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    : 
0.00/0.00	#!/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 $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n151.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 17:25:10 CST 2018
0.60/0.78	% done 148 iterations in 0.580s
0.60/0.78	% SZS status Theorem for 'stdin'
0.60/0.78	% SZS output start Refutation
0.60/0.78	tff(zf_stmt_8, conjecture,
0.60/0.78	  (((app_encode_app(a,a,cL,cZ) = cZ) & (app_encode_app(a,a,cR,cZ) = cZ) & 
0.60/0.78	    (![Xx:a,Xy:a]:
0.60/0.78	       (app_encode_app(a,a,cL,
0.60/0.78	                       app_encode_app(a,a,
0.60/0.78	                                      app_encode_app(a,app_encode_fun(a,a),
0.60/0.78	                                                     cP,Xx),
0.60/0.78	                                      Xy)) =
0.60/0.78	        Xx)) & 
0.60/0.78	    (![Xx:a,Xy:a]:
0.60/0.78	       (app_encode_app(a,a,cR,
0.60/0.78	                       app_encode_app(a,a,
0.60/0.78	                                      app_encode_app(a,app_encode_fun(a,a),
0.60/0.78	                                                     cP,Xx),
0.60/0.78	                                      Xy)) =
0.60/0.78	        Xy)) & 
0.60/0.78	    (![Xt:a]:
0.60/0.78	       ((Xt != cZ) <=>
0.60/0.78	        (Xt =
0.60/0.78	         app_encode_app(a,a,
0.60/0.78	                        app_encode_app(a,app_encode_fun(a,a),cP,
0.60/0.78	                                       app_encode_app(a,a,cL,Xt)),
0.60/0.78	                        app_encode_app(a,a,cR,Xt))))) & 
0.60/0.78	    (![X:app_encode_fun(a,$o)]:
0.60/0.78	       ((![Xt:a,Xu:a]:
0.60/0.78	           (app_encode_app(a,$o,X,
0.60/0.78	                           app_encode_app(a,a,
0.60/0.78	                                          app_encode_app(a,
0.60/0.78	                                                         app_encode_fun(a,a),
0.60/0.78	                                                         cP,Xt),
0.60/0.78	                                          Xu)) =>
0.60/0.78	            (((Xt = cZ) <=> (Xu = cZ)) & 
0.60/0.78	             app_encode_app(a,$o,X,
0.60/0.78	                            app_encode_app(a,a,
0.60/0.78	                                           app_encode_app(a,
0.60/0.78	                                                          app_encode_fun(a,a),
0.60/0.78	                                                          cP,
0.60/0.78	                                                          app_encode_app(
0.60/0.78	                                                          a,a,cL,Xt)),
0.60/0.78	                                           app_encode_app(a,a,cL,Xu))) & 
0.60/0.78	             app_encode_app(a,$o,X,
0.60/0.78	                            app_encode_app(a,a,
0.60/0.78	                                           app_encode_app(a,
0.60/0.78	                                                          app_encode_fun(a,a),
0.60/0.78	                                                          cP,
0.60/0.78	                                                          app_encode_app(
0.60/0.78	                                                          a,a,cR,Xt)),
0.60/0.78	                                           app_encode_app(a,a,cR,Xu)))))) =>
0.60/0.78	        (![Xt:a,Xu:a]:
0.60/0.78	           (app_encode_app(a,$o,X,
0.60/0.78	                           app_encode_app(a,a,
0.60/0.78	                                          app_encode_app(a,
0.60/0.78	                                                         app_encode_fun(a,a),
0.60/0.78	                                                         cP,Xt),
0.60/0.78	                                          Xu)) =>
0.60/0.78	            (Xt = Xu)))))) =>
0.60/0.78	   (![Xx:a,Xy:a]:
0.60/0.78	      ((?[X:app_encode_fun(a,$o)]:
0.60/0.78	          (app_encode_app(a,$o,X,
0.60/0.78	                          app_encode_app(a,a,
0.60/0.78	                                         app_encode_app(a,
0.60/0.78	                                                        app_encode_fun(a,a),
0.60/0.78	                                                        cP,Xx),
0.60/0.78	                                         Xy)) & 
0.60/0.78	           (![Xt:a,Xu:a]:
0.60/0.78	              (app_encode_app(a,$o,X,
0.60/0.78	                              app_encode_app(a,a,
0.60/0.78	                                             app_encode_app(a,
0.60/0.78	                                                            app_encode_fun(
0.60/0.78	                                                            a,a),cP,Xt),
0.60/0.78	                                             Xu)) =>
0.60/0.78	               (((Xu = cZ) => (Xt = cZ)) & 
0.60/0.78	                app_encode_app(a,$o,X,
0.60/0.78	                               app_encode_app(a,a,
0.60/0.78	                                              app_encode_app(a,
0.60/0.78	                                                             app_encode_fun(
0.60/0.78	                                                             a,a),cP,
0.60/0.78	                                                             app_encode_app(
0.60/0.78	                                                             a,a,cL,Xt)),
0.60/0.78	                                              app_encode_app(a,a,cL,Xu))) & 
0.60/0.78	                app_encode_app(a,$o,X,
0.60/0.78	                               app_encode_app(a,a,
0.60/0.78	                                              app_encode_app(a,
