0.00/0.00	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : app
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : kbo
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n146.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 17:30:08 CST 2018
0.37/0.58	% done 1191 iterations in 0.375s
0.37/0.58	% SZS status Theorem for 'stdin'
0.37/0.58	% SZS output start Refutation
0.37/0.58	tff(zf_stmt_3, conjecture,
0.37/0.58	  (![P:app_encode_fun(app_encode_fun(a,$o),$o)]:
0.37/0.58	     ((![Xx:a]:
0.37/0.58	         (?[Xp:app_encode_fun(a,$o)]:
0.37/0.58	            (app_encode_app(app_encode_fun(a,$o),$o,P,Xp) & 
0.37/0.58	             app_encode_app(a,$o,Xp,Xx) & 
0.37/0.58	             (![Xq:app_encode_fun(a,$o)]:
0.37/0.58	                ((app_encode_app(app_encode_fun(a,$o),$o,P,Xq) & 
0.37/0.58	                  app_encode_app(a,$o,Xq,Xx)) =>
0.37/0.58	                 (Xq = Xp)))))) =>
0.37/0.58	      ((![Xx:a]:
0.37/0.58	          (?[S:app_encode_fun(a,$o)]:
0.37/0.58	             (app_encode_app(app_encode_fun(a,$o),$o,P,S) & 
0.37/0.58	              app_encode_app(a,$o,S,Xx) & app_encode_app(a,$o,S,Xx)))) & 
0.37/0.58	       (![Xx:a,Xy:a]:
0.37/0.58	          ((?[S:app_encode_fun(a,$o)]:
0.37/0.58	              (app_encode_app(app_encode_fun(a,$o),$o,P,S) & 
0.37/0.58	               app_encode_app(a,$o,S,Xx) & app_encode_app(a,$o,S,Xy))) =>
0.37/0.58	           (?[S:app_encode_fun(a,$o)]:
0.37/0.58	              (app_encode_app(app_encode_fun(a,$o),$o,P,S) & 
0.37/0.58	               app_encode_app(a,$o,S,Xy) & app_encode_app(a,$o,S,Xx))))) & 
0.37/0.58	       (![Xx:a,Xy:a,Xz:a]:
0.37/0.58	          (((?[S:app_encode_fun(a,$o)]:
0.37/0.58	               (app_encode_app(app_encode_fun(a,$o),$o,P,S) & 
0.37/0.58	                app_encode_app(a,$o,S,Xx) & app_encode_app(a,$o,S,Xy))) & 
0.37/0.58	            (?[S:app_encode_fun(a,$o)]:
0.37/0.58	               (app_encode_app(app_encode_fun(a,$o),$o,P,S) & 
0.37/0.58	                app_encode_app(a,$o,S,Xy) & app_encode_app(a,$o,S,Xz)))) =>
0.37/0.58	           (?[S:app_encode_fun(a,$o)]:
0.37/0.58	              (app_encode_app(app_encode_fun(a,$o),$o,P,S) & 
0.37/0.58	               app_encode_app(a,$o,S,Xx) & app_encode_app(a,$o,S,Xz))))))))).
0.37/0.58	tff(zf_stmt_0, negated_conjecture,
0.37/0.58	  (~
0.37/0.58	    (![P:app_encode_fun(app_encode_fun(a,$o),$o)]:
0.37/0.58	       ((![Xx:a]:
0.37/0.58	           (?[Xp:app_encode_fun(a,$o)]:
0.37/0.58	              (app_encode_app(app_encode_fun(a,$o),$o,P,Xp) & 
0.37/0.58	               app_encode_app(a,$o,Xp,Xx) & 
0.37/0.58	               (![Xq:app_encode_fun(a,$o)]:
0.37/0.58	                  ((app_encode_app(app_encode_fun(a,$o),$o,P,Xq) & 
0.37/0.58	                    app_encode_app(a,$o,Xq,Xx)) =>
0.37/0.58	                   (Xq = Xp)))))) =>
0.37/0.58	        ((![Xx:a]:
0.37/0.58	            (?[S:app_encode_fun(a,$o)]:
0.37/0.58	               (app_encode_app(app_encode_fun(a,$o),$o,P,S) & 
0.37/0.58	                app_encode_app(a,$o,S,Xx) & app_encode_app(a,$o,S,Xx)))) & 
0.37/0.58	         (![Xx:a,Xy:a]:
0.37/0.58	            ((?[S:app_encode_fun(a,$o)]:
0.37/0.58	                (app_encode_app(app_encode_fun(a,$o),$o,P,S) & 
0.37/0.58	                 app_encode_app(a,$o,S,Xx) & app_encode_app(a,$o,S,Xy))) =>
0.37/0.58	             (?[S:app_encode_fun(a,$o)]:
0.37/0.58	                (app_encode_app(app_encode_fun(a,$o),$o,P,S) & 
0.37/0.58	                 app_encode_app(a,$o,S,Xy) & app_encode_app(a,$o,S,Xx))))) & 
0.37/0.58	         (![Xx:a,Xy:a,Xz:a]:
0.37/0.58	            (((?[S:app_encode_fun(a,$o)]:
0.37/0.58	                 (app_encode_app(app_encode_fun(a,$o),$o,P,S) & 
0.37/0.58	                  app_encode_app(a,$o,S,Xx) & app_encode_app(a,$o,S,Xy))) & 
0.37/0.58	              (?[S:app_encode_fun(a,$o)]:
0.37/0.58	                 (app_encode_app(app_encode_fun(a,$o),$o,P,S) & 
0.37/0.58	                  app_encode_app(a,$o,S,Xy) & app_encode_app(a,$o,S,Xz)))) =>
0.37/0.58	             (?[S:app_encode_fun(a,$o)]:
0.37/0.58	                (app_encode_app(app_encode_fun(a,$o),$o,P,S) & 
0.37/0.58	                 app_encode_app(a,$o,S,Xx) & app_encode_app(a,$o,S,Xz)))))))))).
0.37/0.58	tff('0', plain, ![X0 : a]: app_encode_app(a, $o, sk_Xp(X0), X0),
0.37/0.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.37/0.58	tff('1', plain,
0.37/0.58	    ![X0 : a]: app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_Xp(X0)),
0.37/0.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.37/0.58	tff('2', plain,
0.37/0.58	    ![X2 : app_encode_fun(a, $o)]:
0.37/0.58	      (~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.58	       | ~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.37/0.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.37/0.58	tff('3', plain,
0.37/0.58	    ![X2 : app_encode_fun(a, $o)]:
0.37/0.58	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.37/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.58	       | ~ app_encode_app(a, $o, X2, sk_Xx)),
0.37/0.58	    inference('simplify', [status(thm)], ['2'])).
0.37/0.58	tff('4', plain,
0.37/0.58	    ![X0 : a]:
0.37/0.58	      (~ $true
0.37/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.37/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.37/0.58	    inference('sup-', [status(thm)], ['1', '3'])).
0.37/0.58	tff('5', plain,
0.37/0.58	    ![X0 : a]:
0.37/0.58	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.37/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.37/0.58	    inference('simplify', [status(thm)], ['4'])).
0.37/0.58	tff('6', plain,
0.37/0.58	    (~ $true
0.37/0.58	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.58	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.37/0.58	    inference('sup-', [status(thm)], ['0', '5'])).
0.37/0.58	tff('7', plain,
0.37/0.58	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.37/0.58	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.37/0.58	    inference('simplify', [status(thm)], ['6'])).
0.37/0.58	tff('8', plain,
0.37/0.58	    ![X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o)]:
0.37/0.58	      (~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.58	       | ~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X3)
0.37/0.58	       | ~ app_encode_app(a, $o, X3, sk_Xx2)
0.37/0.58	       | ~ app_encode_app(a, $o, X3, sk_Xz)),
0.37/0.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.37/0.58	tff('9', plain,
0.37/0.58	    ![X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o)]:
0.37/0.58	      (~ app_encode_app(a, $o, X3, sk_Xz)
0.37/0.58	       | ~ app_encode_app(a, $o, X3, sk_Xx2)
0.37/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X3)
0.37/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.58	       | ~ app_encode_app(a, $o, X2, sk_Xx)),
0.37/0.58	    inference('simplify', [status(thm)], ['8'])).
0.37/0.58	tff('10', plain,
0.37/0.58	    ![X0 : app_encode_fun(a, $o)]:
0.37/0.58	      (~ $true
0.37/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.58	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.37/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.37/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.58	       | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)
0.37/0.58	       | ~ app_encode_app(a, $o, sk_S2, sk_Xz)),
0.37/0.58	    inference('sup-', [status(thm)], ['7', '9'])).
0.37/0.58	tff('11', plain,
0.37/0.58	    ![X0 : app_encode_fun(a, $o)]:
0.37/0.58	      (~ app_encode_app(a, $o, sk_S2, sk_Xz)
0.37/0.58	       | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)
0.37/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.37/0.58	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.37/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.37/0.58	    inference('simplify', [status(thm)], ['10'])).
0.37/0.58	tff('12', plain,
0.37/0.58	    ![X2 : app_encode_fun(a, $o)]:
0.37/0.58	      (~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.58	       | ~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.58	       | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.37/0.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.37/0.58	tff('13', plain,
0.37/0.58	    ![X2 : app_encode_fun(a, $o)]:
0.37/0.58	      (app_encode_app(a, $o, sk_S2, sk_Xz)
0.37/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.58	       | ~ app_encode_app(a, $o, X2, sk_Xx)),
0.37/0.58	    inference('simplify', [status(thm)], ['12'])).
0.37/0.58	tff('14', plain,
0.37/0.58	    ![X0 : a]:
0.37/0.58	      (~ $true
0.37/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.37/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.58	       | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.37/0.58	    inference('sup-', [status(thm)], ['1', '13'])).
0.37/0.58	tff('15', plain,
0.37/0.58	    ![X0 : a]:
0.37/0.58	      (app_encode_app(a, $o, sk_S2, sk_Xz)
0.37/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.37/0.58	    inference('simplify', [status(thm)], ['14'])).
0.37/0.58	tff('16', plain,
0.37/0.58	    (~ $true
0.37/0.58	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.58	     | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.37/0.58	    inference('sup-', [status(thm)], ['0', '15'])).
0.37/0.58	tff('17', plain,
0.37/0.58	    (app_encode_app(a, $o, sk_S2, sk_Xz)
0.37/0.58	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.37/0.58	    inference('simplify', [status(thm)], ['16'])).
0.37/0.58	tff('18', plain,
0.37/0.58	    ![X0 : app_encode_fun(a, $o)]:
0.37/0.58	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.58	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.37/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.37/0.58	       | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)),
0.37/0.58	    inference('clc', [status(thm)], ['11', '17'])).
0.37/0.58	tff('19', plain,
0.37/0.58	    ![X0 : a]:
0.37/0.58	      (~ $true
0.37/0.58	       | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)
0.37/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.37/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.37/0.58	    inference('sup-', [status(thm)], ['1', '18'])).
0.37/0.58	tff('20', plain,
0.37/0.58	    ![X0 : a]:
0.37/0.58	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.37/0.58	       | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)),
0.37/0.58	    inference('simplify', [status(thm)], ['19'])).
0.37/0.58	tff('21', plain,
0.37/0.58	    (~ $true
0.37/0.58	     | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)
0.37/0.58	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.37/0.58	    inference('sup-', [status(thm)], ['0', '20'])).
0.37/0.58	tff('22', plain,
0.37/0.58	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.58	     | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)),
0.37/0.58	    inference('simplify', [status(thm)], ['21'])).
0.37/0.58	tff('23', plain,
0.37/0.58	    ![X2 : app_encode_fun(a, $o)]:
0.37/0.58	      (~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.58	       | ~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.58	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.37/0.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.37/0.58	tff('24', plain,
0.37/0.58	    ![X2 : app_encode_fun(a, $o)]:
0.37/0.58	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.37/0.58	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.58	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.58	       | ~ app_encode_app(a, $o, X2, sk_Xx)),
0.37/0.58	    inference('simplify', [status(thm)], ['23'])).
0.37/0.58	tff('25', plain,
0.37/0.58	    ![X0 : a]:
0.37/0.58	      (~ $true
0.37/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.37/0.58	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.58	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.37/0.58	    inference('sup-', [status(thm)], ['1', '24'])).
