0.00/0.00	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : app
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : kbo
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n107.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 17:25:10 CST 2018
14.53/14.77	% done 1210 iterations in 14.575s
14.53/14.77	% SZS status Theorem for 'stdin'
14.53/14.77	% SZS output start Refutation
14.59/14.77	tff(zf_stmt_7, conjecture,
14.59/14.77	  (((app_encode_app(a,a,cL,cZ) = cZ) & (app_encode_app(a,a,cR,cZ) = cZ) & 
14.59/14.77	    (![Xx:a,Xy:a]:
14.59/14.77	       (app_encode_app(a,a,cL,
14.59/14.77	                       app_encode_app(a,a,
14.59/14.77	                                      app_encode_app(a,app_encode_fun(a,a),
14.59/14.77	                                                     cP,Xx),
14.59/14.77	                                      Xy)) =
14.59/14.77	        Xx)) & 
14.59/14.77	    (![Xx:a,Xy:a]:
14.59/14.77	       (app_encode_app(a,a,cR,
14.59/14.77	                       app_encode_app(a,a,
14.59/14.77	                                      app_encode_app(a,app_encode_fun(a,a),
14.59/14.77	                                                     cP,Xx),
14.59/14.77	                                      Xy)) =
14.59/14.77	        Xy)) & 
14.59/14.77	    (![Xt:a]:
14.59/14.77	       ((Xt != cZ) <=>
14.59/14.77	        (Xt =
14.59/14.77	         app_encode_app(a,a,
14.59/14.77	                        app_encode_app(a,app_encode_fun(a,a),cP,
14.59/14.77	                                       app_encode_app(a,a,cL,Xt)),
14.59/14.77	                        app_encode_app(a,a,cR,Xt))))) & 
14.59/14.77	    (![X:app_encode_fun(a,$o)]:
14.59/14.77	       ((![Xt:a,Xu:a]:
14.59/14.77	           (app_encode_app(a,$o,X,
14.59/14.77	                           app_encode_app(a,a,
14.59/14.77	                                          app_encode_app(a,
14.59/14.77	                                                         app_encode_fun(a,a),
14.59/14.77	                                                         cP,Xt),
14.59/14.77	                                          Xu)) =>
14.59/14.77	            (((Xt = cZ) <=> (Xu = cZ)) & 
14.59/14.77	             app_encode_app(a,$o,X,
14.59/14.77	                            app_encode_app(a,a,
14.59/14.77	                                           app_encode_app(a,
14.59/14.77	                                                          app_encode_fun(a,a),
14.59/14.77	                                                          cP,
14.59/14.77	                                                          app_encode_app(
14.59/14.77	                                                          a,a,cL,Xt)),
14.59/14.77	                                           app_encode_app(a,a,cL,Xu))) & 
14.59/14.77	             app_encode_app(a,$o,X,
14.59/14.77	                            app_encode_app(a,a,
14.59/14.77	                                           app_encode_app(a,
14.59/14.77	                                                          app_encode_fun(a,a),
14.59/14.77	                                                          cP,
14.59/14.77	                                                          app_encode_app(
14.59/14.77	                                                          a,a,cR,Xt)),
14.59/14.77	                                           app_encode_app(a,a,cR,Xu)))))) =>
14.59/14.77	        (![Xt:a,Xu:a]:
14.59/14.77	           (app_encode_app(a,$o,X,
14.59/14.77	                           app_encode_app(a,a,
14.59/14.77	                                          app_encode_app(a,
14.59/14.77	                                                         app_encode_fun(a,a),
14.59/14.77	                                                         cP,Xt),
14.59/14.77	                                          Xu)) =>
14.59/14.77	            (Xt = Xu)))))) =>
14.59/14.77	   (![Xx:a,Xy:a]:
14.59/14.77	      ((?[X:app_encode_fun(a,$o)]:
14.59/14.77	          (app_encode_app(a,$o,X,
14.59/14.77	                          app_encode_app(a,a,
14.59/14.77	                                         app_encode_app(a,
14.59/14.77	                                                        app_encode_fun(a,a),
14.59/14.77	                                                        cP,Xx),
14.59/14.77	                                         Xy)) & 
14.59/14.77	           (![Xt:a,Xu:a]:
14.59/14.77	              (app_encode_app(a,$o,X,
14.59/14.77	                              app_encode_app(a,a,
14.59/14.77	                                             app_encode_app(a,
14.59/14.77	                                                            app_encode_fun(
14.59/14.77	                                                            a,a),cP,Xt),
14.59/14.77	                                             Xu)) =>
14.59/14.77	               (((Xu = cZ) => (Xt = cZ)) & 
14.59/14.77	                app_encode_app(a,$o,X,
14.59/14.77	                               app_encode_app(a,a,
14.59/14.77	                                              app_encode_app(a,
14.59/14.77	                                                             app_encode_fun(
14.59/14.77	                                                             a,a),cP,
14.59/14.77	                                                             app_encode_app(
14.59/14.77	                                                             a,a,cL,Xt)),
14.59/14.77	                                              app_encode_app(a,a,cL,Xu))) & 
14.59/14.77	                app_encode_app(a,$o,X,
14.59/14.77	                               app_encode_app(a,a,
14.59/14.77	                                              app_encode_app(a,