0.60/0.78	                                                             app_encode_fun(
0.60/0.78	                                                             a,a),cP,
0.60/0.78	                                                             app_encode_app(
0.60/0.78	                                                             a,a,cR,Xt)),
0.60/0.78	                                              app_encode_app(a,a,cR,Xu)))))))) =>
0.60/0.78	       (?[X:app_encode_fun(a,$o)]:
0.60/0.78	          (app_encode_app(a,$o,X,
0.60/0.78	                          app_encode_app(a,a,
0.60/0.78	                                         app_encode_app(a,
0.60/0.78	                                                        app_encode_fun(a,a),
0.60/0.78	                                                        cP,
0.60/0.78	                                                        app_encode_app(
0.60/0.78	                                                        a,a,cL,Xx)),
0.60/0.78	                                         app_encode_app(a,a,cL,Xy))) & 
0.60/0.78	           (![Xt:a,Xu:a]:
0.60/0.78	              (app_encode_app(a,$o,X,
0.60/0.78	                              app_encode_app(a,a,
0.60/0.78	                                             app_encode_app(a,
0.60/0.78	                                                            app_encode_fun(
0.60/0.78	                                                            a,a),cP,Xt),
0.60/0.78	                                             Xu)) =>
0.60/0.78	               (((Xu = cZ) => (Xt = cZ)) & 
0.60/0.78	                app_encode_app(a,$o,X,
0.60/0.78	                               app_encode_app(a,a,
0.60/0.78	                                              app_encode_app(a,
0.60/0.78	                                                             app_encode_fun(
0.60/0.78	                                                             a,a),cP,
0.60/0.78	                                                             app_encode_app(
0.60/0.78	                                                             a,a,cL,Xt)),
0.60/0.78	                                              app_encode_app(a,a,cL,Xu))) & 
0.60/0.78	                app_encode_app(a,$o,X,
0.60/0.78	                               app_encode_app(a,a,
0.60/0.78	                                              app_encode_app(a,
0.60/0.78	                                                             app_encode_fun(
0.60/0.78	                                                             a,a),cP,
0.60/0.78	                                                             app_encode_app(
0.60/0.78	                                                             a,a,cR,Xt)),
0.60/0.78	                                              app_encode_app(a,a,cR,Xu)))))))))))).
0.60/0.78	tff(zf_stmt_0, negated_conjecture,
0.60/0.78	  (~
0.60/0.78	    (((app_encode_app(a,a,cL,cZ) = cZ) & (app_encode_app(a,a,cR,cZ) = cZ) & 
0.60/0.78	      (![Xx:a,Xy:a]:
0.60/0.78	         (app_encode_app(a,a,cL,
0.60/0.78	                         app_encode_app(a,a,
0.60/0.78	                                        app_encode_app(a,app_encode_fun(a,a),
0.60/0.78	                                                       cP,Xx),
0.60/0.78	                                        Xy)) =
0.60/0.78	          Xx)) & 
0.60/0.78	      (![Xx:a,Xy:a]:
0.60/0.78	         (app_encode_app(a,a,cR,
0.60/0.78	                         app_encode_app(a,a,
0.60/0.78	                                        app_encode_app(a,app_encode_fun(a,a),
0.60/0.78	                                                       cP,Xx),
0.60/0.78	                                        Xy)) =
0.60/0.78	          Xy)) & 
0.60/0.78	      (![Xt:a]:
0.60/0.78	         ((Xt != cZ) <=>
0.60/0.78	          (Xt =
0.60/0.78	           app_encode_app(a,a,
0.60/0.78	                          app_encode_app(a,app_encode_fun(a,a),cP,
0.60/0.78	                                         app_encode_app(a,a,cL,Xt)),
0.60/0.78	                          app_encode_app(a,a,cR,Xt))))) & 
0.60/0.78	      (![X:app_encode_fun(a,$o)]:
0.60/0.78	         ((![Xt:a,Xu:a]:
0.60/0.78	             (app_encode_app(a,$o,X,
0.60/0.78	                             app_encode_app(a,a,
0.60/0.78	                                            app_encode_app(a,
0.60/0.78	                                                           app_encode_fun(
0.60/0.78	                                                           a,a),cP,Xt),
0.60/0.78	                                            Xu)) =>
0.60/0.78	              (((Xt = cZ) <=> (Xu = cZ)) & 
0.60/0.78	               app_encode_app(a,$o,X,
0.60/0.78	                              app_encode_app(a,a,
0.60/0.78	                                             app_encode_app(a,
0.60/0.78	                                                            app_encode_fun(
0.60/0.78	                                                            a,a),cP,
0.60/0.78	                                                            app_encode_app(
0.60/0.78	                                                            a,a,cL,Xt)),
0.60/0.78	                                             app_encode_app(a,a,cL,Xu))) & 
0.60/0.78	               app_encode_app(a,$o,X,
0.60/0.78	                              app_encode_app(a,a,
0.60/0.78	                                             app_encode_app(a,
0.60/0.78	                                                            app_encode_fun(
