0.00/0.00	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : appext
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : kbo
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n132.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 17:30:23 CST 2018
0.71/0.88	% done 2881 iterations in 0.686s
0.71/0.88	% SZS status Theorem for 'stdin'
0.71/0.88	% SZS output start Refutation
0.72/0.89	tff(zf_stmt_4, conjecture,
0.72/0.89	  (![P:app_encode_fun(app_encode_fun(a,$o),$o)]:
0.72/0.89	     (((![Xp:app_encode_fun(a,$o)]:
0.72/0.89	          (app_encode_app(app_encode_fun(a,$o),$o,P,Xp) =>
0.72/0.89	           (?[Xz:a]: app_encode_app(a,$o,Xp,Xz)))) & 
0.72/0.89	       (![Xx:a]:
0.72/0.89	          (?[Xp:app_encode_fun(a,$o)]:
0.72/0.89	             (app_encode_app(app_encode_fun(a,$o),$o,P,Xp) & 
0.72/0.89	              app_encode_app(a,$o,Xp,Xx) & 
0.72/0.89	              (![Xq:app_encode_fun(a,$o)]:
0.72/0.89	                 ((app_encode_app(app_encode_fun(a,$o),$o,P,Xq) & 
0.72/0.89	                   app_encode_app(a,$o,Xq,Xx)) =>
0.72/0.89	                  (Xq = Xp))))))) =>
0.72/0.89	      ((![Xx:a]:
0.72/0.89	          (?[S:app_encode_fun(a,$o)]:
0.72/0.89	             (app_encode_app(app_encode_fun(a,$o),$o,P,S) & 
0.72/0.89	              app_encode_app(a,$o,S,Xx) & app_encode_app(a,$o,S,Xx)))) & 
0.72/0.89	       (![Xx:a,Xy:a]:
0.72/0.89	          ((?[S:app_encode_fun(a,$o)]:
0.72/0.89	              (app_encode_app(app_encode_fun(a,$o),$o,P,S) & 
0.72/0.89	               app_encode_app(a,$o,S,Xx) & app_encode_app(a,$o,S,Xy))) =>
0.72/0.89	           (?[S:app_encode_fun(a,$o)]:
0.72/0.89	              (app_encode_app(app_encode_fun(a,$o),$o,P,S) & 
0.72/0.89	               app_encode_app(a,$o,S,Xy) & app_encode_app(a,$o,S,Xx))))) & 
0.72/0.89	       (![Xx:a,Xy:a,Xz:a]:
0.72/0.89	          (((?[S:app_encode_fun(a,$o)]:
0.72/0.89	               (app_encode_app(app_encode_fun(a,$o),$o,P,S) & 
0.72/0.89	                app_encode_app(a,$o,S,Xx) & app_encode_app(a,$o,S,Xy))) & 
0.72/0.89	            (?[S:app_encode_fun(a,$o)]:
0.72/0.89	               (app_encode_app(app_encode_fun(a,$o),$o,P,S) & 
0.72/0.89	                app_encode_app(a,$o,S,Xy) & app_encode_app(a,$o,S,Xz)))) =>
0.72/0.89	           (?[S:app_encode_fun(a,$o)]:
0.72/0.89	              (app_encode_app(app_encode_fun(a,$o),$o,P,S) & 
0.72/0.89	               app_encode_app(a,$o,S,Xx) & app_encode_app(a,$o,S,Xz))))))))).