14.59/14.77	                                                             app_encode_fun(
14.59/14.77	                                                             a,a),cP,
14.59/14.77	                                                             app_encode_app(
14.59/14.77	                                                             a,a,cR,Xt)),
14.59/14.77	                                              app_encode_app(a,a,cR,Xu)))))))) =>
14.59/14.77	       (?[X:app_encode_fun(a,$o)]:
14.59/14.77	          (app_encode_app(a,$o,X,
14.59/14.77	                          app_encode_app(a,a,
14.59/14.77	                                         app_encode_app(a,
14.59/14.77	                                                        app_encode_fun(a,a),
14.59/14.77	                                                        cP,
14.59/14.77	                                                        app_encode_app(
14.59/14.77	                                                        a,a,cL,Xx)),
14.59/14.77	                                         app_encode_app(a,a,cL,Xy))) & 
14.59/14.77	           (![Xt:a,Xu:a]:
14.59/14.77	              (app_encode_app(a,$o,X,
14.59/14.77	                              app_encode_app(a,a,
14.59/14.77	                                             app_encode_app(a,
14.59/14.77	                                                            app_encode_fun(
14.59/14.77	                                                            a,a),cP,Xt),
14.59/14.77	                                             Xu)) =>
14.59/14.77	               (((Xu = cZ) => (Xt = cZ)) & 
14.59/14.77	                app_encode_app(a,$o,X,
14.59/14.77	                               app_encode_app(a,a,
14.59/14.77	                                              app_encode_app(a,
14.59/14.77	                                                             app_encode_fun(
14.59/14.77	                                                             a,a),cP,
14.59/14.77	                                                             app_encode_app(
14.59/14.77	                                                             a,a,cL,Xt)),
14.59/14.77	                                              app_encode_app(a,a,cL,Xu))) & 
14.59/14.77	                app_encode_app(a,$o,X,
14.59/14.77	                               app_encode_app(a,a,
14.59/14.77	                                              app_encode_app(a,
14.59/14.77	                                                             app_encode_fun(
14.59/14.77	                                                             a,a),cP,
14.59/14.77	                                                             app_encode_app(
14.59/14.77	                                                             a,a,cR,Xt)),
14.59/14.77	                                              app_encode_app(a,a,cR,Xu)))))))))))).
14.59/14.77	tff(zf_stmt_0, negated_conjecture,
14.59/14.77	  (~
14.59/14.77	    (((app_encode_app(a,a,cL,cZ) = cZ) & (app_encode_app(a,a,cR,cZ) = cZ) & 
14.59/14.77	      (![Xx:a,Xy:a]:
14.59/14.77	         (app_encode_app(a,a,cL,
14.59/14.77	                         app_encode_app(a,a,
14.59/14.77	                                        app_encode_app(a,app_encode_fun(a,a),
14.59/14.77	                                                       cP,Xx),
14.59/14.77	                                        Xy)) =
14.59/14.77	          Xx)) & 
14.59/14.77	      (![Xx:a,Xy:a]:
14.59/14.77	         (app_encode_app(a,a,cR,
14.59/14.77	                         app_encode_app(a,a,
14.59/14.77	                                        app_encode_app(a,app_encode_fun(a,a),
14.59/14.77	                                                       cP,Xx),
14.59/14.77	                                        Xy)) =
14.59/14.77	          Xy)) & 
14.59/14.77	      (![Xt:a]:
14.59/14.77	         ((Xt != cZ) <=>
14.59/14.77	          (Xt =
14.59/14.77	           app_encode_app(a,a,
14.59/14.77	                          app_encode_app(a,app_encode_fun(a,a),cP,
14.59/14.77	                                         app_encode_app(a,a,cL,Xt)),
14.59/14.77	                          app_encode_app(a,a,cR,Xt))))) & 
14.59/14.77	      (![X:app_encode_fun(a,$o)]:
14.59/14.77	         ((![Xt:a,Xu:a]:
14.59/14.77	             (app_encode_app(a,$o,X,
14.59/14.77	                             app_encode_app(a,a,
14.59/14.77	                                            app_encode_app(a,
14.59/14.77	                                                           app_encode_fun(
14.59/14.77	                                                           a,a),cP,Xt),
14.59/14.77	                                            Xu)) =>
14.59/14.77	              (((Xt = cZ) <=> (Xu = cZ)) & 
14.59/14.77	               app_encode_app(a,$o,X,
14.59/14.77	                              app_encode_app(a,a,
14.59/14.77	                                             app_encode_app(a,
14.59/14.77	                                                            app_encode_fun(
14.59/14.77	                                                            a,a),cP,
14.59/14.77	                                                            app_encode_app(
14.59/14.77	                                                            a,a,cL,Xt)),
14.59/14.77	                                             app_encode_app(a,a,cL,Xu))) & 
14.59/14.77	               app_encode_app(a,$o,X,
14.59/14.77	                              app_encode_app(a,a,
14.59/14.77	                                             app_encode_app(a,
14.59/14.77	                                                            app_encode_fun(