0.60/0.78	                                                            a,a),cP,
0.60/0.78	                                                            app_encode_app(
0.60/0.78	                                                            a,a,cR,Xt)),
0.60/0.78	                                             app_encode_app(a,a,cR,Xu)))))) =>
0.60/0.78	          (![Xt:a,Xu:a]:
0.60/0.78	             (app_encode_app(a,$o,X,
0.60/0.78	                             app_encode_app(a,a,
0.60/0.78	                                            app_encode_app(a,
0.60/0.78	                                                           app_encode_fun(
0.60/0.78	                                                           a,a),cP,Xt),
0.60/0.78	                                            Xu)) =>
0.60/0.78	              (Xt = Xu)))))) =>
0.60/0.78	     (![Xx:a,Xy:a]:
0.60/0.78	        ((?[X:app_encode_fun(a,$o)]:
0.60/0.78	            (app_encode_app(a,$o,X,
0.60/0.78	                            app_encode_app(a,a,
0.60/0.78	                                           app_encode_app(a,
0.60/0.78	                                                          app_encode_fun(a,a),
0.60/0.78	                                                          cP,Xx),
0.60/0.78	                                           Xy)) & 
0.60/0.78	             (![Xt:a,Xu:a]:
0.60/0.78	                (app_encode_app(a,$o,X,
0.60/0.78	                                app_encode_app(a,a,
0.60/0.78	                                               app_encode_app(a,
0.60/0.78	                                                              app_encode_fun(
0.60/0.78	                                                              a,a),cP,Xt),
0.60/0.78	                                               Xu)) =>
0.60/0.78	                 (((Xu = cZ) => (Xt = cZ)) & 
0.60/0.78	                  app_encode_app(a,$o,X,
0.60/0.78	                                 app_encode_app(a,a,
0.60/0.78	                                                app_encode_app(a,
0.60/0.78	                                                               app_encode_fun(
0.60/0.78	                                                               a,a),cP,
0.60/0.78	                                                               app_encode_app(
0.60/0.78	                                                               a,a,cL,Xt)),
0.60/0.78	                                                app_encode_app(a,a,cL,Xu))) & 
0.60/0.78	                  app_encode_app(a,$o,X,
0.60/0.78	                                 app_encode_app(a,a,
0.60/0.78	                                                app_encode_app(a,
0.60/0.78	                                                               app_encode_fun(
0.60/0.78	                                                               a,a),cP,
0.60/0.78	                                                               app_encode_app(
0.60/0.78	                                                               a,a,cR,Xt)),
0.60/0.78	                                                app_encode_app(a,a,cR,Xu)))))))) =>
0.60/0.78	         (?[X:app_encode_fun(a,$o)]:
0.60/0.78	            (app_encode_app(a,$o,X,
0.60/0.78	                            app_encode_app(a,a,
0.60/0.78	                                           app_encode_app(a,
0.60/0.78	                                                          app_encode_fun(a,a),
0.60/0.78	                                                          cP,
0.60/0.78	                                                          app_encode_app(
0.60/0.78	                                                          a,a,cL,Xx)),
0.60/0.78	                                           app_encode_app(a,a,cL,Xy))) & 
0.60/0.78	             (![Xt:a,Xu:a]:
0.60/0.78	                (app_encode_app(a,$o,X,
0.60/0.78	                                app_encode_app(a,a,
0.60/0.78	                                               app_encode_app(a,
0.60/0.78	                                                              app_encode_fun(
0.60/0.78	                                                              a,a),cP,Xt),
0.60/0.78	                                               Xu)) =>
0.60/0.78	                 (((Xu = cZ) => (Xt = cZ)) & 
0.60/0.78	                  app_encode_app(a,$o,X,
0.60/0.78	                                 app_encode_app(a,a,
0.60/0.78	                                                app_encode_app(a,
0.60/0.78	                                                               app_encode_fun(
0.60/0.78	                                                               a,a),cP,
0.60/0.78	                                                               app_encode_app(
0.60/0.78	                                                               a,a,cL,Xt)),
0.60/0.78	                                                app_encode_app(a,a,cL,Xu))) & 
0.60/0.78	                  app_encode_app(a,$o,X,
0.60/0.78	                                 app_encode_app(a,a,
0.60/0.78	                                                app_encode_app(a,
0.60/0.78	                                                               app_encode_fun(
0.60/0.78	                                                               a,a),cP,
0.60/0.78	                                                               app_encode_app(
0.60/0.78	                                                               a,a,cR,Xt)),
0.60/0.78	                                                app_encode_app(a,a,cR,Xu))))))))))))).