0.72/0.89	tff(zf_stmt_0, negated_conjecture,
0.72/0.89	  (~
0.72/0.89	    (![P:app_encode_fun(app_encode_fun(a,$o),$o)]:
0.72/0.89	       (((![Xp:app_encode_fun(a,$o)]:
0.72/0.89	            (app_encode_app(app_encode_fun(a,$o),$o,P,Xp) =>
0.72/0.89	             (?[Xz:a]: app_encode_app(a,$o,Xp,Xz)))) & 
0.72/0.89	         (![Xx:a]:
0.72/0.89	            (?[Xp:app_encode_fun(a,$o)]:
0.72/0.89	               (app_encode_app(app_encode_fun(a,$o),$o,P,Xp) & 
0.72/0.89	                app_encode_app(a,$o,Xp,Xx) & 
0.72/0.89	                (![Xq:app_encode_fun(a,$o)]:
0.72/0.89	                   ((app_encode_app(app_encode_fun(a,$o),$o,P,Xq) & 
0.72/0.89	                     app_encode_app(a,$o,Xq,Xx)) =>
0.72/0.89	                    (Xq = Xp))))))) =>
0.72/0.89	        ((![Xx:a]:
0.72/0.89	            (?[S:app_encode_fun(a,$o)]:
0.72/0.89	               (app_encode_app(app_encode_fun(a,$o),$o,P,S) & 
0.72/0.89	                app_encode_app(a,$o,S,Xx) & app_encode_app(a,$o,S,Xx)))) & 
0.72/0.89	         (![Xx:a,Xy:a]:
0.72/0.89	            ((?[S:app_encode_fun(a,$o)]:
0.72/0.89	                (app_encode_app(app_encode_fun(a,$o),$o,P,S) & 
0.72/0.89	                 app_encode_app(a,$o,S,Xx) & app_encode_app(a,$o,S,Xy))) =>
0.72/0.89	             (?[S:app_encode_fun(a,$o)]:
0.72/0.89	                (app_encode_app(app_encode_fun(a,$o),$o,P,S) & 
0.72/0.89	                 app_encode_app(a,$o,S,Xy) & app_encode_app(a,$o,S,Xx))))) & 
0.72/0.89	         (![Xx:a,Xy:a,Xz:a]:
0.72/0.89	            (((?[S:app_encode_fun(a,$o)]:
0.72/0.89	                 (app_encode_app(app_encode_fun(a,$o),$o,P,S) & 
0.72/0.89	                  app_encode_app(a,$o,S,Xx) & app_encode_app(a,$o,S,Xy))) & 
0.72/0.89	              (?[S:app_encode_fun(a,$o)]:
0.72/0.89	                 (app_encode_app(app_encode_fun(a,$o),$o,P,S) & 
0.72/0.89	                  app_encode_app(a,$o,S,Xy) & app_encode_app(a,$o,S,Xz)))) =>
0.72/0.89	             (?[S:app_encode_fun(a,$o)]:
0.72/0.89	                (app_encode_app(app_encode_fun(a,$o),$o,P,S) & 
0.72/0.89	                 app_encode_app(a,$o,S,Xx) & app_encode_app(a,$o,S,Xz)))))))))).
0.72/0.89	tff('0', plain, ![X5 : a]: app_encode_app(a, $o, sk_Xp(X5), X5),
0.72/0.89	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.72/0.89	tff('1', plain,
0.72/0.89	    ![X5 : a]: app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_Xp(X5)),
0.72/0.89	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.72/0.89	tff('2', plain,
0.72/0.89	    ![X7 : app_encode_fun(a, $o)]:
0.72/0.89	      (~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.89	       | ~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.89	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.72/0.89	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.72/0.89	tff('3', plain,
0.72/0.89	    ![X7 : app_encode_fun(a, $o)]:
0.72/0.89	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.72/0.89	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.89	       | ~ app_encode_app(a, $o, X7, sk_Xx)),
0.72/0.89	    inference('simplify', [status(thm)], ['2'])).
0.72/0.89	tff('4', plain,
0.72/0.89	    ![X0 : a]:
0.72/0.89	      (~ $true
0.72/0.89	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.72/0.89	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.72/0.89	    inference('sup-', [status(thm)], ['1', '3'])).
0.72/0.89	tff('5', plain,
0.72/0.89	    ![X0 : a]:
0.72/0.89	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.72/0.89	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.72/0.89	    inference('simplify', [status(thm)], ['4'])).
0.72/0.89	tff('6', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.72/0.89	    inference('sup-', [status(thm)], ['0', '5'])).
0.72/0.89	tff('7', plain,
0.72/0.89	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.72/0.89	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.72/0.89	    inference('simplify', [status(thm)], ['6'])).
