0.00/0.00	% File    : /export/starexec/sandbox2/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 $2 \
0.00/0.01	  --simultaneous-sup false \
0.00/0.01	  --no-max-vars \
0.00/0.01	  --no-fool
0.00/0.19	% Computer   : n092.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 17:47:09 CST 2018
0.00/0.45	% done 404 iterations in 0.248s
0.00/0.45	% SZS status Theorem for 'stdin'
0.00/0.45	% SZS output start Refutation
0.00/0.45	tff(zf_stmt_8, conjecture,
0.00/0.45	  (((![Xu:a,Xv:a,Xw:a]:
0.00/0.45	       ((app_encode_app(a,$o,app_encode_app(a,app_encode_fun(a,$o),cR,Xu),Xv) & 
0.00/0.45	         app_encode_app(a,$o,app_encode_app(a,app_encode_fun(a,$o),cR,Xw),Xv)) =>
0.00/0.45	        app_encode_app(a,$o,app_encode_app(a,app_encode_fun(a,$o),cR,Xu),Xw))) & 
0.00/0.45	    (![Xx:a]:
0.00/0.45	       app_encode_app(a,$o,app_encode_app(a,app_encode_fun(a,$o),cR,Xx),Xx))) =>
0.00/0.45	   (((![Xx:a]:
0.00/0.45	        (?[Xy]:
0.00/0.45	           app_encode_app($i,$o,app_encode_app(a,app_encode_fun($i,$o),f,Xx),
0.00/0.45	                          Xy))) & 
0.00/0.45	     (![Xx:a,Xy1,Xy2]:
0.00/0.45	        ((app_encode_app($i,$o,app_encode_app(a,app_encode_fun($i,$o),f,Xx),
0.00/0.45	                         Xy1) & 
0.00/0.45	          app_encode_app($i,$o,app_encode_app(a,app_encode_fun($i,$o),f,Xx),
0.00/0.45	                         Xy2)) =>
0.00/0.45	         app_encode_app($i,$o,
0.00/0.45	                        app_encode_app($i,app_encode_fun($i,$o),cS,Xy1),Xy2))) & 
0.00/0.45	     (![Xx1:a,Xx2:a,Xy]:
0.00/0.45	        ((app_encode_app($i,$o,app_encode_app(a,app_encode_fun($i,$o),f,Xx1),
0.00/0.45	                         Xy) & 
0.00/0.45	          app_encode_app($i,$o,app_encode_app(a,app_encode_fun($i,$o),f,Xx2),
0.00/0.45	                         Xy)) =>
0.00/0.45	         app_encode_app(a,$o,app_encode_app(a,app_encode_fun(a,$o),cR,Xx1),
0.00/0.45	                        Xx2)))) =>
0.00/0.45	    ((![Xx:a]:
0.00/0.45	        (?[Xy]:
0.00/0.45	           (![Xw:a]:
0.00/0.45	              (app_encode_app($i,$o,
0.00/0.45	                              app_encode_app(a,app_encode_fun($i,$o),f,Xx),Xy) | 
0.00/0.45	               ((~
0.00/0.45	                  app_encode_app($i,$o,
0.00/0.45	                                 app_encode_app(a,app_encode_fun($i,$o),f,Xw),
0.00/0.45	                                 Xy)) & 
0.00/0.45	                app_encode_app(a,$o,
0.00/0.45	                               app_encode_app(a,app_encode_fun(a,$o),cR,Xx),z)))))) & 
0.00/0.45	     (![Xy,Xx1:a,Xx2:a]:
0.00/0.45	        (((![Xw:a]:
0.00/0.45	             (app_encode_app($i,$o,
0.00/0.45	                             app_encode_app(a,app_encode_fun($i,$o),f,Xx1),Xy) | 
0.00/0.45	              ((~
0.00/0.45	                 app_encode_app($i,$o,
0.00/0.45	                                app_encode_app(a,app_encode_fun($i,$o),f,Xw),
0.00/0.45	                                Xy)) & 
0.00/0.45	               app_encode_app(a,$o,
0.00/0.45	                              app_encode_app(a,app_encode_fun(a,$o),cR,Xx1),z)))) & 
0.00/0.45	          (![Xw:a]:
0.00/0.45	             (app_encode_app($i,$o,
0.00/0.45	                             app_encode_app(a,app_encode_fun($i,$o),f,Xx2),Xy) | 
0.00/0.45	              ((~
0.00/0.45	                 app_encode_app($i,$o,
0.00/0.45	                                app_encode_app(a,app_encode_fun($i,$o),f,Xw),
0.00/0.45	                                Xy)) & 
0.00/0.45	               app_encode_app(a,$o,
0.00/0.45	                              app_encode_app(a,app_encode_fun(a,$o),cR,Xx2),z))))) =>
0.00/0.45	         app_encode_app(a,$o,app_encode_app(a,app_encode_fun(a,$o),cR,Xx1),
0.00/0.45	                        Xx2))) & 
0.00/0.45	     (![Xy]:
0.00/0.45	        (?[Xx:a]:
0.00/0.45	           (![Xw:a]:
0.00/0.45	              (app_encode_app($i,$o,
0.00/0.45	                              app_encode_app(a,app_encode_fun($i,$o),f,Xx),Xy) | 
0.00/0.45	               ((~
0.00/0.45	                  app_encode_app($i,$o,
0.00/0.45	                                 app_encode_app(a,app_encode_fun($i,$o),f,Xw),
0.00/0.45	                                 Xy)) & 
0.00/0.45	                app_encode_app(a,$o,
0.00/0.45	                               app_encode_app(a,app_encode_fun(a,$o),cR,Xx),z)))))))))).