0.60/0.78	tff('0', plain,
0.60/0.78	    ![X14 : a, X15 : a]:
0.60/0.78	      (app_encode_app(a, $o, sk_X, 
0.60/0.78	         app_encode_app(a, a, 
0.60/0.78	           app_encode_app(a, app_encode_fun(a, a), cP, 
0.60/0.78	             app_encode_app(a, a, cL, X15)), app_encode_app(a, a, cL, X14)))
0.60/0.78	       | ~ app_encode_app(a, $o, sk_X, 
0.60/0.78	             app_encode_app(a, a, 
0.60/0.78	               app_encode_app(a, app_encode_fun(a, a), cP, X15), X14))),
0.60/0.78	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.60/0.78	tff('1', plain,
0.60/0.78	    ![X13 : app_encode_fun(a, $o)]:
0.60/0.78	      (~ app_encode_app(a, $o, X13, 
0.60/0.78	           app_encode_app(a, a, 
0.60/0.78	             app_encode_app(a, app_encode_fun(a, a), cP, 
0.60/0.78	               app_encode_app(a, a, cL, sk_Xx)), 
0.60/0.78	             app_encode_app(a, a, cL, sk_Xy)))
0.60/0.78	       | app_encode_app(a, $o, X13, 
0.60/0.78	           app_encode_app(a, a, 
0.60/0.78	             app_encode_app(a, app_encode_fun(a, a), cP, sk_Xt(X13)), 
0.60/0.78	             sk_Xu(X13)))),
0.60/0.78	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.60/0.78	tff('2', plain,
0.60/0.78	    (~ $true
0.60/0.78	     | ~ app_encode_app(a, $o, sk_X, 
0.60/0.78	           app_encode_app(a, a, 
0.60/0.78	             app_encode_app(a, app_encode_fun(a, a), cP, sk_Xx), sk_Xy))
0.60/0.78	     | app_encode_app(a, $o, sk_X, 
0.60/0.78	         app_encode_app(a, a, 
0.60/0.78	           app_encode_app(a, app_encode_fun(a, a), cP, sk_Xt(sk_X)), 
0.60/0.78	           sk_Xu(sk_X)))),
0.60/0.78	    inference('sup-', [status(thm)], ['0', '1'])).
0.60/0.78	tff('3', plain,
0.60/0.78	    app_encode_app(a, $o, sk_X, 
0.60/0.78	      app_encode_app(a, a, 
0.60/0.78	        app_encode_app(a, app_encode_fun(a, a), cP, sk_Xx), sk_Xy)),
0.60/0.78	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.60/0.78	tff('4', plain,
0.60/0.78	    (~ $true
0.60/0.78	     | ~ $true
0.60/0.78	     | app_encode_app(a, $o, sk_X, 
0.60/0.78	         app_encode_app(a, a, 
0.60/0.78	           app_encode_app(a, app_encode_fun(a, a), cP, sk_Xt(sk_X)), 
0.60/0.78	           sk_Xu(sk_X)))),
0.60/0.78	    inference('demod', [status(thm)], ['2', '3'])).
0.60/0.78	tff('5', plain,
0.60/0.78	    app_encode_app(a, $o, sk_X, 
0.60/0.78	      app_encode_app(a, a, 
0.60/0.78	        app_encode_app(a, app_encode_fun(a, a), cP, sk_Xt(sk_X)), 
0.60/0.78	        sk_Xu(sk_X))),
0.60/0.78	    inference('simplify', [status(thm)], ['4'])).