0.72/0.89	tff('8', plain,
0.72/0.89	    ![X7 : app_encode_fun(a, $o), X8 : app_encode_fun(a, $o)]:
0.72/0.89	      (~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.89	       | ~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.89	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X8)
0.72/0.89	       | ~ app_encode_app(a, $o, X8, sk_Xx2)
0.72/0.89	       | ~ app_encode_app(a, $o, X8, sk_Xz)),
0.72/0.89	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.72/0.89	tff('9', plain,
0.72/0.89	    ![X7 : app_encode_fun(a, $o), X8 : app_encode_fun(a, $o)]:
0.72/0.89	      (~ app_encode_app(a, $o, X8, sk_Xz)
0.72/0.89	       | ~ app_encode_app(a, $o, X8, sk_Xx2)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X8)
0.72/0.89	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.89	       | ~ app_encode_app(a, $o, X7, sk_Xx)),
0.72/0.89	    inference('simplify', [status(thm)], ['8'])).
0.72/0.89	tff('10', plain,
0.72/0.89	    ![X0 : app_encode_fun(a, $o)]:
0.72/0.89	      (~ $true
0.72/0.89	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.72/0.89	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	       | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)
0.72/0.89	       | ~ app_encode_app(a, $o, sk_S2, sk_Xz)),
0.72/0.89	    inference('sup-', [status(thm)], ['7', '9'])).
0.72/0.89	tff('11', plain,
0.72/0.89	    ![X0 : app_encode_fun(a, $o)]:
0.72/0.89	      (~ app_encode_app(a, $o, sk_S2, sk_Xz)
0.72/0.89	       | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.72/0.89	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.72/0.89	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.72/0.89	    inference('simplify', [status(thm)], ['10'])).
0.72/0.89	tff('12', plain,
0.72/0.89	    ![X7 : app_encode_fun(a, $o)]:
0.72/0.89	      (~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.89	       | ~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.89	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	       | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.72/0.89	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.72/0.89	tff('13', plain,
0.72/0.89	    ![X7 : app_encode_fun(a, $o)]:
0.72/0.89	      (app_encode_app(a, $o, sk_S2, sk_Xz)
0.72/0.89	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.89	       | ~ app_encode_app(a, $o, X7, sk_Xx)),
0.72/0.89	    inference('simplify', [status(thm)], ['12'])).
0.72/0.89	tff('14', plain,
0.72/0.89	    ![X0 : a]:
0.72/0.89	      (~ $true
0.72/0.89	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.72/0.89	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	       | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.72/0.89	    inference('sup-', [status(thm)], ['1', '13'])).
0.72/0.89	tff('15', plain,
0.72/0.89	    ![X0 : a]:
0.72/0.89	      (app_encode_app(a, $o, sk_S2, sk_Xz)
0.72/0.89	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.72/0.89	    inference('simplify', [status(thm)], ['14'])).
0.72/0.89	tff('16', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	     | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.72/0.89	    inference('sup-', [status(thm)], ['0', '15'])).
0.72/0.89	tff('17', plain,
0.72/0.89	    (app_encode_app(a, $o, sk_S2, sk_Xz)
0.72/0.89	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.72/0.89	    inference('simplify', [status(thm)], ['16'])).
0.72/0.89	tff('18', plain,
0.72/0.89	    ![X0 : app_encode_fun(a, $o)]:
0.72/0.89	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.72/0.89	       | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)),
0.72/0.89	    inference('clc', [status(thm)], ['11', '17'])).
0.72/0.89	tff('19', plain,
0.72/0.89	    ![X0 : a]:
0.72/0.89	      (~ $true
0.72/0.89	       | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)
0.72/0.89	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.72/0.89	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.72/0.89	    inference('sup-', [status(thm)], ['1', '18'])).
0.72/0.89	tff('20', plain,
0.72/0.89	    ![X0 : a]:
0.72/0.89	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.72/0.89	       | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)),
0.72/0.89	    inference('simplify', [status(thm)], ['19'])).
0.72/0.89	tff('21', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)
0.72/0.89	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.72/0.89	    inference('sup-', [status(thm)], ['0', '20'])).