0.37/0.58	tff('26', plain,
0.37/0.58	    ![X0 : a]:
0.37/0.58	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.37/0.58	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.58	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.37/0.58	    inference('simplify', [status(thm)], ['25'])).
0.37/0.58	tff('27', plain,
0.37/0.58	    (~ $true
0.37/0.58	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.58	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.37/0.58	    inference('sup-', [status(thm)], ['0', '26'])).
0.37/0.58	tff('28', plain,
0.37/0.58	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.37/0.58	     | app_encode_app(a, $o, sk_S, sk_Xy)),
0.37/0.58	    inference('simplify', [status(thm)], ['27'])).
0.37/0.58	tff('29', plain,
0.37/0.58	    ![X2 : app_encode_fun(a, $o)]:
0.37/0.58	      (~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.58	       | ~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	       | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.37/0.59	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.37/0.59	tff('30', plain,
0.37/0.59	    ![X2 : app_encode_fun(a, $o)]:
0.37/0.59	      (app_encode_app(a, $o, sk_S2, sk_Xz)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.59	       | ~ app_encode_app(a, $o, X2, sk_Xx)),
0.37/0.59	    inference('simplify', [status(thm)], ['29'])).
0.37/0.59	tff('31', plain,
0.37/0.59	    ![X0 : a]:
0.37/0.59	      (~ $true
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	       | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.37/0.59	    inference('sup-', [status(thm)], ['1', '30'])).
0.37/0.59	tff('32', plain,
0.37/0.59	    ![X0 : a]:
0.37/0.59	      (app_encode_app(a, $o, sk_S2, sk_Xz)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.37/0.59	    inference('simplify', [status(thm)], ['31'])).
0.37/0.59	tff('33', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	     | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.37/0.59	    inference('sup-', [status(thm)], ['0', '32'])).
0.37/0.59	tff('34', plain,
0.37/0.59	    (app_encode_app(a, $o, sk_S2, sk_Xz) | app_encode_app(a, $o, sk_S, sk_Xy)),
0.37/0.59	    inference('simplify', [status(thm)], ['33'])).
0.37/0.59	tff('35', plain,
0.37/0.59	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
0.37/0.59	      (X1 = sk_Xp(X0)
0.37/0.59	       | ~ app_encode_app(a, $o, X1, X0)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X1)),
0.37/0.59	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.37/0.59	tff('36', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.37/0.59	     | sk_S2 = sk_Xp(sk_Xz)),
0.37/0.59	    inference('sup-', [status(thm)], ['34', '35'])).
0.37/0.59	tff('37', plain,
0.37/0.59	    (sk_S2 = sk_Xp(sk_Xz)
0.37/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xy)),
0.37/0.59	    inference('simplify', [status(thm)], ['36'])).
0.37/0.59	tff('38', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	     | sk_S2 = sk_Xp(sk_Xz)),
0.37/0.59	    inference('sup-', [status(thm)], ['28', '37'])).
0.37/0.59	tff('39', plain, (sk_S2 = sk_Xp(sk_Xz) | app_encode_app(a, $o, sk_S, sk_Xy)),
0.37/0.59	    inference('simplify', [status(thm)], ['38'])).
0.37/0.59	tff('40', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | sk_S2 = sk_Xp(sk_Xz)
0.37/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.59	     | sk_S = sk_Xp(sk_Xy)),
0.37/0.59	    inference('sup-', [status(thm)], ['39', '35'])).
0.37/0.59	tff('41', plain,
0.37/0.59	    (sk_S = sk_Xp(sk_Xy)
0.37/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.59	     | sk_S2 = sk_Xp(sk_Xz)),
0.37/0.59	    inference('simplify', [status(thm)], ['40'])).
0.37/0.59	tff('42', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | app_encode_app(a, $o, sk_S2, sk_Xz)
0.37/0.59	     | sk_S2 = sk_Xp(sk_Xz)
0.37/0.59	     | sk_S = sk_Xp(sk_Xy)),
0.37/0.59	    inference('sup-', [status(thm)], ['17', '41'])).
0.37/0.59	tff('43', plain,
0.37/0.59	    (sk_S = sk_Xp(sk_Xy)
0.37/0.59	     | sk_S2 = sk_Xp(sk_Xz)
0.37/0.59	     | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.37/0.59	    inference('simplify', [status(thm)], ['42'])).
0.37/0.59	tff('44', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | sk_S2 = sk_Xp(sk_Xz)
0.37/0.59	     | sk_S = sk_Xp(sk_Xy)
0.37/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.37/0.59	     | sk_S2 = sk_Xp(sk_Xz)),
0.37/0.59	    inference('sup-', [status(thm)], ['43', '35'])).
0.37/0.59	tff('45', plain,
0.37/0.59	    (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.37/0.59	     | sk_S = sk_Xp(sk_Xy)
0.37/0.59	     | sk_S2 = sk_Xp(sk_Xz)),
0.37/0.59	    inference('simplify', [status(thm)], ['44'])).
0.37/0.59	tff('46', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.59	     | sk_S2 = sk_Xp(sk_Xz)
0.37/0.59	     | sk_S = sk_Xp(sk_Xy)),
0.37/0.59	    inference('sup-', [status(thm)], ['7', '45'])).
0.37/0.59	tff('47', plain,
0.37/0.59	    (sk_S = sk_Xp(sk_Xy)
0.37/0.59	     | sk_S2 = sk_Xp(sk_Xz)
0.37/0.59	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.37/0.59	    inference('simplify', [status(thm)], ['46'])).
0.37/0.59	tff('48', plain, (sk_S2 = sk_Xp(sk_Xz) | sk_S = sk_Xp(sk_Xy)),
0.37/0.59	    inference('clc', [status(thm)], ['47', '41'])).
0.37/0.59	tff('49', plain,
0.37/0.59	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.37/0.59	     | sk_S = sk_Xp(sk_Xy)),
0.37/0.59	    inference('sup+', [status(thm)], ['48', '1'])).
0.37/0.59	tff('50', plain,
0.37/0.59	    ![X2 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.59	       | ~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.59	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.59	       | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.37/0.59	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.37/0.59	tff('51', plain,
0.37/0.59	    ![X2 : app_encode_fun(a, $o)]:
0.37/0.59	      (app_encode_app(a, $o, sk_S2, sk_Xy1)
0.37/0.59	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.59	       | ~ app_encode_app(a, $o, X2, sk_Xx)),
0.37/0.59	    inference('simplify', [status(thm)], ['50'])).
0.37/0.59	tff('52', plain,
0.37/0.59	    ![X0 : a]:
0.37/0.59	      (~ $true
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.37/0.59	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.59	       | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.37/0.59	    inference('sup-', [status(thm)], ['1', '51'])).
0.37/0.59	tff('53', plain,
0.37/0.59	    ![X0 : a]:
0.37/0.59	      (app_encode_app(a, $o, sk_S2, sk_Xy1)
0.37/0.59	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.37/0.59	    inference('simplify', [status(thm)], ['52'])).
0.37/0.59	tff('54', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.59	     | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.37/0.59	    inference('sup-', [status(thm)], ['0', '53'])).
0.37/0.59	tff('55', plain,
0.37/0.59	    (app_encode_app(a, $o, sk_S2, sk_Xy1)
0.37/0.59	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.37/0.59	    inference('simplify', [status(thm)], ['54'])).
0.37/0.59	tff('56', plain,
0.37/0.59	    ![X2 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.59	       | ~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	       | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.37/0.59	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.37/0.59	tff('57', plain,
0.37/0.59	    ![X2 : app_encode_fun(a, $o)]:
0.37/0.59	      (app_encode_app(a, $o, sk_S2, sk_Xy1)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.59	       | ~ app_encode_app(a, $o, X2, sk_Xx)),
0.37/0.59	    inference('simplify', [status(thm)], ['56'])).
0.37/0.59	tff('58', plain,
0.37/0.59	    ![X0 : a]:
0.37/0.59	      (~ $true
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	       | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.37/0.59	    inference('sup-', [status(thm)], ['1', '57'])).
0.37/0.59	tff('59', plain,
0.37/0.59	    ![X0 : a]:
0.37/0.59	      (app_encode_app(a, $o, sk_S2, sk_Xy1)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.37/0.59	    inference('simplify', [status(thm)], ['58'])).
0.37/0.59	tff('60', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	     | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.37/0.59	    inference('sup-', [status(thm)], ['0', '59'])).
0.37/0.59	tff('61', plain,
0.37/0.59	    (app_encode_app(a, $o, sk_S2, sk_Xy1)
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xy)),
0.37/0.59	    inference('simplify', [status(thm)], ['60'])).
0.37/0.59	tff('62', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.37/0.59	     | sk_S2 = sk_Xp(sk_Xy1)),
0.37/0.59	    inference('sup-', [status(thm)], ['61', '35'])).
0.37/0.59	tff('63', plain,
0.37/0.59	    (sk_S2 = sk_Xp(sk_Xy1)
0.37/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xy)),
0.37/0.59	    inference('simplify', [status(thm)], ['62'])).
0.37/0.59	tff('64', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	     | sk_S2 = sk_Xp(sk_Xy1)),
0.37/0.59	    inference('sup-', [status(thm)], ['28', '63'])).
0.37/0.59	tff('65', plain,
0.37/0.59	    (sk_S2 = sk_Xp(sk_Xy1) | app_encode_app(a, $o, sk_S, sk_Xy)),
0.37/0.59	    inference('simplify', [status(thm)], ['64'])).
0.37/0.59	tff('66', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | sk_S2 = sk_Xp(sk_Xy1)
0.37/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.59	     | sk_S = sk_Xp(sk_Xy)),
0.37/0.59	    inference('sup-', [status(thm)], ['65', '35'])).
0.37/0.59	tff('67', plain,
0.37/0.59	    (sk_S = sk_Xp(sk_Xy)
0.37/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.59	     | sk_S2 = sk_Xp(sk_Xy1)),
0.37/0.59	    inference('simplify', [status(thm)], ['66'])).
0.37/0.59	tff('68', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | app_encode_app(a, $o, sk_S2, sk_Xy1)
0.37/0.59	     | sk_S2 = sk_Xp(sk_Xy1)
0.37/0.59	     | sk_S = sk_Xp(sk_Xy)),
0.37/0.59	    inference('sup-', [status(thm)], ['55', '67'])).
0.37/0.59	tff('69', plain,
0.37/0.59	    (sk_S = sk_Xp(sk_Xy)
0.37/0.59	     | sk_S2 = sk_Xp(sk_Xy1)
0.37/0.59	     | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.37/0.59	    inference('simplify', [status(thm)], ['68'])).
0.37/0.59	tff('70', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | sk_S2 = sk_Xp(sk_Xy1)
0.37/0.59	     | sk_S = sk_Xp(sk_Xy)
0.37/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.37/0.59	     | sk_S2 = sk_Xp(sk_Xy1)),
0.37/0.59	    inference('sup-', [status(thm)], ['69', '35'])).
0.37/0.59	tff('71', plain,
0.37/0.59	    (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.37/0.59	     | sk_S = sk_Xp(sk_Xy)
0.37/0.59	     | sk_S2 = sk_Xp(sk_Xy1)),
0.37/0.59	    inference('simplify', [status(thm)], ['70'])).
0.37/0.59	tff('72', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | sk_S = sk_Xp(sk_Xy)
0.37/0.59	     | sk_S2 = sk_Xp(sk_Xy1)
0.37/0.59	     | sk_S = sk_Xp(sk_Xy)),
0.37/0.59	    inference('sup-', [status(thm)], ['49', '71'])).
0.37/0.59	tff('73', plain, (sk_S2 = sk_Xp(sk_Xy1) | sk_S = sk_Xp(sk_Xy)),
0.37/0.59	    inference('simplify', [status(thm)], ['72'])).
0.37/0.59	tff('74', plain,
0.37/0.59	    ![X2 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.59	       | ~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.37/0.59	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.37/0.59	tff('75', plain,
0.37/0.59	    ![X2 : app_encode_fun(a, $o)]:
0.37/0.59	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.59	       | ~ app_encode_app(a, $o, X2, sk_Xx)),
0.37/0.59	    inference('simplify', [status(thm)], ['74'])).
