0.00/0.00	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : appext
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : kbo
0.00/0.00	% 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 $2 \
0.00/0.01	  --simultaneous-sup false \
0.00/0.01	  --no-max-vars \
0.00/0.01	  --no-fool
0.00/0.20	% Computer   : n186.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 17:51:53 CST 2018
0.83/1.06	% done 392 iterations in 0.856s
0.83/1.06	% SZS status Theorem for 'stdin'
0.83/1.06	% SZS output start Refutation
0.83/1.07	tff(zf_stmt_4, conjecture,
0.83/1.07	  (![P:app_encode_fun(app_encode_fun(a,app_encode_fun(a,$o)),$o),
0.83/1.07	     R:app_encode_fun(a,app_encode_fun(a,$o)),
0.83/1.07	     S:app_encode_fun(a,app_encode_fun(a,$o)),Xx:a,Xy:a]:
0.83/1.07	     ((![Xp:app_encode_fun(a,app_encode_fun(a,$o))]:
0.83/1.07	         (((![Xx0:a,Xy0:a]:
0.83/1.07	              (((![Xp0:app_encode_fun(a,app_encode_fun(a,$o))]:
0.83/1.07	                   (((![Xx1:a,Xy1:a]:
0.83/1.07	                        (app_encode_app(a,$o,
0.83/1.07	                                        app_encode_app(a,
0.83/1.07	                                                       app_encode_fun(a,$o),
0.83/1.07	                                                       R,Xx1),
0.83/1.07	                                        Xy1) =>
0.83/1.07	                         app_encode_app(a,$o,
0.83/1.07	                                        app_encode_app(a,
0.83/1.07	                                                       app_encode_fun(a,$o),
0.83/1.07	                                                       Xp0,Xx1),
0.83/1.07	                                        Xy1))) & 
0.83/1.07	                     app_encode_app(app_encode_fun(a,app_encode_fun(a,$o)),
0.83/1.07	                                    $o,P,Xp0)) =>
0.83/1.07	                    app_encode_app(a,$o,
0.83/1.07	                                   app_encode_app(a,app_encode_fun(a,$o),Xp0,
0.83/1.07	                                                  Xx0),
0.83/1.07	                                   Xy0))) | 
0.83/1.07	                (![Xp0:app_encode_fun(a,app_encode_fun(a,$o))]:
0.83/1.07	                   (((![Xx1:a,Xy1:a]:
0.83/1.07	                        (app_encode_app(a,$o,
0.83/1.07	                                        app_encode_app(a,
0.83/1.07	                                                       app_encode_fun(a,$o),
0.83/1.07	                                                       S,Xx1),
0.83/1.07	                                        Xy1) =>
0.83/1.07	                         app_encode_app(a,$o,
0.83/1.07	                                        app_encode_app(a,
0.83/1.07	                                                       app_encode_fun(a,$o),
0.83/1.07	                                                       Xp0,Xx1),
0.83/1.07	                                        Xy1))) & 
0.83/1.07	                     app_encode_app(app_encode_fun(a,app_encode_fun(a,$o)),
0.83/1.07	                                    $o,P,Xp0)) =>
0.83/1.07	                    app_encode_app(a,$o,
0.83/1.07	                                   app_encode_app(a,app_encode_fun(a,$o),Xp0,
0.83/1.07	                                                  Xx0),
0.83/1.07	                                   Xy0)))) =>
0.83/1.07	               app_encode_app(a,$o,
0.83/1.07	                              app_encode_app(a,app_encode_fun(a,$o),Xp,Xx0),
0.83/1.07	                              Xy0))) & 
0.83/1.07	           app_encode_app(app_encode_fun(a,app_encode_fun(a,$o)),$o,P,Xp)) =>
0.83/1.07	          app_encode_app(a,$o,app_encode_app(a,app_encode_fun(a,$o),Xp,Xx),Xy))) =>
0.83/1.07	      (![Xp:app_encode_fun(a,app_encode_fun(a,$o))]:
0.83/1.07	         (((![Xx0:a,Xy0:a]:
0.83/1.07	              ((app_encode_app(a,$o,
0.83/1.07	                               app_encode_app(a,app_encode_fun(a,$o),R,Xx0),
0.83/1.07	                               Xy0) | 
0.83/1.07	                app_encode_app(a,$o,
0.83/1.07	                               app_encode_app(a,app_encode_fun(a,$o),S,Xx0),
0.83/1.07	                               Xy0)) =>
0.83/1.07	               app_encode_app(a,$o,
0.83/1.07	                              app_encode_app(a,app_encode_fun(a,$o),Xp,Xx0),
0.83/1.07	                              Xy0))) & 
0.83/1.07	           app_encode_app(app_encode_fun(a,app_encode_fun(a,$o)),$o,P,Xp)) =>
0.83/1.07	          app_encode_app(a,$o,app_encode_app(a,app_encode_fun(a,$o),Xp,Xx),Xy)))))).