0.72/0.89	tff('22', plain,
0.72/0.89	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	     | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)),
0.72/0.89	    inference('simplify', [status(thm)], ['21'])).
0.72/0.89	tff('23', plain,
0.72/0.89	    ![X7 : app_encode_fun(a, $o)]:
0.72/0.89	      (~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.89	       | ~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.89	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.72/0.89	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.72/0.89	tff('24', plain,
0.72/0.89	    ![X7 : app_encode_fun(a, $o)]:
0.72/0.89	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.89	       | ~ app_encode_app(a, $o, X7, sk_Xx)),
0.72/0.89	    inference('simplify', [status(thm)], ['23'])).
0.72/0.89	tff('25', plain,
0.72/0.89	    ![X0 : a]:
0.72/0.89	      (~ $true
0.72/0.89	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.89	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.72/0.89	    inference('sup-', [status(thm)], ['1', '24'])).
0.72/0.89	tff('26', plain,
0.72/0.89	    ![X0 : a]:
0.72/0.89	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.89	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.72/0.89	    inference('simplify', [status(thm)], ['25'])).
0.72/0.89	tff('27', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.89	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.72/0.89	    inference('sup-', [status(thm)], ['0', '26'])).
0.72/0.89	tff('28', plain,
0.72/0.89	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.72/0.89	    inference('simplify', [status(thm)], ['27'])).
0.72/0.89	tff('29', plain,
0.72/0.89	    ![X7 : app_encode_fun(a, $o)]:
0.72/0.89	      (~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.89	       | ~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.89	       | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.72/0.89	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.72/0.89	tff('30', plain,
0.72/0.89	    ![X7 : app_encode_fun(a, $o)]:
0.72/0.89	      (app_encode_app(a, $o, sk_S2, sk_Xy1)
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.89	       | ~ app_encode_app(a, $o, X7, sk_Xx)),
0.72/0.89	    inference('simplify', [status(thm)], ['29'])).
0.72/0.89	tff('31', plain,
0.72/0.89	    ![X0 : a]:
0.72/0.89	      (~ $true
0.72/0.89	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.89	       | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.72/0.89	    inference('sup-', [status(thm)], ['1', '30'])).
0.72/0.89	tff('32', plain,
0.72/0.89	    ![X0 : a]:
0.72/0.89	      (app_encode_app(a, $o, sk_S2, sk_Xy1)
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.89	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.72/0.89	    inference('simplify', [status(thm)], ['31'])).
0.72/0.89	tff('33', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.89	     | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.72/0.89	    inference('sup-', [status(thm)], ['0', '32'])).
0.72/0.89	tff('34', plain,
0.72/0.89	    (app_encode_app(a, $o, sk_S2, sk_Xy1)
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.72/0.89	    inference('simplify', [status(thm)], ['33'])).
0.72/0.89	tff('35', plain,
0.72/0.89	    ![X5 : a, X6 : app_encode_fun(a, $o)]:
0.72/0.89	      (X6 = sk_Xp(X5)
0.72/0.89	       | ~ app_encode_app(a, $o, X6, X5)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)),
0.72/0.89	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.72/0.89	tff('36', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.89	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.72/0.89	     | sk_S2 = sk_Xp(sk_Xy1)),
0.72/0.89	    inference('sup-', [status(thm)], ['34', '35'])).
0.72/0.89	tff('37', plain,
0.72/0.89	    (sk_S2 = sk_Xp(sk_Xy1)
0.72/0.89	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.72/0.89	    inference('simplify', [status(thm)], ['36'])).
0.72/0.89	tff('38', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.89	     | sk_S2 = sk_Xp(sk_Xy1)),
0.72/0.89	    inference('sup-', [status(thm)], ['28', '37'])).
0.72/0.89	tff('39', plain,
0.72/0.89	    (sk_S2 = sk_Xp(sk_Xy1) | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.72/0.89	    inference('simplify', [status(thm)], ['38'])).
0.72/0.89	tff('40', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | sk_S2 = sk_Xp(sk_Xy1)
0.72/0.89	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	     | sk_S = sk_Xp(sk_Xx1)),
0.72/0.89	    inference('sup-', [status(thm)], ['39', '35'])).