0.60/0.78	tff('6', plain,
0.60/0.78	    ![X14 : a, X15 : a]:
0.60/0.78	      (app_encode_app(a, $o, sk_X, 
0.60/0.78	         app_encode_app(a, a, 
0.60/0.78	           app_encode_app(a, app_encode_fun(a, a), cP, 
0.60/0.78	             app_encode_app(a, a, cR, X15)), app_encode_app(a, a, cR, X14)))
0.60/0.78	       | ~ app_encode_app(a, $o, sk_X, 
0.60/0.78	             app_encode_app(a, a, 
0.60/0.78	               app_encode_app(a, app_encode_fun(a, a), cP, X15), X14))),
0.60/0.78	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.60/0.78	tff('7', plain,
0.60/0.78	    ![X13 : app_encode_fun(a, $o)]:
0.60/0.78	      (~ app_encode_app(a, $o, X13, 
0.60/0.78	           app_encode_app(a, a, 
0.60/0.78	             app_encode_app(a, app_encode_fun(a, a), cP, 
0.60/0.78	               app_encode_app(a, a, cL, sk_Xx)), 
0.60/0.78	             app_encode_app(a, a, cL, sk_Xy)))
0.60/0.78	       | sk_Xu(X13) = cZ
0.60/0.78	       | ~ app_encode_app(a, $o, X13, 
0.60/0.78	             app_encode_app(a, a, 
0.60/0.78	               app_encode_app(a, app_encode_fun(a, a), cP, 
0.60/0.78	                 app_encode_app(a, a, cL, sk_Xt(X13))), 
0.60/0.78	               app_encode_app(a, a, cL, sk_Xu(X13))))
0.60/0.78	       | ~ app_encode_app(a, $o, X13, 
0.60/0.78	             app_encode_app(a, a, 
0.60/0.78	               app_encode_app(a, app_encode_fun(a, a), cP, 
0.60/0.78	                 app_encode_app(a, a, cR, sk_Xt(X13))), 
0.60/0.78	               app_encode_app(a, a, cR, sk_Xu(X13))))),
0.60/0.78	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.60/0.78	tff('8', plain,
0.60/0.78	    (~ $true
0.60/0.78	     | ~ app_encode_app(a, $o, sk_X, 
0.60/0.78	           app_encode_app(a, a, 
0.60/0.78	             app_encode_app(a, app_encode_fun(a, a), cP, sk_Xt(sk_X)), 
0.60/0.78	             sk_Xu(sk_X)))
0.60/0.78	     | ~ app_encode_app(a, $o, sk_X, 
0.60/0.78	           app_encode_app(a, a, 
0.60/0.78	             app_encode_app(a, app_encode_fun(a, a), cP, 
0.60/0.78	               app_encode_app(a, a, cL, sk_Xt(sk_X))), 
0.60/0.78	             app_encode_app(a, a, cL, sk_Xu(sk_X))))
0.60/0.78	     | sk_Xu(sk_X) = cZ
0.60/0.78	     | ~ app_encode_app(a, $o, sk_X, 
0.60/0.78	           app_encode_app(a, a, 
0.60/0.78	             app_encode_app(a, app_encode_fun(a, a), cP, 
0.60/0.78	               app_encode_app(a, a, cL, sk_Xx)), 
0.60/0.78	             app_encode_app(a, a, cL, sk_Xy)))),
0.60/0.78	    inference('sup-', [status(thm)], ['6', '7'])).
0.60/0.78	tff('9', plain,
0.60/0.78	    (~ $true
0.60/0.78	     | ~ $true
0.60/0.78	     | ~ app_encode_app(a, $o, sk_X, 
0.60/0.78	           app_encode_app(a, a, 
0.60/0.78	             app_encode_app(a, app_encode_fun(a, a), cP, 
0.60/0.78	               app_encode_app(a, a, cL, sk_Xt(sk_X))), 
0.60/0.78	             app_encode_app(a, a, cL, sk_Xu(sk_X))))
0.60/0.78	     | sk_Xu(sk_X) = cZ
0.60/0.78	     | ~ app_encode_app(a, $o, sk_X, 
0.60/0.78	           app_encode_app(a, a, 
0.60/0.78	             app_encode_app(a, app_encode_fun(a, a), cP, 
0.60/0.78	               app_encode_app(a, a, cL, sk_Xx)), 
0.60/0.78	             app_encode_app(a, a, cL, sk_Xy)))),
0.60/0.78	    inference('demod', [status(thm)], ['8', '5'])).