0.83/1.07	tff(zf_stmt_0, negated_conjecture,
0.83/1.07	  (~
0.83/1.07	    (![P:app_encode_fun(app_encode_fun(a,app_encode_fun(a,$o)),$o),
0.83/1.07	       R:app_encode_fun(a,app_encode_fun(a,$o)),
0.83/1.07	       S:app_encode_fun(a,app_encode_fun(a,$o)),Xx:a,Xy:a]:
0.83/1.07	       ((![Xp:app_encode_fun(a,app_encode_fun(a,$o))]:
0.83/1.07	           (((![Xx0:a,Xy0:a]:
0.83/1.07	                (((![Xp0:app_encode_fun(a,app_encode_fun(a,$o))]:
0.83/1.07	                     (((![Xx1:a,Xy1:a]:
0.83/1.07	                          (app_encode_app(a,$o,
0.83/1.07	                                          app_encode_app(a,
0.83/1.07	                                                         app_encode_fun(a,$o),
0.83/1.07	                                                         R,Xx1),
0.83/1.07	                                          Xy1) =>
0.83/1.07	                           app_encode_app(a,$o,
0.83/1.07	                                          app_encode_app(a,
0.83/1.07	                                                         app_encode_fun(a,$o),
0.83/1.07	                                                         Xp0,Xx1),
0.83/1.07	                                          Xy1))) & 
0.83/1.07	                       app_encode_app(app_encode_fun(a,app_encode_fun(a,$o)),
0.83/1.07	                                      $o,P,Xp0)) =>
0.83/1.07	                      app_encode_app(a,$o,
0.83/1.07	                                     app_encode_app(a,app_encode_fun(a,$o),
0.83/1.07	                                                    Xp0,Xx0),
0.83/1.07	                                     Xy0))) | 
0.83/1.07	                  (![Xp0:app_encode_fun(a,app_encode_fun(a,$o))]:
0.83/1.07	                     (((![Xx1:a,Xy1:a]:
0.83/1.07	                          (app_encode_app(a,$o,
0.83/1.07	                                          app_encode_app(a,
0.83/1.07	                                                         app_encode_fun(a,$o),
0.83/1.07	                                                         S,Xx1),
0.83/1.07	                                          Xy1) =>
0.83/1.07	                           app_encode_app(a,$o,
0.83/1.07	                                          app_encode_app(a,
0.83/1.07	                                                         app_encode_fun(a,$o),
0.83/1.07	                                                         Xp0,Xx1),
0.83/1.07	                                          Xy1))) & 
0.83/1.07	                       app_encode_app(app_encode_fun(a,app_encode_fun(a,$o)),
0.83/1.07	                                      $o,P,Xp0)) =>
0.83/1.07	                      app_encode_app(a,$o,
0.83/1.07	                                     app_encode_app(a,app_encode_fun(a,$o),
0.83/1.07	                                                    Xp0,Xx0),
0.83/1.07	                                     Xy0)))) =>
0.83/1.07	                 app_encode_app(a,$o,
0.83/1.07	                                app_encode_app(a,app_encode_fun(a,$o),Xp,Xx0),
0.83/1.07	                                Xy0))) & 
0.83/1.07	             app_encode_app(app_encode_fun(a,app_encode_fun(a,$o)),$o,P,Xp)) =>
0.83/1.07	            app_encode_app(a,$o,app_encode_app(a,app_encode_fun(a,$o),Xp,Xx),
0.83/1.07	                           Xy))) =>
0.83/1.07	        (![Xp:app_encode_fun(a,app_encode_fun(a,$o))]:
0.83/1.07	           (((![Xx0:a,Xy0:a]:
0.83/1.07	                ((app_encode_app(a,$o,
0.83/1.07	                                 app_encode_app(a,app_encode_fun(a,$o),R,Xx0),
0.83/1.07	                                 Xy0) | 
0.83/1.07	                  app_encode_app(a,$o,
0.83/1.07	                                 app_encode_app(a,app_encode_fun(a,$o),S,Xx0),
0.83/1.07	                                 Xy0)) =>
0.83/1.07	                 app_encode_app(a,$o,
0.83/1.07	                                app_encode_app(a,app_encode_fun(a,$o),Xp,Xx0),
0.83/1.07	                                Xy0))) & 
0.83/1.07	             app_encode_app(app_encode_fun(a,app_encode_fun(a,$o)),$o,P,Xp)) =>
0.83/1.07	            app_encode_app(a,$o,app_encode_app(a,app_encode_fun(a,$o),Xp,Xx),
0.83/1.07	                           Xy))))))).
