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    : 
0.00/0.00	#!/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 $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n095.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 17:29:53 CST 2018
0.38/0.57	% done 1176 iterations in 0.370s
0.38/0.57	% SZS status Theorem for 'stdin'
0.38/0.57	% SZS output start Refutation
0.38/0.58	tff(zf_stmt_4, conjecture,
0.38/0.58	  (![P:app_encode_fun(app_encode_fun(a,$o),$o)]:
0.38/0.58	     ((![Xx:a]:
0.38/0.58	         (?[Xp:app_encode_fun(a,$o)]:
0.38/0.58	            (app_encode_app(app_encode_fun(a,$o),$o,P,Xp) & 
0.38/0.58	             app_encode_app(a,$o,Xp,Xx) & 
0.38/0.58	             (![Xq:app_encode_fun(a,$o)]:
0.38/0.58	                ((app_encode_app(app_encode_fun(a,$o),$o,P,Xq) & 
0.38/0.58	                  app_encode_app(a,$o,Xq,Xx)) =>
0.38/0.58	                 (Xq = Xp)))))) =>
0.38/0.58	      ((![Xx:a]:
0.38/0.58	          (?[S:app_encode_fun(a,$o)]:
0.38/0.58	             (app_encode_app(app_encode_fun(a,$o),$o,P,S) & 
0.38/0.58	              app_encode_app(a,$o,S,Xx) & app_encode_app(a,$o,S,Xx)))) & 
0.38/0.58	       (![Xx:a,Xy:a]:
0.38/0.58	          ((?[S:app_encode_fun(a,$o)]:
0.38/0.58	              (app_encode_app(app_encode_fun(a,$o),$o,P,S) & 
0.38/0.58	               app_encode_app(a,$o,S,Xx) & app_encode_app(a,$o,S,Xy))) =>
0.38/0.58	           (?[S:app_encode_fun(a,$o)]:
0.38/0.58	              (app_encode_app(app_encode_fun(a,$o),$o,P,S) & 
0.38/0.58	               app_encode_app(a,$o,S,Xy) & app_encode_app(a,$o,S,Xx))))) & 
0.38/0.58	       (![Xx:a,Xy:a,Xz:a]:
0.38/0.58	          (((?[S:app_encode_fun(a,$o)]:
0.38/0.58	               (app_encode_app(app_encode_fun(a,$o),$o,P,S) & 
0.38/0.58	                app_encode_app(a,$o,S,Xx) & app_encode_app(a,$o,S,Xy))) & 
0.38/0.58	            (?[S:app_encode_fun(a,$o)]:
0.38/0.58	               (app_encode_app(app_encode_fun(a,$o),$o,P,S) & 
0.38/0.58	                app_encode_app(a,$o,S,Xy) & app_encode_app(a,$o,S,Xz)))) =>
0.38/0.58	           (?[S:app_encode_fun(a,$o)]:
0.38/0.58	              (app_encode_app(app_encode_fun(a,$o),$o,P,S) & 
0.38/0.58	               app_encode_app(a,$o,S,Xx) & app_encode_app(a,$o,S,Xz))))))))).
0.38/0.58	tff(zf_stmt_0, negated_conjecture,
0.38/0.58	  (~
0.38/0.58	    (![P:app_encode_fun(app_encode_fun(a,$o),$o)]:
0.38/0.58	       ((![Xx:a]:
0.38/0.58	           (?[Xp:app_encode_fun(a,$o)]:
0.38/0.58	              (app_encode_app(app_encode_fun(a,$o),$o,P,Xp) & 
0.38/0.58	               app_encode_app(a,$o,Xp,Xx) & 
0.38/0.58	               (![Xq:app_encode_fun(a,$o)]:
0.38/0.58	                  ((app_encode_app(app_encode_fun(a,$o),$o,P,Xq) & 
0.38/0.58	                    app_encode_app(a,$o,Xq,Xx)) =>
0.38/0.58	                   (Xq = Xp)))))) =>
0.38/0.58	        ((![Xx:a]:
0.38/0.58	            (?[S:app_encode_fun(a,$o)]:
0.38/0.58	               (app_encode_app(app_encode_fun(a,$o),$o,P,S) & 
0.38/0.58	                app_encode_app(a,$o,S,Xx) & app_encode_app(a,$o,S,Xx)))) & 
0.38/0.58	         (![Xx:a,Xy:a]:
0.38/0.58	            ((?[S:app_encode_fun(a,$o)]:
0.38/0.58	                (app_encode_app(app_encode_fun(a,$o),$o,P,S) & 
0.38/0.58	                 app_encode_app(a,$o,S,Xx) & app_encode_app(a,$o,S,Xy))) =>
0.38/0.58	             (?[S:app_encode_fun(a,$o)]:
0.38/0.58	                (app_encode_app(app_encode_fun(a,$o),$o,P,S) & 
0.38/0.58	                 app_encode_app(a,$o,S,Xy) & app_encode_app(a,$o,S,Xx))))) & 
0.38/0.58	         (![Xx:a,Xy:a,Xz:a]:
0.38/0.58	            (((?[S:app_encode_fun(a,$o)]:
0.38/0.58	                 (app_encode_app(app_encode_fun(a,$o),$o,P,S) & 
0.38/0.58	                  app_encode_app(a,$o,S,Xx) & app_encode_app(a,$o,S,Xy))) & 
0.38/0.58	              (?[S:app_encode_fun(a,$o)]:
0.38/0.58	                 (app_encode_app(app_encode_fun(a,$o),$o,P,S) & 
0.38/0.58	                  app_encode_app(a,$o,S,Xy) & app_encode_app(a,$o,S,Xz)))) =>
0.38/0.58	             (?[S:app_encode_fun(a,$o)]:
0.38/0.58	                (app_encode_app(app_encode_fun(a,$o),$o,P,S) & 
0.38/0.58	                 app_encode_app(a,$o,S,Xx) & app_encode_app(a,$o,S,Xz)))))))))).
0.38/0.58	tff('0', plain, ![X4 : a]: app_encode_app(a, $o, sk_Xp(X4), X4),
0.38/0.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.38/0.58	tff('1', plain,
0.38/0.58	    ![X4 : a]: app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_Xp(X4)),
0.38/0.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.38/0.58	tff('2', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.38/0.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.38/0.58	tff('3', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o)]:
0.38/0.58	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['2'])).
0.38/0.58	tff('4', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (~ $true
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.38/0.58	    inference('sup-', [status(thm)], ['1', '3'])).
0.38/0.58	tff('5', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['4'])).
0.38/0.58	tff('6', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.38/0.58	    inference('sup-', [status(thm)], ['0', '5'])).
0.38/0.58	tff('7', plain,
0.38/0.58	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.38/0.58	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.38/0.58	    inference('simplify', [status(thm)], ['6'])).
0.38/0.58	tff('8', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o), X7 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.38/0.58	       | ~ app_encode_app(a, $o, X7, sk_Xx2)
0.38/0.58	       | ~ app_encode_app(a, $o, X7, sk_Xz)),
0.38/0.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.38/0.58	tff('9', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o), X7 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ app_encode_app(a, $o, X7, sk_Xz)
0.38/0.58	       | ~ app_encode_app(a, $o, X7, sk_Xx2)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['8'])).
0.38/0.58	tff('10', plain,
0.38/0.58	    ![X0 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ $true
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_S2, sk_Xz)),
0.38/0.58	    inference('sup-', [status(thm)], ['7', '9'])).
0.38/0.58	tff('11', plain,
0.38/0.58	    ![X0 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ app_encode_app(a, $o, sk_S2, sk_Xz)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.38/0.58	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.38/0.58	    inference('simplify', [status(thm)], ['10'])).
0.38/0.58	tff('12', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	       | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.38/0.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.38/0.58	tff('13', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o)]:
0.38/0.58	      (app_encode_app(a, $o, sk_S2, sk_Xz)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['12'])).
0.38/0.58	tff('14', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (~ $true
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	       | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.38/0.58	    inference('sup-', [status(thm)], ['1', '13'])).
0.38/0.58	tff('15', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (app_encode_app(a, $o, sk_S2, sk_Xz)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['14'])).
0.38/0.58	tff('16', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	     | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.38/0.58	    inference('sup-', [status(thm)], ['0', '15'])).
0.38/0.58	tff('17', plain,
0.38/0.58	    (app_encode_app(a, $o, sk_S2, sk_Xz)
0.38/0.58	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.38/0.58	    inference('simplify', [status(thm)], ['16'])).
0.38/0.58	tff('18', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o), X8 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | ~ app_encode_app(a, $o, X8, sk_Xx1)
0.38/0.58	       | ~ app_encode_app(a, $o, X8, sk_Xy)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X8)
0.38/0.58	       | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.38/0.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.38/0.58	tff('19', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o), X8 : app_encode_fun(a, $o)]:
0.38/0.58	      (app_encode_app(a, $o, sk_S2, sk_Xz)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X8)
0.38/0.58	       | ~ app_encode_app(a, $o, X8, sk_Xy)
0.38/0.58	       | ~ app_encode_app(a, $o, X8, sk_Xx1)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['18'])).
0.38/0.58	tff('20', plain,
0.38/0.58	    ![X0 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ $true
0.38/0.58	       | app_encode_app(a, $o, sk_S2, sk_Xz)
0.38/0.58	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	       | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.38/0.58	    inference('sup-', [status(thm)], ['17', '19'])).
0.38/0.58	tff('21', plain,
0.38/0.58	    ![X0 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.38/0.58	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.38/0.58	       | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.38/0.58	    inference('simplify', [status(thm)], ['20'])).
0.38/0.58	tff('22', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	       | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.38/0.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.38/0.58	tff('23', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o)]:
0.38/0.58	      (app_encode_app(a, $o, sk_S2, sk_Xz)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['22'])).
0.38/0.58	tff('24', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (~ $true
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	       | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.38/0.58	    inference('sup-', [status(thm)], ['1', '23'])).
0.38/0.58	tff('25', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (app_encode_app(a, $o, sk_S2, sk_Xz)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['24'])).
0.38/0.58	tff('26', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	     | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.38/0.58	    inference('sup-', [status(thm)], ['0', '25'])).
0.38/0.58	tff('27', plain,
0.38/0.58	    (app_encode_app(a, $o, sk_S2, sk_Xz) | app_encode_app(a, $o, sk_S, sk_Xy)),
0.38/0.58	    inference('simplify', [status(thm)], ['26'])).
0.38/0.58	tff('28', plain,
0.38/0.58	    ![X0 : app_encode_fun(a, $o)]:
0.38/0.58	      (app_encode_app(a, $o, sk_S2, sk_Xz)
0.38/0.58	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_S, sk_Xx1)),
0.38/0.58	    inference('clc', [status(thm)], ['21', '27'])).
0.38/0.58	tff('29', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	       | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.38/0.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.38/0.58	tff('30', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o)]:
0.38/0.58	      (app_encode_app(a, $o, sk_S2, sk_Xz)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['29'])).