0.37/0.59	tff('76', plain,
0.37/0.59	    ![X0 : a]:
0.37/0.59	      (~ $true
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.37/0.59	    inference('sup-', [status(thm)], ['1', '75'])).
0.37/0.59	tff('77', plain,
0.37/0.59	    ![X0 : a]:
0.37/0.59	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.37/0.59	    inference('simplify', [status(thm)], ['76'])).
0.37/0.59	tff('78', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.37/0.59	    inference('sup-', [status(thm)], ['0', '77'])).
0.37/0.59	tff('79', plain,
0.37/0.59	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.37/0.59	    inference('simplify', [status(thm)], ['78'])).
0.37/0.59	tff('80', plain,
0.37/0.59	    ![X2 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.59	       | ~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	       | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.37/0.59	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.37/0.59	tff('81', plain,
0.37/0.59	    ![X2 : app_encode_fun(a, $o)]:
0.37/0.59	      (app_encode_app(a, $o, sk_S2, sk_Xz)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.59	       | ~ app_encode_app(a, $o, X2, sk_Xx)),
0.37/0.59	    inference('simplify', [status(thm)], ['80'])).
0.37/0.59	tff('82', plain,
0.37/0.59	    ![X0 : a]:
0.37/0.59	      (~ $true
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	       | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.37/0.59	    inference('sup-', [status(thm)], ['1', '81'])).
0.37/0.59	tff('83', plain,
0.37/0.59	    ![X0 : a]:
0.37/0.59	      (app_encode_app(a, $o, sk_S2, sk_Xz)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.37/0.59	    inference('simplify', [status(thm)], ['82'])).
0.37/0.59	tff('84', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	     | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.37/0.59	    inference('sup-', [status(thm)], ['0', '83'])).
0.37/0.59	tff('85', plain,
0.37/0.59	    (app_encode_app(a, $o, sk_S2, sk_Xz)
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.37/0.59	    inference('simplify', [status(thm)], ['84'])).
0.37/0.59	tff('86', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.37/0.59	     | sk_S2 = sk_Xp(sk_Xz)),
0.37/0.59	    inference('sup-', [status(thm)], ['85', '35'])).
0.37/0.59	tff('87', plain,
0.37/0.59	    (sk_S2 = sk_Xp(sk_Xz)
0.37/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.37/0.59	    inference('simplify', [status(thm)], ['86'])).
0.37/0.59	tff('88', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	     | sk_S2 = sk_Xp(sk_Xz)),
0.37/0.59	    inference('sup-', [status(thm)], ['79', '87'])).
0.37/0.59	tff('89', plain,
0.37/0.59	    (sk_S2 = sk_Xp(sk_Xz) | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.37/0.59	    inference('simplify', [status(thm)], ['88'])).
0.37/0.59	tff('90', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | sk_S2 = sk_Xp(sk_Xz)
0.37/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.59	     | sk_S = sk_Xp(sk_Xx1)),
0.37/0.59	    inference('sup-', [status(thm)], ['89', '35'])).
0.37/0.59	tff('91', plain,
0.37/0.59	    (sk_S = sk_Xp(sk_Xx1)
0.37/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.59	     | sk_S2 = sk_Xp(sk_Xz)),
0.37/0.59	    inference('simplify', [status(thm)], ['90'])).
0.37/0.59	tff('92', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | app_encode_app(a, $o, sk_S2, sk_Xz)
0.37/0.59	     | sk_S2 = sk_Xp(sk_Xz)
0.37/0.59	     | sk_S = sk_Xp(sk_Xx1)),
0.37/0.59	    inference('sup-', [status(thm)], ['17', '91'])).
0.37/0.59	tff('93', plain,
0.37/0.59	    (sk_S = sk_Xp(sk_Xx1)
0.37/0.59	     | sk_S2 = sk_Xp(sk_Xz)
0.37/0.59	     | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.37/0.59	    inference('simplify', [status(thm)], ['92'])).
0.37/0.59	tff('94', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | sk_S2 = sk_Xp(sk_Xz)
0.37/0.59	     | sk_S = sk_Xp(sk_Xx1)
0.37/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.37/0.59	     | sk_S2 = sk_Xp(sk_Xz)),
0.37/0.59	    inference('sup-', [status(thm)], ['93', '35'])).
0.37/0.59	tff('95', plain,
0.37/0.59	    (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.37/0.59	     | sk_S = sk_Xp(sk_Xx1)
0.37/0.59	     | sk_S2 = sk_Xp(sk_Xz)),
0.37/0.59	    inference('simplify', [status(thm)], ['94'])).
0.37/0.59	tff('96', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.59	     | sk_S2 = sk_Xp(sk_Xz)
0.37/0.59	     | sk_S = sk_Xp(sk_Xx1)),
0.37/0.59	    inference('sup-', [status(thm)], ['7', '95'])).
0.37/0.59	tff('97', plain,
0.37/0.59	    (sk_S = sk_Xp(sk_Xx1)
0.37/0.59	     | sk_S2 = sk_Xp(sk_Xz)
0.37/0.59	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.37/0.59	    inference('simplify', [status(thm)], ['96'])).
0.37/0.59	tff('98', plain, (sk_S2 = sk_Xp(sk_Xz) | sk_S = sk_Xp(sk_Xx1)),
0.37/0.59	    inference('clc', [status(thm)], ['97', '91'])).
0.37/0.59	tff('99', plain,
0.37/0.59	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.37/0.59	     | sk_S = sk_Xp(sk_Xx1)),
0.37/0.59	    inference('sup+', [status(thm)], ['98', '1'])).
0.37/0.59	tff('100', plain,
0.37/0.59	    ![X2 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.59	       | ~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	       | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.37/0.59	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.37/0.59	tff('101', plain,
0.37/0.59	    ![X2 : app_encode_fun(a, $o)]:
0.37/0.59	      (app_encode_app(a, $o, sk_S2, sk_Xy1)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.59	       | ~ app_encode_app(a, $o, X2, sk_Xx)),
0.37/0.59	    inference('simplify', [status(thm)], ['100'])).
0.37/0.59	tff('102', plain,
0.37/0.59	    ![X0 : a]:
0.37/0.59	      (~ $true
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	       | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.37/0.59	    inference('sup-', [status(thm)], ['1', '101'])).
0.37/0.59	tff('103', plain,
0.37/0.59	    ![X0 : a]:
0.37/0.59	      (app_encode_app(a, $o, sk_S2, sk_Xy1)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.37/0.59	    inference('simplify', [status(thm)], ['102'])).
0.37/0.59	tff('104', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	     | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.37/0.59	    inference('sup-', [status(thm)], ['0', '103'])).
0.37/0.59	tff('105', plain,
0.37/0.59	    (app_encode_app(a, $o, sk_S2, sk_Xy1)
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.37/0.59	    inference('simplify', [status(thm)], ['104'])).
0.37/0.59	tff('106', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.37/0.59	     | sk_S2 = sk_Xp(sk_Xy1)),
0.37/0.59	    inference('sup-', [status(thm)], ['105', '35'])).
0.37/0.59	tff('107', plain,
0.37/0.59	    (sk_S2 = sk_Xp(sk_Xy1)
0.37/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.37/0.59	    inference('simplify', [status(thm)], ['106'])).
0.37/0.59	tff('108', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	     | sk_S2 = sk_Xp(sk_Xy1)),
0.37/0.59	    inference('sup-', [status(thm)], ['79', '107'])).
0.37/0.59	tff('109', plain,
0.37/0.59	    (sk_S2 = sk_Xp(sk_Xy1) | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.37/0.59	    inference('simplify', [status(thm)], ['108'])).
0.37/0.59	tff('110', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | sk_S2 = sk_Xp(sk_Xy1)
0.37/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.59	     | sk_S = sk_Xp(sk_Xx1)),
0.37/0.59	    inference('sup-', [status(thm)], ['109', '35'])).
0.37/0.59	tff('111', plain,
0.37/0.59	    (sk_S = sk_Xp(sk_Xx1)
0.37/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.59	     | sk_S2 = sk_Xp(sk_Xy1)),
0.37/0.59	    inference('simplify', [status(thm)], ['110'])).
0.37/0.59	tff('112', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | app_encode_app(a, $o, sk_S2, sk_Xy1)
0.37/0.59	     | sk_S2 = sk_Xp(sk_Xy1)
0.37/0.59	     | sk_S = sk_Xp(sk_Xx1)),
0.37/0.59	    inference('sup-', [status(thm)], ['55', '111'])).
0.37/0.59	tff('113', plain,
0.37/0.59	    (sk_S = sk_Xp(sk_Xx1)
0.37/0.59	     | sk_S2 = sk_Xp(sk_Xy1)
0.37/0.59	     | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.37/0.59	    inference('simplify', [status(thm)], ['112'])).
0.37/0.59	tff('114', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | sk_S2 = sk_Xp(sk_Xy1)
0.37/0.59	     | sk_S = sk_Xp(sk_Xx1)
0.37/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.37/0.59	     | sk_S2 = sk_Xp(sk_Xy1)),
0.37/0.59	    inference('sup-', [status(thm)], ['113', '35'])).
0.37/0.59	tff('115', plain,
0.37/0.59	    (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.37/0.59	     | sk_S = sk_Xp(sk_Xx1)
0.37/0.59	     | sk_S2 = sk_Xp(sk_Xy1)),
0.37/0.59	    inference('simplify', [status(thm)], ['114'])).
0.37/0.59	tff('116', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | sk_S = sk_Xp(sk_Xx1)
0.37/0.59	     | sk_S2 = sk_Xp(sk_Xy1)
0.37/0.59	     | sk_S = sk_Xp(sk_Xx1)),
0.37/0.59	    inference('sup-', [status(thm)], ['99', '115'])).
0.37/0.59	tff('117', plain, (sk_S2 = sk_Xp(sk_Xy1) | sk_S = sk_Xp(sk_Xx1)),
0.37/0.59	    inference('simplify', [status(thm)], ['116'])).
0.37/0.59	tff('118', plain,
0.37/0.59	    ![X2 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.59	       | ~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.59	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.59	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.37/0.59	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.37/0.59	tff('119', plain,
0.37/0.59	    ![X2 : app_encode_fun(a, $o)]:
0.37/0.59	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.37/0.59	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.59	       | ~ app_encode_app(a, $o, X2, sk_Xx)),
0.37/0.59	    inference('simplify', [status(thm)], ['118'])).
0.37/0.59	tff('120', plain,
0.37/0.59	    ![X0 : a]:
0.37/0.59	      (~ $true
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.37/0.59	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.59	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.37/0.59	    inference('sup-', [status(thm)], ['1', '119'])).
0.37/0.59	tff('121', plain,
0.37/0.59	    ![X0 : a]:
0.37/0.59	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.37/0.59	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.37/0.59	    inference('simplify', [status(thm)], ['120'])).
0.37/0.59	tff('122', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.59	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.37/0.59	    inference('sup-', [status(thm)], ['0', '121'])).
0.37/0.59	tff('123', plain,
0.37/0.59	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.37/0.59	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.37/0.59	    inference('simplify', [status(thm)], ['122'])).
0.37/0.59	tff('124', plain,
0.37/0.59	    ![X2 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.59	       | ~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.59	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.59	       | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.37/0.59	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.37/0.59	tff('125', plain,
0.37/0.59	    ![X2 : app_encode_fun(a, $o)]:
0.37/0.59	      (app_encode_app(a, $o, sk_S1, sk_Xx2)
0.37/0.59	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.59	       | ~ app_encode_app(a, $o, X2, sk_Xx)),
0.37/0.59	    inference('simplify', [status(thm)], ['124'])).
0.37/0.59	tff('126', plain,
0.37/0.59	    ![X0 : a]:
0.37/0.59	      (~ $true
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.37/0.59	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.59	       | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.37/0.59	    inference('sup-', [status(thm)], ['1', '125'])).
0.37/0.59	tff('127', plain,
0.37/0.59	    ![X0 : a]:
0.37/0.59	      (app_encode_app(a, $o, sk_S1, sk_Xx2)
0.37/0.59	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.37/0.59	    inference('simplify', [status(thm)], ['126'])).
0.37/0.59	tff('128', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.59	     | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.37/0.59	    inference('sup-', [status(thm)], ['0', '127'])).