0.83/1.07	tff('0', plain,
0.83/1.07	    ![X4 : app_encode_fun(a, app_encode_fun(a, $o)), 
0.83/1.07	      X5 : app_encode_fun(a, app_encode_fun(a, $o)), 
0.83/1.07	      X6 : app_encode_fun(a, app_encode_fun(a, $o))]:
0.83/1.07	      (app_encode_app(a, $o, 
0.83/1.07	         app_encode_app(a, app_encode_fun(a, $o), X4, sk_Xx), sk_Xy)
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X4)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xx1(X5)), 
0.83/1.07	           sk_Xy1(X5))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X5)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X5, sk_Xx0(X4)), 
0.83/1.07	           sk_Xy0(X4))
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xx11(X6)), 
0.83/1.07	           sk_Xy11(X6))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X6)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X6, sk_Xx0(X4)), 
0.83/1.07	           sk_Xy0(X4))),
0.83/1.07	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.83/1.07	tff('1', plain,
0.83/1.07	    ![X4 : app_encode_fun(a, app_encode_fun(a, $o))]:
0.83/1.07	      (app_encode_app(a, $o, 
0.83/1.07	         app_encode_app(a, app_encode_fun(a, $o), X4, sk_Xx), sk_Xy)
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X4)
0.83/1.07	       | ~ app_encode_app(a, $o, 
0.83/1.07	             app_encode_app(a, app_encode_fun(a, $o), X4, sk_Xx0(X4)), 
0.83/1.07	             sk_Xy0(X4))),
0.83/1.07	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.83/1.07	tff('2', plain,
0.83/1.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, $o)), 
0.83/1.07	      X1 : app_encode_fun(a, app_encode_fun(a, $o))]:
0.83/1.07	      (~ $true
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X1, sk_Xx0(X0)), 
0.83/1.07	           sk_Xy0(X0))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X1)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xx11(X1)), 
0.83/1.07	           sk_Xy11(X1))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X0)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xx1(X0)), 
0.83/1.07	           sk_Xy1(X0))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X0)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xx), sk_Xy)
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X0)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xx), sk_Xy)),
0.83/1.07	    inference('sup-', [status(thm)], ['0', '1'])).
0.83/1.07	tff('3', plain,
0.83/1.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, $o)), 
0.83/1.07	      X1 : app_encode_fun(a, app_encode_fun(a, $o))]:
0.83/1.07	      (app_encode_app(a, $o, 
0.83/1.07	         app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xx), sk_Xy)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xx1(X0)), 
0.83/1.07	           sk_Xy1(X0))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X0)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xx11(X1)), 
0.83/1.07	           sk_Xy11(X1))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X1)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X1, sk_Xx0(X0)), 
0.83/1.07	           sk_Xy0(X0))),
0.83/1.07	    inference('simplify', [status(thm)], ['2'])).
0.83/1.07	tff('4', plain,
0.83/1.07	    ![X7 : a, X8 : a]:
0.83/1.07	      (app_encode_app(a, $o, 
0.83/1.07	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X7), X8)
0.83/1.07	       | ~ app_encode_app(a, $o, 
0.83/1.07	             app_encode_app(a, app_encode_fun(a, $o), sk_R, X7), X8)),
0.83/1.07	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.83/1.07	tff('5', plain,
0.83/1.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, $o)), 
0.83/1.07	      X1 : app_encode_fun(a, app_encode_fun(a, $o))]:
0.83/1.07	      (~ $true
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X1, sk_Xx0(X0)), 
0.83/1.07	           sk_Xy0(X0))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X1)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xx11(X1)), 
0.83/1.07	           sk_Xy11(X1))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X0)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xx), sk_Xy)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx1(X0)), 
0.83/1.07	           sk_Xy1(X0))),
0.83/1.07	    inference('sup-', [status(thm)], ['3', '4'])).
0.83/1.07	tff('6', plain,
0.83/1.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, $o)), 
0.83/1.07	      X1 : app_encode_fun(a, app_encode_fun(a, $o))]:
0.83/1.07	      (app_encode_app(a, $o, 
0.83/1.07	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx1(X0)), 
0.83/1.07	         sk_Xy1(X0))
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xx), sk_Xy)
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X0)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xx11(X1)), 
0.83/1.07	           sk_Xy11(X1))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X1)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X1, sk_Xx0(X0)), 
0.83/1.07	           sk_Xy0(X0))),
0.83/1.07	    inference('simplify', [status(thm)], ['5'])).
0.83/1.07	tff('7', plain,
0.83/1.07	    ![X4 : app_encode_fun(a, app_encode_fun(a, $o)), 
0.83/1.07	      X5 : app_encode_fun(a, app_encode_fun(a, $o)), 
0.83/1.07	      X6 : app_encode_fun(a, app_encode_fun(a, $o))]:
0.83/1.07	      (app_encode_app(a, $o, 
0.83/1.07	         app_encode_app(a, app_encode_fun(a, $o), X4, sk_Xx), sk_Xy)
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X4)
0.83/1.07	       | ~ app_encode_app(a, $o, 
0.83/1.07	             app_encode_app(a, app_encode_fun(a, $o), X5, sk_Xx1(X5)), 
0.83/1.07	             sk_Xy1(X5))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X5)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X5, sk_Xx0(X4)), 
0.83/1.07	           sk_Xy0(X4))
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xx11(X6)), 
0.83/1.07	           sk_Xy11(X6))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X6)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X6, sk_Xx0(X4)), 
0.83/1.07	           sk_Xy0(X4))),
0.83/1.07	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.83/1.07	tff('8', plain,
0.83/1.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, $o)), 
0.83/1.07	      X1 : app_encode_fun(a, app_encode_fun(a, $o)), 
0.83/1.07	      X2 : app_encode_fun(a, app_encode_fun(a, $o))]:
0.83/1.07	      (~ $true
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X2, sk_Xx0(sk_Xp)), 
0.83/1.07	           sk_Xy0(sk_Xp))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X2)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xx11(X2)), 
0.83/1.07	           sk_Xy11(X2))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, sk_Xp)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx), sk_Xy)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X1, sk_Xx0(X0)), 
0.83/1.07	           sk_Xy0(X0))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X1)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xx11(X1)), 
0.83/1.07	           sk_Xy11(X1))
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0(X0)), 
0.83/1.07	           sk_Xy0(X0))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, sk_Xp)
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X0)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xx), sk_Xy)),
0.83/1.07	    inference('sup-', [status(thm)], ['6', '7'])).