0.38/0.58	tff('31', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (~ $true
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	       | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.38/0.58	    inference('sup-', [status(thm)], ['1', '30'])).
0.38/0.58	tff('32', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (app_encode_app(a, $o, sk_S2, sk_Xz)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['31'])).
0.38/0.58	tff('33', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	     | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.38/0.58	    inference('sup-', [status(thm)], ['0', '32'])).
0.38/0.58	tff('34', plain,
0.38/0.58	    (app_encode_app(a, $o, sk_S2, sk_Xz)
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.38/0.58	    inference('simplify', [status(thm)], ['33'])).
0.38/0.58	tff('35', plain,
0.38/0.58	    ![X0 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.38/0.58	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.38/0.58	       | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.38/0.58	    inference('clc', [status(thm)], ['28', '34'])).
0.38/0.58	tff('36', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (~ $true
0.38/0.58	       | app_encode_app(a, $o, sk_S2, sk_Xz)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.38/0.58	    inference('sup-', [status(thm)], ['1', '35'])).
0.38/0.58	tff('37', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.38/0.58	       | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.38/0.58	    inference('simplify', [status(thm)], ['36'])).
0.38/0.58	tff('38', plain, (~ $true | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.38/0.58	    inference('sup-', [status(thm)], ['0', '37'])).
0.38/0.58	tff('39', plain, app_encode_app(a, $o, sk_S2, sk_Xz),
0.38/0.58	    inference('simplify', [status(thm)], ['38'])).
0.38/0.58	tff('40', plain,
0.38/0.58	    ![X0 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ $true
0.38/0.58	       | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.38/0.58	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.38/0.58	    inference('demod', [status(thm)], ['11', '39'])).
0.38/0.58	tff('41', plain,
0.38/0.58	    ![X0 : app_encode_fun(a, $o)]:
0.38/0.58	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)),
0.38/0.58	    inference('simplify', [status(thm)], ['40'])).
0.38/0.58	tff('42', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (~ $true
0.38/0.58	       | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.38/0.58	    inference('sup-', [status(thm)], ['1', '41'])).
0.38/0.58	tff('43', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)),
0.38/0.58	    inference('simplify', [status(thm)], ['42'])).
0.38/0.58	tff('44', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)
0.38/0.58	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.38/0.58	    inference('sup-', [status(thm)], ['0', '43'])).
0.38/0.58	tff('45', plain,
0.38/0.58	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	     | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)),
0.38/0.58	    inference('simplify', [status(thm)], ['44'])).
0.38/0.58	tff('46', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.38/0.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.38/0.58	tff('47', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o)]:
0.38/0.58	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['46'])).
0.38/0.58	tff('48', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (~ $true
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.38/0.58	    inference('sup-', [status(thm)], ['1', '47'])).
0.38/0.58	tff('49', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['48'])).
0.38/0.58	tff('50', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.38/0.58	    inference('sup-', [status(thm)], ['0', '49'])).
0.38/0.58	tff('51', plain,
0.38/0.58	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xy)),
0.38/0.58	    inference('simplify', [status(thm)], ['50'])).
0.38/0.58	tff('52', plain,
0.38/0.58	    ![X4 : a, X5 : app_encode_fun(a, $o)]:
0.38/0.58	      (X5 = sk_Xp(X4)
0.38/0.58	       | ~ app_encode_app(a, $o, X5, X4)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X5)),
0.38/0.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.38/0.58	tff('53', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.38/0.58	     | sk_S2 = sk_Xp(sk_Xz)),
0.38/0.58	    inference('sup-', [status(thm)], ['27', '52'])).
0.38/0.58	tff('54', plain,
0.38/0.58	    (sk_S2 = sk_Xp(sk_Xz)
0.38/0.58	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xy)),
0.38/0.58	    inference('simplify', [status(thm)], ['53'])).
0.38/0.58	tff('55', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	     | sk_S2 = sk_Xp(sk_Xz)),
0.38/0.58	    inference('sup-', [status(thm)], ['51', '54'])).
0.38/0.58	tff('56', plain, (sk_S2 = sk_Xp(sk_Xz) | app_encode_app(a, $o, sk_S, sk_Xy)),
0.38/0.58	    inference('simplify', [status(thm)], ['55'])).
0.38/0.58	tff('57', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | sk_S2 = sk_Xp(sk_Xz)
0.38/0.58	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	     | sk_S = sk_Xp(sk_Xy)),
0.38/0.58	    inference('sup-', [status(thm)], ['56', '52'])).
0.38/0.58	tff('58', plain,
0.38/0.58	    (sk_S = sk_Xp(sk_Xy)
0.38/0.58	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	     | sk_S2 = sk_Xp(sk_Xz)),
0.38/0.58	    inference('simplify', [status(thm)], ['57'])).
0.38/0.58	tff('59', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | app_encode_app(a, $o, sk_S2, sk_Xz)
0.38/0.58	     | sk_S2 = sk_Xp(sk_Xz)
0.38/0.58	     | sk_S = sk_Xp(sk_Xy)),
0.38/0.58	    inference('sup-', [status(thm)], ['17', '58'])).
0.38/0.58	tff('60', plain,
0.38/0.58	    (sk_S = sk_Xp(sk_Xy)
0.38/0.58	     | sk_S2 = sk_Xp(sk_Xz)
0.38/0.58	     | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.38/0.58	    inference('simplify', [status(thm)], ['59'])).
0.38/0.58	tff('61', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | sk_S2 = sk_Xp(sk_Xz)
0.38/0.58	     | sk_S = sk_Xp(sk_Xy)
0.38/0.58	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.38/0.58	     | sk_S2 = sk_Xp(sk_Xz)),
0.38/0.58	    inference('sup-', [status(thm)], ['60', '52'])).
0.38/0.58	tff('62', plain,
0.38/0.58	    (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.38/0.58	     | sk_S = sk_Xp(sk_Xy)
0.38/0.58	     | sk_S2 = sk_Xp(sk_Xz)),
0.38/0.58	    inference('simplify', [status(thm)], ['61'])).
0.38/0.58	tff('63', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	     | sk_S2 = sk_Xp(sk_Xz)
0.38/0.58	     | sk_S = sk_Xp(sk_Xy)),
0.38/0.58	    inference('sup-', [status(thm)], ['7', '62'])).
0.38/0.58	tff('64', plain,
0.38/0.58	    (sk_S = sk_Xp(sk_Xy)
0.38/0.58	     | sk_S2 = sk_Xp(sk_Xz)
0.38/0.58	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.38/0.58	    inference('simplify', [status(thm)], ['63'])).
0.38/0.58	tff('65', plain, (sk_S2 = sk_Xp(sk_Xz) | sk_S = sk_Xp(sk_Xy)),
0.38/0.58	    inference('clc', [status(thm)], ['64', '58'])).
0.38/0.58	tff('66', plain,
0.38/0.58	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.38/0.58	     | sk_S = sk_Xp(sk_Xy)),
0.38/0.58	    inference('sup+', [status(thm)], ['65', '1'])).
0.38/0.58	tff('67', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	       | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.38/0.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.38/0.58	tff('68', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o)]:
0.38/0.58	      (app_encode_app(a, $o, sk_S2, sk_Xy1)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['67'])).
0.38/0.58	tff('69', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (~ $true
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	       | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.38/0.58	    inference('sup-', [status(thm)], ['1', '68'])).
0.38/0.58	tff('70', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (app_encode_app(a, $o, sk_S2, sk_Xy1)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['69'])).
0.38/0.58	tff('71', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	     | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.38/0.58	    inference('sup-', [status(thm)], ['0', '70'])).
0.38/0.58	tff('72', plain,
0.38/0.58	    (app_encode_app(a, $o, sk_S2, sk_Xy1)
0.38/0.58	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.38/0.58	    inference('simplify', [status(thm)], ['71'])).
0.38/0.58	tff('73', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	       | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.38/0.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.38/0.58	tff('74', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o)]:
0.38/0.58	      (app_encode_app(a, $o, sk_S2, sk_Xy1)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['73'])).
0.38/0.58	tff('75', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (~ $true
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	       | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.38/0.58	    inference('sup-', [status(thm)], ['1', '74'])).
0.38/0.58	tff('76', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (app_encode_app(a, $o, sk_S2, sk_Xy1)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['75'])).
0.38/0.58	tff('77', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	     | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.38/0.58	    inference('sup-', [status(thm)], ['0', '76'])).
0.38/0.58	tff('78', plain,
0.38/0.58	    (app_encode_app(a, $o, sk_S2, sk_Xy1)
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xy)),
0.38/0.58	    inference('simplify', [status(thm)], ['77'])).
0.38/0.58	tff('79', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.38/0.58	     | sk_S2 = sk_Xp(sk_Xy1)),
0.38/0.58	    inference('sup-', [status(thm)], ['78', '52'])).
0.38/0.58	tff('80', plain,
0.38/0.58	    (sk_S2 = sk_Xp(sk_Xy1)
0.38/0.58	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xy)),
0.38/0.58	    inference('simplify', [status(thm)], ['79'])).
0.38/0.58	tff('81', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	     | sk_S2 = sk_Xp(sk_Xy1)),
0.38/0.58	    inference('sup-', [status(thm)], ['51', '80'])).
0.38/0.58	tff('82', plain,
0.38/0.58	    (sk_S2 = sk_Xp(sk_Xy1) | app_encode_app(a, $o, sk_S, sk_Xy)),
0.38/0.58	    inference('simplify', [status(thm)], ['81'])).
0.38/0.58	tff('83', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | sk_S2 = sk_Xp(sk_Xy1)
0.38/0.58	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	     | sk_S = sk_Xp(sk_Xy)),
0.38/0.58	    inference('sup-', [status(thm)], ['82', '52'])).
0.38/0.58	tff('84', plain,
0.38/0.58	    (sk_S = sk_Xp(sk_Xy)
0.38/0.58	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	     | sk_S2 = sk_Xp(sk_Xy1)),
0.38/0.58	    inference('simplify', [status(thm)], ['83'])).
0.38/0.58	tff('85', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | app_encode_app(a, $o, sk_S2, sk_Xy1)
0.38/0.58	     | sk_S2 = sk_Xp(sk_Xy1)
0.38/0.58	     | sk_S = sk_Xp(sk_Xy)),
0.38/0.58	    inference('sup-', [status(thm)], ['72', '84'])).
0.38/0.58	tff('86', plain,
0.38/0.58	    (sk_S = sk_Xp(sk_Xy)
0.38/0.58	     | sk_S2 = sk_Xp(sk_Xy1)
0.38/0.58	     | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.38/0.58	    inference('simplify', [status(thm)], ['85'])).
0.38/0.58	tff('87', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | sk_S2 = sk_Xp(sk_Xy1)
0.38/0.58	     | sk_S = sk_Xp(sk_Xy)
0.38/0.58	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.38/0.58	     | sk_S2 = sk_Xp(sk_Xy1)),
0.38/0.58	    inference('sup-', [status(thm)], ['86', '52'])).