0.00/0.45	tff(zf_stmt_0, negated_conjecture,
0.00/0.45	  (~
0.00/0.45	    (((![Xu:a,Xv:a,Xw:a]:
0.00/0.45	         ((app_encode_app(a,$o,app_encode_app(a,app_encode_fun(a,$o),cR,Xu),
0.00/0.45	                          Xv) & 
0.00/0.45	           app_encode_app(a,$o,app_encode_app(a,app_encode_fun(a,$o),cR,Xw),
0.00/0.45	                          Xv)) =>
0.00/0.45	          app_encode_app(a,$o,app_encode_app(a,app_encode_fun(a,$o),cR,Xu),Xw))) & 
0.00/0.45	      (![Xx:a]:
0.00/0.45	         app_encode_app(a,$o,app_encode_app(a,app_encode_fun(a,$o),cR,Xx),Xx))) =>
0.00/0.45	     (((![Xx:a]:
0.00/0.45	          (?[Xy]:
0.00/0.45	             app_encode_app($i,$o,
0.00/0.45	                            app_encode_app(a,app_encode_fun($i,$o),f,Xx),Xy))) & 
0.00/0.45	       (![Xx:a,Xy1,Xy2]:
0.00/0.45	          ((app_encode_app($i,$o,
0.00/0.45	                           app_encode_app(a,app_encode_fun($i,$o),f,Xx),Xy1) & 
0.00/0.45	            app_encode_app($i,$o,
0.00/0.45	                           app_encode_app(a,app_encode_fun($i,$o),f,Xx),Xy2)) =>
0.00/0.45	           app_encode_app($i,$o,
0.00/0.45	                          app_encode_app($i,app_encode_fun($i,$o),cS,Xy1),Xy2))) & 
0.00/0.45	       (![Xx1:a,Xx2:a,Xy]:
0.00/0.45	          ((app_encode_app($i,$o,
0.00/0.45	                           app_encode_app(a,app_encode_fun($i,$o),f,Xx1),Xy) & 
0.00/0.45	            app_encode_app($i,$o,
0.00/0.45	                           app_encode_app(a,app_encode_fun($i,$o),f,Xx2),Xy)) =>
0.00/0.45	           app_encode_app(a,$o,app_encode_app(a,app_encode_fun(a,$o),cR,Xx1),
0.00/0.45	                          Xx2)))) =>
0.00/0.45	      ((![Xx:a]:
0.00/0.45	          (?[Xy]:
0.00/0.45	             (![Xw:a]:
0.00/0.45	                (app_encode_app($i,$o,
0.00/0.45	                                app_encode_app(a,app_encode_fun($i,$o),f,Xx),
0.00/0.45	                                Xy) | 
0.00/0.45	                 ((~
0.00/0.45	                    app_encode_app($i,$o,
0.00/0.45	                                   app_encode_app(a,app_encode_fun($i,$o),f,
0.00/0.45	                                                  Xw),
0.00/0.45	                                   Xy)) & 
0.00/0.45	                  app_encode_app(a,$o,
0.00/0.45	                                 app_encode_app(a,app_encode_fun(a,$o),cR,Xx),
0.00/0.45	                                 z)))))) & 
0.00/0.45	       (![Xy,Xx1:a,Xx2:a]:
0.00/0.45	          (((![Xw:a]:
0.00/0.45	               (app_encode_app($i,$o,
0.00/0.45	                               app_encode_app(a,app_encode_fun($i,$o),f,Xx1),
0.00/0.45	                               Xy) | 
0.00/0.45	                ((~
0.00/0.45	                   app_encode_app($i,$o,
0.00/0.45	                                  app_encode_app(a,app_encode_fun($i,$o),f,Xw),
0.00/0.45	                                  Xy)) & 
0.00/0.45	                 app_encode_app(a,$o,
0.00/0.45	                                app_encode_app(a,app_encode_fun(a,$o),cR,Xx1),
0.00/0.45	                                z)))) & 
0.00/0.45	            (![Xw:a]:
0.00/0.45	               (app_encode_app($i,$o,
0.00/0.45	                               app_encode_app(a,app_encode_fun($i,$o),f,Xx2),
0.00/0.45	                               Xy) | 
0.00/0.45	                ((~
0.00/0.45	                   app_encode_app($i,$o,
0.00/0.45	                                  app_encode_app(a,app_encode_fun($i,$o),f,Xw),
0.00/0.45	                                  Xy)) & 
0.00/0.45	                 app_encode_app(a,$o,
0.00/0.45	                                app_encode_app(a,app_encode_fun(a,$o),cR,Xx2),
0.00/0.45	                                z))))) =>
0.00/0.45	           app_encode_app(a,$o,app_encode_app(a,app_encode_fun(a,$o),cR,Xx1),
0.00/0.45	                          Xx2))) & 
0.00/0.45	       (![Xy]:
0.00/0.45	          (?[Xx:a]:
0.00/0.45	             (![Xw:a]:
0.00/0.45	                (app_encode_app($i,$o,
0.00/0.45	                                app_encode_app(a,app_encode_fun($i,$o),f,Xx),
0.00/0.45	                                Xy) | 
0.00/0.45	                 ((~
0.00/0.45	                    app_encode_app($i,$o,
0.00/0.45	                                   app_encode_app(a,app_encode_fun($i,$o),f,
0.00/0.45	                                                  Xw),
0.00/0.45	                                   Xy)) & 
0.00/0.45	                  app_encode_app(a,$o,
0.00/0.45	                                 app_encode_app(a,app_encode_fun(a,$o),cR,Xx),
0.00/0.45	                                 z))))))))))).
0.00/0.45	tff('0', plain,
0.00/0.45	    ![X7 : a]:
0.00/0.45	      app_encode_app(a, $o, 
0.00/0.45	        app_encode_app(a, app_encode_fun(a, $o), cR, X7), X7),
0.00/0.45	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.45	tff('1', plain,
0.00/0.45	    ![X18 : a]:
0.00/0.45	      app_encode_app($i, $o, 
0.00/0.45	        app_encode_app(a, app_encode_fun($i, $o), f, X18), sk_Xy(X18)),
0.00/0.45	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.45	tff('2', plain,
0.00/0.45	    ![X12 : a, X13 : a, X14]:
0.00/0.45	      (app_encode_app(a, $o, 
0.00/0.45	         app_encode_app(a, app_encode_fun(a, $o), cR, X12), X13)
0.00/0.45	       | ~ app_encode_app($i, $o, 
0.00/0.45	             app_encode_app(a, app_encode_fun($i, $o), f, X12), X14)
0.00/0.45	       | ~ app_encode_app($i, $o, 
0.00/0.45	             app_encode_app(a, app_encode_fun($i, $o), f, X13), X14)),
0.00/0.45	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.45	tff('3', plain,
0.00/0.45	    ![X0 : a, X1 : a]:
0.00/0.45	      (~ $true
0.00/0.45	       | ~ app_encode_app($i, $o, 
0.00/0.45	             app_encode_app(a, app_encode_fun($i, $o), f, X1), sk_Xy(X0))
0.00/0.45	       | app_encode_app(a, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun(a, $o), cR, X0), X1)),
0.00/0.45	    inference('sup-', [status(thm)], ['1', '2'])).