0.60/0.78	tff('10', plain,
0.60/0.78	    (~ app_encode_app(a, $o, sk_X, 
0.60/0.78	         app_encode_app(a, a, 
0.60/0.78	           app_encode_app(a, app_encode_fun(a, a), cP, 
0.60/0.78	             app_encode_app(a, a, cL, sk_Xx)), 
0.60/0.78	           app_encode_app(a, a, cL, sk_Xy)))
0.60/0.78	     | sk_Xu(sk_X) = cZ
0.60/0.78	     | ~ app_encode_app(a, $o, sk_X, 
0.60/0.78	           app_encode_app(a, a, 
0.60/0.78	             app_encode_app(a, app_encode_fun(a, a), cP, 
0.60/0.78	               app_encode_app(a, a, cL, sk_Xt(sk_X))), 
0.60/0.78	             app_encode_app(a, a, cL, sk_Xu(sk_X))))),
0.60/0.78	    inference('simplify', [status(thm)], ['9'])).
0.60/0.78	tff('11', plain,
0.60/0.78	    (~ $true
0.60/0.78	     | ~ app_encode_app(a, $o, sk_X, 
0.60/0.78	           app_encode_app(a, a, 
0.60/0.78	             app_encode_app(a, app_encode_fun(a, a), cP, sk_Xt(sk_X)), 
0.60/0.78	             sk_Xu(sk_X)))
0.60/0.78	     | sk_Xu(sk_X) = cZ
0.60/0.78	     | ~ app_encode_app(a, $o, sk_X, 
0.60/0.78	           app_encode_app(a, a, 
0.60/0.78	             app_encode_app(a, app_encode_fun(a, a), cP, 
0.60/0.78	               app_encode_app(a, a, cL, sk_Xx)), 
0.60/0.78	             app_encode_app(a, a, cL, sk_Xy)))),
0.60/0.78	    inference('sup-', [status(thm)], ['0', '10'])).
0.60/0.78	tff('12', plain,
0.60/0.78	    (~ $true
0.60/0.78	     | ~ $true
0.60/0.78	     | sk_Xu(sk_X) = cZ
0.60/0.78	     | ~ app_encode_app(a, $o, sk_X, 
0.60/0.78	           app_encode_app(a, a, 
0.60/0.78	             app_encode_app(a, app_encode_fun(a, a), cP, 
0.60/0.78	               app_encode_app(a, a, cL, sk_Xx)), 
0.60/0.78	             app_encode_app(a, a, cL, sk_Xy)))),
0.60/0.78	    inference('demod', [status(thm)], ['11', '5'])).
0.60/0.78	tff('13', plain,
0.60/0.78	    (~ app_encode_app(a, $o, sk_X, 
0.60/0.78	         app_encode_app(a, a, 
0.60/0.78	           app_encode_app(a, app_encode_fun(a, a), cP, 
0.60/0.78	             app_encode_app(a, a, cL, sk_Xx)), 
0.60/0.78	           app_encode_app(a, a, cL, sk_Xy)))
0.60/0.78	     | sk_Xu(sk_X) = cZ),
0.60/0.78	    inference('simplify', [status(thm)], ['12'])).
0.60/0.78	tff('14', plain,
0.60/0.78	    (~ $true
0.60/0.78	     | ~ app_encode_app(a, $o, sk_X, 
0.60/0.78	           app_encode_app(a, a, 
0.60/0.78	             app_encode_app(a, app_encode_fun(a, a), cP, sk_Xx), sk_Xy))
0.60/0.78	     | sk_Xu(sk_X) = cZ),
0.60/0.78	    inference('sup-', [status(thm)], ['0', '13'])).
0.60/0.78	tff('15', plain, (~ $true | ~ $true | sk_Xu(sk_X) = cZ),
0.60/0.78	    inference('demod', [status(thm)], ['14', '3'])).
0.60/0.78	tff('16', plain, sk_Xu(sk_X) = cZ,
0.60/0.78	    inference('simplify', [status(thm)], ['15'])).
0.60/0.78	tff('17', plain,
0.60/0.78	    app_encode_app(a, $o, sk_X, 
0.60/0.78	      app_encode_app(a, a, 
0.60/0.78	        app_encode_app(a, app_encode_fun(a, a), cP, sk_Xt(sk_X)), cZ)),
0.60/0.78	    inference('demod', [status(thm)], ['5', '16'])).