0.38/0.58	tff('88', plain,
0.38/0.58	    (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.38/0.58	     | sk_S = sk_Xp(sk_Xy)
0.38/0.58	     | sk_S2 = sk_Xp(sk_Xy1)),
0.38/0.58	    inference('simplify', [status(thm)], ['87'])).
0.38/0.58	tff('89', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | sk_S = sk_Xp(sk_Xy)
0.38/0.58	     | sk_S2 = sk_Xp(sk_Xy1)
0.38/0.58	     | sk_S = sk_Xp(sk_Xy)),
0.38/0.58	    inference('sup-', [status(thm)], ['66', '88'])).
0.38/0.58	tff('90', plain, (sk_S2 = sk_Xp(sk_Xy1) | sk_S = sk_Xp(sk_Xy)),
0.38/0.58	    inference('simplify', [status(thm)], ['89'])).
0.38/0.58	tff('91', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.38/0.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.38/0.58	tff('92', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o)]:
0.38/0.58	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['91'])).
0.38/0.58	tff('93', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (~ $true
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.38/0.58	    inference('sup-', [status(thm)], ['1', '92'])).
0.38/0.58	tff('94', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['93'])).
0.38/0.58	tff('95', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.38/0.58	    inference('sup-', [status(thm)], ['0', '94'])).
0.38/0.58	tff('96', plain,
0.38/0.58	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.38/0.58	    inference('simplify', [status(thm)], ['95'])).
0.38/0.58	tff('97', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.38/0.58	     | sk_S2 = sk_Xp(sk_Xz)),
0.38/0.58	    inference('sup-', [status(thm)], ['34', '52'])).
0.38/0.58	tff('98', plain,
0.38/0.58	    (sk_S2 = sk_Xp(sk_Xz)
0.38/0.58	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.38/0.58	    inference('simplify', [status(thm)], ['97'])).
0.38/0.58	tff('99', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	     | sk_S2 = sk_Xp(sk_Xz)),
0.38/0.58	    inference('sup-', [status(thm)], ['96', '98'])).
0.38/0.58	tff('100', plain,
0.38/0.58	    (sk_S2 = sk_Xp(sk_Xz) | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.38/0.58	    inference('simplify', [status(thm)], ['99'])).
0.38/0.58	tff('101', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | sk_S2 = sk_Xp(sk_Xz)
0.38/0.58	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	     | sk_S = sk_Xp(sk_Xx1)),
0.38/0.58	    inference('sup-', [status(thm)], ['100', '52'])).
0.38/0.58	tff('102', plain,
0.38/0.58	    (sk_S = sk_Xp(sk_Xx1)
0.38/0.58	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	     | sk_S2 = sk_Xp(sk_Xz)),
0.38/0.58	    inference('simplify', [status(thm)], ['101'])).
0.38/0.58	tff('103', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | app_encode_app(a, $o, sk_S2, sk_Xz)
0.38/0.58	     | sk_S2 = sk_Xp(sk_Xz)
0.38/0.58	     | sk_S = sk_Xp(sk_Xx1)),
0.38/0.58	    inference('sup-', [status(thm)], ['17', '102'])).
0.38/0.58	tff('104', plain,
0.38/0.58	    (sk_S = sk_Xp(sk_Xx1)
0.38/0.58	     | sk_S2 = sk_Xp(sk_Xz)
0.38/0.58	     | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.38/0.58	    inference('simplify', [status(thm)], ['103'])).
0.38/0.58	tff('105', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | sk_S2 = sk_Xp(sk_Xz)
0.38/0.58	     | sk_S = sk_Xp(sk_Xx1)
0.38/0.58	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.38/0.58	     | sk_S2 = sk_Xp(sk_Xz)),
0.38/0.58	    inference('sup-', [status(thm)], ['104', '52'])).
0.38/0.58	tff('106', plain,
0.38/0.58	    (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.38/0.58	     | sk_S = sk_Xp(sk_Xx1)
0.38/0.58	     | sk_S2 = sk_Xp(sk_Xz)),
0.38/0.58	    inference('simplify', [status(thm)], ['105'])).
0.38/0.58	tff('107', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	     | sk_S2 = sk_Xp(sk_Xz)
0.38/0.58	     | sk_S = sk_Xp(sk_Xx1)),
0.38/0.58	    inference('sup-', [status(thm)], ['7', '106'])).
0.38/0.58	tff('108', plain,
0.38/0.58	    (sk_S = sk_Xp(sk_Xx1)
0.38/0.58	     | sk_S2 = sk_Xp(sk_Xz)
0.38/0.58	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.38/0.58	    inference('simplify', [status(thm)], ['107'])).
0.38/0.58	tff('109', plain, (sk_S2 = sk_Xp(sk_Xz) | sk_S = sk_Xp(sk_Xx1)),
0.38/0.58	    inference('clc', [status(thm)], ['108', '102'])).
0.38/0.58	tff('110', plain,
0.38/0.58	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.38/0.58	     | sk_S = sk_Xp(sk_Xx1)),
0.38/0.58	    inference('sup+', [status(thm)], ['109', '1'])).
0.38/0.58	tff('111', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	       | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.38/0.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.38/0.58	tff('112', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o)]:
0.38/0.58	      (app_encode_app(a, $o, sk_S2, sk_Xy1)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['111'])).
0.38/0.58	tff('113', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (~ $true
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	       | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.38/0.58	    inference('sup-', [status(thm)], ['1', '112'])).
0.38/0.58	tff('114', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (app_encode_app(a, $o, sk_S2, sk_Xy1)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['113'])).
0.38/0.58	tff('115', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	     | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.38/0.58	    inference('sup-', [status(thm)], ['0', '114'])).
0.38/0.58	tff('116', plain,
0.38/0.58	    (app_encode_app(a, $o, sk_S2, sk_Xy1)
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.38/0.58	    inference('simplify', [status(thm)], ['115'])).
0.38/0.58	tff('117', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.38/0.58	     | sk_S2 = sk_Xp(sk_Xy1)),
0.38/0.58	    inference('sup-', [status(thm)], ['116', '52'])).
0.38/0.58	tff('118', plain,
0.38/0.58	    (sk_S2 = sk_Xp(sk_Xy1)
0.38/0.58	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.38/0.58	    inference('simplify', [status(thm)], ['117'])).
0.38/0.58	tff('119', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	     | sk_S2 = sk_Xp(sk_Xy1)),
0.38/0.58	    inference('sup-', [status(thm)], ['96', '118'])).
0.38/0.58	tff('120', plain,
0.38/0.58	    (sk_S2 = sk_Xp(sk_Xy1) | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.38/0.58	    inference('simplify', [status(thm)], ['119'])).
0.38/0.58	tff('121', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | sk_S2 = sk_Xp(sk_Xy1)
0.38/0.58	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	     | sk_S = sk_Xp(sk_Xx1)),
0.38/0.58	    inference('sup-', [status(thm)], ['120', '52'])).
0.38/0.58	tff('122', plain,
0.38/0.58	    (sk_S = sk_Xp(sk_Xx1)
0.38/0.58	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	     | sk_S2 = sk_Xp(sk_Xy1)),
0.38/0.58	    inference('simplify', [status(thm)], ['121'])).
0.38/0.58	tff('123', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | app_encode_app(a, $o, sk_S2, sk_Xy1)
0.38/0.58	     | sk_S2 = sk_Xp(sk_Xy1)
0.38/0.58	     | sk_S = sk_Xp(sk_Xx1)),
0.38/0.58	    inference('sup-', [status(thm)], ['72', '122'])).
0.38/0.58	tff('124', plain,
0.38/0.58	    (sk_S = sk_Xp(sk_Xx1)
0.38/0.58	     | sk_S2 = sk_Xp(sk_Xy1)
0.38/0.58	     | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.38/0.58	    inference('simplify', [status(thm)], ['123'])).
0.38/0.58	tff('125', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | sk_S2 = sk_Xp(sk_Xy1)
0.38/0.58	     | sk_S = sk_Xp(sk_Xx1)
0.38/0.58	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.38/0.58	     | sk_S2 = sk_Xp(sk_Xy1)),
0.38/0.58	    inference('sup-', [status(thm)], ['124', '52'])).
0.38/0.58	tff('126', plain,
0.38/0.58	    (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.38/0.58	     | sk_S = sk_Xp(sk_Xx1)
0.38/0.58	     | sk_S2 = sk_Xp(sk_Xy1)),
0.38/0.58	    inference('simplify', [status(thm)], ['125'])).
0.38/0.58	tff('127', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | sk_S = sk_Xp(sk_Xx1)
0.38/0.58	     | sk_S2 = sk_Xp(sk_Xy1)
0.38/0.58	     | sk_S = sk_Xp(sk_Xx1)),
0.38/0.58	    inference('sup-', [status(thm)], ['110', '126'])).
0.38/0.58	tff('128', plain, (sk_S2 = sk_Xp(sk_Xy1) | sk_S = sk_Xp(sk_Xx1)),
0.38/0.58	    inference('simplify', [status(thm)], ['127'])).
0.38/0.58	tff('129', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.38/0.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.38/0.58	tff('130', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o)]:
0.38/0.58	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['129'])).
0.38/0.58	tff('131', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (~ $true
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.38/0.58	    inference('sup-', [status(thm)], ['1', '130'])).
0.38/0.58	tff('132', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['131'])).
0.38/0.58	tff('133', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.38/0.58	    inference('sup-', [status(thm)], ['0', '132'])).
0.38/0.58	tff('134', plain,
0.38/0.58	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.38/0.58	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.38/0.58	    inference('simplify', [status(thm)], ['133'])).
0.38/0.58	tff('135', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	       | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.38/0.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.38/0.58	tff('136', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o)]:
0.38/0.58	      (app_encode_app(a, $o, sk_S1, sk_Xx2)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['135'])).
0.38/0.58	tff('137', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (~ $true
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	       | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.38/0.58	    inference('sup-', [status(thm)], ['1', '136'])).
0.38/0.58	tff('138', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (app_encode_app(a, $o, sk_S1, sk_Xx2)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['137'])).
0.38/0.58	tff('139', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	     | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.38/0.58	    inference('sup-', [status(thm)], ['0', '138'])).
0.38/0.58	tff('140', plain,
0.38/0.58	    (app_encode_app(a, $o, sk_S1, sk_Xx2)
0.38/0.58	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.38/0.58	    inference('simplify', [status(thm)], ['139'])).
0.38/0.58	tff('141', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.38/0.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.38/0.58	tff('142', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o)]:
0.38/0.58	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['141'])).
0.38/0.58	tff('143', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (~ $true
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.38/0.58	    inference('sup-', [status(thm)], ['1', '142'])).
0.38/0.58	tff('144', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['143'])).
0.38/0.58	tff('145', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.38/0.58	    inference('sup-', [status(thm)], ['0', '144'])).
0.38/0.58	tff('146', plain,
0.38/0.58	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.38/0.58	    inference('simplify', [status(thm)], ['145'])).