0.00/0.45	tff('4', plain,
0.00/0.45	    ![X0 : a, X1 : a]:
0.00/0.45	      (app_encode_app(a, $o, 
0.00/0.45	         app_encode_app(a, app_encode_fun(a, $o), cR, X0), X1)
0.00/0.45	       | ~ app_encode_app($i, $o, 
0.00/0.45	             app_encode_app(a, app_encode_fun($i, $o), f, X1), sk_Xy(X0))),
0.00/0.45	    inference('simplify', [status(thm)], ['3'])).
0.00/0.45	tff('5', plain,
0.00/0.45	    ![X8, X9 : a]:
0.00/0.45	      (~ app_encode_app($i, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx), X8)
0.00/0.45	       | app_encode_app(a, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun(a, $o), cR, sk_Xx2), z)
0.00/0.45	       | app_encode_app($i, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx2), sk_Xy1)
0.00/0.45	       | app_encode_app($i, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xw1(X9)), sk_Xy2)
0.00/0.45	       | ~ app_encode_app(a, $o, 
0.00/0.45	             app_encode_app(a, app_encode_fun(a, $o), cR, X9), z)),
0.00/0.45	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.45	tff('6', plain,
0.00/0.45	    ![X8, X9 : a]:
0.00/0.45	      (~ app_encode_app($i, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx), X8)
0.00/0.45	       | app_encode_app(a, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun(a, $o), cR, sk_Xx2), z)
0.00/0.45	       | app_encode_app($i, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx2), sk_Xy1)
0.00/0.45	       | ~ app_encode_app($i, $o, 
0.00/0.45	             app_encode_app(a, app_encode_fun($i, $o), f, X9), sk_Xy2)),
0.00/0.45	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.45	tff('7', plain,
0.00/0.45	    ![X0 : a]:
0.00/0.45	      (~ $true
0.00/0.45	       | ~ app_encode_app($i, $o, 
0.00/0.45	             app_encode_app(a, app_encode_fun($i, $o), f, X0), sk_Xy2)
0.00/0.45	       | app_encode_app($i, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx2), sk_Xy1)
0.00/0.45	       | app_encode_app(a, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun(a, $o), cR, sk_Xx2), z)),
0.00/0.45	    inference('sup-', [status(thm)], ['1', '6'])).
0.00/0.45	tff('8', plain,
0.00/0.45	    ![X0 : a]:
0.00/0.45	      (app_encode_app(a, $o, 
0.00/0.45	         app_encode_app(a, app_encode_fun(a, $o), cR, sk_Xx2), z)
0.00/0.45	       | app_encode_app($i, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx2), sk_Xy1)
0.00/0.45	       | ~ app_encode_app($i, $o, 
0.00/0.45	             app_encode_app(a, app_encode_fun($i, $o), f, X0), sk_Xy2)),
0.00/0.45	    inference('simplify', [status(thm)], ['7'])).
0.00/0.45	tff('9', plain,
0.00/0.45	    ![X8, X9 : a]:
0.00/0.45	      (~ app_encode_app(a, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun(a, $o), cR, X9), z)
0.00/0.45	       | app_encode_app($i, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx2), sk_Xy1)
0.00/0.45	       | app_encode_app(a, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun(a, $o), cR, sk_Xx2), z)
0.00/0.45	       | ~ app_encode_app($i, $o, 
0.00/0.45	             app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx), X8)),
0.00/0.45	    inference('clc', [status(thm)], ['5', '8'])).
0.00/0.45	tff('10', plain,
0.00/0.45	    ![X0]:
0.00/0.45	      (~ $true
0.00/0.45	       | ~ app_encode_app($i, $o, 
0.00/0.45	             app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx), X0)
0.00/0.45	       | app_encode_app(a, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun(a, $o), cR, sk_Xx2), z)
0.00/0.45	       | app_encode_app($i, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx2), sk_Xy1)),
0.00/0.45	    inference('sup-', [status(thm)], ['0', '9'])).
0.00/0.45	tff('11', plain,
0.00/0.45	    ![X0]:
0.00/0.45	      (app_encode_app($i, $o, 
0.00/0.45	         app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx2), sk_Xy1)
0.00/0.45	       | app_encode_app(a, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun(a, $o), cR, sk_Xx2), z)
0.00/0.45	       | ~ app_encode_app($i, $o, 
0.00/0.45	             app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx), X0)),
0.00/0.45	    inference('simplify', [status(thm)], ['10'])).
0.00/0.45	tff('12', plain,
0.00/0.45	    (~ $true
0.00/0.45	     | app_encode_app(a, $o, 
0.00/0.45	         app_encode_app(a, app_encode_fun(a, $o), cR, sk_Xx2), z)
0.00/0.45	     | app_encode_app($i, $o, 
0.00/0.45	         app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx2), sk_Xy1)),
0.00/0.45	    inference('sup-', [status(thm)], ['1', '11'])).
0.00/0.45	tff('13', plain,
0.00/0.45	    (app_encode_app($i, $o, 
0.00/0.45	       app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx2), sk_Xy1)
0.00/0.45	     | app_encode_app(a, $o, 
0.00/0.45	         app_encode_app(a, app_encode_fun(a, $o), cR, sk_Xx2), z)),
0.00/0.45	    inference('simplify', [status(thm)], ['12'])).
0.00/0.45	tff('14', plain,
0.00/0.45	    ![X4 : a, X5 : a, X6 : a]:
0.00/0.45	      (~ app_encode_app(a, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun(a, $o), cR, X4), X5)
0.00/0.45	       | ~ app_encode_app(a, $o, 
0.00/0.45	             app_encode_app(a, app_encode_fun(a, $o), cR, X6), X5)
0.00/0.45	       | app_encode_app(a, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun(a, $o), cR, X4), X6)),
0.00/0.45	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.45	tff('15', plain,
0.00/0.45	    ![X0 : a]:
0.00/0.45	      (~ $true
0.00/0.45	       | app_encode_app($i, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx2), sk_Xy1)
0.00/0.45	       | app_encode_app(a, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun(a, $o), cR, sk_Xx2), X0)
0.00/0.45	       | ~ app_encode_app(a, $o, 
0.00/0.45	             app_encode_app(a, app_encode_fun(a, $o), cR, X0), z)),
0.00/0.45	    inference('sup-', [status(thm)], ['13', '14'])).