14.59/14.77	                                                            a,a),cP,
14.59/14.77	                                                            app_encode_app(
14.59/14.77	                                                            a,a,cR,Xt)),
14.59/14.77	                                             app_encode_app(a,a,cR,Xu)))))) =>
14.59/14.77	          (![Xt:a,Xu:a]:
14.59/14.77	             (app_encode_app(a,$o,X,
14.59/14.77	                             app_encode_app(a,a,
14.59/14.77	                                            app_encode_app(a,
14.59/14.77	                                                           app_encode_fun(
14.59/14.77	                                                           a,a),cP,Xt),
14.59/14.77	                                            Xu)) =>
14.59/14.77	              (Xt = Xu)))))) =>
14.59/14.77	     (![Xx:a,Xy:a]:
14.59/14.77	        ((?[X:app_encode_fun(a,$o)]:
14.59/14.77	            (app_encode_app(a,$o,X,
14.59/14.77	                            app_encode_app(a,a,
14.59/14.77	                                           app_encode_app(a,
14.59/14.77	                                                          app_encode_fun(a,a),
14.59/14.77	                                                          cP,Xx),
14.59/14.77	                                           Xy)) & 
14.59/14.77	             (![Xt:a,Xu:a]:
14.59/14.77	                (app_encode_app(a,$o,X,
14.59/14.77	                                app_encode_app(a,a,
14.59/14.77	                                               app_encode_app(a,
14.59/14.77	                                                              app_encode_fun(
14.59/14.77	                                                              a,a),cP,Xt),
14.59/14.77	                                               Xu)) =>
14.59/14.77	                 (((Xu = cZ) => (Xt = cZ)) & 
14.59/14.77	                  app_encode_app(a,$o,X,
14.59/14.77	                                 app_encode_app(a,a,
14.59/14.77	                                                app_encode_app(a,
14.59/14.77	                                                               app_encode_fun(
14.59/14.77	                                                               a,a),cP,
14.59/14.77	                                                               app_encode_app(
14.59/14.77	                                                               a,a,cL,Xt)),
14.59/14.77	                                                app_encode_app(a,a,cL,Xu))) & 
14.59/14.77	                  app_encode_app(a,$o,X,
14.59/14.77	                                 app_encode_app(a,a,
14.59/14.77	                                                app_encode_app(a,
14.59/14.77	                                                               app_encode_fun(
14.59/14.77	                                                               a,a),cP,
14.59/14.77	                                                               app_encode_app(
14.59/14.77	                                                               a,a,cR,Xt)),
14.59/14.77	                                                app_encode_app(a,a,cR,Xu)))))))) =>
14.59/14.77	         (?[X:app_encode_fun(a,$o)]:
14.59/14.77	            (app_encode_app(a,$o,X,
14.59/14.77	                            app_encode_app(a,a,
14.59/14.77	                                           app_encode_app(a,
14.59/14.77	                                                          app_encode_fun(a,a),
14.59/14.77	                                                          cP,
14.59/14.77	                                                          app_encode_app(
14.59/14.77	                                                          a,a,cL,Xx)),
14.59/14.77	                                           app_encode_app(a,a,cL,Xy))) & 
14.59/14.77	             (![Xt:a,Xu:a]:
14.59/14.77	                (app_encode_app(a,$o,X,
14.59/14.77	                                app_encode_app(a,a,
14.59/14.77	                                               app_encode_app(a,
14.59/14.77	                                                              app_encode_fun(
14.59/14.77	                                                              a,a),cP,Xt),
14.59/14.77	                                               Xu)) =>
14.59/14.77	                 (((Xu = cZ) => (Xt = cZ)) & 
14.59/14.77	                  app_encode_app(a,$o,X,
14.59/14.77	                                 app_encode_app(a,a,
14.59/14.77	                                                app_encode_app(a,
14.59/14.77	                                                               app_encode_fun(
14.59/14.77	                                                               a,a),cP,
14.59/14.77	                                                               app_encode_app(
14.59/14.77	                                                               a,a,cL,Xt)),
14.59/14.77	                                                app_encode_app(a,a,cL,Xu))) & 
14.59/14.77	                  app_encode_app(a,$o,X,
14.59/14.77	                                 app_encode_app(a,a,
14.59/14.77	                                                app_encode_app(a,
14.59/14.77	                                                               app_encode_fun(
14.59/14.77	                                                               a,a),cP,
14.59/14.77	                                                               app_encode_app(
14.59/14.77	                                                               a,a,cR,Xt)),
14.59/14.77	                                                app_encode_app(a,a,cR,Xu))))))))))))).