0.60/0.78	tff('18', plain,
0.60/0.78	    ![X14 : a, X15 : a]:
0.60/0.78	      (X14 != cZ
0.60/0.78	       | X15 = cZ
0.60/0.78	       | ~ app_encode_app(a, $o, sk_X, 
0.60/0.78	             app_encode_app(a, a, 
0.60/0.78	               app_encode_app(a, app_encode_fun(a, a), cP, X15), X14))),
0.60/0.78	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.60/0.78	tff('19', plain,
0.60/0.78	    ![X15 : a]:
0.60/0.78	      (~ app_encode_app(a, $o, sk_X, 
0.60/0.78	           app_encode_app(a, a, 
0.60/0.78	             app_encode_app(a, app_encode_fun(a, a), cP, X15), cZ))
0.60/0.78	       | X15 = cZ),
0.60/0.78	    inference('simplify', [status(thm)], ['18'])).
0.60/0.78	tff('20', plain, (~ $true | sk_Xt(sk_X) = cZ),
0.60/0.78	    inference('sup-', [status(thm)], ['17', '19'])).
0.60/0.78	tff('21', plain, sk_Xt(sk_X) = cZ,
0.60/0.78	    inference('simplify', [status(thm)], ['20'])).
0.60/0.78	tff('22', plain,
0.60/0.78	    ![X13 : app_encode_fun(a, $o)]:
0.60/0.78	      (~ app_encode_app(a, $o, X13, 
0.60/0.78	           app_encode_app(a, a, 
0.60/0.78	             app_encode_app(a, app_encode_fun(a, a), cP, 
0.60/0.78	               app_encode_app(a, a, cL, sk_Xx)), 
0.60/0.78	             app_encode_app(a, a, cL, sk_Xy)))
0.60/0.78	       | sk_Xt(X13) != cZ
0.60/0.78	       | ~ app_encode_app(a, $o, X13, 
0.60/0.78	             app_encode_app(a, a, 
0.60/0.78	               app_encode_app(a, app_encode_fun(a, a), cP, 
0.60/0.78	                 app_encode_app(a, a, cL, sk_Xt(X13))), 
0.60/0.78	               app_encode_app(a, a, cL, sk_Xu(X13))))
0.60/0.78	       | ~ app_encode_app(a, $o, X13, 
0.60/0.78	             app_encode_app(a, a, 
0.60/0.78	               app_encode_app(a, app_encode_fun(a, a), cP, 
0.60/0.78	                 app_encode_app(a, a, cR, sk_Xt(X13))), 
0.60/0.78	               app_encode_app(a, a, cR, sk_Xu(X13))))),
0.60/0.78	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.60/0.78	tff('23', plain,
0.60/0.78	    (~ $true
0.60/0.78	     | ~ app_encode_app(a, $o, sk_X, 
0.60/0.78	           app_encode_app(a, a, 
0.60/0.78	             app_encode_app(a, app_encode_fun(a, a), cP, sk_Xt(sk_X)), 
0.60/0.78	             sk_Xu(sk_X)))
0.60/0.78	     | ~ app_encode_app(a, $o, sk_X, 
0.60/0.78	           app_encode_app(a, a, 
0.60/0.78	             app_encode_app(a, app_encode_fun(a, a), cP, 
0.60/0.78	               app_encode_app(a, a, cL, sk_Xt(sk_X))), 
0.60/0.78	             app_encode_app(a, a, cL, sk_Xu(sk_X))))
0.60/0.78	     | sk_Xt(sk_X) != cZ
0.60/0.78	     | ~ app_encode_app(a, $o, sk_X, 
0.60/0.78	           app_encode_app(a, a, 
0.60/0.78	             app_encode_app(a, app_encode_fun(a, a), cP, 
0.60/0.78	               app_encode_app(a, a, cL, sk_Xx)), 
0.60/0.78	             app_encode_app(a, a, cL, sk_Xy)))),
0.60/0.78	    inference('sup-', [status(thm)], ['6', '22'])).
0.60/0.78	tff('24', plain,
0.60/0.78	    (~ $true
0.60/0.78	     | ~ $true
0.60/0.78	     | ~ app_encode_app(a, $o, sk_X, 
0.60/0.78	           app_encode_app(a, a, 
0.60/0.78	             app_encode_app(a, app_encode_fun(a, a), cP, 
0.60/0.78	               app_encode_app(a, a, cL, sk_Xt(sk_X))), 
0.60/0.78	             app_encode_app(a, a, cL, sk_Xu(sk_X))))
0.60/0.78	     | sk_Xt(sk_X) != cZ
0.60/0.78	     | ~ app_encode_app(a, $o, sk_X, 
0.60/0.78	           app_encode_app(a, a, 
0.60/0.78	             app_encode_app(a, app_encode_fun(a, a), cP, 
0.60/0.78	               app_encode_app(a, a, cL, sk_Xx)), 
0.60/0.78	             app_encode_app(a, a, cL, sk_Xy)))),
0.60/0.78	    inference('demod', [status(thm)], ['23', '5'])).