0.37/0.59	tff('129', plain,
0.37/0.59	    (app_encode_app(a, $o, sk_S1, sk_Xx2)
0.37/0.59	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.37/0.59	    inference('simplify', [status(thm)], ['128'])).
0.37/0.59	tff('130', plain,
0.37/0.59	    ![X2 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.59	       | ~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.37/0.59	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.37/0.59	tff('131', plain,
0.37/0.59	    ![X2 : app_encode_fun(a, $o)]:
0.37/0.59	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.59	       | ~ app_encode_app(a, $o, X2, sk_Xx)),
0.37/0.59	    inference('simplify', [status(thm)], ['130'])).
0.37/0.59	tff('132', plain,
0.37/0.59	    ![X0 : a]:
0.37/0.59	      (~ $true
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.37/0.59	    inference('sup-', [status(thm)], ['1', '131'])).
0.37/0.59	tff('133', plain,
0.37/0.59	    ![X0 : a]:
0.37/0.59	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.37/0.59	    inference('simplify', [status(thm)], ['132'])).
0.37/0.59	tff('134', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.37/0.59	    inference('sup-', [status(thm)], ['0', '133'])).
0.37/0.59	tff('135', plain,
0.37/0.59	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.37/0.59	    inference('simplify', [status(thm)], ['134'])).
0.37/0.59	tff('136', plain,
0.37/0.59	    ![X2 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.59	       | ~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	       | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.37/0.59	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.37/0.59	tff('137', plain,
0.37/0.59	    ![X2 : app_encode_fun(a, $o)]:
0.37/0.59	      (app_encode_app(a, $o, sk_S1, sk_Xx2)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.59	       | ~ app_encode_app(a, $o, X2, sk_Xx)),
0.37/0.59	    inference('simplify', [status(thm)], ['136'])).
0.37/0.59	tff('138', plain,
0.37/0.59	    ![X0 : a]:
0.37/0.59	      (~ $true
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	       | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.37/0.59	    inference('sup-', [status(thm)], ['1', '137'])).
0.37/0.59	tff('139', plain,
0.37/0.59	    ![X0 : a]:
0.37/0.59	      (app_encode_app(a, $o, sk_S1, sk_Xx2)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.37/0.59	    inference('simplify', [status(thm)], ['138'])).
0.37/0.59	tff('140', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	     | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.37/0.59	    inference('sup-', [status(thm)], ['0', '139'])).
0.37/0.59	tff('141', plain,
0.37/0.59	    (app_encode_app(a, $o, sk_S1, sk_Xx2)
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.37/0.59	    inference('simplify', [status(thm)], ['140'])).
0.37/0.59	tff('142', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.37/0.59	     | sk_S1 = sk_Xp(sk_Xx2)),
0.37/0.59	    inference('sup-', [status(thm)], ['141', '35'])).
0.37/0.59	tff('143', plain,
0.37/0.59	    (sk_S1 = sk_Xp(sk_Xx2)
0.37/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.37/0.59	    inference('simplify', [status(thm)], ['142'])).
0.37/0.59	tff('144', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	     | sk_S1 = sk_Xp(sk_Xx2)),
0.37/0.59	    inference('sup-', [status(thm)], ['135', '143'])).
0.37/0.59	tff('145', plain,
0.37/0.59	    (sk_S1 = sk_Xp(sk_Xx2) | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.37/0.59	    inference('simplify', [status(thm)], ['144'])).
0.37/0.59	tff('146', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | sk_S1 = sk_Xp(sk_Xx2)
0.37/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.59	     | sk_S = sk_Xp(sk_Xx1)),
0.37/0.59	    inference('sup-', [status(thm)], ['145', '35'])).
0.37/0.59	tff('147', plain,
0.37/0.59	    (sk_S = sk_Xp(sk_Xx1)
0.37/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.59	     | sk_S1 = sk_Xp(sk_Xx2)),
0.37/0.59	    inference('simplify', [status(thm)], ['146'])).
0.37/0.59	tff('148', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | app_encode_app(a, $o, sk_S1, sk_Xx2)
0.37/0.59	     | sk_S1 = sk_Xp(sk_Xx2)
0.37/0.59	     | sk_S = sk_Xp(sk_Xx1)),
0.37/0.59	    inference('sup-', [status(thm)], ['129', '147'])).
0.37/0.59	tff('149', plain,
0.37/0.59	    (sk_S = sk_Xp(sk_Xx1)
0.37/0.59	     | sk_S1 = sk_Xp(sk_Xx2)
0.37/0.59	     | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.37/0.59	    inference('simplify', [status(thm)], ['148'])).
0.37/0.59	tff('150', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | sk_S1 = sk_Xp(sk_Xx2)
0.37/0.59	     | sk_S = sk_Xp(sk_Xx1)
0.37/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.37/0.59	     | sk_S1 = sk_Xp(sk_Xx2)),
0.37/0.59	    inference('sup-', [status(thm)], ['149', '35'])).
0.37/0.59	tff('151', plain,
0.37/0.59	    (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.37/0.59	     | sk_S = sk_Xp(sk_Xx1)
0.37/0.59	     | sk_S1 = sk_Xp(sk_Xx2)),
0.37/0.59	    inference('simplify', [status(thm)], ['150'])).
0.37/0.59	tff('152', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.59	     | sk_S1 = sk_Xp(sk_Xx2)
0.37/0.59	     | sk_S = sk_Xp(sk_Xx1)),
0.37/0.59	    inference('sup-', [status(thm)], ['123', '151'])).
0.37/0.59	tff('153', plain,
0.37/0.59	    (sk_S = sk_Xp(sk_Xx1)
0.37/0.59	     | sk_S1 = sk_Xp(sk_Xx2)
0.37/0.59	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.37/0.59	    inference('simplify', [status(thm)], ['152'])).
0.37/0.59	tff('154', plain, (sk_S1 = sk_Xp(sk_Xx2) | sk_S = sk_Xp(sk_Xx1)),
0.37/0.59	    inference('clc', [status(thm)], ['153', '147'])).
0.37/0.59	tff('155', plain,
0.37/0.59	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.37/0.59	     | sk_S = sk_Xp(sk_Xx1)),
0.37/0.59	    inference('sup+', [status(thm)], ['154', '1'])).
0.37/0.59	tff('156', plain,
0.37/0.59	    ![X2 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.59	       | ~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.59	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.59	       | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.37/0.59	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.37/0.59	tff('157', plain,
0.37/0.59	    ![X2 : app_encode_fun(a, $o)]:
0.37/0.59	      (app_encode_app(a, $o, sk_S1, sk_Xy1)
0.37/0.59	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.59	       | ~ app_encode_app(a, $o, X2, sk_Xx)),
0.37/0.59	    inference('simplify', [status(thm)], ['156'])).
0.37/0.59	tff('158', plain,
0.37/0.59	    ![X0 : a]:
0.37/0.59	      (~ $true
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.37/0.59	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.59	       | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.37/0.59	    inference('sup-', [status(thm)], ['1', '157'])).
0.37/0.59	tff('159', plain,
0.37/0.59	    ![X0 : a]:
0.37/0.59	      (app_encode_app(a, $o, sk_S1, sk_Xy1)
0.37/0.59	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.37/0.59	    inference('simplify', [status(thm)], ['158'])).
0.37/0.59	tff('160', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.59	     | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.37/0.59	    inference('sup-', [status(thm)], ['0', '159'])).
0.37/0.59	tff('161', plain,
0.37/0.59	    (app_encode_app(a, $o, sk_S1, sk_Xy1)
0.37/0.59	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.37/0.59	    inference('simplify', [status(thm)], ['160'])).
0.37/0.59	tff('162', plain,
0.37/0.59	    ![X2 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.59	       | ~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	       | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.37/0.59	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.37/0.59	tff('163', plain,
0.37/0.59	    ![X2 : app_encode_fun(a, $o)]:
0.37/0.59	      (app_encode_app(a, $o, sk_S1, sk_Xy1)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.59	       | ~ app_encode_app(a, $o, X2, sk_Xx)),
0.37/0.59	    inference('simplify', [status(thm)], ['162'])).
0.37/0.59	tff('164', plain,
0.37/0.59	    ![X0 : a]:
0.37/0.59	      (~ $true
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	       | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.37/0.59	    inference('sup-', [status(thm)], ['1', '163'])).
0.37/0.59	tff('165', plain,
0.37/0.59	    ![X0 : a]:
0.37/0.59	      (app_encode_app(a, $o, sk_S1, sk_Xy1)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.37/0.59	    inference('simplify', [status(thm)], ['164'])).
0.37/0.59	tff('166', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	     | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.37/0.59	    inference('sup-', [status(thm)], ['0', '165'])).
0.37/0.59	tff('167', plain,
0.37/0.59	    (app_encode_app(a, $o, sk_S1, sk_Xy1)
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.37/0.59	    inference('simplify', [status(thm)], ['166'])).
0.37/0.59	tff('168', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.37/0.59	     | sk_S1 = sk_Xp(sk_Xy1)),
0.37/0.59	    inference('sup-', [status(thm)], ['167', '35'])).
0.37/0.59	tff('169', plain,
0.37/0.59	    (sk_S1 = sk_Xp(sk_Xy1)
0.37/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.37/0.59	    inference('simplify', [status(thm)], ['168'])).
0.37/0.59	tff('170', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	     | sk_S1 = sk_Xp(sk_Xy1)),
0.37/0.59	    inference('sup-', [status(thm)], ['135', '169'])).
0.37/0.59	tff('171', plain,
0.37/0.59	    (sk_S1 = sk_Xp(sk_Xy1) | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.37/0.59	    inference('simplify', [status(thm)], ['170'])).
0.37/0.59	tff('172', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | sk_S1 = sk_Xp(sk_Xy1)
0.37/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.59	     | sk_S = sk_Xp(sk_Xx1)),
0.37/0.59	    inference('sup-', [status(thm)], ['171', '35'])).
0.37/0.59	tff('173', plain,
0.37/0.59	    (sk_S = sk_Xp(sk_Xx1)
0.37/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.59	     | sk_S1 = sk_Xp(sk_Xy1)),
0.37/0.59	    inference('simplify', [status(thm)], ['172'])).
0.37/0.59	tff('174', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | app_encode_app(a, $o, sk_S1, sk_Xy1)
0.37/0.59	     | sk_S1 = sk_Xp(sk_Xy1)
0.37/0.59	     | sk_S = sk_Xp(sk_Xx1)),
0.37/0.59	    inference('sup-', [status(thm)], ['161', '173'])).
0.37/0.59	tff('175', plain,
0.37/0.59	    (sk_S = sk_Xp(sk_Xx1)
0.37/0.59	     | sk_S1 = sk_Xp(sk_Xy1)
0.37/0.59	     | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.37/0.59	    inference('simplify', [status(thm)], ['174'])).
0.37/0.59	tff('176', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | sk_S1 = sk_Xp(sk_Xy1)
0.37/0.59	     | sk_S = sk_Xp(sk_Xx1)
0.37/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.37/0.59	     | sk_S1 = sk_Xp(sk_Xy1)),
0.37/0.59	    inference('sup-', [status(thm)], ['175', '35'])).
0.37/0.59	tff('177', plain,
0.37/0.59	    (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.37/0.59	     | sk_S = sk_Xp(sk_Xx1)
0.37/0.59	     | sk_S1 = sk_Xp(sk_Xy1)),
0.37/0.59	    inference('simplify', [status(thm)], ['176'])).
0.37/0.59	tff('178', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | sk_S = sk_Xp(sk_Xx1)
0.37/0.59	     | sk_S1 = sk_Xp(sk_Xy1)
0.37/0.59	     | sk_S = sk_Xp(sk_Xx1)),
0.37/0.59	    inference('sup-', [status(thm)], ['155', '177'])).
0.37/0.59	tff('179', plain, (sk_S1 = sk_Xp(sk_Xy1) | sk_S = sk_Xp(sk_Xx1)),
0.37/0.59	    inference('simplify', [status(thm)], ['178'])).
0.37/0.59	tff('180', plain,
0.37/0.59	    (sk_S1 = sk_S2 | sk_S = sk_Xp(sk_Xx1) | sk_S = sk_Xp(sk_Xx1)),
0.37/0.59	    inference('sup+', [status(thm)], ['117', '179'])).