14.59/14.77	tff('0', plain,
14.59/14.77	    ![X10 : a, X11 : a]:
14.59/14.77	      (app_encode_app(a, $o, sk_X, 
14.59/14.77	         app_encode_app(a, a, 
14.59/14.77	           app_encode_app(a, app_encode_fun(a, a), cP, 
14.59/14.77	             app_encode_app(a, a, cL, X11)), app_encode_app(a, a, cL, X10)))
14.59/14.77	       | ~ app_encode_app(a, $o, sk_X, 
14.59/14.77	             app_encode_app(a, a, 
14.59/14.77	               app_encode_app(a, app_encode_fun(a, a), cP, X11), X10))),
14.59/14.77	    inference('cnf', [status(esa)], [zf_stmt_0])).
14.59/14.77	tff('1', plain,
14.59/14.77	    ![X9 : app_encode_fun(a, $o)]:
14.59/14.77	      (~ app_encode_app(a, $o, X9, 
14.59/14.77	           app_encode_app(a, a, 
14.59/14.77	             app_encode_app(a, app_encode_fun(a, a), cP, 
14.59/14.77	               app_encode_app(a, a, cL, sk_Xx)), 
14.59/14.77	             app_encode_app(a, a, cL, sk_Xy)))
14.59/14.77	       | app_encode_app(a, $o, X9, 
14.59/14.77	           app_encode_app(a, a, 
14.59/14.77	             app_encode_app(a, app_encode_fun(a, a), cP, sk_Xt(X9)), 
14.59/14.77	             sk_Xu(X9)))),
14.59/14.77	    inference('cnf', [status(esa)], [zf_stmt_0])).
14.59/14.77	tff('2', plain,
14.59/14.77	    (~ $true
14.59/14.77	     | ~ app_encode_app(a, $o, sk_X, 
14.59/14.77	           app_encode_app(a, a, 
14.59/14.77	             app_encode_app(a, app_encode_fun(a, a), cP, sk_Xx), sk_Xy))
14.59/14.77	     | app_encode_app(a, $o, sk_X, 
14.59/14.77	         app_encode_app(a, a, 
14.59/14.77	           app_encode_app(a, app_encode_fun(a, a), cP, sk_Xt(sk_X)), 
14.59/14.77	           sk_Xu(sk_X)))),
14.59/14.77	    inference('sup-', [status(thm)], ['0', '1'])).
14.59/14.77	tff('3', plain,
14.59/14.77	    app_encode_app(a, $o, sk_X, 
14.59/14.77	      app_encode_app(a, a, 
14.59/14.77	        app_encode_app(a, app_encode_fun(a, a), cP, sk_Xx), sk_Xy)),
14.59/14.77	    inference('cnf', [status(esa)], [zf_stmt_0])).
14.59/14.77	tff('4', plain,
14.59/14.77	    (~ $true
14.59/14.77	     | ~ $true
14.59/14.77	     | app_encode_app(a, $o, sk_X, 
14.59/14.77	         app_encode_app(a, a, 
14.59/14.77	           app_encode_app(a, app_encode_fun(a, a), cP, sk_Xt(sk_X)), 
14.59/14.77	           sk_Xu(sk_X)))),
14.59/14.77	    inference('demod', [status(thm)], ['2', '3'])).
14.59/14.77	tff('5', plain,
14.59/14.77	    app_encode_app(a, $o, sk_X, 
14.59/14.77	      app_encode_app(a, a, 
14.59/14.77	        app_encode_app(a, app_encode_fun(a, a), cP, sk_Xt(sk_X)), 
14.59/14.77	        sk_Xu(sk_X))),
14.59/14.77	    inference('simplify', [status(thm)], ['4'])).
14.59/14.77	tff('6', plain,
14.59/14.77	    ![X10 : a, X11 : a]:
14.59/14.77	      (app_encode_app(a, $o, sk_X, 
14.59/14.77	         app_encode_app(a, a, 
14.59/14.77	           app_encode_app(a, app_encode_fun(a, a), cP, 
14.59/14.77	             app_encode_app(a, a, cR, X11)), app_encode_app(a, a, cR, X10)))
14.59/14.77	       | ~ app_encode_app(a, $o, sk_X, 
14.59/14.77	             app_encode_app(a, a, 
14.59/14.77	               app_encode_app(a, app_encode_fun(a, a), cP, X11), X10))),
14.59/14.77	    inference('cnf', [status(esa)], [zf_stmt_0])).