0.00/0.45	tff('16', plain,
0.00/0.45	    ![X0 : a]:
0.00/0.45	      (~ app_encode_app(a, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun(a, $o), cR, X0), z)
0.00/0.45	       | app_encode_app(a, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun(a, $o), cR, sk_Xx2), X0)
0.00/0.45	       | app_encode_app($i, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx2), sk_Xy1)),
0.00/0.45	    inference('simplify', [status(thm)], ['15'])).
0.00/0.45	tff('17', plain,
0.00/0.45	    ![X0 : a]:
0.00/0.45	      (~ $true
0.00/0.45	       | ~ app_encode_app($i, $o, 
0.00/0.45	             app_encode_app(a, app_encode_fun($i, $o), f, z), sk_Xy(X0))
0.00/0.45	       | app_encode_app($i, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx2), sk_Xy1)
0.00/0.45	       | app_encode_app(a, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun(a, $o), cR, sk_Xx2), X0)),
0.00/0.45	    inference('sup-', [status(thm)], ['4', '16'])).
0.00/0.45	tff('18', plain,
0.00/0.45	    ![X0 : a]:
0.00/0.45	      (app_encode_app(a, $o, 
0.00/0.45	         app_encode_app(a, app_encode_fun(a, $o), cR, sk_Xx2), X0)
0.00/0.45	       | app_encode_app($i, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx2), sk_Xy1)
0.00/0.45	       | ~ app_encode_app($i, $o, 
0.00/0.45	             app_encode_app(a, app_encode_fun($i, $o), f, z), sk_Xy(X0))),
0.00/0.45	    inference('simplify', [status(thm)], ['17'])).
0.00/0.45	tff('19', plain,
0.00/0.45	    ![X8, X9 : a]:
0.00/0.45	      (~ app_encode_app($i, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx), X8)
0.00/0.45	       | app_encode_app(a, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun(a, $o), cR, sk_Xx1), z)
0.00/0.45	       | app_encode_app($i, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx1), sk_Xy1)
0.00/0.45	       | app_encode_app($i, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xw1(X9)), sk_Xy2)
0.00/0.45	       | ~ app_encode_app(a, $o, 
0.00/0.45	             app_encode_app(a, app_encode_fun(a, $o), cR, X9), z)),
0.00/0.45	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.45	tff('20', plain,
0.00/0.45	    ![X8, X9 : a]:
0.00/0.45	      (~ app_encode_app($i, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx), X8)
0.00/0.45	       | app_encode_app(a, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun(a, $o), cR, sk_Xx1), z)
0.00/0.45	       | app_encode_app($i, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx1), sk_Xy1)
0.00/0.45	       | ~ app_encode_app($i, $o, 
0.00/0.45	             app_encode_app(a, app_encode_fun($i, $o), f, X9), sk_Xy2)),
0.00/0.45	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.45	tff('21', plain,
0.00/0.45	    ![X0 : a]:
0.00/0.45	      (~ $true
0.00/0.45	       | ~ app_encode_app($i, $o, 
0.00/0.45	             app_encode_app(a, app_encode_fun($i, $o), f, X0), sk_Xy2)
0.00/0.45	       | app_encode_app($i, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx1), sk_Xy1)
0.00/0.45	       | app_encode_app(a, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun(a, $o), cR, sk_Xx1), z)),
0.00/0.45	    inference('sup-', [status(thm)], ['1', '20'])).
0.00/0.45	tff('22', plain,
0.00/0.45	    ![X0 : a]:
0.00/0.45	      (app_encode_app(a, $o, 
0.00/0.45	         app_encode_app(a, app_encode_fun(a, $o), cR, sk_Xx1), z)
0.00/0.45	       | app_encode_app($i, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx1), sk_Xy1)
0.00/0.45	       | ~ app_encode_app($i, $o, 
0.00/0.45	             app_encode_app(a, app_encode_fun($i, $o), f, X0), sk_Xy2)),
0.00/0.45	    inference('simplify', [status(thm)], ['21'])).
0.00/0.45	tff('23', plain,
0.00/0.45	    ![X8, X9 : a]:
0.00/0.45	      (~ app_encode_app(a, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun(a, $o), cR, X9), z)
0.00/0.45	       | app_encode_app($i, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx1), sk_Xy1)
0.00/0.45	       | app_encode_app(a, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun(a, $o), cR, sk_Xx1), z)
0.00/0.45	       | ~ app_encode_app($i, $o, 
0.00/0.45	             app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx), X8)),
0.00/0.45	    inference('clc', [status(thm)], ['19', '22'])).
0.00/0.45	tff('24', plain,
0.00/0.45	    ![X0]:
0.00/0.45	      (~ $true
0.00/0.45	       | ~ app_encode_app($i, $o, 
0.00/0.45	             app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx), X0)
0.00/0.45	       | app_encode_app(a, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun(a, $o), cR, sk_Xx1), z)
0.00/0.45	       | app_encode_app($i, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx1), sk_Xy1)),
0.00/0.45	    inference('sup-', [status(thm)], ['0', '23'])).
0.00/0.45	tff('25', plain,
0.00/0.45	    ![X0]:
0.00/0.45	      (app_encode_app($i, $o, 
0.00/0.45	         app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx1), sk_Xy1)
0.00/0.45	       | app_encode_app(a, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun(a, $o), cR, sk_Xx1), z)
0.00/0.45	       | ~ app_encode_app($i, $o, 
0.00/0.45	             app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx), X0)),
0.00/0.45	    inference('simplify', [status(thm)], ['24'])).
0.00/0.45	tff('26', plain,
0.00/0.45	    (~ $true
0.00/0.45	     | app_encode_app(a, $o, 
0.00/0.45	         app_encode_app(a, app_encode_fun(a, $o), cR, sk_Xx1), z)
0.00/0.45	     | app_encode_app($i, $o, 
0.00/0.45	         app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx1), sk_Xy1)),
0.00/0.45	    inference('sup-', [status(thm)], ['1', '25'])).