0.37/0.59	tff('181', plain, (sk_S = sk_Xp(sk_Xx1) | sk_S1 = sk_S2),
0.37/0.59	    inference('simplify', [status(thm)], ['180'])).
0.37/0.59	tff('182', plain,
0.37/0.59	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S) | sk_S1 = sk_S2),
0.37/0.59	    inference('sup+', [status(thm)], ['181', '1'])).
0.37/0.59	tff('183', plain,
0.37/0.59	    ![X2 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.59	       | ~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.37/0.59	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.37/0.59	tff('184', plain,
0.37/0.59	    ![X2 : app_encode_fun(a, $o)]:
0.37/0.59	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.59	       | ~ app_encode_app(a, $o, X2, sk_Xx)),
0.37/0.59	    inference('simplify', [status(thm)], ['183'])).
0.37/0.59	tff('185', plain,
0.37/0.59	    ![X0 : a]:
0.37/0.59	      (~ $true
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.37/0.59	    inference('sup-', [status(thm)], ['1', '184'])).
0.37/0.59	tff('186', plain,
0.37/0.59	    ![X0 : a]:
0.37/0.59	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.37/0.59	    inference('simplify', [status(thm)], ['185'])).
0.37/0.59	tff('187', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.37/0.59	    inference('sup-', [status(thm)], ['0', '186'])).
0.37/0.59	tff('188', plain,
0.37/0.59	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xy)),
0.37/0.59	    inference('simplify', [status(thm)], ['187'])).
0.37/0.59	tff('189', plain,
0.37/0.59	    ![X2 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.59	       | ~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	       | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.37/0.59	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.37/0.59	tff('190', plain,
0.37/0.59	    ![X2 : app_encode_fun(a, $o)]:
0.37/0.59	      (app_encode_app(a, $o, sk_S1, sk_Xy1)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.59	       | ~ app_encode_app(a, $o, X2, sk_Xx)),
0.37/0.59	    inference('simplify', [status(thm)], ['189'])).
0.37/0.59	tff('191', plain,
0.37/0.59	    ![X0 : a]:
0.37/0.59	      (~ $true
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	       | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.37/0.59	    inference('sup-', [status(thm)], ['1', '190'])).
0.37/0.59	tff('192', plain,
0.37/0.59	    ![X0 : a]:
0.37/0.59	      (app_encode_app(a, $o, sk_S1, sk_Xy1)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.37/0.59	    inference('simplify', [status(thm)], ['191'])).
0.37/0.59	tff('193', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	     | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.37/0.59	    inference('sup-', [status(thm)], ['0', '192'])).
0.37/0.59	tff('194', plain,
0.37/0.59	    (app_encode_app(a, $o, sk_S1, sk_Xy1)
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xy)),
0.37/0.59	    inference('simplify', [status(thm)], ['193'])).
0.37/0.59	tff('195', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.37/0.59	     | sk_S1 = sk_Xp(sk_Xy1)),
0.37/0.59	    inference('sup-', [status(thm)], ['194', '35'])).
0.37/0.59	tff('196', plain,
0.37/0.59	    (sk_S1 = sk_Xp(sk_Xy1)
0.37/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xy)),
0.37/0.59	    inference('simplify', [status(thm)], ['195'])).
0.37/0.59	tff('197', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	     | sk_S1 = sk_Xp(sk_Xy1)),
0.37/0.59	    inference('sup-', [status(thm)], ['188', '196'])).
0.37/0.59	tff('198', plain,
0.37/0.59	    (sk_S1 = sk_Xp(sk_Xy1) | app_encode_app(a, $o, sk_S, sk_Xy)),
0.37/0.59	    inference('simplify', [status(thm)], ['197'])).
0.37/0.59	tff('199', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | sk_S1 = sk_Xp(sk_Xy1)
0.37/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.59	     | sk_S = sk_Xp(sk_Xy)),
0.37/0.59	    inference('sup-', [status(thm)], ['198', '35'])).
0.37/0.59	tff('200', plain,
0.37/0.59	    (sk_S = sk_Xp(sk_Xy)
0.37/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.59	     | sk_S1 = sk_Xp(sk_Xy1)),
0.37/0.59	    inference('simplify', [status(thm)], ['199'])).
0.37/0.59	tff('201', plain,
0.37/0.59	    (~ $true | sk_S1 = sk_S2 | sk_S1 = sk_Xp(sk_Xy1) | sk_S = sk_Xp(sk_Xy)),
0.37/0.59	    inference('sup-', [status(thm)], ['182', '200'])).
0.37/0.59	tff('202', plain,
0.37/0.59	    (sk_S = sk_Xp(sk_Xy) | sk_S1 = sk_Xp(sk_Xy1) | sk_S1 = sk_S2),
0.37/0.59	    inference('simplify', [status(thm)], ['201'])).
0.37/0.59	tff('203', plain,
0.37/0.59	    (sk_S1 = sk_S2
0.37/0.59	     | sk_S = sk_Xp(sk_Xy)
0.37/0.59	     | sk_S1 = sk_S2
0.37/0.59	     | sk_S = sk_Xp(sk_Xy)),
0.37/0.59	    inference('sup+', [status(thm)], ['73', '202'])).
0.37/0.59	tff('204', plain, (sk_S = sk_Xp(sk_Xy) | sk_S1 = sk_S2),
0.37/0.59	    inference('simplify', [status(thm)], ['203'])).
0.37/0.59	tff('205', plain,
0.37/0.59	    ![X2 : app_encode_fun(a, $o), X4 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.59	       | ~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.59	       | ~ app_encode_app(a, $o, X4, sk_Xx1)
0.37/0.59	       | ~ app_encode_app(a, $o, X4, sk_Xy)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X4)
0.37/0.59	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.37/0.59	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.37/0.59	tff('206', plain,
0.37/0.59	    ![X2 : app_encode_fun(a, $o), X4 : app_encode_fun(a, $o)]:
0.37/0.59	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X4)
0.37/0.59	       | ~ app_encode_app(a, $o, X4, sk_Xy)
0.37/0.59	       | ~ app_encode_app(a, $o, X4, sk_Xx1)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.59	       | ~ app_encode_app(a, $o, X2, sk_Xx)),
0.37/0.59	    inference('simplify', [status(thm)], ['205'])).
0.37/0.59	tff('207', plain,
0.37/0.59	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ $true
0.37/0.59	       | ~ app_encode_app(a, $o, X1, sk_Xx)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X1)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx1)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xy)
0.37/0.59	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.37/0.59	    inference('sup-', [status(thm)], ['1', '206'])).
0.37/0.59	tff('208', plain,
0.37/0.59	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
0.37/0.59	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xy)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx1)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X1)
0.37/0.59	       | ~ app_encode_app(a, $o, X1, sk_Xx)),
0.37/0.59	    inference('simplify', [status(thm)], ['207'])).
0.37/0.59	tff('209', plain,
0.37/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ $true
0.37/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(sk_Xy), sk_Xx1)
0.37/0.59	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.37/0.59	    inference('sup-', [status(thm)], ['0', '208'])).
0.37/0.59	tff('210', plain,
0.37/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.37/0.59	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(sk_Xy), sk_Xx1)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.37/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)),
0.37/0.59	    inference('simplify', [status(thm)], ['209'])).
0.37/0.59	tff('211', plain,
0.37/0.59	    ![X0 : a]:
0.37/0.59	      (~ $true
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(sk_Xy), sk_Xx1)
0.37/0.59	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.37/0.59	    inference('sup-', [status(thm)], ['1', '210'])).
0.37/0.59	tff('212', plain,
0.37/0.59	    ![X0 : a]:
0.37/0.59	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(sk_Xy), sk_Xx1)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.37/0.59	    inference('simplify', [status(thm)], ['211'])).
0.37/0.59	tff('213', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | ~ app_encode_app(a, $o, sk_Xp(sk_Xy), sk_Xx1)
0.37/0.59	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.37/0.59	    inference('sup-', [status(thm)], ['0', '212'])).
0.37/0.59	tff('214', plain,
0.37/0.59	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.37/0.59	     | ~ app_encode_app(a, $o, sk_Xp(sk_Xy), sk_Xx1)),
0.37/0.59	    inference('simplify', [status(thm)], ['213'])).
0.37/0.59	tff('215', plain,
0.37/0.59	    ![X2 : app_encode_fun(a, $o), X4 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.59	       | ~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.59	       | ~ app_encode_app(a, $o, X4, sk_Xx1)
0.37/0.59	       | ~ app_encode_app(a, $o, X4, sk_Xy)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X4)
0.37/0.59	       | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.37/0.59	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.37/0.59	tff('216', plain,
0.37/0.59	    ![X2 : app_encode_fun(a, $o), X4 : app_encode_fun(a, $o)]:
0.37/0.59	      (app_encode_app(a, $o, sk_S2, sk_Xz)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X4)
0.37/0.59	       | ~ app_encode_app(a, $o, X4, sk_Xy)
0.37/0.59	       | ~ app_encode_app(a, $o, X4, sk_Xx1)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.59	       | ~ app_encode_app(a, $o, X2, sk_Xx)),
0.37/0.59	    inference('simplify', [status(thm)], ['215'])).
0.37/0.59	tff('217', plain,
0.37/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ $true
0.37/0.59	       | app_encode_app(a, $o, sk_S2, sk_Xz)
0.37/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	       | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.37/0.59	    inference('sup-', [status(thm)], ['17', '216'])).
0.37/0.59	tff('218', plain,
0.37/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.37/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.37/0.59	       | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.37/0.59	    inference('simplify', [status(thm)], ['217'])).
0.37/0.59	tff('219', plain,
0.37/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.37/0.59	      (app_encode_app(a, $o, sk_S2, sk_Xz)
0.37/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_S, sk_Xx1)),
0.37/0.59	    inference('clc', [status(thm)], ['218', '34'])).
0.37/0.59	tff('220', plain,
0.37/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.37/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.37/0.59	       | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.37/0.59	    inference('clc', [status(thm)], ['219', '85'])).
0.37/0.59	tff('221', plain,
0.37/0.59	    ![X0 : a]:
0.37/0.59	      (~ $true
0.37/0.59	       | app_encode_app(a, $o, sk_S2, sk_Xz)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.37/0.59	    inference('sup-', [status(thm)], ['1', '220'])).
0.37/0.59	tff('222', plain,
0.37/0.59	    ![X0 : a]:
0.37/0.59	      (~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.37/0.59	       | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.37/0.59	    inference('simplify', [status(thm)], ['221'])).
0.37/0.59	tff('223', plain, (~ $true | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.37/0.59	    inference('sup-', [status(thm)], ['0', '222'])).
0.37/0.59	tff('224', plain, app_encode_app(a, $o, sk_S2, sk_Xz),
0.37/0.59	    inference('simplify', [status(thm)], ['223'])).
0.37/0.59	tff('225', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.37/0.59	     | sk_S2 = sk_Xp(sk_Xz)),
0.37/0.59	    inference('sup-', [status(thm)], ['224', '35'])).
0.37/0.59	tff('226', plain,
0.37/0.59	    (sk_S2 = sk_Xp(sk_Xz)
0.37/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.37/0.59	    inference('simplify', [status(thm)], ['225'])).
0.37/0.59	tff('227', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | ~ app_encode_app(a, $o, sk_Xp(sk_Xy), sk_Xx1)
0.37/0.59	     | sk_S2 = sk_Xp(sk_Xz)),
0.37/0.59	    inference('sup-', [status(thm)], ['214', '226'])).
0.37/0.59	tff('228', plain,
0.37/0.59	    (sk_S2 = sk_Xp(sk_Xz) | ~ app_encode_app(a, $o, sk_Xp(sk_Xy), sk_Xx1)),
0.37/0.59	    inference('simplify', [status(thm)], ['227'])).
0.37/0.59	tff('229', plain,
0.37/0.59	    (~ app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	     | sk_S1 = sk_S2
0.37/0.59	     | sk_S2 = sk_Xp(sk_Xz)),
0.37/0.59	    inference('sup-', [status(thm)], ['204', '228'])).
0.37/0.59	tff('230', plain, (app_encode_app(a, $o, sk_S, sk_Xx1) | sk_S1 = sk_S2),
0.37/0.59	    inference('sup+', [status(thm)], ['181', '0'])).