14.59/14.77	tff('7', plain,
14.59/14.77	    ![X9 : app_encode_fun(a, $o)]:
14.59/14.77	      (~ app_encode_app(a, $o, X9, 
14.59/14.77	           app_encode_app(a, a, 
14.59/14.77	             app_encode_app(a, app_encode_fun(a, a), cP, 
14.59/14.77	               app_encode_app(a, a, cL, sk_Xx)), 
14.59/14.77	             app_encode_app(a, a, cL, sk_Xy)))
14.59/14.77	       | sk_Xu(X9) = cZ
14.59/14.77	       | ~ app_encode_app(a, $o, X9, 
14.59/14.77	             app_encode_app(a, a, 
14.59/14.77	               app_encode_app(a, app_encode_fun(a, a), cP, 
14.59/14.77	                 app_encode_app(a, a, cL, sk_Xt(X9))), 
14.59/14.77	               app_encode_app(a, a, cL, sk_Xu(X9))))
14.59/14.77	       | ~ app_encode_app(a, $o, X9, 
14.59/14.77	             app_encode_app(a, a, 
14.59/14.77	               app_encode_app(a, app_encode_fun(a, a), cP, 
14.59/14.77	                 app_encode_app(a, a, cR, sk_Xt(X9))), 
14.59/14.77	               app_encode_app(a, a, cR, sk_Xu(X9))))),
14.59/14.77	    inference('cnf', [status(esa)], [zf_stmt_0])).
14.59/14.77	tff('8', plain,
14.59/14.77	    (~ $true
14.59/14.77	     | ~ app_encode_app(a, $o, sk_X, 
14.59/14.77	           app_encode_app(a, a, 
14.59/14.77	             app_encode_app(a, app_encode_fun(a, a), cP, sk_Xt(sk_X)), 
14.59/14.77	             sk_Xu(sk_X)))
14.59/14.77	     | ~ app_encode_app(a, $o, sk_X, 
14.59/14.77	           app_encode_app(a, a, 
14.59/14.77	             app_encode_app(a, app_encode_fun(a, a), cP, 
14.59/14.77	               app_encode_app(a, a, cL, sk_Xt(sk_X))), 
14.59/14.77	             app_encode_app(a, a, cL, sk_Xu(sk_X))))
14.59/14.77	     | sk_Xu(sk_X) = cZ
14.59/14.77	     | ~ app_encode_app(a, $o, sk_X, 
14.59/14.77	           app_encode_app(a, a, 
14.59/14.77	             app_encode_app(a, app_encode_fun(a, a), cP, 
14.59/14.77	               app_encode_app(a, a, cL, sk_Xx)), 
14.59/14.77	             app_encode_app(a, a, cL, sk_Xy)))),
14.59/14.77	    inference('sup-', [status(thm)], ['6', '7'])).
14.59/14.77	tff('9', plain,
14.59/14.77	    (~ app_encode_app(a, $o, sk_X, 
14.59/14.77	         app_encode_app(a, a, 
14.59/14.77	           app_encode_app(a, app_encode_fun(a, a), cP, 
14.59/14.77	             app_encode_app(a, a, cL, sk_Xx)), 
14.59/14.77	           app_encode_app(a, a, cL, sk_Xy)))
14.59/14.77	     | sk_Xu(sk_X) = cZ
14.59/14.77	     | ~ app_encode_app(a, $o, sk_X, 
14.59/14.77	           app_encode_app(a, a, 
14.59/14.77	             app_encode_app(a, app_encode_fun(a, a), cP, 
14.59/14.77	               app_encode_app(a, a, cL, sk_Xt(sk_X))), 
14.59/14.77	             app_encode_app(a, a, cL, sk_Xu(sk_X))))
14.59/14.77	     | ~ app_encode_app(a, $o, sk_X, 
14.59/14.77	           app_encode_app(a, a, 
14.59/14.77	             app_encode_app(a, app_encode_fun(a, a), cP, sk_Xt(sk_X)), 
14.59/14.77	             sk_Xu(sk_X)))),
14.59/14.77	    inference('simplify', [status(thm)], ['8'])).