0.38/0.58	tff('147', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	       | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.38/0.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.38/0.58	tff('148', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o)]:
0.38/0.58	      (app_encode_app(a, $o, sk_S1, sk_Xx2)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['147'])).
0.38/0.58	tff('149', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (~ $true
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	       | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.38/0.58	    inference('sup-', [status(thm)], ['1', '148'])).
0.38/0.58	tff('150', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (app_encode_app(a, $o, sk_S1, sk_Xx2)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['149'])).
0.38/0.58	tff('151', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	     | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.38/0.58	    inference('sup-', [status(thm)], ['0', '150'])).
0.38/0.58	tff('152', plain,
0.38/0.58	    (app_encode_app(a, $o, sk_S1, sk_Xx2)
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.38/0.58	    inference('simplify', [status(thm)], ['151'])).
0.38/0.58	tff('153', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.38/0.58	     | sk_S1 = sk_Xp(sk_Xx2)),
0.38/0.58	    inference('sup-', [status(thm)], ['152', '52'])).
0.38/0.58	tff('154', plain,
0.38/0.58	    (sk_S1 = sk_Xp(sk_Xx2)
0.38/0.58	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.38/0.58	    inference('simplify', [status(thm)], ['153'])).
0.38/0.58	tff('155', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	     | sk_S1 = sk_Xp(sk_Xx2)),
0.38/0.58	    inference('sup-', [status(thm)], ['146', '154'])).
0.38/0.58	tff('156', plain,
0.38/0.58	    (sk_S1 = sk_Xp(sk_Xx2) | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.38/0.58	    inference('simplify', [status(thm)], ['155'])).
0.38/0.58	tff('157', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | sk_S1 = sk_Xp(sk_Xx2)
0.38/0.58	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	     | sk_S = sk_Xp(sk_Xx1)),
0.38/0.58	    inference('sup-', [status(thm)], ['156', '52'])).
0.38/0.58	tff('158', plain,
0.38/0.58	    (sk_S = sk_Xp(sk_Xx1)
0.38/0.58	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	     | sk_S1 = sk_Xp(sk_Xx2)),
0.38/0.58	    inference('simplify', [status(thm)], ['157'])).
0.38/0.58	tff('159', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | app_encode_app(a, $o, sk_S1, sk_Xx2)
0.38/0.58	     | sk_S1 = sk_Xp(sk_Xx2)
0.38/0.58	     | sk_S = sk_Xp(sk_Xx1)),
0.38/0.58	    inference('sup-', [status(thm)], ['140', '158'])).
0.38/0.58	tff('160', plain,
0.38/0.58	    (sk_S = sk_Xp(sk_Xx1)
0.38/0.58	     | sk_S1 = sk_Xp(sk_Xx2)
0.38/0.58	     | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.38/0.58	    inference('simplify', [status(thm)], ['159'])).
0.38/0.58	tff('161', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | sk_S1 = sk_Xp(sk_Xx2)
0.38/0.58	     | sk_S = sk_Xp(sk_Xx1)
0.38/0.58	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.38/0.58	     | sk_S1 = sk_Xp(sk_Xx2)),
0.38/0.58	    inference('sup-', [status(thm)], ['160', '52'])).
0.38/0.58	tff('162', plain,
0.38/0.58	    (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.38/0.58	     | sk_S = sk_Xp(sk_Xx1)
0.38/0.58	     | sk_S1 = sk_Xp(sk_Xx2)),
0.38/0.58	    inference('simplify', [status(thm)], ['161'])).
0.38/0.58	tff('163', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	     | sk_S1 = sk_Xp(sk_Xx2)
0.38/0.58	     | sk_S = sk_Xp(sk_Xx1)),
0.38/0.58	    inference('sup-', [status(thm)], ['134', '162'])).
0.38/0.58	tff('164', plain,
0.38/0.58	    (sk_S = sk_Xp(sk_Xx1)
0.38/0.58	     | sk_S1 = sk_Xp(sk_Xx2)
0.38/0.58	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.38/0.58	    inference('simplify', [status(thm)], ['163'])).
0.38/0.58	tff('165', plain, (sk_S1 = sk_Xp(sk_Xx2) | sk_S = sk_Xp(sk_Xx1)),
0.38/0.58	    inference('clc', [status(thm)], ['164', '158'])).
0.38/0.58	tff('166', plain,
0.38/0.58	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.38/0.58	     | sk_S = sk_Xp(sk_Xx1)),
0.38/0.58	    inference('sup+', [status(thm)], ['165', '1'])).
0.38/0.58	tff('167', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	       | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.38/0.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.38/0.58	tff('168', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o)]:
0.38/0.58	      (app_encode_app(a, $o, sk_S1, sk_Xy1)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['167'])).
0.38/0.58	tff('169', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (~ $true
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	       | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.38/0.58	    inference('sup-', [status(thm)], ['1', '168'])).
0.38/0.58	tff('170', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (app_encode_app(a, $o, sk_S1, sk_Xy1)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['169'])).
0.38/0.58	tff('171', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	     | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.38/0.58	    inference('sup-', [status(thm)], ['0', '170'])).
0.38/0.58	tff('172', plain,
0.38/0.58	    (app_encode_app(a, $o, sk_S1, sk_Xy1)
0.38/0.58	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.38/0.58	    inference('simplify', [status(thm)], ['171'])).
0.38/0.58	tff('173', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	       | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.38/0.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.38/0.58	tff('174', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o)]:
0.38/0.58	      (app_encode_app(a, $o, sk_S1, sk_Xy1)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['173'])).
0.38/0.58	tff('175', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (~ $true
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	       | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.38/0.58	    inference('sup-', [status(thm)], ['1', '174'])).
0.38/0.58	tff('176', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (app_encode_app(a, $o, sk_S1, sk_Xy1)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['175'])).
0.38/0.58	tff('177', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	     | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.38/0.58	    inference('sup-', [status(thm)], ['0', '176'])).
0.38/0.58	tff('178', plain,
0.38/0.58	    (app_encode_app(a, $o, sk_S1, sk_Xy1)
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.38/0.58	    inference('simplify', [status(thm)], ['177'])).
0.38/0.58	tff('179', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.38/0.58	     | sk_S1 = sk_Xp(sk_Xy1)),
0.38/0.58	    inference('sup-', [status(thm)], ['178', '52'])).
0.38/0.58	tff('180', plain,
0.38/0.58	    (sk_S1 = sk_Xp(sk_Xy1)
0.38/0.58	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.38/0.58	    inference('simplify', [status(thm)], ['179'])).
0.38/0.58	tff('181', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	     | sk_S1 = sk_Xp(sk_Xy1)),
0.38/0.58	    inference('sup-', [status(thm)], ['146', '180'])).
0.38/0.58	tff('182', plain,
0.38/0.58	    (sk_S1 = sk_Xp(sk_Xy1) | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.38/0.58	    inference('simplify', [status(thm)], ['181'])).
0.38/0.58	tff('183', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | sk_S1 = sk_Xp(sk_Xy1)
0.38/0.58	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	     | sk_S = sk_Xp(sk_Xx1)),
0.38/0.58	    inference('sup-', [status(thm)], ['182', '52'])).
0.38/0.58	tff('184', plain,
0.38/0.58	    (sk_S = sk_Xp(sk_Xx1)
0.38/0.58	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	     | sk_S1 = sk_Xp(sk_Xy1)),
0.38/0.58	    inference('simplify', [status(thm)], ['183'])).
0.38/0.58	tff('185', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | app_encode_app(a, $o, sk_S1, sk_Xy1)
0.38/0.58	     | sk_S1 = sk_Xp(sk_Xy1)
0.38/0.58	     | sk_S = sk_Xp(sk_Xx1)),
0.38/0.58	    inference('sup-', [status(thm)], ['172', '184'])).
0.38/0.58	tff('186', plain,
0.38/0.58	    (sk_S = sk_Xp(sk_Xx1)
0.38/0.58	     | sk_S1 = sk_Xp(sk_Xy1)
0.38/0.58	     | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.38/0.58	    inference('simplify', [status(thm)], ['185'])).
0.38/0.58	tff('187', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | sk_S1 = sk_Xp(sk_Xy1)
0.38/0.58	     | sk_S = sk_Xp(sk_Xx1)
0.38/0.58	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.38/0.58	     | sk_S1 = sk_Xp(sk_Xy1)),
0.38/0.58	    inference('sup-', [status(thm)], ['186', '52'])).
0.38/0.58	tff('188', plain,
0.38/0.58	    (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.38/0.58	     | sk_S = sk_Xp(sk_Xx1)
0.38/0.58	     | sk_S1 = sk_Xp(sk_Xy1)),
0.38/0.58	    inference('simplify', [status(thm)], ['187'])).
0.38/0.58	tff('189', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | sk_S = sk_Xp(sk_Xx1)
0.38/0.58	     | sk_S1 = sk_Xp(sk_Xy1)
0.38/0.58	     | sk_S = sk_Xp(sk_Xx1)),
0.38/0.58	    inference('sup-', [status(thm)], ['166', '188'])).
0.38/0.58	tff('190', plain, (sk_S1 = sk_Xp(sk_Xy1) | sk_S = sk_Xp(sk_Xx1)),
0.38/0.58	    inference('simplify', [status(thm)], ['189'])).
0.38/0.58	tff('191', plain,
0.38/0.58	    (sk_S1 = sk_S2 | sk_S = sk_Xp(sk_Xx1) | sk_S = sk_Xp(sk_Xx1)),
0.38/0.58	    inference('sup+', [status(thm)], ['128', '190'])).
0.38/0.58	tff('192', plain, (sk_S = sk_Xp(sk_Xx1) | sk_S1 = sk_S2),
0.38/0.58	    inference('simplify', [status(thm)], ['191'])).
0.38/0.58	tff('193', plain,
0.38/0.58	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S) | sk_S1 = sk_S2),
0.38/0.58	    inference('sup+', [status(thm)], ['192', '1'])).
0.38/0.58	tff('194', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.38/0.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.38/0.58	tff('195', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o)]:
0.38/0.58	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['194'])).
0.38/0.58	tff('196', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (~ $true
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.38/0.58	    inference('sup-', [status(thm)], ['1', '195'])).
0.38/0.58	tff('197', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['196'])).
0.38/0.58	tff('198', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.38/0.58	    inference('sup-', [status(thm)], ['0', '197'])).
0.38/0.58	tff('199', plain,
0.38/0.58	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xy)),
0.38/0.58	    inference('simplify', [status(thm)], ['198'])).
0.38/0.58	tff('200', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	       | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.38/0.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.38/0.58	tff('201', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o)]:
0.38/0.58	      (app_encode_app(a, $o, sk_S1, sk_Xy1)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['200'])).
0.38/0.58	tff('202', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (~ $true
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	       | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.38/0.58	    inference('sup-', [status(thm)], ['1', '201'])).
0.38/0.58	tff('203', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (app_encode_app(a, $o, sk_S1, sk_Xy1)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['202'])).