0.00/0.45	tff('27', plain,
0.00/0.45	    (app_encode_app($i, $o, 
0.00/0.45	       app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx1), sk_Xy1)
0.00/0.45	     | app_encode_app(a, $o, 
0.00/0.45	         app_encode_app(a, app_encode_fun(a, $o), cR, sk_Xx1), z)),
0.00/0.45	    inference('simplify', [status(thm)], ['26'])).
0.00/0.45	tff('28', plain,
0.00/0.45	    ![X0 : a]:
0.00/0.45	      (~ $true
0.00/0.45	       | app_encode_app($i, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx1), sk_Xy1)
0.00/0.45	       | app_encode_app(a, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun(a, $o), cR, sk_Xx1), X0)
0.00/0.45	       | ~ app_encode_app(a, $o, 
0.00/0.45	             app_encode_app(a, app_encode_fun(a, $o), cR, X0), z)),
0.00/0.45	    inference('sup-', [status(thm)], ['27', '14'])).
0.00/0.45	tff('29', plain,
0.00/0.45	    ![X0 : a]:
0.00/0.45	      (~ app_encode_app(a, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun(a, $o), cR, X0), z)
0.00/0.45	       | app_encode_app(a, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun(a, $o), cR, sk_Xx1), X0)
0.00/0.45	       | app_encode_app($i, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx1), sk_Xy1)),
0.00/0.45	    inference('simplify', [status(thm)], ['28'])).
0.00/0.45	tff('30', plain,
0.00/0.45	    (~ $true
0.00/0.45	     | ~ app_encode_app($i, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun($i, $o), f, z), sk_Xy(z))
0.00/0.45	     | app_encode_app($i, $o, 
0.00/0.45	         app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx2), sk_Xy1)
0.00/0.45	     | app_encode_app($i, $o, 
0.00/0.45	         app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx1), sk_Xy1)
0.00/0.45	     | app_encode_app(a, $o, 
0.00/0.45	         app_encode_app(a, app_encode_fun(a, $o), cR, sk_Xx1), sk_Xx2)),
0.00/0.45	    inference('sup-', [status(thm)], ['18', '29'])).
0.00/0.45	tff('31', plain,
0.00/0.45	    (~ $true
0.00/0.45	     | ~ $true
0.00/0.45	     | app_encode_app($i, $o, 
0.00/0.45	         app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx2), sk_Xy1)
0.00/0.45	     | app_encode_app($i, $o, 
0.00/0.45	         app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx1), sk_Xy1)
0.00/0.45	     | app_encode_app(a, $o, 
0.00/0.45	         app_encode_app(a, app_encode_fun(a, $o), cR, sk_Xx1), sk_Xx2)),
0.00/0.45	    inference('demod', [status(thm)], ['30', '1'])).
0.00/0.45	tff('32', plain,
0.00/0.45	    (app_encode_app(a, $o, 
0.00/0.45	       app_encode_app(a, app_encode_fun(a, $o), cR, sk_Xx1), sk_Xx2)
0.00/0.45	     | app_encode_app($i, $o, 
0.00/0.45	         app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx1), sk_Xy1)
0.00/0.45	     | app_encode_app($i, $o, 
0.00/0.45	         app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx2), sk_Xy1)),
0.00/0.45	    inference('simplify', [status(thm)], ['31'])).
0.00/0.45	tff('33', plain,
0.00/0.45	    ![X8, X9 : a]:
0.00/0.45	      (~ app_encode_app($i, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx), X8)
0.00/0.45	       | ~ app_encode_app(a, $o, 
0.00/0.45	             app_encode_app(a, app_encode_fun(a, $o), cR, sk_Xx1), sk_Xx2)
0.00/0.45	       | app_encode_app($i, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xw1(X9)), sk_Xy2)
0.00/0.45	       | ~ app_encode_app(a, $o, 
0.00/0.45	             app_encode_app(a, app_encode_fun(a, $o), cR, X9), z)),
0.00/0.45	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.45	tff('34', plain,
0.00/0.45	    ![X8, X9 : a]:
0.00/0.45	      (~ app_encode_app($i, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx), X8)
0.00/0.45	       | ~ app_encode_app(a, $o, 
0.00/0.45	             app_encode_app(a, app_encode_fun(a, $o), cR, sk_Xx1), sk_Xx2)
0.00/0.45	       | ~ app_encode_app($i, $o, 
0.00/0.45	             app_encode_app(a, app_encode_fun($i, $o), f, X9), sk_Xy2)),
0.00/0.45	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.45	tff('35', plain,
0.00/0.45	    ![X0 : a]:
0.00/0.45	      (~ $true
0.00/0.45	       | ~ app_encode_app($i, $o, 
0.00/0.45	             app_encode_app(a, app_encode_fun($i, $o), f, X0), sk_Xy2)
0.00/0.45	       | ~ app_encode_app(a, $o, 
0.00/0.45	             app_encode_app(a, app_encode_fun(a, $o), cR, sk_Xx1), sk_Xx2)),
0.00/0.45	    inference('sup-', [status(thm)], ['1', '34'])).
0.00/0.45	tff('36', plain,
0.00/0.45	    ![X0 : a]:
0.00/0.45	      (~ app_encode_app(a, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun(a, $o), cR, sk_Xx1), sk_Xx2)
0.00/0.45	       | ~ app_encode_app($i, $o, 
0.00/0.45	             app_encode_app(a, app_encode_fun($i, $o), f, X0), sk_Xy2)),
0.00/0.45	    inference('simplify', [status(thm)], ['35'])).
0.00/0.45	tff('37', plain,
0.00/0.45	    ![X8, X9 : a]:
0.00/0.45	      (~ app_encode_app(a, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun(a, $o), cR, X9), z)
0.00/0.45	       | ~ app_encode_app(a, $o, 
0.00/0.45	             app_encode_app(a, app_encode_fun(a, $o), cR, sk_Xx1), sk_Xx2)
0.00/0.45	       | ~ app_encode_app($i, $o, 
0.00/0.45	             app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx), X8)),
0.00/0.45	    inference('clc', [status(thm)], ['33', '36'])).
0.00/0.45	tff('38', plain,
0.00/0.45	    ![X0]:
0.00/0.45	      (~ $true
0.00/0.45	       | ~ app_encode_app($i, $o, 
0.00/0.45	             app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx), X0)
0.00/0.45	       | ~ app_encode_app(a, $o, 
0.00/0.45	             app_encode_app(a, app_encode_fun(a, $o), cR, sk_Xx1), sk_Xx2)),
0.00/0.45	    inference('sup-', [status(thm)], ['0', '37'])).