14.59/14.77	tff('10', plain,
14.59/14.77	    (~ app_encode_app(a, $o, sk_X, 
14.59/14.77	         app_encode_app(a, a, 
14.59/14.77	           app_encode_app(a, app_encode_fun(a, a), cP, 
14.59/14.77	             app_encode_app(a, a, cL, sk_Xx)), 
14.59/14.77	           app_encode_app(a, a, cL, sk_Xy)))
14.59/14.77	     | sk_Xu(sk_X) = cZ
14.59/14.77	     | ~ app_encode_app(a, $o, sk_X, 
14.59/14.77	           app_encode_app(a, a, 
14.59/14.77	             app_encode_app(a, app_encode_fun(a, a), cP, 
14.59/14.77	               app_encode_app(a, a, cL, sk_Xt(sk_X))), 
14.59/14.77	             app_encode_app(a, a, cL, sk_Xu(sk_X))))
14.59/14.77	     | ~ $true),
14.59/14.77	    inference('demod', [status(thm)], ['9', '5'])).
14.59/14.77	tff('11', plain,
14.59/14.77	    (~ app_encode_app(a, $o, sk_X, 
14.59/14.77	         app_encode_app(a, a, 
14.59/14.77	           app_encode_app(a, app_encode_fun(a, a), cP, 
14.59/14.77	             app_encode_app(a, a, cL, sk_Xt(sk_X))), 
14.59/14.77	           app_encode_app(a, a, cL, sk_Xu(sk_X))))
14.59/14.77	     | sk_Xu(sk_X) = cZ
14.59/14.77	     | ~ app_encode_app(a, $o, sk_X, 
14.59/14.77	           app_encode_app(a, a, 
14.59/14.77	             app_encode_app(a, app_encode_fun(a, a), cP, 
14.59/14.77	               app_encode_app(a, a, cL, sk_Xx)), 
14.59/14.77	             app_encode_app(a, a, cL, sk_Xy)))),
14.59/14.77	    inference('simplify', [status(thm)], ['10'])).
14.59/14.77	tff('12', plain,
14.59/14.77	    (~ $true
14.59/14.77	     | ~ app_encode_app(a, $o, sk_X, 
14.59/14.77	           app_encode_app(a, a, 
14.59/14.77	             app_encode_app(a, app_encode_fun(a, a), cP, sk_Xt(sk_X)), 
14.59/14.77	             sk_Xu(sk_X)))
14.59/14.77	     | ~ app_encode_app(a, $o, sk_X, 
14.59/14.77	           app_encode_app(a, a, 
14.59/14.77	             app_encode_app(a, app_encode_fun(a, a), cP, 
14.59/14.77	               app_encode_app(a, a, cL, sk_Xx)), 
14.59/14.77	             app_encode_app(a, a, cL, sk_Xy)))
14.59/14.77	     | sk_Xu(sk_X) = cZ),
14.59/14.77	    inference('sup-', [status(thm)], ['0', '11'])).
14.59/14.77	tff('13', plain,
14.59/14.77	    (~ $true
14.59/14.77	     | ~ $true
14.59/14.77	     | ~ app_encode_app(a, $o, sk_X, 
14.59/14.77	           app_encode_app(a, a, 
14.59/14.77	             app_encode_app(a, app_encode_fun(a, a), cP, 
14.59/14.77	               app_encode_app(a, a, cL, sk_Xx)), 
14.59/14.77	             app_encode_app(a, a, cL, sk_Xy)))
14.59/14.77	     | sk_Xu(sk_X) = cZ),
14.59/14.77	    inference('demod', [status(thm)], ['12', '5'])).
14.59/14.77	tff('14', plain,
14.59/14.77	    (sk_Xu(sk_X) = cZ
14.59/14.77	     | ~ app_encode_app(a, $o, sk_X, 
14.59/14.77	           app_encode_app(a, a, 
14.59/14.77	             app_encode_app(a, app_encode_fun(a, a), cP, 
14.59/14.77	               app_encode_app(a, a, cL, sk_Xx)), 
14.59/14.77	             app_encode_app(a, a, cL, sk_Xy)))),
14.59/14.77	    inference('simplify', [status(thm)], ['13'])).
14.59/14.77	tff('15', plain,
14.59/14.77	    (~ $true
14.59/14.77	     | ~ app_encode_app(a, $o, sk_X, 
14.59/14.77	           app_encode_app(a, a, 
14.59/14.77	             app_encode_app(a, app_encode_fun(a, a), cP, sk_Xx), sk_Xy))
14.59/14.77	     | sk_Xu(sk_X) = cZ),
14.59/14.77	    inference('sup-', [status(thm)], ['0', '14'])).
14.59/14.77	tff('16', plain, (~ $true | ~ $true | sk_Xu(sk_X) = cZ),
14.59/14.77	    inference('demod', [status(thm)], ['15', '3'])).
14.59/14.77	tff('17', plain, sk_Xu(sk_X) = cZ,
14.59/14.77	    inference('simplify', [status(thm)], ['16'])).
14.59/14.77	tff('18', plain,
14.59/14.77	    app_encode_app(a, $o, sk_X, 
14.59/14.77	      app_encode_app(a, a, 
14.59/14.77	        app_encode_app(a, app_encode_fun(a, a), cP, sk_Xt(sk_X)), cZ)),
14.59/14.77	    inference('demod', [status(thm)], ['5', '17'])).