0.38/0.58	tff('204', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	     | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.38/0.58	    inference('sup-', [status(thm)], ['0', '203'])).
0.38/0.58	tff('205', plain,
0.38/0.58	    (app_encode_app(a, $o, sk_S1, sk_Xy1)
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xy)),
0.38/0.58	    inference('simplify', [status(thm)], ['204'])).
0.38/0.58	tff('206', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.38/0.58	     | sk_S1 = sk_Xp(sk_Xy1)),
0.38/0.58	    inference('sup-', [status(thm)], ['205', '52'])).
0.38/0.58	tff('207', plain,
0.38/0.58	    (sk_S1 = sk_Xp(sk_Xy1)
0.38/0.58	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xy)),
0.38/0.58	    inference('simplify', [status(thm)], ['206'])).
0.38/0.58	tff('208', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	     | sk_S1 = sk_Xp(sk_Xy1)),
0.38/0.58	    inference('sup-', [status(thm)], ['199', '207'])).
0.38/0.58	tff('209', plain,
0.38/0.58	    (sk_S1 = sk_Xp(sk_Xy1) | app_encode_app(a, $o, sk_S, sk_Xy)),
0.38/0.58	    inference('simplify', [status(thm)], ['208'])).
0.38/0.58	tff('210', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | sk_S1 = sk_Xp(sk_Xy1)
0.38/0.58	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	     | sk_S = sk_Xp(sk_Xy)),
0.38/0.58	    inference('sup-', [status(thm)], ['209', '52'])).
0.38/0.58	tff('211', plain,
0.38/0.58	    (sk_S = sk_Xp(sk_Xy)
0.38/0.58	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	     | sk_S1 = sk_Xp(sk_Xy1)),
0.38/0.58	    inference('simplify', [status(thm)], ['210'])).
0.38/0.58	tff('212', plain,
0.38/0.58	    (~ $true | sk_S1 = sk_S2 | sk_S1 = sk_Xp(sk_Xy1) | sk_S = sk_Xp(sk_Xy)),
0.38/0.58	    inference('sup-', [status(thm)], ['193', '211'])).
0.38/0.58	tff('213', plain,
0.38/0.58	    (sk_S = sk_Xp(sk_Xy) | sk_S1 = sk_Xp(sk_Xy1) | sk_S1 = sk_S2),
0.38/0.58	    inference('simplify', [status(thm)], ['212'])).
0.38/0.58	tff('214', plain,
0.38/0.58	    (sk_S1 = sk_S2
0.38/0.58	     | sk_S = sk_Xp(sk_Xy)
0.38/0.58	     | sk_S1 = sk_S2
0.38/0.58	     | sk_S = sk_Xp(sk_Xy)),
0.38/0.58	    inference('sup+', [status(thm)], ['90', '213'])).
0.38/0.58	tff('215', plain, (sk_S = sk_Xp(sk_Xy) | sk_S1 = sk_S2),
0.38/0.58	    inference('simplify', [status(thm)], ['214'])).
0.38/0.58	tff('216', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o), X8 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | ~ app_encode_app(a, $o, X8, sk_Xx1)
0.38/0.58	       | ~ app_encode_app(a, $o, X8, sk_Xy)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X8)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.38/0.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.38/0.58	tff('217', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o), X8 : app_encode_fun(a, $o)]:
0.38/0.58	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X8)
0.38/0.58	       | ~ app_encode_app(a, $o, X8, sk_Xy)
0.38/0.58	       | ~ app_encode_app(a, $o, X8, sk_Xx1)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['216'])).
0.38/0.58	tff('218', plain,
0.38/0.58	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ $true
0.38/0.58	       | ~ app_encode_app(a, $o, X1, sk_Xx)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X1)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx1)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xy)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.38/0.58	    inference('sup-', [status(thm)], ['1', '217'])).
0.38/0.58	tff('219', plain,
0.38/0.58	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
0.38/0.58	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xy)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx1)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X1)
0.38/0.58	       | ~ app_encode_app(a, $o, X1, sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['218'])).
0.38/0.58	tff('220', plain,
0.38/0.58	    ![X0 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ $true
0.38/0.58	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(sk_Xy), sk_Xx1)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.38/0.58	    inference('sup-', [status(thm)], ['0', '219'])).
0.38/0.58	tff('221', plain,
0.38/0.58	    ![X0 : app_encode_fun(a, $o)]:
0.38/0.58	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(sk_Xy), sk_Xx1)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.38/0.58	       | ~ app_encode_app(a, $o, X0, sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['220'])).
0.38/0.58	tff('222', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (~ $true
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(sk_Xy), sk_Xx1)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.38/0.58	    inference('sup-', [status(thm)], ['1', '221'])).
0.38/0.58	tff('223', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(sk_Xy), sk_Xx1)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['222'])).
0.38/0.58	tff('224', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | ~ app_encode_app(a, $o, sk_Xp(sk_Xy), sk_Xx1)
0.38/0.58	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.38/0.58	    inference('sup-', [status(thm)], ['0', '223'])).
0.38/0.58	tff('225', plain,
0.38/0.58	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.38/0.58	     | ~ app_encode_app(a, $o, sk_Xp(sk_Xy), sk_Xx1)),
0.38/0.58	    inference('simplify', [status(thm)], ['224'])).
0.38/0.58	tff('226', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.38/0.58	     | sk_S2 = sk_Xp(sk_Xz)),
0.38/0.58	    inference('sup-', [status(thm)], ['39', '52'])).
0.38/0.58	tff('227', plain,
0.38/0.58	    (sk_S2 = sk_Xp(sk_Xz)
0.38/0.58	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.38/0.58	    inference('simplify', [status(thm)], ['226'])).
0.38/0.58	tff('228', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | ~ app_encode_app(a, $o, sk_Xp(sk_Xy), sk_Xx1)
0.38/0.58	     | sk_S2 = sk_Xp(sk_Xz)),
0.38/0.58	    inference('sup-', [status(thm)], ['225', '227'])).
0.38/0.58	tff('229', plain,
0.38/0.58	    (sk_S2 = sk_Xp(sk_Xz) | ~ app_encode_app(a, $o, sk_Xp(sk_Xy), sk_Xx1)),
0.38/0.58	    inference('simplify', [status(thm)], ['228'])).
0.38/0.58	tff('230', plain,
0.38/0.58	    (~ app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	     | sk_S1 = sk_S2
0.38/0.58	     | sk_S2 = sk_Xp(sk_Xz)),
0.38/0.58	    inference('sup-', [status(thm)], ['215', '229'])).
0.38/0.58	tff('231', plain, (app_encode_app(a, $o, sk_S, sk_Xx1) | sk_S1 = sk_S2),
0.38/0.58	    inference('sup+', [status(thm)], ['192', '0'])).
0.38/0.58	tff('232', plain, (sk_S2 = sk_Xp(sk_Xz) | sk_S1 = sk_S2),
0.38/0.58	    inference('clc', [status(thm)], ['230', '231'])).
0.38/0.58	tff('233', plain,
0.38/0.58	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2) | sk_S1 = sk_S2),
0.38/0.58	    inference('sup+', [status(thm)], ['232', '1'])).
0.38/0.58	tff('234', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o), X8 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | ~ app_encode_app(a, $o, X8, sk_Xx1)
0.38/0.58	       | ~ app_encode_app(a, $o, X8, sk_Xy)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X8)
0.38/0.58	       | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.38/0.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.38/0.58	tff('235', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o), X8 : app_encode_fun(a, $o)]:
0.38/0.58	      (app_encode_app(a, $o, sk_S2, sk_Xy1)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X8)
0.38/0.58	       | ~ app_encode_app(a, $o, X8, sk_Xy)
0.38/0.58	       | ~ app_encode_app(a, $o, X8, sk_Xx1)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['234'])).
0.38/0.58	tff('236', plain,
0.38/0.58	    ![X0 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ $true
0.38/0.58	       | app_encode_app(a, $o, sk_S2, sk_Xy1)
0.38/0.58	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	       | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.38/0.58	    inference('sup-', [status(thm)], ['72', '235'])).
0.38/0.58	tff('237', plain,
0.38/0.58	    ![X0 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.38/0.58	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.38/0.58	       | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.38/0.58	    inference('simplify', [status(thm)], ['236'])).
0.38/0.58	tff('238', plain,
0.38/0.58	    ![X0 : app_encode_fun(a, $o)]:
0.38/0.58	      (app_encode_app(a, $o, sk_S2, sk_Xy1)
0.38/0.58	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_S, sk_Xx1)),
0.38/0.58	    inference('clc', [status(thm)], ['237', '78'])).
0.38/0.58	tff('239', plain,
0.38/0.58	    ![X0 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.38/0.58	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.38/0.58	       | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.38/0.58	    inference('clc', [status(thm)], ['238', '116'])).
0.38/0.58	tff('240', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (~ $true
0.38/0.58	       | app_encode_app(a, $o, sk_S2, sk_Xy1)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.38/0.58	    inference('sup-', [status(thm)], ['1', '239'])).
0.38/0.58	tff('241', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.38/0.58	       | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.38/0.58	    inference('simplify', [status(thm)], ['240'])).
0.38/0.58	tff('242', plain, (~ $true | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.38/0.58	    inference('sup-', [status(thm)], ['0', '241'])).
0.38/0.58	tff('243', plain, app_encode_app(a, $o, sk_S2, sk_Xy1),
0.38/0.58	    inference('simplify', [status(thm)], ['242'])).
0.38/0.58	tff('244', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.38/0.58	     | sk_S2 = sk_Xp(sk_Xy1)),
0.38/0.58	    inference('sup-', [status(thm)], ['243', '52'])).
0.38/0.58	tff('245', plain,
0.38/0.58	    (sk_S2 = sk_Xp(sk_Xy1)
0.38/0.58	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.38/0.58	    inference('simplify', [status(thm)], ['244'])).
0.38/0.58	tff('246', plain, (~ $true | sk_S1 = sk_S2 | sk_S2 = sk_Xp(sk_Xy1)),
0.38/0.58	    inference('sup-', [status(thm)], ['233', '245'])).
0.38/0.58	tff('247', plain, (sk_S2 = sk_Xp(sk_Xy1) | sk_S1 = sk_S2),
0.38/0.58	    inference('simplify', [status(thm)], ['246'])).
0.38/0.58	tff('248', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o), X8 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | ~ app_encode_app(a, $o, X8, sk_Xx1)
0.38/0.58	       | ~ app_encode_app(a, $o, X8, sk_Xy)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X8)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.38/0.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.38/0.58	tff('249', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o), X8 : app_encode_fun(a, $o)]:
0.38/0.58	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X8)
0.38/0.58	       | ~ app_encode_app(a, $o, X8, sk_Xy)
0.38/0.58	       | ~ app_encode_app(a, $o, X8, sk_Xx1)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['248'])).
0.38/0.58	tff('250', plain,
0.38/0.58	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ $true
0.38/0.58	       | ~ app_encode_app(a, $o, X1, sk_Xx)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X1)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx1)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xy)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.38/0.58	    inference('sup-', [status(thm)], ['1', '249'])).