0.83/1.07	tff('9', plain,
0.83/1.07	    app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, sk_P, sk_Xp),
0.83/1.07	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.83/1.07	tff('10', plain,
0.83/1.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, $o)), 
0.83/1.07	      X1 : app_encode_fun(a, app_encode_fun(a, $o)), 
0.83/1.07	      X2 : app_encode_fun(a, app_encode_fun(a, $o))]:
0.83/1.07	      (~ $true
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X2, sk_Xx0(sk_Xp)), 
0.83/1.07	           sk_Xy0(sk_Xp))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X2)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xx11(X2)), 
0.83/1.07	           sk_Xy11(X2))
0.83/1.07	       | ~ $true
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx), sk_Xy)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X1, sk_Xx0(X0)), 
0.83/1.07	           sk_Xy0(X0))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X1)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xx11(X1)), 
0.83/1.07	           sk_Xy11(X1))
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0(X0)), 
0.83/1.07	           sk_Xy0(X0))
0.83/1.07	       | ~ $true
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X0)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xx), sk_Xy)),
0.83/1.07	    inference('demod', [status(thm)], ['8', '9', '9'])).
0.83/1.07	tff('11', plain,
0.83/1.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, $o)), 
0.83/1.07	      X1 : app_encode_fun(a, app_encode_fun(a, $o)), 
0.83/1.07	      X2 : app_encode_fun(a, app_encode_fun(a, $o))]:
0.83/1.07	      (app_encode_app(a, $o, 
0.83/1.07	         app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xx), sk_Xy)
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X0)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0(X0)), 
0.83/1.07	           sk_Xy0(X0))
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xx11(X1)), 
0.83/1.07	           sk_Xy11(X1))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X1)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X1, sk_Xx0(X0)), 
0.83/1.07	           sk_Xy0(X0))
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx), sk_Xy)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xx11(X2)), 
0.83/1.07	           sk_Xy11(X2))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X2)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X2, sk_Xx0(sk_Xp)), 
0.83/1.07	           sk_Xy0(sk_Xp))),
0.83/1.07	    inference('simplify', [status(thm)], ['10'])).
0.83/1.07	tff('12', plain,
0.83/1.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, $o))]:
0.83/1.07	      (~ $true
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X0)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xx11(X0)), 
0.83/1.07	           sk_Xy11(X0))
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx), sk_Xy)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xx0(sk_Xp)), 
0.83/1.07	           sk_Xy0(sk_Xp))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X0)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xx11(X0)), 
0.83/1.07	           sk_Xy11(X0))
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0(sk_Xp)), 
0.83/1.07	           sk_Xy0(sk_Xp))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, sk_Xp)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx), sk_Xy)),
0.83/1.07	    inference('eq_fact', [status(thm)], ['11'])).
0.83/1.07	tff('13', plain,
0.83/1.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, $o))]:
0.83/1.07	      (~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, sk_P, 
0.83/1.07	           sk_Xp)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0(sk_Xp)), 
0.83/1.07	           sk_Xy0(sk_Xp))
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xx0(sk_Xp)), 
0.83/1.07	           sk_Xy0(sk_Xp))
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx), sk_Xy)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xx11(X0)), 
0.83/1.07	           sk_Xy11(X0))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X0)),
0.83/1.07	    inference('simplify', [status(thm)], ['12'])).
0.83/1.07	tff('14', plain,
0.83/1.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, $o))]:
0.83/1.07	      (~ $true
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0(sk_Xp)), 
0.83/1.07	           sk_Xy0(sk_Xp))
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xx0(sk_Xp)), 
0.83/1.07	           sk_Xy0(sk_Xp))
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx), sk_Xy)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xx11(X0)), 
0.83/1.07	           sk_Xy11(X0))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X0)),
0.83/1.07	    inference('demod', [status(thm)], ['13', '9'])).
0.83/1.07	tff('15', plain,
0.83/1.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, $o))]:
0.83/1.07	      (~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, sk_P, 
0.83/1.07	           X0)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xx11(X0)), 
0.83/1.07	           sk_Xy11(X0))
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx), sk_Xy)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xx0(sk_Xp)), 
0.83/1.07	           sk_Xy0(sk_Xp))
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0(sk_Xp)), 
0.83/1.07	           sk_Xy0(sk_Xp))),
0.83/1.07	    inference('simplify', [status(thm)], ['14'])).
0.83/1.07	tff('16', plain,
0.83/1.07	    ~ app_encode_app(a, $o, 
0.83/1.07	        app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx), sk_Xy),
0.83/1.07	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.83/1.07	tff('17', plain,
0.83/1.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, $o))]:
0.83/1.07	      (app_encode_app(a, $o, 
0.83/1.07	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0(sk_Xp)), 
0.83/1.07	         sk_Xy0(sk_Xp))
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xx0(sk_Xp)), 
0.83/1.07	           sk_Xy0(sk_Xp))
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xx11(X0)), 
0.83/1.07	           sk_Xy11(X0))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X0)),
0.83/1.07	    inference('clc', [status(thm)], ['15', '16'])).