14.59/14.77	tff('19', plain,
14.59/14.77	    ![X10 : a, X11 : a]:
14.59/14.77	      (X10 != cZ
14.59/14.77	       | X11 = cZ
14.59/14.77	       | ~ app_encode_app(a, $o, sk_X, 
14.59/14.77	             app_encode_app(a, a, 
14.59/14.77	               app_encode_app(a, app_encode_fun(a, a), cP, X11), X10))),
14.59/14.77	    inference('cnf', [status(esa)], [zf_stmt_0])).
14.59/14.77	tff('20', plain,
14.59/14.77	    ![X11 : a]:
14.59/14.77	      (~ app_encode_app(a, $o, sk_X, 
14.59/14.77	           app_encode_app(a, a, 
14.59/14.77	             app_encode_app(a, app_encode_fun(a, a), cP, X11), cZ))
14.59/14.77	       | X11 = cZ),
14.59/14.77	    inference('simplify', [status(thm)], ['19'])).
14.59/14.77	tff('21', plain, (~ $true | sk_Xt(sk_X) = cZ),
14.59/14.77	    inference('sup-', [status(thm)], ['18', '20'])).
14.59/14.77	tff('22', plain, sk_Xt(sk_X) = cZ,
14.59/14.77	    inference('simplify', [status(thm)], ['21'])).
14.59/14.77	tff('23', plain,
14.59/14.77	    ![X9 : app_encode_fun(a, $o)]:
14.59/14.77	      (~ app_encode_app(a, $o, X9, 
14.59/14.77	           app_encode_app(a, a, 
14.59/14.77	             app_encode_app(a, app_encode_fun(a, a), cP, 
14.59/14.77	               app_encode_app(a, a, cL, sk_Xx)), 
14.59/14.77	             app_encode_app(a, a, cL, sk_Xy)))
14.59/14.77	       | sk_Xt(X9) != cZ
14.59/14.77	       | ~ app_encode_app(a, $o, X9, 
14.59/14.77	             app_encode_app(a, a, 
14.59/14.77	               app_encode_app(a, app_encode_fun(a, a), cP, 
14.59/14.77	                 app_encode_app(a, a, cL, sk_Xt(X9))), 
14.59/14.77	               app_encode_app(a, a, cL, sk_Xu(X9))))
14.59/14.77	       | ~ app_encode_app(a, $o, X9, 
14.59/14.77	             app_encode_app(a, a, 
14.59/14.77	               app_encode_app(a, app_encode_fun(a, a), cP, 
14.59/14.77	                 app_encode_app(a, a, cR, sk_Xt(X9))), 
14.59/14.77	               app_encode_app(a, a, cR, sk_Xu(X9))))),
14.59/14.77	    inference('cnf', [status(esa)], [zf_stmt_0])).
14.59/14.77	tff('24', plain,
14.59/14.77	    (~ $true
14.59/14.77	     | ~ app_encode_app(a, $o, sk_X, 
14.59/14.77	           app_encode_app(a, a, 
14.59/14.77	             app_encode_app(a, app_encode_fun(a, a), cP, sk_Xt(sk_X)), 
14.59/14.77	             sk_Xu(sk_X)))
14.59/14.77	     | ~ app_encode_app(a, $o, sk_X, 
14.59/14.77	           app_encode_app(a, a, 
14.59/14.77	             app_encode_app(a, app_encode_fun(a, a), cP, 
14.59/14.77	               app_encode_app(a, a, cL, sk_Xt(sk_X))), 
14.59/14.77	             app_encode_app(a, a, cL, sk_Xu(sk_X))))
14.59/14.77	     | sk_Xt(sk_X) != cZ
14.59/14.77	     | ~ app_encode_app(a, $o, sk_X, 
14.59/14.77	           app_encode_app(a, a, 
14.59/14.77	             app_encode_app(a, app_encode_fun(a, a), cP, 
14.59/14.77	               app_encode_app(a, a, cL, sk_Xx)), 
14.59/14.77	             app_encode_app(a, a, cL, sk_Xy)))),
14.59/14.77	    inference('sup-', [status(thm)], ['6', '23'])).