0.72/0.89	tff('41', plain,
0.72/0.89	    (sk_S = sk_Xp(sk_Xx1)
0.72/0.89	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	     | sk_S2 = sk_Xp(sk_Xy1)),
0.72/0.89	    inference('simplify', [status(thm)], ['40'])).
0.72/0.89	tff('42', plain,
0.72/0.89	    ![X7 : app_encode_fun(a, $o)]:
0.72/0.89	      (~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.89	       | ~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.89	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	       | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.72/0.89	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.72/0.89	tff('43', plain,
0.72/0.89	    ![X7 : app_encode_fun(a, $o)]:
0.72/0.89	      (app_encode_app(a, $o, sk_S2, sk_Xy1)
0.72/0.89	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.89	       | ~ app_encode_app(a, $o, X7, sk_Xx)),
0.72/0.89	    inference('simplify', [status(thm)], ['42'])).
0.72/0.89	tff('44', plain,
0.72/0.89	    ![X0 : a]:
0.72/0.89	      (~ $true
0.72/0.89	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.72/0.89	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	       | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.72/0.89	    inference('sup-', [status(thm)], ['1', '43'])).
0.72/0.89	tff('45', plain,
0.72/0.89	    ![X0 : a]:
0.72/0.89	      (app_encode_app(a, $o, sk_S2, sk_Xy1)
0.72/0.89	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.72/0.89	    inference('simplify', [status(thm)], ['44'])).
0.72/0.89	tff('46', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	     | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.72/0.89	    inference('sup-', [status(thm)], ['0', '45'])).
0.72/0.89	tff('47', plain,
0.72/0.89	    (app_encode_app(a, $o, sk_S2, sk_Xy1)
0.72/0.89	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.72/0.89	    inference('simplify', [status(thm)], ['46'])).
0.72/0.89	tff('48', plain,
0.72/0.89	    ![X4 : app_encode_fun(a, $o)]:
0.72/0.89	      (app_encode_app(a, $o, X4, sk_Xz1(X4))
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X4)),
0.72/0.89	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.72/0.89	tff('49', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | app_encode_app(a, $o, sk_S2, sk_Xy1)
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xz1(sk_S))),
0.72/0.89	    inference('sup-', [status(thm)], ['47', '48'])).
0.72/0.89	tff('50', plain,
0.72/0.89	    (app_encode_app(a, $o, sk_S, sk_Xz1(sk_S))
0.72/0.89	     | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.72/0.89	    inference('simplify', [status(thm)], ['49'])).
0.72/0.89	tff('51', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | app_encode_app(a, $o, sk_S2, sk_Xy1)
0.72/0.89	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	     | sk_S = sk_Xp(sk_Xz1(sk_S))),
0.72/0.89	    inference('sup-', [status(thm)], ['50', '35'])).
0.72/0.89	tff('52', plain,
0.72/0.89	    (sk_S = sk_Xp(sk_Xz1(sk_S))
0.72/0.89	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	     | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.72/0.89	    inference('simplify', [status(thm)], ['51'])).
0.72/0.89	tff('53', plain,
0.72/0.89	    (app_encode_app(a, $o, sk_S2, sk_Xy1) | sk_S = sk_Xp(sk_Xz1(sk_S))),
0.72/0.89	    inference('clc', [status(thm)], ['52', '47'])).
0.72/0.89	tff('54', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | sk_S = sk_Xp(sk_Xz1(sk_S))
0.72/0.89	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.72/0.89	     | sk_S2 = sk_Xp(sk_Xy1)),
0.72/0.89	    inference('sup-', [status(thm)], ['53', '35'])).
0.72/0.89	tff('55', plain,
0.72/0.89	    (sk_S2 = sk_Xp(sk_Xy1)
0.72/0.89	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.72/0.89	     | sk_S = sk_Xp(sk_Xz1(sk_S))),
0.72/0.89	    inference('simplify', [status(thm)], ['54'])).