0.37/0.59	tff('231', plain, (sk_S2 = sk_Xp(sk_Xz) | sk_S1 = sk_S2),
0.37/0.59	    inference('clc', [status(thm)], ['229', '230'])).
0.37/0.59	tff('232', plain,
0.37/0.59	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2) | sk_S1 = sk_S2),
0.37/0.59	    inference('sup+', [status(thm)], ['231', '1'])).
0.37/0.59	tff('233', plain,
0.37/0.59	    ![X2 : app_encode_fun(a, $o), X4 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.59	       | ~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.59	       | ~ app_encode_app(a, $o, X4, sk_Xx1)
0.37/0.59	       | ~ app_encode_app(a, $o, X4, sk_Xy)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X4)
0.37/0.59	       | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.37/0.59	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.37/0.59	tff('234', plain,
0.37/0.59	    ![X2 : app_encode_fun(a, $o), X4 : app_encode_fun(a, $o)]:
0.37/0.59	      (app_encode_app(a, $o, sk_S2, sk_Xy1)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X4)
0.37/0.59	       | ~ app_encode_app(a, $o, X4, sk_Xy)
0.37/0.59	       | ~ app_encode_app(a, $o, X4, sk_Xx1)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.59	       | ~ app_encode_app(a, $o, X2, sk_Xx)),
0.37/0.59	    inference('simplify', [status(thm)], ['233'])).
0.37/0.59	tff('235', plain,
0.37/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ $true
0.37/0.59	       | app_encode_app(a, $o, sk_S2, sk_Xy1)
0.37/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	       | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.37/0.59	    inference('sup-', [status(thm)], ['55', '234'])).
0.37/0.59	tff('236', plain,
0.37/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.37/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.37/0.59	       | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.37/0.59	    inference('simplify', [status(thm)], ['235'])).
0.37/0.59	tff('237', plain,
0.37/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.37/0.59	      (app_encode_app(a, $o, sk_S2, sk_Xy1)
0.37/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_S, sk_Xx1)),
0.37/0.59	    inference('clc', [status(thm)], ['236', '61'])).
0.37/0.59	tff('238', plain,
0.37/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.37/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.37/0.59	       | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.37/0.59	    inference('clc', [status(thm)], ['237', '105'])).
0.37/0.59	tff('239', plain,
0.37/0.59	    ![X0 : a]:
0.37/0.59	      (~ $true
0.37/0.59	       | app_encode_app(a, $o, sk_S2, sk_Xy1)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.37/0.59	    inference('sup-', [status(thm)], ['1', '238'])).
0.37/0.59	tff('240', plain,
0.37/0.59	    ![X0 : a]:
0.37/0.59	      (~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.37/0.59	       | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.37/0.59	    inference('simplify', [status(thm)], ['239'])).
0.37/0.59	tff('241', plain, (~ $true | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.37/0.59	    inference('sup-', [status(thm)], ['0', '240'])).
0.37/0.59	tff('242', plain, app_encode_app(a, $o, sk_S2, sk_Xy1),
0.37/0.59	    inference('simplify', [status(thm)], ['241'])).
0.37/0.59	tff('243', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.37/0.59	     | sk_S2 = sk_Xp(sk_Xy1)),
0.37/0.59	    inference('sup-', [status(thm)], ['242', '35'])).
0.37/0.59	tff('244', plain,
0.37/0.59	    (sk_S2 = sk_Xp(sk_Xy1)
0.37/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.37/0.59	    inference('simplify', [status(thm)], ['243'])).
0.37/0.59	tff('245', plain, (~ $true | sk_S1 = sk_S2 | sk_S2 = sk_Xp(sk_Xy1)),
0.37/0.59	    inference('sup-', [status(thm)], ['232', '244'])).
0.37/0.59	tff('246', plain, (sk_S2 = sk_Xp(sk_Xy1) | sk_S1 = sk_S2),
0.37/0.59	    inference('simplify', [status(thm)], ['245'])).
0.37/0.59	tff('247', plain,
0.37/0.59	    ![X2 : app_encode_fun(a, $o), X4 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.59	       | ~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.59	       | ~ app_encode_app(a, $o, X4, sk_Xx1)
0.37/0.59	       | ~ app_encode_app(a, $o, X4, sk_Xy)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X4)
0.37/0.59	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.37/0.59	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.37/0.59	tff('248', plain,
0.37/0.59	    ![X2 : app_encode_fun(a, $o), X4 : app_encode_fun(a, $o)]:
0.37/0.59	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X4)
0.37/0.59	       | ~ app_encode_app(a, $o, X4, sk_Xy)
0.37/0.59	       | ~ app_encode_app(a, $o, X4, sk_Xx1)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.59	       | ~ app_encode_app(a, $o, X2, sk_Xx)),
0.37/0.59	    inference('simplify', [status(thm)], ['247'])).
0.37/0.59	tff('249', plain,
0.37/0.59	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ $true
0.37/0.59	       | ~ app_encode_app(a, $o, X1, sk_Xx)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X1)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx1)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xy)
0.37/0.59	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.37/0.59	    inference('sup-', [status(thm)], ['1', '248'])).
0.37/0.59	tff('250', plain,
0.37/0.59	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
0.37/0.59	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xy)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx1)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X1)
0.37/0.59	       | ~ app_encode_app(a, $o, X1, sk_Xx)),
0.37/0.59	    inference('simplify', [status(thm)], ['249'])).
0.37/0.59	tff('251', plain,
0.37/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ $true
0.37/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(sk_Xy), sk_Xx1)
0.37/0.59	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.37/0.59	    inference('sup-', [status(thm)], ['0', '250'])).
0.37/0.59	tff('252', plain,
0.37/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.37/0.59	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(sk_Xy), sk_Xx1)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.37/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)),
0.37/0.59	    inference('simplify', [status(thm)], ['251'])).
0.37/0.59	tff('253', plain,
0.37/0.59	    ![X0 : a]:
0.37/0.59	      (~ $true
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(sk_Xy), sk_Xx1)
0.37/0.59	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.37/0.59	    inference('sup-', [status(thm)], ['1', '252'])).
0.37/0.59	tff('254', plain,
0.37/0.59	    ![X0 : a]:
0.37/0.59	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(sk_Xy), sk_Xx1)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.37/0.59	    inference('simplify', [status(thm)], ['253'])).
0.37/0.59	tff('255', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | ~ app_encode_app(a, $o, sk_Xp(sk_Xy), sk_Xx1)
0.37/0.59	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.37/0.59	    inference('sup-', [status(thm)], ['0', '254'])).
0.37/0.59	tff('256', plain,
0.37/0.59	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.37/0.59	     | ~ app_encode_app(a, $o, sk_Xp(sk_Xy), sk_Xx1)),
0.37/0.59	    inference('simplify', [status(thm)], ['255'])).
0.37/0.59	tff('257', plain,
0.37/0.59	    ![X2 : app_encode_fun(a, $o), X4 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.59	       | ~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.59	       | ~ app_encode_app(a, $o, X4, sk_Xx1)
0.37/0.59	       | ~ app_encode_app(a, $o, X4, sk_Xy)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X4)
0.37/0.59	       | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.37/0.59	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.37/0.59	tff('258', plain,
0.37/0.59	    ![X2 : app_encode_fun(a, $o), X4 : app_encode_fun(a, $o)]:
0.37/0.59	      (app_encode_app(a, $o, sk_S1, sk_Xx2)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X4)
0.37/0.59	       | ~ app_encode_app(a, $o, X4, sk_Xy)
0.37/0.59	       | ~ app_encode_app(a, $o, X4, sk_Xx1)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.59	       | ~ app_encode_app(a, $o, X2, sk_Xx)),
0.37/0.59	    inference('simplify', [status(thm)], ['257'])).
0.37/0.59	tff('259', plain,
0.37/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ $true
0.37/0.59	       | app_encode_app(a, $o, sk_S1, sk_Xx2)
0.37/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	       | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.37/0.59	    inference('sup-', [status(thm)], ['129', '258'])).
0.37/0.59	tff('260', plain,
0.37/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.37/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.37/0.59	       | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.37/0.59	    inference('simplify', [status(thm)], ['259'])).
0.37/0.59	tff('261', plain,
0.37/0.59	    ![X2 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.59	       | ~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	       | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.37/0.59	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.37/0.59	tff('262', plain,
0.37/0.59	    ![X2 : app_encode_fun(a, $o)]:
0.37/0.59	      (app_encode_app(a, $o, sk_S1, sk_Xx2)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.59	       | ~ app_encode_app(a, $o, X2, sk_Xx)),
0.37/0.59	    inference('simplify', [status(thm)], ['261'])).
0.37/0.59	tff('263', plain,
0.37/0.59	    ![X0 : a]:
0.37/0.59	      (~ $true
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	       | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.37/0.59	    inference('sup-', [status(thm)], ['1', '262'])).
0.37/0.59	tff('264', plain,
0.37/0.59	    ![X0 : a]:
0.37/0.59	      (app_encode_app(a, $o, sk_S1, sk_Xx2)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.37/0.59	    inference('simplify', [status(thm)], ['263'])).
0.37/0.59	tff('265', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	     | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.37/0.59	    inference('sup-', [status(thm)], ['0', '264'])).
0.37/0.59	tff('266', plain,
0.37/0.59	    (app_encode_app(a, $o, sk_S1, sk_Xx2)
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xy)),
0.37/0.59	    inference('simplify', [status(thm)], ['265'])).
0.37/0.59	tff('267', plain,
0.37/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.37/0.59	      (app_encode_app(a, $o, sk_S1, sk_Xx2)
0.37/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_S, sk_Xx1)),
0.37/0.59	    inference('clc', [status(thm)], ['260', '266'])).
0.37/0.59	tff('268', plain,
0.37/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.37/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.37/0.59	       | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.37/0.59	    inference('clc', [status(thm)], ['267', '141'])).
0.37/0.59	tff('269', plain,
0.37/0.59	    ![X0 : a]:
0.37/0.59	      (~ $true
0.37/0.59	       | app_encode_app(a, $o, sk_S1, sk_Xx2)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.37/0.59	    inference('sup-', [status(thm)], ['1', '268'])).
0.37/0.59	tff('270', plain,
0.37/0.59	    ![X0 : a]:
0.37/0.59	      (~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.37/0.59	       | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.37/0.59	    inference('simplify', [status(thm)], ['269'])).
0.37/0.59	tff('271', plain, (~ $true | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.37/0.59	    inference('sup-', [status(thm)], ['0', '270'])).
0.37/0.59	tff('272', plain, app_encode_app(a, $o, sk_S1, sk_Xx2),
0.37/0.59	    inference('simplify', [status(thm)], ['271'])).
0.37/0.59	tff('273', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.37/0.59	     | sk_S1 = sk_Xp(sk_Xx2)),
0.37/0.59	    inference('sup-', [status(thm)], ['272', '35'])).
0.37/0.59	tff('274', plain,
0.37/0.59	    (sk_S1 = sk_Xp(sk_Xx2)
0.37/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.37/0.59	    inference('simplify', [status(thm)], ['273'])).
0.37/0.59	tff('275', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | ~ app_encode_app(a, $o, sk_Xp(sk_Xy), sk_Xx1)
0.37/0.59	     | sk_S1 = sk_Xp(sk_Xx2)),
0.37/0.59	    inference('sup-', [status(thm)], ['256', '274'])).
0.37/0.59	tff('276', plain,
0.37/0.59	    (sk_S1 = sk_Xp(sk_Xx2) | ~ app_encode_app(a, $o, sk_Xp(sk_Xy), sk_Xx1)),
0.37/0.59	    inference('simplify', [status(thm)], ['275'])).
0.37/0.59	tff('277', plain,
0.37/0.59	    (~ app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	     | sk_S1 = sk_S2
0.37/0.59	     | sk_S1 = sk_Xp(sk_Xx2)),
0.37/0.59	    inference('sup-', [status(thm)], ['204', '276'])).
0.37/0.59	tff('278', plain, (sk_S1 = sk_Xp(sk_Xx2) | sk_S1 = sk_S2),
0.37/0.59	    inference('clc', [status(thm)], ['277', '230'])).
0.37/0.59	tff('279', plain,
0.37/0.59	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1) | sk_S1 = sk_S2),
0.37/0.59	    inference('sup+', [status(thm)], ['278', '1'])).