0.00/0.45	tff('39', plain,
0.00/0.45	    ![X0]:
0.00/0.45	      (~ app_encode_app(a, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun(a, $o), cR, sk_Xx1), sk_Xx2)
0.00/0.45	       | ~ app_encode_app($i, $o, 
0.00/0.45	             app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx), X0)),
0.00/0.45	    inference('simplify', [status(thm)], ['38'])).
0.00/0.45	tff('40', plain,
0.00/0.45	    ![X0]:
0.00/0.45	      (~ $true
0.00/0.45	       | app_encode_app($i, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx2), sk_Xy1)
0.00/0.45	       | app_encode_app($i, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx1), sk_Xy1)
0.00/0.45	       | ~ app_encode_app($i, $o, 
0.00/0.45	             app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx), X0)),
0.00/0.45	    inference('sup-', [status(thm)], ['32', '39'])).
0.00/0.45	tff('41', plain,
0.00/0.45	    ![X0]:
0.00/0.45	      (~ app_encode_app($i, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx), X0)
0.00/0.45	       | app_encode_app($i, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx1), sk_Xy1)
0.00/0.45	       | app_encode_app($i, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx2), sk_Xy1)),
0.00/0.45	    inference('simplify', [status(thm)], ['40'])).
0.00/0.45	tff('42', plain,
0.00/0.45	    ![X8, X9 : a, X11 : a]:
0.00/0.45	      (~ app_encode_app($i, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx), X8)
0.00/0.45	       | ~ app_encode_app($i, $o, 
0.00/0.45	             app_encode_app(a, app_encode_fun($i, $o), f, X11), sk_Xy1)
0.00/0.45	       | app_encode_app($i, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx1), sk_Xy1)
0.00/0.45	       | app_encode_app($i, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xw1(X9)), sk_Xy2)
0.00/0.45	       | ~ app_encode_app(a, $o, 
0.00/0.45	             app_encode_app(a, app_encode_fun(a, $o), cR, X9), z)),
0.00/0.45	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.45	tff('43', plain,
0.00/0.45	    ![X8, X9 : a, X11 : a]:
0.00/0.45	      (~ app_encode_app($i, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx), X8)
0.00/0.45	       | ~ app_encode_app($i, $o, 
0.00/0.45	             app_encode_app(a, app_encode_fun($i, $o), f, X11), sk_Xy1)
0.00/0.45	       | app_encode_app($i, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx1), sk_Xy1)
0.00/0.45	       | ~ app_encode_app($i, $o, 
0.00/0.45	             app_encode_app(a, app_encode_fun($i, $o), f, X9), sk_Xy2)),
0.00/0.45	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.45	tff('44', plain,
0.00/0.45	    ![X0 : a, X1 : a]:
0.00/0.45	      (~ $true
0.00/0.45	       | ~ app_encode_app($i, $o, 
0.00/0.45	             app_encode_app(a, app_encode_fun($i, $o), f, X0), sk_Xy2)
0.00/0.45	       | app_encode_app($i, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx1), sk_Xy1)
0.00/0.45	       | ~ app_encode_app($i, $o, 
0.00/0.45	             app_encode_app(a, app_encode_fun($i, $o), f, X1), sk_Xy1)),
0.00/0.45	    inference('sup-', [status(thm)], ['1', '43'])).
0.00/0.45	tff('45', plain,
0.00/0.45	    ![X0 : a, X1 : a]:
0.00/0.45	      (~ app_encode_app($i, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun($i, $o), f, X1), sk_Xy1)
0.00/0.45	       | app_encode_app($i, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx1), sk_Xy1)
0.00/0.45	       | ~ app_encode_app($i, $o, 
0.00/0.45	             app_encode_app(a, app_encode_fun($i, $o), f, X0), sk_Xy2)),
0.00/0.45	    inference('simplify', [status(thm)], ['44'])).
0.00/0.45	tff('46', plain,
0.00/0.45	    ![X8, X9 : a, X11 : a]:
0.00/0.45	      (~ app_encode_app(a, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun(a, $o), cR, X9), z)
0.00/0.45	       | app_encode_app($i, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx1), sk_Xy1)
0.00/0.45	       | ~ app_encode_app($i, $o, 
0.00/0.45	             app_encode_app(a, app_encode_fun($i, $o), f, X11), sk_Xy1)
0.00/0.45	       | ~ app_encode_app($i, $o, 
0.00/0.45	             app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx), X8)),
0.00/0.45	    inference('clc', [status(thm)], ['42', '45'])).
0.00/0.45	tff('47', plain,
0.00/0.45	    ![X0, X1 : a]:
0.00/0.45	      (~ $true
0.00/0.45	       | ~ app_encode_app($i, $o, 
0.00/0.45	             app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx), X0)
0.00/0.45	       | ~ app_encode_app($i, $o, 
0.00/0.45	             app_encode_app(a, app_encode_fun($i, $o), f, X1), sk_Xy1)
0.00/0.45	       | app_encode_app($i, $o, 
0.00/0.45	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx1), sk_Xy1)),
0.00/0.45	    inference('sup-', [status(thm)], ['0', '46'])).
0.00/0.45	tff('48', plain,
0.00/0.45	    ![X0, X1 : a]:
0.00/0.45	      (app_encode_app($i, $o, 
0.00/0.45	         app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx1), sk_Xy1)
0.00/0.45	       | ~ app_encode_app($i, $o, 
0.00/0.45	             app_encode_app(a, app_encode_fun($i, $o), f, X1), sk_Xy1)
0.00/0.45	       | ~ app_encode_app($i, $o, 
0.00/0.45	             app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx), X0)),
0.00/0.45	    inference('simplify', [status(thm)], ['47'])).
0.00/0.45	tff('49', plain,
0.00/0.45	    ![X0]:
0.00/0.45	      (app_encode_app($i, $o, 
0.00/0.45	         app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx1), sk_Xy1)
0.00/0.46	       | ~ app_encode_app($i, $o, 
0.00/0.46	             app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx), X0)),
0.00/0.46	    inference('clc', [status(thm)], ['41', '48'])).