0.38/0.58	tff('251', plain,
0.38/0.58	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
0.38/0.58	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xy)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx1)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X1)
0.38/0.58	       | ~ app_encode_app(a, $o, X1, sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['250'])).
0.38/0.58	tff('252', plain,
0.38/0.58	    ![X0 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ $true
0.38/0.58	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(sk_Xy), sk_Xx1)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.38/0.58	    inference('sup-', [status(thm)], ['0', '251'])).
0.38/0.58	tff('253', plain,
0.38/0.58	    ![X0 : app_encode_fun(a, $o)]:
0.38/0.58	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(sk_Xy), sk_Xx1)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.38/0.58	       | ~ app_encode_app(a, $o, X0, sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['252'])).
0.38/0.58	tff('254', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (~ $true
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(sk_Xy), sk_Xx1)
0.38/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.38/0.58	    inference('sup-', [status(thm)], ['1', '253'])).
0.38/0.58	tff('255', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(sk_Xy), sk_Xx1)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['254'])).
0.38/0.58	tff('256', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | ~ app_encode_app(a, $o, sk_Xp(sk_Xy), sk_Xx1)
0.38/0.58	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.38/0.58	    inference('sup-', [status(thm)], ['0', '255'])).
0.38/0.58	tff('257', plain,
0.38/0.58	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.38/0.58	     | ~ app_encode_app(a, $o, sk_Xp(sk_Xy), sk_Xx1)),
0.38/0.58	    inference('simplify', [status(thm)], ['256'])).
0.38/0.58	tff('258', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o), X8 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | ~ app_encode_app(a, $o, X8, sk_Xx1)
0.38/0.58	       | ~ app_encode_app(a, $o, X8, sk_Xy)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X8)
0.38/0.58	       | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.38/0.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.38/0.58	tff('259', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o), X8 : app_encode_fun(a, $o)]:
0.38/0.58	      (app_encode_app(a, $o, sk_S1, sk_Xx2)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X8)
0.38/0.58	       | ~ app_encode_app(a, $o, X8, sk_Xy)
0.38/0.58	       | ~ app_encode_app(a, $o, X8, sk_Xx1)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['258'])).
0.38/0.58	tff('260', plain,
0.38/0.58	    ![X0 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ $true
0.38/0.58	       | app_encode_app(a, $o, sk_S1, sk_Xx2)
0.38/0.58	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	       | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.38/0.58	    inference('sup-', [status(thm)], ['140', '259'])).
0.38/0.58	tff('261', plain,
0.38/0.58	    ![X0 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.38/0.58	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.38/0.58	       | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.38/0.58	    inference('simplify', [status(thm)], ['260'])).
0.38/0.58	tff('262', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	       | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.38/0.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.38/0.58	tff('263', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o)]:
0.38/0.58	      (app_encode_app(a, $o, sk_S1, sk_Xx2)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['262'])).
0.38/0.58	tff('264', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (~ $true
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	       | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.38/0.58	    inference('sup-', [status(thm)], ['1', '263'])).
0.38/0.58	tff('265', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (app_encode_app(a, $o, sk_S1, sk_Xx2)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['264'])).
0.38/0.58	tff('266', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	     | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.38/0.58	    inference('sup-', [status(thm)], ['0', '265'])).
0.38/0.58	tff('267', plain,
0.38/0.58	    (app_encode_app(a, $o, sk_S1, sk_Xx2)
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xy)),
0.38/0.58	    inference('simplify', [status(thm)], ['266'])).
0.38/0.58	tff('268', plain,
0.38/0.58	    ![X0 : app_encode_fun(a, $o)]:
0.38/0.58	      (app_encode_app(a, $o, sk_S1, sk_Xx2)
0.38/0.58	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_S, sk_Xx1)),
0.38/0.58	    inference('clc', [status(thm)], ['261', '267'])).
0.38/0.58	tff('269', plain,
0.38/0.58	    ![X0 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.38/0.58	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.38/0.58	       | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.38/0.58	    inference('clc', [status(thm)], ['268', '152'])).
0.38/0.58	tff('270', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (~ $true
0.38/0.58	       | app_encode_app(a, $o, sk_S1, sk_Xx2)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.38/0.58	    inference('sup-', [status(thm)], ['1', '269'])).
0.38/0.58	tff('271', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.38/0.58	       | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.38/0.58	    inference('simplify', [status(thm)], ['270'])).
0.38/0.58	tff('272', plain, (~ $true | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.38/0.58	    inference('sup-', [status(thm)], ['0', '271'])).
0.38/0.58	tff('273', plain, app_encode_app(a, $o, sk_S1, sk_Xx2),
0.38/0.58	    inference('simplify', [status(thm)], ['272'])).
0.38/0.58	tff('274', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.38/0.58	     | sk_S1 = sk_Xp(sk_Xx2)),
0.38/0.58	    inference('sup-', [status(thm)], ['273', '52'])).
0.38/0.58	tff('275', plain,
0.38/0.58	    (sk_S1 = sk_Xp(sk_Xx2)
0.38/0.58	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.38/0.58	    inference('simplify', [status(thm)], ['274'])).
0.38/0.58	tff('276', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | ~ app_encode_app(a, $o, sk_Xp(sk_Xy), sk_Xx1)
0.38/0.58	     | sk_S1 = sk_Xp(sk_Xx2)),
0.38/0.58	    inference('sup-', [status(thm)], ['257', '275'])).
0.38/0.58	tff('277', plain,
0.38/0.58	    (sk_S1 = sk_Xp(sk_Xx2) | ~ app_encode_app(a, $o, sk_Xp(sk_Xy), sk_Xx1)),
0.38/0.58	    inference('simplify', [status(thm)], ['276'])).
0.38/0.58	tff('278', plain,
0.38/0.58	    (~ app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	     | sk_S1 = sk_S2
0.38/0.58	     | sk_S1 = sk_Xp(sk_Xx2)),
0.38/0.58	    inference('sup-', [status(thm)], ['215', '277'])).
0.38/0.58	tff('279', plain, (sk_S1 = sk_Xp(sk_Xx2) | sk_S1 = sk_S2),
0.38/0.58	    inference('clc', [status(thm)], ['278', '231'])).
0.38/0.58	tff('280', plain,
0.38/0.58	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1) | sk_S1 = sk_S2),
0.38/0.58	    inference('sup+', [status(thm)], ['279', '1'])).
0.38/0.58	tff('281', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o), X8 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | ~ app_encode_app(a, $o, X8, sk_Xx1)
0.38/0.58	       | ~ app_encode_app(a, $o, X8, sk_Xy)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X8)
0.38/0.58	       | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.38/0.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.38/0.58	tff('282', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o), X8 : app_encode_fun(a, $o)]:
0.38/0.58	      (app_encode_app(a, $o, sk_S1, sk_Xy1)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X8)
0.38/0.58	       | ~ app_encode_app(a, $o, X8, sk_Xy)
0.38/0.58	       | ~ app_encode_app(a, $o, X8, sk_Xx1)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['281'])).
0.38/0.58	tff('283', plain,
0.38/0.58	    ![X0 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ $true
0.38/0.58	       | app_encode_app(a, $o, sk_S1, sk_Xy1)
0.38/0.58	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	       | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.38/0.58	    inference('sup-', [status(thm)], ['172', '282'])).
0.38/0.58	tff('284', plain,
0.38/0.58	    ![X0 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.38/0.58	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.38/0.58	       | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.38/0.58	    inference('simplify', [status(thm)], ['283'])).
0.38/0.58	tff('285', plain,
0.38/0.58	    ![X0 : app_encode_fun(a, $o)]:
0.38/0.58	      (app_encode_app(a, $o, sk_S1, sk_Xy1)
0.38/0.58	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_S, sk_Xx1)),
0.38/0.58	    inference('clc', [status(thm)], ['284', '205'])).
0.38/0.58	tff('286', plain,
0.38/0.58	    ![X0 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.38/0.58	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.38/0.58	       | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.38/0.58	    inference('clc', [status(thm)], ['285', '178'])).
0.38/0.58	tff('287', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (~ $true
0.38/0.58	       | app_encode_app(a, $o, sk_S1, sk_Xy1)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.38/0.58	    inference('sup-', [status(thm)], ['1', '286'])).
0.38/0.58	tff('288', plain,
0.38/0.58	    ![X0 : a]:
0.38/0.58	      (~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.38/0.58	       | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.38/0.58	    inference('simplify', [status(thm)], ['287'])).
0.38/0.58	tff('289', plain, (~ $true | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.38/0.58	    inference('sup-', [status(thm)], ['0', '288'])).
0.38/0.58	tff('290', plain, app_encode_app(a, $o, sk_S1, sk_Xy1),
0.38/0.58	    inference('simplify', [status(thm)], ['289'])).
0.38/0.58	tff('291', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.38/0.58	     | sk_S1 = sk_Xp(sk_Xy1)),
0.38/0.58	    inference('sup-', [status(thm)], ['290', '52'])).
0.38/0.58	tff('292', plain,
0.38/0.58	    (sk_S1 = sk_Xp(sk_Xy1)
0.38/0.58	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.38/0.58	    inference('simplify', [status(thm)], ['291'])).
0.38/0.58	tff('293', plain, (~ $true | sk_S1 = sk_S2 | sk_S1 = sk_Xp(sk_Xy1)),
0.38/0.58	    inference('sup-', [status(thm)], ['280', '292'])).
0.38/0.58	tff('294', plain, (sk_S1 = sk_Xp(sk_Xy1) | sk_S1 = sk_S2),
0.38/0.58	    inference('simplify', [status(thm)], ['293'])).
0.38/0.58	tff('295', plain, (sk_S1 = sk_S2 | sk_S1 = sk_S2 | sk_S1 = sk_S2),
0.38/0.58	    inference('sup+', [status(thm)], ['247', '294'])).
0.38/0.58	tff('296', plain, sk_S1 = sk_S2,
0.38/0.58	    inference('simplify', [status(thm)], ['295'])).
0.38/0.58	tff('297', plain,
0.38/0.58	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S) | ~ $true),
0.38/0.58	    inference('demod', [status(thm)], ['45', '296', '273'])).
0.38/0.58	tff('298', plain, app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S),
0.38/0.58	    inference('simplify', [status(thm)], ['297'])).
0.38/0.58	tff('299', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.38/0.58	     | sk_S1 = sk_Xp(sk_Xx2)),
0.38/0.58	    inference('sup-', [status(thm)], ['267', '52'])).
0.38/0.58	tff('300', plain,
0.38/0.58	    (sk_S1 = sk_Xp(sk_Xx2)
0.38/0.58	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xy)),
0.38/0.58	    inference('simplify', [status(thm)], ['299'])).
0.38/0.58	tff('301', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	     | sk_S1 = sk_Xp(sk_Xx2)),
0.38/0.58	    inference('sup-', [status(thm)], ['199', '300'])).