0.37/0.59	tff('280', plain,
0.37/0.59	    ![X2 : app_encode_fun(a, $o), X4 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.59	       | ~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.59	       | ~ app_encode_app(a, $o, X4, sk_Xx1)
0.37/0.59	       | ~ app_encode_app(a, $o, X4, sk_Xy)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X4)
0.37/0.59	       | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.37/0.59	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.37/0.59	tff('281', plain,
0.37/0.59	    ![X2 : app_encode_fun(a, $o), X4 : app_encode_fun(a, $o)]:
0.37/0.59	      (app_encode_app(a, $o, sk_S1, sk_Xy1)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X4)
0.37/0.59	       | ~ app_encode_app(a, $o, X4, sk_Xy)
0.37/0.59	       | ~ app_encode_app(a, $o, X4, sk_Xx1)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.59	       | ~ app_encode_app(a, $o, X2, sk_Xx)),
0.37/0.59	    inference('simplify', [status(thm)], ['280'])).
0.37/0.59	tff('282', plain,
0.37/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ $true
0.37/0.59	       | app_encode_app(a, $o, sk_S1, sk_Xy1)
0.37/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	       | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.37/0.59	    inference('sup-', [status(thm)], ['161', '281'])).
0.37/0.59	tff('283', plain,
0.37/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.37/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.37/0.59	       | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.37/0.59	    inference('simplify', [status(thm)], ['282'])).
0.37/0.59	tff('284', plain,
0.37/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.37/0.59	      (app_encode_app(a, $o, sk_S1, sk_Xy1)
0.37/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_S, sk_Xx1)),
0.37/0.59	    inference('clc', [status(thm)], ['283', '194'])).
0.37/0.59	tff('285', plain,
0.37/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.37/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.37/0.59	       | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.37/0.59	    inference('clc', [status(thm)], ['284', '167'])).
0.37/0.59	tff('286', plain,
0.37/0.59	    ![X0 : a]:
0.37/0.59	      (~ $true
0.37/0.59	       | app_encode_app(a, $o, sk_S1, sk_Xy1)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.37/0.59	    inference('sup-', [status(thm)], ['1', '285'])).
0.37/0.59	tff('287', plain,
0.37/0.59	    ![X0 : a]:
0.37/0.59	      (~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.37/0.59	       | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.37/0.59	    inference('simplify', [status(thm)], ['286'])).
0.37/0.59	tff('288', plain, (~ $true | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.37/0.59	    inference('sup-', [status(thm)], ['0', '287'])).
0.37/0.59	tff('289', plain, app_encode_app(a, $o, sk_S1, sk_Xy1),
0.37/0.59	    inference('simplify', [status(thm)], ['288'])).
0.37/0.59	tff('290', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.37/0.59	     | sk_S1 = sk_Xp(sk_Xy1)),
0.37/0.59	    inference('sup-', [status(thm)], ['289', '35'])).
0.37/0.59	tff('291', plain,
0.37/0.59	    (sk_S1 = sk_Xp(sk_Xy1)
0.37/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.37/0.59	    inference('simplify', [status(thm)], ['290'])).
0.37/0.59	tff('292', plain, (~ $true | sk_S1 = sk_S2 | sk_S1 = sk_Xp(sk_Xy1)),
0.37/0.59	    inference('sup-', [status(thm)], ['279', '291'])).
0.37/0.59	tff('293', plain, (sk_S1 = sk_Xp(sk_Xy1) | sk_S1 = sk_S2),
0.37/0.59	    inference('simplify', [status(thm)], ['292'])).
0.37/0.59	tff('294', plain, (sk_S1 = sk_S2 | sk_S1 = sk_S2 | sk_S1 = sk_S2),
0.37/0.59	    inference('sup+', [status(thm)], ['246', '293'])).
0.37/0.59	tff('295', plain, sk_S1 = sk_S2,
0.37/0.59	    inference('simplify', [status(thm)], ['294'])).
0.37/0.59	tff('296', plain,
0.37/0.59	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S) | ~ $true),
0.37/0.59	    inference('demod', [status(thm)], ['22', '295', '272'])).
0.37/0.59	tff('297', plain, app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S),
0.37/0.59	    inference('simplify', [status(thm)], ['296'])).
0.37/0.59	tff('298', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.37/0.59	     | sk_S1 = sk_Xp(sk_Xx2)),
0.37/0.59	    inference('sup-', [status(thm)], ['266', '35'])).
0.37/0.59	tff('299', plain,
0.37/0.59	    (sk_S1 = sk_Xp(sk_Xx2)
0.37/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xy)),
0.37/0.59	    inference('simplify', [status(thm)], ['298'])).
0.37/0.59	tff('300', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	     | sk_S1 = sk_Xp(sk_Xx2)),
0.37/0.59	    inference('sup-', [status(thm)], ['188', '299'])).
0.37/0.59	tff('301', plain,
0.37/0.59	    (sk_S1 = sk_Xp(sk_Xx2) | app_encode_app(a, $o, sk_S, sk_Xy)),
0.37/0.59	    inference('simplify', [status(thm)], ['300'])).
0.37/0.59	tff('302', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | sk_S1 = sk_Xp(sk_Xx2)
0.37/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.59	     | sk_S = sk_Xp(sk_Xy)),
0.37/0.59	    inference('sup-', [status(thm)], ['301', '35'])).
0.37/0.59	tff('303', plain,
0.37/0.59	    (sk_S = sk_Xp(sk_Xy)
0.37/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.59	     | sk_S1 = sk_Xp(sk_Xx2)),
0.37/0.59	    inference('simplify', [status(thm)], ['302'])).
0.37/0.59	tff('304', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | app_encode_app(a, $o, sk_S1, sk_Xx2)
0.37/0.59	     | sk_S1 = sk_Xp(sk_Xx2)
0.37/0.59	     | sk_S = sk_Xp(sk_Xy)),
0.37/0.59	    inference('sup-', [status(thm)], ['129', '303'])).
0.37/0.59	tff('305', plain,
0.37/0.59	    (sk_S = sk_Xp(sk_Xy)
0.37/0.59	     | sk_S1 = sk_Xp(sk_Xx2)
0.37/0.59	     | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.37/0.59	    inference('simplify', [status(thm)], ['304'])).
0.37/0.59	tff('306', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | sk_S1 = sk_Xp(sk_Xx2)
0.37/0.59	     | sk_S = sk_Xp(sk_Xy)
0.37/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.37/0.59	     | sk_S1 = sk_Xp(sk_Xx2)),
0.37/0.59	    inference('sup-', [status(thm)], ['305', '35'])).
0.37/0.59	tff('307', plain,
0.37/0.59	    (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.37/0.59	     | sk_S = sk_Xp(sk_Xy)
0.37/0.59	     | sk_S1 = sk_Xp(sk_Xx2)),
0.37/0.59	    inference('simplify', [status(thm)], ['306'])).
0.37/0.59	tff('308', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.59	     | sk_S1 = sk_Xp(sk_Xx2)
0.37/0.59	     | sk_S = sk_Xp(sk_Xy)),
0.37/0.59	    inference('sup-', [status(thm)], ['123', '307'])).
0.37/0.59	tff('309', plain,
0.37/0.59	    (sk_S = sk_Xp(sk_Xy)
0.37/0.59	     | sk_S1 = sk_Xp(sk_Xx2)
0.37/0.59	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.37/0.59	    inference('simplify', [status(thm)], ['308'])).
0.37/0.59	tff('310', plain, (sk_S1 = sk_Xp(sk_Xx2) | sk_S = sk_Xp(sk_Xy)),
0.37/0.59	    inference('clc', [status(thm)], ['309', '303'])).
0.37/0.59	tff('311', plain,
0.37/0.59	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.37/0.59	     | sk_S = sk_Xp(sk_Xy)),
0.37/0.59	    inference('sup+', [status(thm)], ['310', '1'])).
0.37/0.59	tff('312', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | app_encode_app(a, $o, sk_S1, sk_Xy1)
0.37/0.59	     | sk_S1 = sk_Xp(sk_Xy1)
0.37/0.59	     | sk_S = sk_Xp(sk_Xy)),
0.37/0.59	    inference('sup-', [status(thm)], ['161', '200'])).
0.37/0.59	tff('313', plain,
0.37/0.59	    (sk_S = sk_Xp(sk_Xy)
0.37/0.59	     | sk_S1 = sk_Xp(sk_Xy1)
0.37/0.59	     | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.37/0.59	    inference('simplify', [status(thm)], ['312'])).
0.37/0.59	tff('314', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | sk_S1 = sk_Xp(sk_Xy1)
0.37/0.59	     | sk_S = sk_Xp(sk_Xy)
0.37/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.37/0.59	     | sk_S1 = sk_Xp(sk_Xy1)),
0.37/0.59	    inference('sup-', [status(thm)], ['313', '35'])).
0.37/0.59	tff('315', plain,
0.37/0.59	    (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.37/0.59	     | sk_S = sk_Xp(sk_Xy)
0.37/0.59	     | sk_S1 = sk_Xp(sk_Xy1)),
0.37/0.59	    inference('simplify', [status(thm)], ['314'])).
0.37/0.59	tff('316', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | sk_S = sk_Xp(sk_Xy)
0.37/0.59	     | sk_S1 = sk_Xp(sk_Xy1)
0.37/0.59	     | sk_S = sk_Xp(sk_Xy)),
0.37/0.59	    inference('sup-', [status(thm)], ['311', '315'])).
0.37/0.59	tff('317', plain, (sk_S1 = sk_Xp(sk_Xy1) | sk_S = sk_Xp(sk_Xy)),
0.37/0.59	    inference('simplify', [status(thm)], ['316'])).
0.37/0.59	tff('318', plain,
0.37/0.59	    ![X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.59	       | ~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X3)
0.37/0.59	       | ~ app_encode_app(a, $o, X3, sk_Xx2)
0.37/0.59	       | ~ app_encode_app(a, $o, X3, sk_Xz)),
0.37/0.59	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.37/0.59	tff('319', plain,
0.37/0.59	    ![X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ app_encode_app(a, $o, X3, sk_Xz)
0.37/0.59	       | ~ app_encode_app(a, $o, X3, sk_Xx2)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X3)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.59	       | ~ app_encode_app(a, $o, X2, sk_Xx)),
0.37/0.59	    inference('simplify', [status(thm)], ['318'])).
0.37/0.59	tff('320', plain,
0.37/0.59	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ $true
0.37/0.59	       | ~ app_encode_app(a, $o, X1, sk_Xx)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X1)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx2)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xz)),
0.37/0.59	    inference('sup-', [status(thm)], ['1', '319'])).
0.37/0.59	tff('321', plain,
0.37/0.59	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ app_encode_app(a, $o, sk_Xp(X0), sk_Xz)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx2)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X1)
0.37/0.59	       | ~ app_encode_app(a, $o, X1, sk_Xx)),
0.37/0.59	    inference('simplify', [status(thm)], ['320'])).
0.37/0.59	tff('322', plain,
0.37/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ app_encode_app(a, $o, sk_S2, sk_Xz)
0.37/0.59	       | sk_S = sk_Xp(sk_Xy)
0.37/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(sk_Xy1), sk_Xx2)),
0.37/0.59	    inference('sup-', [status(thm)], ['73', '321'])).
0.37/0.59	tff('323', plain,
0.37/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ $true
0.37/0.59	       | sk_S = sk_Xp(sk_Xy)
0.37/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(sk_Xy1), sk_Xx2)),
0.37/0.59	    inference('demod', [status(thm)], ['322', '224'])).
0.37/0.59	tff('324', plain,
0.37/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ app_encode_app(a, $o, sk_Xp(sk_Xy1), sk_Xx2)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.37/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.37/0.59	       | sk_S = sk_Xp(sk_Xy)),
0.37/0.59	    inference('simplify', [status(thm)], ['323'])).
0.37/0.59	tff('325', plain,
0.37/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ app_encode_app(a, $o, sk_S1, sk_Xx2)
0.37/0.59	       | sk_S = sk_Xp(sk_Xy)
0.37/0.59	       | sk_S = sk_Xp(sk_Xy)
0.37/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xy)),
0.37/0.59	    inference('sup-', [status(thm)], ['317', '324'])).
