0.26	             app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xs(X0)), 
0.00/0.26	             sk_Xt(X0))),
0.00/0.26	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.26	tff('29', plain,
0.00/0.26	    (~ app_encode_app(a, $o, 
0.00/0.26	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, sk_Xs(sk_Xp1)), 
0.00/0.26	         sk_Xt(sk_Xp1))
0.00/0.26	     | app_encode_app(a, $o, 
0.00/0.26	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, sk_Xx), sk_Xy)),
0.00/0.26	    inference('clc', [status(thm)], ['27', '28'])).
0.00/0.26	tff('30', plain,
0.00/0.26	    ~ app_encode_app(a, $o, 
0.00/0.26	        app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, sk_Xs(sk_Xp1)), 
0.00/0.26	        sk_Xt(sk_Xp1)),
0.00/0.26	    inference('clc', [status(thm)], ['29', '5'])).
0.00/0.26	tff('31', plain,
0.00/0.26	    ![X0 : a, X1 : a]:
0.00/0.26	      (app_encode_app(a, $o, 
0.00/0.26	         app_encode_app(a, app_encode_fun(a, $o), sk_Xq2(X1, X0), 
0.00/0.26	           sk_Xs(sk_Xp1)), sk_Xt(sk_Xp1))
0.00/0.26	       | app_encode_app(a, $o, 
0.00/0.26	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, X0), X1)),
0.00/0.26	    inference('clc', [status(thm)], ['20', '30'])).
0.00/0.26	tff('32', plain,
0.00/0.26	    ![X4 : a, X5 : a]:
0.00/0.26	      (app_encode_app(a, $o, 
0.00/0.26	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, X4), X5)
0.00/0.26	       | ~ app_encode_app(a, $o, 
0.00/0.26	             app_encode_app(a, app_encode_fun(a, $o), sk_Xq2(X5, X4), X4), 
0.00/0.26	             X5)),
0.00/0.26	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.26	tff('33', plain,
0.00/0.26	    (~ $true
0.00/0.26	     | app_encode_app(a, $o, 
0.00/0.26	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, sk_Xs(sk_Xp1)), 
0.00/0.26	         sk_Xt(sk_Xp1))
0.00/0.26	     | app_encode_app(a, $o, 
0.00/0.26	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, sk_Xs(sk_Xp1)), 
0.00/0.26	         sk_Xt(sk_Xp1))),
0.00/0.26	    inference('sup-', [status(thm)], ['31', '32'])).
0.00/0.26	tff('34', plain,
0.00/0.26	    app_encode_app(a, $o, 
0.00/0.26	      app_encode_app(a, app_encode_fun(a, $o), sk_Xp1, sk_Xs(sk_Xp1)), 
0.00/0.26	      sk_Xt(sk_Xp1)),
0.00/0.26	    inference('simplify', [status(thm)], ['33'])).
0.00/0.26	tff('35', plain, ~ $true, inference('sup-', [status(thm)], ['34', '30'])).
0.00/0.26	tff('36', plain, $false, inference('simplify', [status(thm)], ['35'])).
0.00/0.26	
0.00/0.26	% SZS output end Refutation
0.00/0.26	EOF