0.38/0.58	tff('302', plain,
0.38/0.58	    (sk_S1 = sk_Xp(sk_Xx2) | app_encode_app(a, $o, sk_S, sk_Xy)),
0.38/0.58	    inference('simplify', [status(thm)], ['301'])).
0.38/0.58	tff('303', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | sk_S1 = sk_Xp(sk_Xx2)
0.38/0.58	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	     | sk_S = sk_Xp(sk_Xy)),
0.38/0.58	    inference('sup-', [status(thm)], ['302', '52'])).
0.38/0.58	tff('304', plain,
0.38/0.58	    (sk_S = sk_Xp(sk_Xy)
0.38/0.58	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	     | sk_S1 = sk_Xp(sk_Xx2)),
0.38/0.58	    inference('simplify', [status(thm)], ['303'])).
0.38/0.58	tff('305', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | app_encode_app(a, $o, sk_S1, sk_Xx2)
0.38/0.58	     | sk_S1 = sk_Xp(sk_Xx2)
0.38/0.58	     | sk_S = sk_Xp(sk_Xy)),
0.38/0.58	    inference('sup-', [status(thm)], ['140', '304'])).
0.38/0.58	tff('306', plain,
0.38/0.58	    (sk_S = sk_Xp(sk_Xy)
0.38/0.58	     | sk_S1 = sk_Xp(sk_Xx2)
0.38/0.58	     | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.38/0.58	    inference('simplify', [status(thm)], ['305'])).
0.38/0.58	tff('307', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | sk_S1 = sk_Xp(sk_Xx2)
0.38/0.58	     | sk_S = sk_Xp(sk_Xy)
0.38/0.58	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.38/0.58	     | sk_S1 = sk_Xp(sk_Xx2)),
0.38/0.58	    inference('sup-', [status(thm)], ['306', '52'])).
0.38/0.58	tff('308', plain,
0.38/0.58	    (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.38/0.58	     | sk_S = sk_Xp(sk_Xy)
0.38/0.58	     | sk_S1 = sk_Xp(sk_Xx2)),
0.38/0.58	    inference('simplify', [status(thm)], ['307'])).
0.38/0.58	tff('309', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.58	     | sk_S1 = sk_Xp(sk_Xx2)
0.38/0.58	     | sk_S = sk_Xp(sk_Xy)),
0.38/0.58	    inference('sup-', [status(thm)], ['134', '308'])).
0.38/0.58	tff('310', plain,
0.38/0.58	    (sk_S = sk_Xp(sk_Xy)
0.38/0.58	     | sk_S1 = sk_Xp(sk_Xx2)
0.38/0.58	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.38/0.58	    inference('simplify', [status(thm)], ['309'])).
0.38/0.58	tff('311', plain, (sk_S1 = sk_Xp(sk_Xx2) | sk_S = sk_Xp(sk_Xy)),
0.38/0.58	    inference('clc', [status(thm)], ['310', '304'])).
0.38/0.58	tff('312', plain,
0.38/0.58	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.38/0.58	     | sk_S = sk_Xp(sk_Xy)),
0.38/0.58	    inference('sup+', [status(thm)], ['311', '1'])).
0.38/0.58	tff('313', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | app_encode_app(a, $o, sk_S1, sk_Xy1)
0.38/0.58	     | sk_S1 = sk_Xp(sk_Xy1)
0.38/0.58	     | sk_S = sk_Xp(sk_Xy)),
0.38/0.58	    inference('sup-', [status(thm)], ['172', '211'])).
0.38/0.58	tff('314', plain,
0.38/0.58	    (sk_S = sk_Xp(sk_Xy)
0.38/0.58	     | sk_S1 = sk_Xp(sk_Xy1)
0.38/0.58	     | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.38/0.58	    inference('simplify', [status(thm)], ['313'])).
0.38/0.58	tff('315', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | sk_S1 = sk_Xp(sk_Xy1)
0.38/0.58	     | sk_S = sk_Xp(sk_Xy)
0.38/0.58	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.38/0.58	     | sk_S1 = sk_Xp(sk_Xy1)),
0.38/0.58	    inference('sup-', [status(thm)], ['314', '52'])).
0.38/0.58	tff('316', plain,
0.38/0.58	    (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.38/0.58	     | sk_S = sk_Xp(sk_Xy)
0.38/0.58	     | sk_S1 = sk_Xp(sk_Xy1)),
0.38/0.58	    inference('simplify', [status(thm)], ['315'])).
0.38/0.58	tff('317', plain,
0.38/0.58	    (~ $true
0.38/0.58	     | sk_S = sk_Xp(sk_Xy)
0.38/0.58	     | sk_S1 = sk_Xp(sk_Xy1)
0.38/0.58	     | sk_S = sk_Xp(sk_Xy)),
0.38/0.58	    inference('sup-', [status(thm)], ['312', '316'])).
0.38/0.58	tff('318', plain, (sk_S1 = sk_Xp(sk_Xy1) | sk_S = sk_Xp(sk_Xy)),
0.38/0.58	    inference('simplify', [status(thm)], ['317'])).
0.38/0.58	tff('319', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o), X7 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.38/0.58	       | ~ app_encode_app(a, $o, X7, sk_Xx2)
0.38/0.58	       | ~ app_encode_app(a, $o, X7, sk_Xz)),
0.38/0.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.38/0.58	tff('320', plain,
0.38/0.58	    ![X6 : app_encode_fun(a, $o), X7 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ app_encode_app(a, $o, X7, sk_Xz)
0.38/0.58	       | ~ app_encode_app(a, $o, X7, sk_Xx2)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.58	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['319'])).
0.38/0.58	tff('321', plain,
0.38/0.58	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ $true
0.38/0.58	       | ~ app_encode_app(a, $o, X1, sk_Xx)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X1)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx2)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xz)),
0.38/0.58	    inference('sup-', [status(thm)], ['1', '320'])).
0.38/0.58	tff('322', plain,
0.38/0.58	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ app_encode_app(a, $o, sk_Xp(X0), sk_Xz)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx2)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X1)
0.38/0.58	       | ~ app_encode_app(a, $o, X1, sk_Xx)),
0.38/0.58	    inference('simplify', [status(thm)], ['321'])).
0.38/0.58	tff('323', plain,
0.38/0.58	    ![X0 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ app_encode_app(a, $o, sk_S2, sk_Xz)
0.38/0.58	       | sk_S = sk_Xp(sk_Xy)
0.38/0.58	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.58	       | ~ app_encode_app(a, $o, sk_Xp(sk_Xy1), sk_Xx2)),
0.38/0.58	    inference('sup-', [status(thm)], ['90', '322'])).
0.38/0.58	tff('324', plain,
0.38/0.58	    ![X0 : app_encode_fun(a, $o)]:
0.38/0.58	      (~ $true
0.38/0.58	       | sk_S = sk_Xp(sk_Xy)
0.38/0.58	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.38/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.38/0.58	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.59	       | ~ app_encode_app(a, $o, sk_Xp(sk_Xy1), sk_Xx2)),
0.38/0.59	    inference('demod', [status(thm)], ['323', '39'])).
0.38/0.59	tff('325', plain,
0.38/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.38/0.59	      (~ app_encode_app(a, $o, sk_Xp(sk_Xy1), sk_Xx2)
0.38/0.59	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.38/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.38/0.59	       | sk_S = sk_Xp(sk_Xy)),
0.38/0.59	    inference('simplify', [status(thm)], ['324'])).
0.38/0.59	tff('326', plain,
0.38/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.38/0.59	      (~ app_encode_app(a, $o, sk_S1, sk_Xx2)
0.38/0.59	       | sk_S = sk_Xp(sk_Xy)
0.38/0.59	       | sk_S = sk_Xp(sk_Xy)
0.38/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.38/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.38/0.59	       | app_encode_app(a, $o, sk_S, sk_Xy)),
0.38/0.59	    inference('sup-', [status(thm)], ['318', '325'])).
0.38/0.59	tff('327', plain,
0.38/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.38/0.59	      (~ $true
0.38/0.59	       | sk_S = sk_Xp(sk_Xy)
0.38/0.59	       | sk_S = sk_Xp(sk_Xy)
0.38/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.38/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.38/0.59	       | app_encode_app(a, $o, sk_S, sk_Xy)),
0.38/0.59	    inference('demod', [status(thm)], ['326', '273'])).
0.38/0.59	tff('328', plain,
0.38/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.38/0.59	      (app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.38/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.38/0.59	       | sk_S = sk_Xp(sk_Xy)),
0.38/0.59	    inference('simplify', [status(thm)], ['327'])).
0.38/0.59	tff('329', plain,
0.38/0.59	    ![X0 : a]:
0.38/0.59	      (~ $true
0.38/0.59	       | sk_S = sk_Xp(sk_Xy)
0.38/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.38/0.59	       | app_encode_app(a, $o, sk_S, sk_Xy)),
0.38/0.59	    inference('sup-', [status(thm)], ['1', '328'])).
0.38/0.59	tff('330', plain,
0.38/0.59	    ![X0 : a]:
0.38/0.59	      (app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.38/0.59	       | sk_S = sk_Xp(sk_Xy)),
0.38/0.59	    inference('simplify', [status(thm)], ['329'])).
0.38/0.59	tff('331', plain,
0.38/0.59	    (~ $true | sk_S = sk_Xp(sk_Xy) | app_encode_app(a, $o, sk_S, sk_Xy)),
0.38/0.59	    inference('sup-', [status(thm)], ['0', '330'])).
0.38/0.59	tff('332', plain, (app_encode_app(a, $o, sk_S, sk_Xy) | sk_S = sk_Xp(sk_Xy)),
0.38/0.59	    inference('simplify', [status(thm)], ['331'])).
0.38/0.59	tff('333', plain,
0.38/0.59	    (~ $true
0.38/0.59	     | sk_S = sk_Xp(sk_Xy)
0.38/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.59	     | sk_S = sk_Xp(sk_Xy)),
0.38/0.59	    inference('sup-', [status(thm)], ['332', '52'])).
0.38/0.59	tff('334', plain,
0.38/0.59	    (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.38/0.59	     | sk_S = sk_Xp(sk_Xy)),
0.38/0.59	    inference('simplify', [status(thm)], ['333'])).
0.38/0.59	tff('335', plain,
0.38/0.59	    (~ $true | ~ app_encode_app(a, $o, sk_S2, sk_Xx2) | sk_S = sk_Xp(sk_Xy)),
0.38/0.59	    inference('sup-', [status(thm)], ['45', '334'])).
0.38/0.59	tff('336', plain,
0.38/0.59	    (sk_S = sk_Xp(sk_Xy) | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)),
0.38/0.59	    inference('simplify', [status(thm)], ['335'])).
0.38/0.59	tff('337', plain, (sk_S = sk_Xp(sk_Xy) | ~ $true),
0.38/0.59	    inference('demod', [status(thm)], ['336', '296', '273'])).
0.38/0.59	tff('338', plain, sk_S = sk_Xp(sk_Xy),
0.38/0.59	    inference('simplify', [status(thm)], ['337'])).