0.83/1.07	tff('18', plain,
0.83/1.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, $o))]:
0.83/1.07	      (~ $true
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X0)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xx11(X0)), 
0.83/1.07	           sk_Xy11(X0))
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xx0(sk_Xp)), 
0.83/1.07	           sk_Xy0(sk_Xp))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, sk_Xp)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx), sk_Xy)),
0.83/1.07	    inference('sup-', [status(thm)], ['17', '1'])).
0.83/1.07	tff('19', plain,
0.83/1.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, $o))]:
0.83/1.07	      (~ $true
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X0)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xx11(X0)), 
0.83/1.07	           sk_Xy11(X0))
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xx0(sk_Xp)), 
0.83/1.07	           sk_Xy0(sk_Xp))
0.83/1.07	       | ~ $true
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx), sk_Xy)),
0.83/1.07	    inference('demod', [status(thm)], ['18', '9'])).
0.83/1.07	tff('20', plain,
0.83/1.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, $o))]:
0.83/1.07	      (app_encode_app(a, $o, 
0.83/1.07	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx), sk_Xy)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xx0(sk_Xp)), 
0.83/1.07	           sk_Xy0(sk_Xp))
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xx11(X0)), 
0.83/1.07	           sk_Xy11(X0))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X0)),
0.83/1.07	    inference('simplify', [status(thm)], ['19'])).
0.83/1.07	tff('21', plain,
0.83/1.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, $o))]:
0.83/1.07	      (~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, sk_P, 
0.83/1.07	           X0)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_S, sk_Xx11(X0)), 
0.83/1.07	           sk_Xy11(X0))
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xx0(sk_Xp)), 
0.83/1.07	           sk_Xy0(sk_Xp))),
0.83/1.07	    inference('clc', [status(thm)], ['20', '16'])).
0.83/1.07	tff('22', plain,
0.83/1.07	    ![X7 : a, X8 : a]:
0.83/1.07	      (app_encode_app(a, $o, 
0.83/1.07	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X7), X8)
0.83/1.07	       | ~ app_encode_app(a, $o, 
0.83/1.07	             app_encode_app(a, app_encode_fun(a, $o), sk_S, X7), X8)),
0.83/1.07	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.83/1.07	tff('23', plain,
0.83/1.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, $o))]:
0.83/1.07	      (~ $true
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xx0(sk_Xp)), 
0.83/1.07	           sk_Xy0(sk_Xp))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X0)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx11(X0)), 
0.83/1.07	           sk_Xy11(X0))),
0.83/1.07	    inference('sup-', [status(thm)], ['21', '22'])).
0.83/1.07	tff('24', plain,
0.83/1.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, $o))]:
0.83/1.07	      (app_encode_app(a, $o, 
0.83/1.07	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx11(X0)), 
0.83/1.07	         sk_Xy11(X0))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X0)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xx0(sk_Xp)), 
0.83/1.07	           sk_Xy0(sk_Xp))),
0.83/1.07	    inference('simplify', [status(thm)], ['23'])).
0.83/1.07	tff('25', plain,
0.83/1.07	    ![X4 : app_encode_fun(a, app_encode_fun(a, $o)), 
0.83/1.07	      X5 : app_encode_fun(a, app_encode_fun(a, $o)), 
0.83/1.07	      X6 : app_encode_fun(a, app_encode_fun(a, $o))]:
0.83/1.07	      (app_encode_app(a, $o, 
0.83/1.07	         app_encode_app(a, app_encode_fun(a, $o), X4, sk_Xx), sk_Xy)
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X4)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xx1(X5)), 
0.83/1.07	           sk_Xy1(X5))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X5)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X5, sk_Xx0(X4)), 
0.83/1.07	           sk_Xy0(X4))
0.83/1.07	       | ~ app_encode_app(a, $o, 
0.83/1.07	             app_encode_app(a, app_encode_fun(a, $o), X6, sk_Xx11(X6)), 
0.83/1.07	             sk_Xy11(X6))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X6)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X6, sk_Xx0(X4)), 
0.83/1.07	           sk_Xy0(X4))),
0.83/1.07	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.83/1.07	tff('26', plain,
0.83/1.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, $o)), 
0.83/1.07	      X1 : app_encode_fun(a, app_encode_fun(a, $o))]:
0.83/1.07	      (~ $true
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0(sk_Xp)), 
0.83/1.07	           sk_Xy0(sk_Xp))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, sk_Xp)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0(X0)), 
0.83/1.07	           sk_Xy0(X0))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, sk_Xp)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X1, sk_Xx0(X0)), 
0.83/1.07	           sk_Xy0(X0))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X1)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xx1(X1)), 
0.83/1.07	           sk_Xy1(X1))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X0)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xx), sk_Xy)),
0.83/1.07	    inference('sup-', [status(thm)], ['24', '25'])).
0.83/1.07	tff('27', plain,
0.83/1.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, $o)), 
0.83/1.07	      X1 : app_encode_fun(a, app_encode_fun(a, $o))]:
0.83/1.07	      (~ $true
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0(sk_Xp)), 
0.83/1.07	           sk_Xy0(sk_Xp))
0.83/1.07	       | ~ $true
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0(X0)), 
0.83/1.07	           sk_Xy0(X0))
0.83/1.07	       | ~ $true
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X1, sk_Xx0(X0)), 
0.83/1.07	           sk_Xy0(X0))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X1)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xx1(X1)), 
0.83/1.07	           sk_Xy1(X1))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X0)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xx), sk_Xy)),
0.83/1.07	    inference('demod', [status(thm)], ['26', '9', '9'])).