0.72/0.89	tff('56', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	     | sk_S = sk_Xp(sk_Xz1(sk_S))
0.72/0.89	     | sk_S2 = sk_Xp(sk_Xy1)),
0.72/0.89	    inference('sup-', [status(thm)], ['7', '55'])).
0.72/0.89	tff('57', plain,
0.72/0.89	    (sk_S2 = sk_Xp(sk_Xy1)
0.72/0.89	     | sk_S = sk_Xp(sk_Xz1(sk_S))
0.72/0.89	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.72/0.89	    inference('simplify', [status(thm)], ['56'])).
0.72/0.89	tff('58', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | sk_S = sk_Xp(sk_Xz1(sk_S))
0.72/0.89	     | sk_S2 = sk_Xp(sk_Xy1)
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xz1(sk_S))),
0.72/0.89	    inference('sup-', [status(thm)], ['57', '48'])).
0.72/0.89	tff('59', plain,
0.72/0.89	    (app_encode_app(a, $o, sk_S, sk_Xz1(sk_S))
0.72/0.89	     | sk_S2 = sk_Xp(sk_Xy1)
0.72/0.89	     | sk_S = sk_Xp(sk_Xz1(sk_S))),
0.72/0.89	    inference('simplify', [status(thm)], ['58'])).
0.72/0.89	tff('60', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | sk_S = sk_Xp(sk_Xz1(sk_S))
0.72/0.89	     | sk_S2 = sk_Xp(sk_Xy1)
0.72/0.89	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	     | sk_S = sk_Xp(sk_Xz1(sk_S))),
0.72/0.89	    inference('sup-', [status(thm)], ['59', '35'])).
0.72/0.89	tff('61', plain,
0.72/0.89	    (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	     | sk_S2 = sk_Xp(sk_Xy1)
0.72/0.89	     | sk_S = sk_Xp(sk_Xz1(sk_S))),
0.72/0.89	    inference('simplify', [status(thm)], ['60'])).
0.72/0.89	tff('62', plain, (sk_S = sk_Xp(sk_Xz1(sk_S)) | sk_S2 = sk_Xp(sk_Xy1)),
0.72/0.89	    inference('clc', [status(thm)], ['61', '57'])).
0.72/0.89	tff('63', plain,
0.72/0.89	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	     | sk_S2 = sk_Xp(sk_Xy1)),
0.72/0.89	    inference('sup+', [status(thm)], ['62', '1'])).
0.72/0.89	tff('64', plain, (sk_S2 = sk_Xp(sk_Xy1) | sk_S = sk_Xp(sk_Xx1)),
0.72/0.89	    inference('clc', [status(thm)], ['41', '63'])).
0.72/0.89	tff('65', plain,
0.72/0.89	    ![X7 : app_encode_fun(a, $o)]:
0.72/0.89	      (~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.89	       | ~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.89	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.72/0.89	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.72/0.89	tff('66', plain,
0.72/0.89	    ![X7 : app_encode_fun(a, $o)]:
0.72/0.89	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.72/0.89	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.89	       | ~ app_encode_app(a, $o, X7, sk_Xx)),
0.72/0.89	    inference('simplify', [status(thm)], ['65'])).
0.72/0.89	tff('67', plain,
0.72/0.89	    ![X0 : a]:
0.72/0.89	      (~ $true
0.72/0.89	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.72/0.89	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.72/0.89	    inference('sup-', [status(thm)], ['1', '66'])).
0.72/0.89	tff('68', plain,
0.72/0.89	    ![X0 : a]:
0.72/0.89	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.72/0.89	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.72/0.89	    inference('simplify', [status(thm)], ['67'])).
0.72/0.89	tff('69', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.72/0.89	    inference('sup-', [status(thm)], ['0', '68'])).
0.72/0.89	tff('70', plain,
0.72/0.89	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.72/0.89	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.72/0.89	    inference('simplify', [status(thm)], ['69'])).