0.00/0.46	tff('50', plain,
0.00/0.46	    (~ $true
0.00/0.46	     | app_encode_app($i, $o, 
0.00/0.46	         app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx1), sk_Xy1)),
0.00/0.46	    inference('sup-', [status(thm)], ['1', '49'])).
0.00/0.46	tff('51', plain,
0.00/0.46	    app_encode_app($i, $o, 
0.00/0.46	      app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx1), sk_Xy1),
0.00/0.46	    inference('simplify', [status(thm)], ['50'])).
0.00/0.46	tff('52', plain,
0.00/0.46	    ![X8, X9 : a, X10 : a]:
0.00/0.46	      (~ app_encode_app($i, $o, 
0.00/0.46	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx), X8)
0.00/0.46	       | ~ app_encode_app($i, $o, 
0.00/0.46	             app_encode_app(a, app_encode_fun($i, $o), f, X10), sk_Xy1)
0.00/0.46	       | app_encode_app($i, $o, 
0.00/0.46	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx2), sk_Xy1)
0.00/0.46	       | app_encode_app($i, $o, 
0.00/0.46	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xw1(X9)), sk_Xy2)
0.00/0.46	       | ~ app_encode_app(a, $o, 
0.00/0.46	             app_encode_app(a, app_encode_fun(a, $o), cR, X9), z)),
0.00/0.46	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.46	tff('53', plain,
0.00/0.46	    ![X0 : a, X1 : a]:
0.00/0.46	      (~ $true
0.00/0.46	       | ~ app_encode_app(a, $o, 
0.00/0.46	             app_encode_app(a, app_encode_fun(a, $o), cR, X0), z)
0.00/0.46	       | app_encode_app($i, $o, 
0.00/0.46	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xw1(X0)), sk_Xy2)
0.00/0.46	       | app_encode_app($i, $o, 
0.00/0.46	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx2), sk_Xy1)
0.00/0.46	       | ~ app_encode_app($i, $o, 
0.00/0.46	             app_encode_app(a, app_encode_fun($i, $o), f, X1), sk_Xy1)),
0.00/0.46	    inference('sup-', [status(thm)], ['1', '52'])).
0.00/0.46	tff('54', plain,
0.00/0.46	    ![X0 : a, X1 : a]:
0.00/0.46	      (~ app_encode_app($i, $o, 
0.00/0.46	           app_encode_app(a, app_encode_fun($i, $o), f, X1), sk_Xy1)
0.00/0.46	       | app_encode_app($i, $o, 
0.00/0.46	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx2), sk_Xy1)
0.00/0.46	       | app_encode_app($i, $o, 
0.00/0.46	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xw1(X0)), sk_Xy2)
0.00/0.46	       | ~ app_encode_app(a, $o, 
0.00/0.46	             app_encode_app(a, app_encode_fun(a, $o), cR, X0), z)),
0.00/0.46	    inference('simplify', [status(thm)], ['53'])).
0.00/0.46	tff('55', plain,
0.00/0.46	    ![X0 : a]:
0.00/0.46	      (~ $true
0.00/0.46	       | ~ app_encode_app($i, $o, 
0.00/0.46	             app_encode_app(a, app_encode_fun($i, $o), f, X0), sk_Xy1)
0.00/0.46	       | app_encode_app(a, $o, 
0.00/0.46	           app_encode_app(a, app_encode_fun(a, $o), cR, sk_Xx1), X0)),
0.00/0.46	    inference('sup-', [status(thm)], ['51', '2'])).
0.00/0.46	tff('56', plain,
0.00/0.46	    ![X0 : a]:
0.00/0.46	      (app_encode_app(a, $o, 
0.00/0.46	         app_encode_app(a, app_encode_fun(a, $o), cR, sk_Xx1), X0)
0.00/0.46	       | ~ app_encode_app($i, $o, 
0.00/0.46	             app_encode_app(a, app_encode_fun($i, $o), f, X0), sk_Xy1)),
0.00/0.46	    inference('simplify', [status(thm)], ['55'])).
0.00/0.46	tff('57', plain,
0.00/0.46	    ![X0]:
0.00/0.46	      (~ $true
0.00/0.46	       | ~ app_encode_app($i, $o, 
0.00/0.46	             app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx2), sk_Xy1)
0.00/0.46	       | ~ app_encode_app($i, $o, 
0.00/0.46	             app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx), X0)),
0.00/0.46	    inference('sup-', [status(thm)], ['56', '39'])).
0.00/0.46	tff('58', plain,
0.00/0.46	    ![X0]:
0.00/0.46	      (~ app_encode_app($i, $o, 
0.00/0.46	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx), X0)
0.00/0.46	       | ~ app_encode_app($i, $o, 
0.00/0.46	             app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx2), sk_Xy1)),
0.00/0.46	    inference('simplify', [status(thm)], ['57'])).
0.00/0.46	tff('59', plain,
0.00/0.46	    (~ $true
0.00/0.46	     | ~ app_encode_app($i, $o, 
0.00/0.46	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx2), sk_Xy1)),
0.00/0.46	    inference('sup-', [status(thm)], ['1', '58'])).
0.00/0.46	tff('60', plain,
0.00/0.46	    ~ app_encode_app($i, $o, 
0.00/0.46	        app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx2), sk_Xy1),
0.00/0.46	    inference('simplify', [status(thm)], ['59'])).
0.00/0.46	tff('61', plain,
0.00/0.46	    ![X0 : a, X1 : a]:
0.00/0.46	      (~ app_encode_app(a, $o, 
0.00/0.46	           app_encode_app(a, app_encode_fun(a, $o), cR, X0), z)
0.00/0.46	       | app_encode_app($i, $o, 
0.00/0.46	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xw1(X0)), sk_Xy2)
0.00/0.46	       | ~ app_encode_app($i, $o, 
0.00/0.46	             app_encode_app(a, app_encode_fun($i, $o), f, X1), sk_Xy1)),
0.00/0.46	    inference('clc', [status(thm)], ['54', '60'])).
0.00/0.46	tff('62', plain,
0.00/0.46	    ![X0 : a]:
0.00/0.46	      (~ $true
0.00/0.46	       | ~ app_encode_app($i, $o, 
0.00/0.46	             app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx2), sk_Xy1)
0.00/0.46	       | ~ app_encode_app($i, $o, 
0.00/0.46	             app_encode_app(a, app_encode_fun($i, $o), f, X0), sk_Xy2)),
0.00/0.46	    inference('sup-', [status(thm)], ['56', '36'])).