0.83/1.07	tff('28', plain,
0.83/1.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, $o)), 
0.83/1.07	      X1 : app_encode_fun(a, app_encode_fun(a, $o))]:
0.83/1.07	      (app_encode_app(a, $o, 
0.83/1.07	         app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xx), sk_Xy)
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X0)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xx1(X1)), 
0.83/1.07	           sk_Xy1(X1))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X1)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X1, sk_Xx0(X0)), 
0.83/1.07	           sk_Xy0(X0))
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0(X0)), 
0.83/1.07	           sk_Xy0(X0))
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0(sk_Xp)), 
0.83/1.07	           sk_Xy0(sk_Xp))),
0.83/1.07	    inference('simplify', [status(thm)], ['27'])).
0.83/1.07	tff('29', plain,
0.83/1.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, $o))]:
0.83/1.07	      (~ $true
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0(sk_Xp)), 
0.83/1.07	           sk_Xy0(sk_Xp))
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xx0(sk_Xp)), 
0.83/1.07	           sk_Xy0(sk_Xp))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X0)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xx1(X0)), 
0.83/1.07	           sk_Xy1(X0))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, sk_Xp)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx), sk_Xy)),
0.83/1.07	    inference('eq_fact', [status(thm)], ['28'])).
0.83/1.07	tff('30', plain,
0.83/1.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, $o))]:
0.83/1.07	      (app_encode_app(a, $o, 
0.83/1.07	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx), sk_Xy)
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, sk_Xp)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xx1(X0)), 
0.83/1.07	           sk_Xy1(X0))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X0)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xx0(sk_Xp)), 
0.83/1.07	           sk_Xy0(sk_Xp))
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0(sk_Xp)), 
0.83/1.07	           sk_Xy0(sk_Xp))),
0.83/1.07	    inference('simplify', [status(thm)], ['29'])).
0.83/1.07	tff('31', plain,
0.83/1.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, $o))]:
0.83/1.07	      (app_encode_app(a, $o, 
0.83/1.07	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx), sk_Xy)
0.83/1.07	       | ~ $true
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xx1(X0)), 
0.83/1.07	           sk_Xy1(X0))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X0)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xx0(sk_Xp)), 
0.83/1.07	           sk_Xy0(sk_Xp))
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0(sk_Xp)), 
0.83/1.07	           sk_Xy0(sk_Xp))),
0.83/1.07	    inference('demod', [status(thm)], ['30', '9'])).
0.83/1.07	tff('32', plain,
0.83/1.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, $o))]:
0.83/1.07	      (app_encode_app(a, $o, 
0.83/1.07	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0(sk_Xp)), 
0.83/1.07	         sk_Xy0(sk_Xp))
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xx0(sk_Xp)), 
0.83/1.07	           sk_Xy0(sk_Xp))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X0)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xx1(X0)), 
0.83/1.07	           sk_Xy1(X0))
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx), sk_Xy)),
0.83/1.07	    inference('simplify', [status(thm)], ['31'])).
0.83/1.07	tff('33', plain,
0.83/1.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, $o))]:
0.83/1.07	      (app_encode_app(a, $o, 
0.83/1.07	         app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xx1(X0)), 
0.83/1.07	         sk_Xy1(X0))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X0)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xx0(sk_Xp)), 
0.83/1.07	           sk_Xy0(sk_Xp))
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0(sk_Xp)), 
0.83/1.07	           sk_Xy0(sk_Xp))),
0.83/1.07	    inference('clc', [status(thm)], ['32', '16'])).
0.83/1.07	tff('34', plain,
0.83/1.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, $o))]:
0.83/1.07	      (~ $true
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xx0(sk_Xp)), 
0.83/1.07	           sk_Xy0(sk_Xp))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X0)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xx1(X0)), 
0.83/1.07	           sk_Xy1(X0))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, sk_Xp)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx), sk_Xy)),
0.83/1.07	    inference('sup-', [status(thm)], ['33', '1'])).
0.83/1.07	tff('35', plain,
0.83/1.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, $o))]:
0.83/1.07	      (~ $true
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xx0(sk_Xp)), 
0.83/1.07	           sk_Xy0(sk_Xp))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X0)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xx1(X0)), 
0.83/1.07	           sk_Xy1(X0))
0.83/1.07	       | ~ $true
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx), sk_Xy)),
0.83/1.07	    inference('demod', [status(thm)], ['34', '9'])).
0.83/1.07	tff('36', plain,
0.83/1.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, $o))]:
0.83/1.07	      (app_encode_app(a, $o, 
0.83/1.07	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx), sk_Xy)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xx1(X0)), 
0.83/1.07	           sk_Xy1(X0))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X0)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xx0(sk_Xp)), 
0.83/1.07	           sk_Xy0(sk_Xp))),
0.83/1.07	    inference('simplify', [status(thm)], ['35'])).