0.72/0.89	tff('71', plain,
0.72/0.89	    ![X7 : app_encode_fun(a, $o)]:
0.72/0.89	      (~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.89	       | ~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.89	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	       | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.72/0.89	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.72/0.89	tff('72', plain,
0.72/0.89	    ![X7 : app_encode_fun(a, $o)]:
0.72/0.89	      (app_encode_app(a, $o, sk_S1, sk_Xx2)
0.72/0.89	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.89	       | ~ app_encode_app(a, $o, X7, sk_Xx)),
0.72/0.89	    inference('simplify', [status(thm)], ['71'])).
0.72/0.89	tff('73', plain,
0.72/0.89	    ![X0 : a]:
0.72/0.89	      (~ $true
0.72/0.89	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.72/0.89	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	       | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.72/0.89	    inference('sup-', [status(thm)], ['1', '72'])).
0.72/0.89	tff('74', plain,
0.72/0.89	    ![X0 : a]:
0.72/0.89	      (app_encode_app(a, $o, sk_S1, sk_Xx2)
0.72/0.89	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.72/0.89	    inference('simplify', [status(thm)], ['73'])).
0.72/0.89	tff('75', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	     | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.72/0.89	    inference('sup-', [status(thm)], ['0', '74'])).
0.72/0.89	tff('76', plain,
0.72/0.89	    (app_encode_app(a, $o, sk_S1, sk_Xx2)
0.72/0.89	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.72/0.89	    inference('simplify', [status(thm)], ['75'])).
0.72/0.89	tff('77', plain,
0.72/0.89	    ![X7 : app_encode_fun(a, $o)]:
0.72/0.89	      (~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.89	       | ~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.89	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.72/0.89	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.72/0.89	tff('78', plain,
0.72/0.89	    ![X7 : app_encode_fun(a, $o)]:
0.72/0.89	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.89	       | ~ app_encode_app(a, $o, X7, sk_Xx)),
0.72/0.89	    inference('simplify', [status(thm)], ['77'])).
0.72/0.89	tff('79', plain,
0.72/0.89	    ![X0 : a]:
0.72/0.89	      (~ $true
0.72/0.89	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.89	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.72/0.89	    inference('sup-', [status(thm)], ['1', '78'])).
0.72/0.89	tff('80', plain,
0.72/0.89	    ![X0 : a]:
0.72/0.89	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.89	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.72/0.89	    inference('simplify', [status(thm)], ['79'])).
0.72/0.89	tff('81', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.89	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.72/0.89	    inference('sup-', [status(thm)], ['0', '80'])).
0.72/0.89	tff('82', plain,
0.72/0.89	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.72/0.89	    inference('simplify', [status(thm)], ['81'])).
0.72/0.89	tff('83', plain,
0.72/0.89	    ![X7 : app_encode_fun(a, $o)]:
0.72/0.89	      (~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.89	       | ~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.89	       | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.72/0.89	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.72/0.89	tff('84', plain,
0.72/0.89	    ![X7 : app_encode_fun(a, $o)]:
0.72/0.89	      (app_encode_app(a, $o, sk_S1, sk_Xx2)
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.89	       | ~ app_encode_app(a, $o, X7, sk_Xx)),
0.72/0.89	    inference('simplify', [status(thm)], ['83'])).
0.72/0.89	tff('85', plain,
0.72/0.89	    ![X0 : a]:
0.72/0.89	      (~ $true
0.72/0.89	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.89	       | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.72/0.89	    inference('sup-', [status(thm)], ['1', '84'])).
0.72/0.89	tff('86', plain,
0.72/0.89	    ![X0 : a]:
0.72/0.89	      (app_encode_app(a, $o, sk_S1, sk_Xx2)
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.89	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.72/0.89	    inference('simplify', [status(thm)], ['85'])).
0.72/0.89	tff('87', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.89	     | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.72/0.89	    inference('sup-', [status(thm)], ['0', '86'])).
0.72/0.89	tff('88', plain,
0.72/0.89	    (app_encode_app(a, $o, sk_S1, sk_Xx2)
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.72/0.89	    inference('simplify', [status(thm)], ['87'])).
0.72/0.89	tff('89', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.89	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.72/0.89	     | sk_S1 = sk_Xp(sk_Xx2)),
0.72/0.89	    inference('sup-', [status(thm)], ['88', '35'])).