0.38/0.59	tff('339', plain,
0.38/0.59	    (sk_S1 = sk_Xp(sk_Xx2) | ~ app_encode_app(a, $o, sk_S, sk_Xx1)),
0.38/0.59	    inference('demod', [status(thm)], ['277', '338'])).
0.38/0.59	tff('340', plain,
0.38/0.59	    ![X6 : app_encode_fun(a, $o), X7 : app_encode_fun(a, $o)]:
0.38/0.59	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.59	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.59	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.38/0.59	       | ~ app_encode_app(a, $o, X7, sk_Xx2)
0.38/0.59	       | ~ app_encode_app(a, $o, X7, sk_Xz)),
0.38/0.59	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.38/0.59	tff('341', plain,
0.38/0.59	    ![X6 : app_encode_fun(a, $o), X7 : app_encode_fun(a, $o)]:
0.38/0.59	      (~ app_encode_app(a, $o, X7, sk_Xz)
0.38/0.59	       | ~ app_encode_app(a, $o, X7, sk_Xx2)
0.38/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.38/0.59	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.59	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.38/0.59	    inference('simplify', [status(thm)], ['340'])).
0.38/0.59	tff('342', plain,
0.38/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.38/0.59	      (~ $true
0.38/0.59	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.38/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.38/0.59	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.59	       | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)
0.38/0.59	       | ~ app_encode_app(a, $o, sk_S2, sk_Xz)),
0.38/0.59	    inference('sup-', [status(thm)], ['96', '341'])).
0.38/0.59	tff('343', plain,
0.38/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.38/0.59	      (~ app_encode_app(a, $o, sk_S2, sk_Xz)
0.38/0.59	       | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)
0.38/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.38/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.38/0.59	       | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.38/0.59	    inference('simplify', [status(thm)], ['342'])).
0.38/0.59	tff('344', plain,
0.38/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.38/0.59	      (app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.38/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.38/0.59	       | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)),
0.38/0.59	    inference('clc', [status(thm)], ['343', '34'])).
0.38/0.59	tff('345', plain,
0.38/0.59	    ![X0 : a]:
0.38/0.59	      (~ $true
0.38/0.59	       | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)
0.38/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.38/0.59	       | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.38/0.59	    inference('sup-', [status(thm)], ['1', '344'])).
0.38/0.59	tff('346', plain,
0.38/0.59	    ![X0 : a]:
0.38/0.59	      (app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.38/0.59	       | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)),
0.38/0.59	    inference('simplify', [status(thm)], ['345'])).
0.38/0.59	tff('347', plain,
0.38/0.59	    (~ $true
0.38/0.59	     | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)
0.38/0.59	     | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.38/0.59	    inference('sup-', [status(thm)], ['0', '346'])).
0.38/0.59	tff('348', plain,
0.38/0.59	    (app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.59	     | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)),
0.38/0.59	    inference('simplify', [status(thm)], ['347'])).
0.38/0.59	tff('349', plain, (app_encode_app(a, $o, sk_S, sk_Xx1) | ~ $true),
0.38/0.59	    inference('demod', [status(thm)], ['348', '296', '273'])).
0.38/0.59	tff('350', plain, app_encode_app(a, $o, sk_S, sk_Xx1),
0.38/0.59	    inference('simplify', [status(thm)], ['349'])).
0.38/0.59	tff('351', plain, (sk_S1 = sk_Xp(sk_Xx2) | ~ $true),
0.38/0.59	    inference('demod', [status(thm)], ['339', '350'])).
0.38/0.59	tff('352', plain, sk_S1 = sk_Xp(sk_Xx2),
0.38/0.59	    inference('simplify', [status(thm)], ['351'])).
0.38/0.59	tff('353', plain, app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1),
0.38/0.59	    inference('sup+', [status(thm)], ['352', '1'])).
0.38/0.59	tff('354', plain,
0.38/0.59	    ![X6 : app_encode_fun(a, $o), X7 : app_encode_fun(a, $o), 
0.38/0.59	      X8 : app_encode_fun(a, $o)]:
0.38/0.59	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.59	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.38/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.59	       | ~ app_encode_app(a, $o, X8, sk_Xx1)
0.38/0.59	       | ~ app_encode_app(a, $o, X8, sk_Xy)
0.38/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X8)
0.38/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.38/0.59	       | ~ app_encode_app(a, $o, X7, sk_Xx2)
0.38/0.59	       | ~ app_encode_app(a, $o, X7, sk_Xz)),
0.38/0.59	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.38/0.59	tff('355', plain,
0.38/0.59	    ![X6 : app_encode_fun(a, $o), X7 : app_encode_fun(a, $o), 
0.38/0.59	      X8 : app_encode_fun(a, $o)]:
0.38/0.59	      (~ app_encode_app(a, $o, X7, sk_Xz)
0.38/0.59	       | ~ app_encode_app(a, $o, X7, sk_Xx2)
0.38/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.38/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X8)
0.38/0.59	       | ~ app_encode_app(a, $o, X8, sk_Xy)
0.38/0.59	       | ~ app_encode_app(a, $o, X8, sk_Xx1)
0.38/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.38/0.59	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.38/0.59	    inference('simplify', [status(thm)], ['354'])).
0.38/0.59	tff('356', plain,
0.38/0.59	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.38/0.59	      (~ $true
0.38/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.38/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.38/0.59	       | ~ app_encode_app(a, $o, X1, sk_Xx1)
0.38/0.59	       | ~ app_encode_app(a, $o, X1, sk_Xy)
0.38/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X1)
0.38/0.59	       | ~ app_encode_app(a, $o, sk_S1, sk_Xx2)
0.38/0.59	       | ~ app_encode_app(a, $o, sk_S1, sk_Xz)),
0.38/0.59	    inference('sup-', [status(thm)], ['353', '355'])).
0.38/0.59	tff('357', plain, app_encode_app(a, $o, sk_S1, sk_Xz),
0.38/0.59	    inference('demod', [status(thm)], ['39', '296'])).
0.38/0.59	tff('358', plain,
0.38/0.59	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.38/0.59	      (~ $true
0.38/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.38/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.38/0.59	       | ~ app_encode_app(a, $o, X1, sk_Xx1)
0.38/0.59	       | ~ app_encode_app(a, $o, X1, sk_Xy)
0.38/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X1)
0.38/0.59	       | ~ $true
0.38/0.59	       | ~ $true),
0.38/0.59	    inference('demod', [status(thm)], ['356', '273', '357'])).
0.38/0.59	tff('359', plain,
0.38/0.59	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.38/0.59	      (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X1)
0.38/0.59	       | ~ app_encode_app(a, $o, X1, sk_Xy)
0.38/0.59	       | ~ app_encode_app(a, $o, X1, sk_Xx1)
0.38/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.38/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)),
0.38/0.59	    inference('simplify', [status(thm)], ['358'])).
0.38/0.59	tff('360', plain,
0.38/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.38/0.59	      (~ $true
0.38/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.38/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.38/0.59	       | ~ app_encode_app(a, $o, sk_S, sk_Xx1)
0.38/0.59	       | ~ app_encode_app(a, $o, sk_S, sk_Xy)),
0.38/0.59	    inference('sup-', [status(thm)], ['298', '359'])).
0.38/0.59	tff('361', plain,
0.38/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.38/0.59	      (~ $true
0.38/0.59	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.38/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.38/0.59	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.59	       | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)
0.38/0.59	       | ~ app_encode_app(a, $o, sk_S2, sk_Xz)),
0.38/0.59	    inference('sup-', [status(thm)], ['51', '320'])).
0.38/0.59	tff('362', plain,
0.38/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.38/0.59	      (~ app_encode_app(a, $o, sk_S2, sk_Xz)
0.38/0.59	       | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)
0.38/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.38/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.38/0.59	       | app_encode_app(a, $o, sk_S, sk_Xy)),
0.38/0.59	    inference('simplify', [status(thm)], ['361'])).
0.38/0.59	tff('363', plain,
0.38/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.38/0.59	      (~ $true
0.38/0.59	       | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)
0.38/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.38/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.38/0.59	       | app_encode_app(a, $o, sk_S, sk_Xy)),
0.38/0.59	    inference('demod', [status(thm)], ['362', '39'])).
0.38/0.59	tff('364', plain,
0.38/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.38/0.59	      (app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.38/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.38/0.59	       | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)),
0.38/0.59	    inference('simplify', [status(thm)], ['363'])).
0.38/0.59	tff('365', plain,
0.38/0.59	    ![X0 : a]:
0.38/0.59	      (~ $true
0.38/0.59	       | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)
0.38/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.38/0.59	       | app_encode_app(a, $o, sk_S, sk_Xy)),
0.38/0.59	    inference('sup-', [status(thm)], ['1', '364'])).
0.38/0.59	tff('366', plain,
0.38/0.59	    ![X0 : a]:
0.38/0.59	      (app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.38/0.59	       | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)),
0.38/0.59	    inference('simplify', [status(thm)], ['365'])).
0.38/0.59	tff('367', plain,
0.38/0.59	    (~ $true
0.38/0.59	     | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)
0.38/0.59	     | app_encode_app(a, $o, sk_S, sk_Xy)),
0.38/0.59	    inference('sup-', [status(thm)], ['0', '366'])).
0.38/0.59	tff('368', plain,
0.38/0.59	    (app_encode_app(a, $o, sk_S, sk_Xy)
0.38/0.59	     | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)),
0.38/0.59	    inference('simplify', [status(thm)], ['367'])).
0.38/0.59	tff('369', plain, (app_encode_app(a, $o, sk_S, sk_Xy) | ~ $true),
0.38/0.59	    inference('demod', [status(thm)], ['368', '296', '273'])).
0.38/0.59	tff('370', plain, app_encode_app(a, $o, sk_S, sk_Xy),
0.38/0.59	    inference('simplify', [status(thm)], ['369'])).
0.38/0.59	tff('371', plain,
0.38/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.38/0.59	      (~ $true
0.38/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.38/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.38/0.59	       | ~ $true
0.38/0.59	       | ~ $true),
0.38/0.59	    inference('demod', [status(thm)], ['360', '350', '370'])).
0.38/0.59	tff('372', plain,
0.38/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.38/0.59	      (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.38/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)),
0.38/0.59	    inference('simplify', [status(thm)], ['371'])).
0.38/0.59	tff('373', plain,
0.38/0.59	    ![X0 : a]: (~ $true | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.38/0.59	    inference('sup-', [status(thm)], ['1', '372'])).
0.38/0.59	tff('374', plain, ![X0 : a]: ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx),
0.38/0.59	    inference('simplify', [status(thm)], ['373'])).
0.38/0.59	tff('375', plain, ~ $true, inference('sup-', [status(thm)], ['0', '374'])).
0.38/0.59	tff('376', plain, $false, inference('simplify', [status(thm)], ['375'])).
0.38/0.59	
0.38/0.59	% SZS output end Refutation
0.38/0.59	EOF