0.60/0.78	tff('25', plain,
0.60/0.78	    (~ app_encode_app(a, $o, sk_X, 
0.60/0.78	         app_encode_app(a, a, 
0.60/0.78	           app_encode_app(a, app_encode_fun(a, a), cP, 
0.60/0.78	             app_encode_app(a, a, cL, sk_Xx)), 
0.60/0.78	           app_encode_app(a, a, cL, sk_Xy)))
0.60/0.78	     | sk_Xt(sk_X) != cZ
0.60/0.78	     | ~ app_encode_app(a, $o, sk_X, 
0.60/0.78	           app_encode_app(a, a, 
0.60/0.78	             app_encode_app(a, app_encode_fun(a, a), cP, 
0.60/0.78	               app_encode_app(a, a, cL, sk_Xt(sk_X))), 
0.60/0.78	             app_encode_app(a, a, cL, sk_Xu(sk_X))))),
0.60/0.78	    inference('simplify', [status(thm)], ['24'])).
0.60/0.78	tff('26', plain,
0.60/0.78	    (~ $true
0.60/0.78	     | ~ app_encode_app(a, $o, sk_X, 
0.60/0.78	           app_encode_app(a, a, 
0.60/0.78	             app_encode_app(a, app_encode_fun(a, a), cP, sk_Xt(sk_X)), 
0.60/0.78	             sk_Xu(sk_X)))
0.60/0.78	     | sk_Xt(sk_X) != cZ
0.60/0.78	     | ~ app_encode_app(a, $o, sk_X, 
0.60/0.78	           app_encode_app(a, a, 
0.60/0.78	             app_encode_app(a, app_encode_fun(a, a), cP, 
0.60/0.78	               app_encode_app(a, a, cL, sk_Xx)), 
0.60/0.78	             app_encode_app(a, a, cL, sk_Xy)))),
0.60/0.78	    inference('sup-', [status(thm)], ['0', '25'])).
0.60/0.78	tff('27', plain,
0.60/0.78	    (~ $true
0.60/0.78	     | ~ $true
0.60/0.78	     | sk_Xt(sk_X) != cZ
0.60/0.78	     | ~ app_encode_app(a, $o, sk_X, 
0.60/0.78	           app_encode_app(a, a, 
0.60/0.78	             app_encode_app(a, app_encode_fun(a, a), cP, 
0.60/0.78	               app_encode_app(a, a, cL, sk_Xx)), 
0.60/0.78	             app_encode_app(a, a, cL, sk_Xy)))),
0.60/0.78	    inference('demod', [status(thm)], ['26', '5'])).
0.60/0.78	tff('28', plain,
0.60/0.78	    (~ app_encode_app(a, $o, sk_X, 
0.60/0.78	         app_encode_app(a, a, 
0.60/0.78	           app_encode_app(a, app_encode_fun(a, a), cP, 
0.60/0.78	             app_encode_app(a, a, cL, sk_Xx)), 
0.60/0.78	           app_encode_app(a, a, cL, sk_Xy)))
0.60/0.78	     | sk_Xt(sk_X) != cZ),
0.60/0.78	    inference('simplify', [status(thm)], ['27'])).
0.60/0.78	tff('29', plain,
0.60/0.78	    (~ $true
0.60/0.78	     | ~ app_encode_app(a, $o, sk_X, 
0.60/0.78	           app_encode_app(a, a, 
0.60/0.78	             app_encode_app(a, app_encode_fun(a, a), cP, sk_Xx), sk_Xy))
0.60/0.78	     | sk_Xt(sk_X) != cZ),
0.60/0.78	    inference('sup-', [status(thm)], ['0', '28'])).
0.60/0.78	tff('30', plain, (~ $true | ~ $true | sk_Xt(sk_X) != cZ),
0.60/0.78	    inference('demod', [status(thm)], ['29', '3'])).
0.60/0.78	tff('31', plain, sk_Xt(sk_X) != cZ,
0.60/0.78	    inference('simplify', [status(thm)], ['30'])).
0.60/0.78	tff('32', plain, $false,
0.60/0.78	    inference('simplify_reflect-', [status(thm)], ['21', '31'])).
0.60/0.78	
0.60/0.78	% SZS output end Refutation
0.60/0.78	EOF