0.83/1.07	tff('37', plain,
0.83/1.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, $o))]:
0.83/1.07	      (app_encode_app(a, $o, 
0.83/1.07	         app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xx0(sk_Xp)), 
0.83/1.07	         sk_Xy0(sk_Xp))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X0)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_R, sk_Xx1(X0)), 
0.83/1.07	           sk_Xy1(X0))),
0.83/1.07	    inference('clc', [status(thm)], ['36', '16'])).
0.83/1.07	tff('38', plain,
0.83/1.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, $o))]:
0.83/1.07	      (~ $true
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X0)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xx0(sk_Xp)), 
0.83/1.07	           sk_Xy0(sk_Xp))
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx1(X0)), 
0.83/1.07	           sk_Xy1(X0))),
0.83/1.07	    inference('sup-', [status(thm)], ['37', '4'])).
0.83/1.07	tff('39', plain,
0.83/1.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, $o))]:
0.83/1.07	      (app_encode_app(a, $o, 
0.83/1.07	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx1(X0)), 
0.83/1.07	         sk_Xy1(X0))
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xx0(sk_Xp)), 
0.83/1.07	           sk_Xy0(sk_Xp))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X0)),
0.83/1.07	    inference('simplify', [status(thm)], ['38'])).
0.83/1.07	tff('40', plain,
0.83/1.07	    ![X4 : app_encode_fun(a, app_encode_fun(a, $o)), 
0.83/1.07	      X5 : app_encode_fun(a, app_encode_fun(a, $o)), 
0.83/1.07	      X6 : app_encode_fun(a, app_encode_fun(a, $o))]:
0.83/1.07	      (app_encode_app(a, $o, 
0.83/1.07	         app_encode_app(a, app_encode_fun(a, $o), X4, sk_Xx), sk_Xy)
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X4)
0.83/1.07	       | ~ app_encode_app(a, $o, 
0.83/1.07	             app_encode_app(a, app_encode_fun(a, $o), X5, sk_Xx1(X5)), 
0.83/1.07	             sk_Xy1(X5))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X5)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X5, sk_Xx0(X4)), 
0.83/1.07	           sk_Xy0(X4))
0.83/1.07	       | ~ app_encode_app(a, $o, 
0.83/1.07	             app_encode_app(a, app_encode_fun(a, $o), X6, sk_Xx11(X6)), 
0.83/1.07	             sk_Xy11(X6))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X6)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X6, sk_Xx0(X4)), 
0.83/1.07	           sk_Xy0(X4))),
0.83/1.07	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.83/1.07	tff('41', plain,
0.83/1.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, $o)), 
0.83/1.07	      X1 : app_encode_fun(a, app_encode_fun(a, $o))]:
0.83/1.07	      (~ $true
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, sk_Xp)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0(sk_Xp)), 
0.83/1.07	           sk_Xy0(sk_Xp))
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X1, sk_Xx0(X0)), 
0.83/1.07	           sk_Xy0(X0))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X1)
0.83/1.07	       | ~ app_encode_app(a, $o, 
0.83/1.07	             app_encode_app(a, app_encode_fun(a, $o), X1, sk_Xx11(X1)), 
0.83/1.07	             sk_Xy11(X1))
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0(X0)), 
0.83/1.07	           sk_Xy0(X0))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, sk_Xp)
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X0)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xx), sk_Xy)),
0.83/1.07	    inference('sup-', [status(thm)], ['39', '40'])).
0.83/1.07	tff('42', plain,
0.83/1.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, $o)), 
0.83/1.07	      X1 : app_encode_fun(a, app_encode_fun(a, $o))]:
0.83/1.07	      (~ $true
0.83/1.07	       | ~ $true
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0(sk_Xp)), 
0.83/1.07	           sk_Xy0(sk_Xp))
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X1, sk_Xx0(X0)), 
0.83/1.07	           sk_Xy0(X0))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X1)
0.83/1.07	       | ~ app_encode_app(a, $o, 
0.83/1.07	             app_encode_app(a, app_encode_fun(a, $o), X1, sk_Xx11(X1)), 
0.83/1.07	             sk_Xy11(X1))
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0(X0)), 
0.83/1.07	           sk_Xy0(X0))
0.83/1.07	       | ~ $true
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X0)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xx), sk_Xy)),
0.83/1.07	    inference('demod', [status(thm)], ['41', '9', '9'])).
0.83/1.07	tff('43', plain,
0.83/1.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, $o)), 
0.83/1.07	      X1 : app_encode_fun(a, app_encode_fun(a, $o))]:
0.83/1.07	      (app_encode_app(a, $o, 
0.83/1.07	         app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xx), sk_Xy)
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X0)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0(X0)), 
0.83/1.07	           sk_Xy0(X0))
0.83/1.07	       | ~ app_encode_app(a, $o, 
0.83/1.07	             app_encode_app(a, app_encode_fun(a, $o), X1, sk_Xx11(X1)), 
0.83/1.07	             sk_Xy11(X1))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X1)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X1, sk_Xx0(X0)), 
0.83/1.07	           sk_Xy0(X0))
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0(sk_Xp)), 
0.83/1.07	           sk_Xy0(sk_Xp))),
0.83/1.07	    inference('simplify', [status(thm)], ['42'])).