14.59/14.77	tff('25', plain,
14.59/14.77	    (~ $true
14.59/14.77	     | ~ $true
14.59/14.77	     | ~ app_encode_app(a, $o, sk_X, 
14.59/14.77	           app_encode_app(a, a, 
14.59/14.77	             app_encode_app(a, app_encode_fun(a, a), cP, 
14.59/14.77	               app_encode_app(a, a, cL, sk_Xt(sk_X))), 
14.59/14.77	             app_encode_app(a, a, cL, sk_Xu(sk_X))))
14.59/14.77	     | sk_Xt(sk_X) != cZ
14.59/14.77	     | ~ app_encode_app(a, $o, sk_X, 
14.59/14.77	           app_encode_app(a, a, 
14.59/14.77	             app_encode_app(a, app_encode_fun(a, a), cP, 
14.59/14.77	               app_encode_app(a, a, cL, sk_Xx)), 
14.59/14.77	             app_encode_app(a, a, cL, sk_Xy)))),
14.59/14.77	    inference('demod', [status(thm)], ['24', '5'])).
14.59/14.77	tff('26', plain,
14.59/14.77	    (~ app_encode_app(a, $o, sk_X, 
14.59/14.77	         app_encode_app(a, a, 
14.59/14.77	           app_encode_app(a, app_encode_fun(a, a), cP, 
14.59/14.77	             app_encode_app(a, a, cL, sk_Xx)), 
14.59/14.77	           app_encode_app(a, a, cL, sk_Xy)))
14.59/14.77	     | sk_Xt(sk_X) != cZ
14.59/14.77	     | ~ app_encode_app(a, $o, sk_X, 
14.59/14.77	           app_encode_app(a, a, 
14.59/14.77	             app_encode_app(a, app_encode_fun(a, a), cP, 
14.59/14.77	               app_encode_app(a, a, cL, sk_Xt(sk_X))), 
14.59/14.77	             app_encode_app(a, a, cL, sk_Xu(sk_X))))),
14.59/14.77	    inference('simplify', [status(thm)], ['25'])).
14.59/14.77	tff('27', plain,
14.59/14.77	    (~ $true
14.59/14.77	     | ~ app_encode_app(a, $o, sk_X, 
14.59/14.77	           app_encode_app(a, a, 
14.59/14.77	             app_encode_app(a, app_encode_fun(a, a), cP, sk_Xt(sk_X)), 
14.59/14.77	             sk_Xu(sk_X)))
14.59/14.77	     | sk_Xt(sk_X) != cZ
14.59/14.77	     | ~ app_encode_app(a, $o, sk_X, 
14.59/14.77	           app_encode_app(a, a, 
14.59/14.77	             app_encode_app(a, app_encode_fun(a, a), cP, 
14.59/14.77	               app_encode_app(a, a, cL, sk_Xx)), 
14.59/14.77	             app_encode_app(a, a, cL, sk_Xy)))),
14.59/14.77	    inference('sup-', [status(thm)], ['0', '26'])).
14.59/14.77	tff('28', plain,
14.59/14.77	    (~ $true
14.59/14.77	     | ~ $true
14.59/14.77	     | sk_Xt(sk_X) != cZ
14.59/14.77	     | ~ app_encode_app(a, $o, sk_X, 
14.59/14.77	           app_encode_app(a, a, 
14.59/14.77	             app_encode_app(a, app_encode_fun(a, a), cP, 
14.59/14.77	               app_encode_app(a, a, cL, sk_Xx)), 
14.59/14.77	             app_encode_app(a, a, cL, sk_Xy)))),
14.59/14.77	    inference('demod', [status(thm)], ['27', '5'])).
14.59/14.77	tff('29', plain,
14.59/14.77	    (~ app_encode_app(a, $o, sk_X, 
14.59/14.77	         app_encode_app(a, a, 
14.59/14.77	           app_encode_app(a, app_encode_fun(a, a), cP, 
14.59/14.77	             app_encode_app(a, a, cL, sk_Xx)), 
14.59/14.77	           app_encode_app(a, a, cL, sk_Xy)))
14.59/14.77	     | sk_Xt(sk_X) != cZ),
14.59/14.77	    inference('simplify', [status(thm)], ['28'])).
14.59/14.77	tff('30', plain,
14.59/14.77	    (~ $true
14.59/14.77	     | ~ app_encode_app(a, $o, sk_X, 
14.59/14.77	           app_encode_app(a, a, 
14.59/14.77	             app_encode_app(a, app_encode_fun(a, a), cP, sk_Xx), sk_Xy))
14.59/14.77	     | sk_Xt(sk_X) != cZ),
14.59/14.77	    inference('sup-', [status(thm)], ['0', '29'])).
14.59/14.77	tff('31', plain, (~ $true | ~ $true | sk_Xt(sk_X) != cZ),
14.59/14.77	    inference('demod', [status(thm)], ['30', '3'])).
14.59/14.77	tff('32', plain, sk_Xt(sk_X) != cZ,
14.59/14.77	    inference('simplify', [status(thm)], ['31'])).
14.59/14.77	tff('33', plain, $false,
14.59/14.77	    inference('simplify_reflect-', [status(thm)], ['22', '32'])).
14.59/14.77	
14.59/14.77	% SZS output end Refutation
14.59/14.78	EOF