0.37/0.59	tff('326', plain,
0.37/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ $true
0.37/0.59	       | sk_S = sk_Xp(sk_Xy)
0.37/0.59	       | sk_S = sk_Xp(sk_Xy)
0.37/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xy)),
0.37/0.59	    inference('demod', [status(thm)], ['325', '272'])).
0.37/0.59	tff('327', plain,
0.37/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.37/0.59	      (app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.37/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.37/0.59	       | sk_S = sk_Xp(sk_Xy)),
0.37/0.59	    inference('simplify', [status(thm)], ['326'])).
0.37/0.59	tff('328', plain,
0.37/0.59	    ![X0 : a]:
0.37/0.59	      (~ $true
0.37/0.59	       | sk_S = sk_Xp(sk_Xy)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xy)),
0.37/0.59	    inference('sup-', [status(thm)], ['1', '327'])).
0.37/0.59	tff('329', plain,
0.37/0.59	    ![X0 : a]:
0.37/0.59	      (app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.37/0.59	       | sk_S = sk_Xp(sk_Xy)),
0.37/0.59	    inference('simplify', [status(thm)], ['328'])).
0.37/0.59	tff('330', plain,
0.37/0.59	    (~ $true | sk_S = sk_Xp(sk_Xy) | app_encode_app(a, $o, sk_S, sk_Xy)),
0.37/0.59	    inference('sup-', [status(thm)], ['0', '329'])).
0.37/0.59	tff('331', plain, (app_encode_app(a, $o, sk_S, sk_Xy) | sk_S = sk_Xp(sk_Xy)),
0.37/0.59	    inference('simplify', [status(thm)], ['330'])).
0.37/0.59	tff('332', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | sk_S = sk_Xp(sk_Xy)
0.37/0.59	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.59	     | sk_S = sk_Xp(sk_Xy)),
0.37/0.59	    inference('sup-', [status(thm)], ['331', '35'])).
0.37/0.59	tff('333', plain,
0.37/0.59	    (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.37/0.59	     | sk_S = sk_Xp(sk_Xy)),
0.37/0.59	    inference('simplify', [status(thm)], ['332'])).
0.37/0.59	tff('334', plain,
0.37/0.59	    (~ $true | ~ app_encode_app(a, $o, sk_S2, sk_Xx2) | sk_S = sk_Xp(sk_Xy)),
0.37/0.59	    inference('sup-', [status(thm)], ['22', '333'])).
0.37/0.59	tff('335', plain,
0.37/0.59	    (sk_S = sk_Xp(sk_Xy) | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)),
0.37/0.59	    inference('simplify', [status(thm)], ['334'])).
0.37/0.59	tff('336', plain, (sk_S = sk_Xp(sk_Xy) | ~ $true),
0.37/0.59	    inference('demod', [status(thm)], ['335', '295', '272'])).
0.37/0.59	tff('337', plain, sk_S = sk_Xp(sk_Xy),
0.37/0.59	    inference('simplify', [status(thm)], ['336'])).
0.37/0.59	tff('338', plain,
0.37/0.59	    (sk_S1 = sk_Xp(sk_Xx2) | ~ app_encode_app(a, $o, sk_S, sk_Xx1)),
0.37/0.59	    inference('demod', [status(thm)], ['276', '337'])).
0.37/0.59	tff('339', plain,
0.37/0.59	    ![X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.59	       | ~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X3)
0.37/0.59	       | ~ app_encode_app(a, $o, X3, sk_Xx2)
0.37/0.59	       | ~ app_encode_app(a, $o, X3, sk_Xz)),
0.37/0.59	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.37/0.59	tff('340', plain,
0.37/0.59	    ![X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ app_encode_app(a, $o, X3, sk_Xz)
0.37/0.59	       | ~ app_encode_app(a, $o, X3, sk_Xx2)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X3)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.59	       | ~ app_encode_app(a, $o, X2, sk_Xx)),
0.37/0.59	    inference('simplify', [status(thm)], ['339'])).
0.37/0.59	tff('341', plain,
0.37/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ $true
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_S2, sk_Xz)),
0.37/0.59	    inference('sup-', [status(thm)], ['79', '340'])).
0.37/0.59	tff('342', plain,
0.37/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ app_encode_app(a, $o, sk_S2, sk_Xz)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.37/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.37/0.59	    inference('simplify', [status(thm)], ['341'])).
0.37/0.59	tff('343', plain,
0.37/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.37/0.59	      (app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)),
0.37/0.59	    inference('clc', [status(thm)], ['342', '85'])).
0.37/0.59	tff('344', plain,
0.37/0.59	    ![X0 : a]:
0.37/0.59	      (~ $true
0.37/0.59	       | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.37/0.59	    inference('sup-', [status(thm)], ['1', '343'])).
0.37/0.59	tff('345', plain,
0.37/0.59	    ![X0 : a]:
0.37/0.59	      (app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)),
0.37/0.59	    inference('simplify', [status(thm)], ['344'])).
0.37/0.59	tff('346', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.37/0.59	    inference('sup-', [status(thm)], ['0', '345'])).
0.37/0.59	tff('347', plain,
0.37/0.59	    (app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	     | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)),
0.37/0.59	    inference('simplify', [status(thm)], ['346'])).
0.37/0.59	tff('348', plain, (app_encode_app(a, $o, sk_S, sk_Xx1) | ~ $true),
0.37/0.59	    inference('demod', [status(thm)], ['347', '295', '272'])).
0.37/0.59	tff('349', plain, app_encode_app(a, $o, sk_S, sk_Xx1),
0.37/0.59	    inference('simplify', [status(thm)], ['348'])).
0.37/0.59	tff('350', plain, (sk_S1 = sk_Xp(sk_Xx2) | ~ $true),
0.37/0.59	    inference('demod', [status(thm)], ['338', '349'])).
0.37/0.59	tff('351', plain, sk_S1 = sk_Xp(sk_Xx2),
0.37/0.59	    inference('simplify', [status(thm)], ['350'])).
0.37/0.59	tff('352', plain, app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1),
0.37/0.59	    inference('sup+', [status(thm)], ['351', '1'])).
0.37/0.59	tff('353', plain,
0.37/0.59	    ![X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o), 
0.37/0.59	      X4 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.59	       | ~ app_encode_app(a, $o, X2, sk_Xx)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.59	       | ~ app_encode_app(a, $o, X4, sk_Xx1)
0.37/0.59	       | ~ app_encode_app(a, $o, X4, sk_Xy)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X4)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X3)
0.37/0.59	       | ~ app_encode_app(a, $o, X3, sk_Xx2)
0.37/0.59	       | ~ app_encode_app(a, $o, X3, sk_Xz)),
0.37/0.59	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.37/0.59	tff('354', plain,
0.37/0.59	    ![X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o), 
0.37/0.59	      X4 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ app_encode_app(a, $o, X3, sk_Xz)
0.37/0.59	       | ~ app_encode_app(a, $o, X3, sk_Xx2)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X3)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X4)
0.37/0.59	       | ~ app_encode_app(a, $o, X4, sk_Xy)
0.37/0.59	       | ~ app_encode_app(a, $o, X4, sk_Xx1)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.37/0.59	       | ~ app_encode_app(a, $o, X2, sk_Xx)),
0.37/0.59	    inference('simplify', [status(thm)], ['353'])).
0.37/0.59	tff('355', plain,
0.37/0.59	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ $true
0.37/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.37/0.59	       | ~ app_encode_app(a, $o, X1, sk_Xx1)
0.37/0.59	       | ~ app_encode_app(a, $o, X1, sk_Xy)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X1)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_S1, sk_Xx2)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_S1, sk_Xz)),
0.37/0.59	    inference('sup-', [status(thm)], ['352', '354'])).
0.37/0.59	tff('356', plain, app_encode_app(a, $o, sk_S1, sk_Xz),
0.37/0.59	    inference('demod', [status(thm)], ['224', '295'])).
0.37/0.59	tff('357', plain,
0.37/0.59	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ $true
0.37/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.37/0.59	       | ~ app_encode_app(a, $o, X1, sk_Xx1)
0.37/0.59	       | ~ app_encode_app(a, $o, X1, sk_Xy)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X1)
0.37/0.59	       | ~ $true
0.37/0.59	       | ~ $true),
0.37/0.59	    inference('demod', [status(thm)], ['355', '272', '356'])).
0.37/0.59	tff('358', plain,
0.37/0.59	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X1)
0.37/0.59	       | ~ app_encode_app(a, $o, X1, sk_Xy)
0.37/0.59	       | ~ app_encode_app(a, $o, X1, sk_Xx1)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.37/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)),
0.37/0.59	    inference('simplify', [status(thm)], ['357'])).
0.37/0.59	tff('359', plain,
0.37/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ $true
0.37/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_S, sk_Xx1)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_S, sk_Xy)),
0.37/0.59	    inference('sup-', [status(thm)], ['297', '358'])).
0.37/0.59	tff('360', plain,
0.37/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ $true
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_S2, sk_Xz)),
0.37/0.59	    inference('sup-', [status(thm)], ['28', '319'])).
0.37/0.59	tff('361', plain,
0.37/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ app_encode_app(a, $o, sk_S2, sk_Xz)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.37/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xy)),
0.37/0.59	    inference('simplify', [status(thm)], ['360'])).
0.37/0.59	tff('362', plain,
0.37/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ $true
0.37/0.59	       | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.37/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xy)),
0.37/0.59	    inference('demod', [status(thm)], ['361', '224'])).
0.37/0.59	tff('363', plain,
0.37/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.37/0.59	      (app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)),
0.37/0.59	    inference('simplify', [status(thm)], ['362'])).
0.37/0.59	tff('364', plain,
0.37/0.59	    ![X0 : a]:
0.37/0.59	      (~ $true
0.37/0.59	       | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.37/0.59	       | app_encode_app(a, $o, sk_S, sk_Xy)),
0.37/0.59	    inference('sup-', [status(thm)], ['1', '363'])).
0.37/0.59	tff('365', plain,
0.37/0.59	    ![X0 : a]:
0.37/0.59	      (app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.37/0.59	       | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)),
0.37/0.59	    inference('simplify', [status(thm)], ['364'])).
0.37/0.59	tff('366', plain,
0.37/0.59	    (~ $true
0.37/0.59	     | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)
0.37/0.59	     | app_encode_app(a, $o, sk_S, sk_Xy)),
0.37/0.59	    inference('sup-', [status(thm)], ['0', '365'])).
0.37/0.59	tff('367', plain,
0.37/0.59	    (app_encode_app(a, $o, sk_S, sk_Xy)
0.37/0.59	     | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)),
0.37/0.59	    inference('simplify', [status(thm)], ['366'])).
0.37/0.59	tff('368', plain, (app_encode_app(a, $o, sk_S, sk_Xy) | ~ $true),
0.37/0.59	    inference('demod', [status(thm)], ['367', '295', '272'])).
0.37/0.59	tff('369', plain, app_encode_app(a, $o, sk_S, sk_Xy),
0.37/0.59	    inference('simplify', [status(thm)], ['368'])).
0.37/0.59	tff('370', plain,
0.37/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ $true
0.37/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.37/0.59	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.37/0.59	       | ~ $true
0.37/0.59	       | ~ $true),
0.37/0.59	    inference('demod', [status(thm)], ['359', '349', '369'])).
0.37/0.59	tff('371', plain,
0.37/0.59	    ![X0 : app_encode_fun(a, $o)]:
0.37/0.59	      (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.37/0.59	       | ~ app_encode_app(a, $o, X0, sk_Xx)),
0.37/0.59	    inference('simplify', [status(thm)], ['370'])).
0.37/0.59	tff('372', plain,
0.37/0.59	    ![X0 : a]: (~ $true | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.37/0.59	    inference('sup-', [status(thm)], ['1', '371'])).
0.37/0.59	tff('373', plain, ![X0 : a]: ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx),
0.37/0.59	    inference('simplify', [status(thm)], ['372'])).
0.37/0.59	tff('374', plain, ~ $true, inference('sup-', [status(thm)], ['0', '373'])).
0.37/0.59	tff('375', plain, $false, inference('simplify', [status(thm)], ['374'])).
0.37/0.59	
0.37/0.59	% SZS output end Refutation
0.37/0.59	EOF