0.83/1.07	tff('44', plain,
0.83/1.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, $o))]:
0.83/1.07	      (~ $true
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0(sk_Xp)), 
0.83/1.07	           sk_Xy0(sk_Xp))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, sk_Xp)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0(sk_Xp)), 
0.83/1.07	           sk_Xy0(sk_Xp))
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0(X0)), 
0.83/1.07	           sk_Xy0(X0))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, sk_Xp)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0(X0)), 
0.83/1.07	           sk_Xy0(X0))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X0)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xx), sk_Xy)),
0.83/1.07	    inference('sup-', [status(thm)], ['24', '43'])).
0.83/1.07	tff('45', plain,
0.83/1.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, $o))]:
0.83/1.07	      (~ $true
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0(sk_Xp)), 
0.83/1.07	           sk_Xy0(sk_Xp))
0.83/1.07	       | ~ $true
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0(sk_Xp)), 
0.83/1.07	           sk_Xy0(sk_Xp))
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0(X0)), 
0.83/1.07	           sk_Xy0(X0))
0.83/1.07	       | ~ $true
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0(X0)), 
0.83/1.07	           sk_Xy0(X0))
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X0)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xx), sk_Xy)),
0.83/1.07	    inference('demod', [status(thm)], ['44', '9', '9'])).
0.83/1.07	tff('46', plain,
0.83/1.07	    ![X0 : app_encode_fun(a, app_encode_fun(a, $o))]:
0.83/1.07	      (app_encode_app(a, $o, 
0.83/1.07	         app_encode_app(a, app_encode_fun(a, $o), X0, sk_Xx), sk_Xy)
0.83/1.07	       | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, 
0.83/1.07	             sk_P, X0)
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0(X0)), 
0.83/1.07	           sk_Xy0(X0))
0.83/1.07	       | app_encode_app(a, $o, 
0.83/1.07	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0(sk_Xp)), 
0.83/1.07	           sk_Xy0(sk_Xp))),
0.83/1.07	    inference('simplify', [status(thm)], ['45'])).
0.83/1.07	tff('47', plain,
0.83/1.07	    (~ $true
0.83/1.07	     | app_encode_app(a, $o, 
0.83/1.07	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0(sk_Xp)), 
0.83/1.07	         sk_Xy0(sk_Xp))
0.83/1.07	     | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, sk_P, 
0.83/1.07	           sk_Xp)
0.83/1.07	     | app_encode_app(a, $o, 
0.83/1.07	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx), sk_Xy)),
0.83/1.07	    inference('eq_fact', [status(thm)], ['46'])).
0.83/1.07	tff('48', plain,
0.83/1.07	    (app_encode_app(a, $o, 
0.83/1.07	       app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx), sk_Xy)
0.83/1.07	     | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, sk_P, 
0.83/1.07	           sk_Xp)
0.83/1.07	     | app_encode_app(a, $o, 
0.83/1.07	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0(sk_Xp)), 
0.83/1.07	         sk_Xy0(sk_Xp))),
0.83/1.07	    inference('simplify', [status(thm)], ['47'])).
0.83/1.07	tff('49', plain,
0.83/1.07	    (app_encode_app(a, $o, 
0.83/1.07	       app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx), sk_Xy)
0.83/1.07	     | ~ $true
0.83/1.07	     | app_encode_app(a, $o, 
0.83/1.07	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0(sk_Xp)), 
0.83/1.07	         sk_Xy0(sk_Xp))),
0.83/1.07	    inference('demod', [status(thm)], ['48', '9'])).
0.83/1.07	tff('50', plain,
0.83/1.07	    (app_encode_app(a, $o, 
0.83/1.07	       app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0(sk_Xp)), 
0.83/1.07	       sk_Xy0(sk_Xp))
0.83/1.07	     | app_encode_app(a, $o, 
0.83/1.07	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx), sk_Xy)),
0.83/1.07	    inference('simplify', [status(thm)], ['49'])).
0.83/1.07	tff('51', plain,
0.83/1.07	    app_encode_app(a, $o, 
0.83/1.07	      app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0(sk_Xp)), 
0.83/1.07	      sk_Xy0(sk_Xp)),
0.83/1.07	    inference('clc', [status(thm)], ['50', '16'])).
0.83/1.07	tff('52', plain,
0.83/1.07	    (~ $true
0.83/1.07	     | ~ app_encode_app(app_encode_fun(a, app_encode_fun(a, $o)), $o, sk_P, 
0.83/1.07	           sk_Xp)
0.83/1.07	     | app_encode_app(a, $o, 
0.83/1.07	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx), sk_Xy)),
0.83/1.07	    inference('sup-', [status(thm)], ['51', '1'])).
0.83/1.07	tff('53', plain,
0.83/1.07	    (~ $true
0.83/1.07	     | ~ $true
0.83/1.07	     | app_encode_app(a, $o, 
0.83/1.07	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx), sk_Xy)),
0.83/1.07	    inference('demod', [status(thm)], ['52', '9'])).
0.83/1.07	tff('54', plain,
0.83/1.07	    app_encode_app(a, $o, 
0.83/1.07	      app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx), sk_Xy),
0.83/1.07	    inference('simplify', [status(thm)], ['53'])).
0.83/1.07	tff('55', plain, ~ $true, inference('sup-', [status(thm)], ['54', '16'])).
0.83/1.07	tff('56', plain, $false, inference('simplify', [status(thm)], ['55'])).
0.83/1.07	
0.83/1.07	% SZS output end Refutation
0.83/1.07	EOF