0.00/0.46	tff('63', plain,
0.00/0.46	    ![X0 : a]:
0.00/0.46	      (~ app_encode_app($i, $o, 
0.00/0.46	           app_encode_app(a, app_encode_fun($i, $o), f, X0), sk_Xy2)
0.00/0.46	       | ~ app_encode_app($i, $o, 
0.00/0.46	             app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx2), sk_Xy1)),
0.00/0.46	    inference('simplify', [status(thm)], ['62'])).
0.00/0.46	tff('64', plain,
0.00/0.46	    ![X0 : a]:
0.00/0.46	      (~ $true
0.00/0.46	       | app_encode_app($i, $o, 
0.00/0.46	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx2), sk_Xy1)
0.00/0.46	       | app_encode_app($i, $o, 
0.00/0.46	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx1), sk_Xy1)
0.00/0.46	       | ~ app_encode_app($i, $o, 
0.00/0.46	             app_encode_app(a, app_encode_fun($i, $o), f, X0), sk_Xy2)),
0.00/0.46	    inference('sup-', [status(thm)], ['32', '36'])).
0.00/0.46	tff('65', plain,
0.00/0.46	    ![X0 : a]:
0.00/0.46	      (~ app_encode_app($i, $o, 
0.00/0.46	           app_encode_app(a, app_encode_fun($i, $o), f, X0), sk_Xy2)
0.00/0.46	       | app_encode_app($i, $o, 
0.00/0.46	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx1), sk_Xy1)
0.00/0.46	       | app_encode_app($i, $o, 
0.00/0.46	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx2), sk_Xy1)),
0.00/0.46	    inference('simplify', [status(thm)], ['64'])).
0.00/0.46	tff('66', plain,
0.00/0.46	    ![X8, X9 : a, X10 : a]:
0.00/0.46	      (~ app_encode_app($i, $o, 
0.00/0.46	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx), X8)
0.00/0.46	       | ~ app_encode_app($i, $o, 
0.00/0.46	             app_encode_app(a, app_encode_fun($i, $o), f, X10), sk_Xy1)
0.00/0.46	       | app_encode_app($i, $o, 
0.00/0.46	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx2), sk_Xy1)
0.00/0.46	       | ~ app_encode_app($i, $o, 
0.00/0.46	             app_encode_app(a, app_encode_fun($i, $o), f, X9), sk_Xy2)),
0.00/0.46	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.46	tff('67', plain,
0.00/0.46	    ![X0 : a, X1 : a]:
0.00/0.46	      (~ $true
0.00/0.46	       | ~ app_encode_app($i, $o, 
0.00/0.46	             app_encode_app(a, app_encode_fun($i, $o), f, X0), sk_Xy2)
0.00/0.46	       | app_encode_app($i, $o, 
0.00/0.46	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx2), sk_Xy1)
0.00/0.46	       | ~ app_encode_app($i, $o, 
0.00/0.46	             app_encode_app(a, app_encode_fun($i, $o), f, X1), sk_Xy1)),
0.00/0.46	    inference('sup-', [status(thm)], ['1', '66'])).
0.00/0.46	tff('68', plain,
0.00/0.46	    ![X0 : a, X1 : a]:
0.00/0.46	      (~ app_encode_app($i, $o, 
0.00/0.46	           app_encode_app(a, app_encode_fun($i, $o), f, X1), sk_Xy1)
0.00/0.46	       | app_encode_app($i, $o, 
0.00/0.46	           app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx2), sk_Xy1)
0.00/0.46	       | ~ app_encode_app($i, $o, 
0.00/0.46	             app_encode_app(a, app_encode_fun($i, $o), f, X0), sk_Xy2)),
0.00/0.46	    inference('simplify', [status(thm)], ['67'])).
0.00/0.46	tff('69', plain,
0.00/0.46	    ![X0 : a]:
0.00/0.46	      (app_encode_app($i, $o, 
0.00/0.46	         app_encode_app(a, app_encode_fun($i, $o), f, sk_Xx2), sk_Xy1)
0.00/0.46	       | ~ app_encode_app($i, $o, 
0.00/0.46	             app_encode_app(a, app_encode_fun($i, $o), f, X0), sk_Xy2)),
0.00/0.46	    inference('clc', [status(thm)], ['65', '68'])).
0.00/0.46	tff('70', plain,
0.00/0.46	    ![X0 : a]:
0.00/0.46	      ~ app_encode_app($i, $o, 
0.00/0.46	          app_encode_app(a, app_encode_fun($i, $o), f, X0), sk_Xy2),
0.00/0.46	    inference('clc', [status(thm)], ['63', '69'])).
0.00/0.46	tff('71', plain,
0.00/0.46	    ![X0 : a, X1 : a]:
0.00/0.46	      (~ app_encode_app($i, $o, 
0.00/0.46	           app_encode_app(a, app_encode_fun($i, $o), f, X1), sk_Xy1)
0.00/0.46	       | ~ app_encode_app(a, $o, 
0.00/0.46	             app_encode_app(a, app_encode_fun(a, $o), cR, X0), z)),
0.00/0.46	    inference('clc', [status(thm)], ['61', '70'])).
0.00/0.46	tff('72', plain,
0.00/0.46	    ![X0 : a]:
0.00/0.46	      (~ $true
0.00/0.46	       | ~ app_encode_app(a, $o, 
0.00/0.46	             app_encode_app(a, app_encode_fun(a, $o), cR, X0), z)),
0.00/0.46	    inference('sup-', [status(thm)], ['51', '71'])).
0.00/0.46	tff('73', plain,
0.00/0.46	    ![X0 : a]:
0.00/0.46	      ~ app_encode_app(a, $o, 
0.00/0.46	          app_encode_app(a, app_encode_fun(a, $o), cR, X0), z),
0.00/0.46	    inference('simplify', [status(thm)], ['72'])).
0.00/0.46	tff('74', plain, ~ $true, inference('sup-', [status(thm)], ['0', '73'])).
0.00/0.46	tff('75', plain, $false, inference('simplify', [status(thm)], ['74'])).
0.00/0.46	
0.00/0.46	% SZS output end Refutation
0.00/0.46	EOF