0.72/0.89	tff('90', plain,
0.72/0.89	    (sk_S1 = sk_Xp(sk_Xx2)
0.72/0.89	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.72/0.89	    inference('simplify', [status(thm)], ['89'])).
0.72/0.89	tff('91', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.89	     | sk_S1 = sk_Xp(sk_Xx2)),
0.72/0.89	    inference('sup-', [status(thm)], ['82', '90'])).
0.72/0.89	tff('92', plain,
0.72/0.89	    (sk_S1 = sk_Xp(sk_Xx2) | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.72/0.89	    inference('simplify', [status(thm)], ['91'])).
0.72/0.89	tff('93', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | sk_S1 = sk_Xp(sk_Xx2)
0.72/0.89	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	     | sk_S = sk_Xp(sk_Xx1)),
0.72/0.89	    inference('sup-', [status(thm)], ['92', '35'])).
0.72/0.89	tff('94', plain,
0.72/0.89	    (sk_S = sk_Xp(sk_Xx1)
0.72/0.89	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	     | sk_S1 = sk_Xp(sk_Xx2)),
0.72/0.89	    inference('simplify', [status(thm)], ['93'])).
0.72/0.89	tff('95', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | app_encode_app(a, $o, sk_S1, sk_Xx2)
0.72/0.89	     | sk_S1 = sk_Xp(sk_Xx2)
0.72/0.89	     | sk_S = sk_Xp(sk_Xx1)),
0.72/0.89	    inference('sup-', [status(thm)], ['76', '94'])).
0.72/0.89	tff('96', plain,
0.72/0.89	    (sk_S = sk_Xp(sk_Xx1)
0.72/0.89	     | sk_S1 = sk_Xp(sk_Xx2)
0.72/0.89	     | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.72/0.89	    inference('simplify', [status(thm)], ['95'])).
0.72/0.89	tff('97', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | sk_S1 = sk_Xp(sk_Xx2)
0.72/0.89	     | sk_S = sk_Xp(sk_Xx1)
0.72/0.89	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.72/0.89	     | sk_S1 = sk_Xp(sk_Xx2)),
0.72/0.89	    inference('sup-', [status(thm)], ['96', '35'])).
0.72/0.89	tff('98', plain,
0.72/0.89	    (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.72/0.89	     | sk_S = sk_Xp(sk_Xx1)
0.72/0.89	     | sk_S1 = sk_Xp(sk_Xx2)),
0.72/0.89	    inference('simplify', [status(thm)], ['97'])).
0.72/0.89	tff('99', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	     | sk_S1 = sk_Xp(sk_Xx2)
0.72/0.89	     | sk_S = sk_Xp(sk_Xx1)),
0.72/0.89	    inference('sup-', [status(thm)], ['70', '98'])).
0.72/0.89	tff('100', plain,
0.72/0.89	    (sk_S = sk_Xp(sk_Xx1)
0.72/0.89	     | sk_S1 = sk_Xp(sk_Xx2)
0.72/0.89	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.72/0.89	    inference('simplify', [status(thm)], ['99'])).
0.72/0.89	tff('101', plain, (sk_S1 = sk_Xp(sk_Xx2) | sk_S = sk_Xp(sk_Xx1)),
0.72/0.89	    inference('clc', [status(thm)], ['100', '94'])).
0.72/0.89	tff('102', plain,
0.72/0.89	    ![X0 : a]:
0.72/0.89	      (~ $true | app_encode_app(a, $o, sk_Xp(X0), sk_Xz1(sk_Xp(X0)))),
0.72/0.89	    inference('sup-', [status(thm)], ['1', '48'])).
0.72/0.89	tff('103', plain,
0.72/0.89	    ![X0 : a]: app_encode_app(a, $o, sk_Xp(X0), sk_Xz1(sk_Xp(X0))),
0.72/0.89	    inference('simplify', [status(thm)], ['102'])).
0.72/0.89	tff('104', plain,
0.72/0.89	    ![X0 : a]:
0.72/0.89	      (~ $true
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_Xp(X0))
0.72/0.89	       | sk_Xp(X0) = sk_Xp(sk_Xz1(sk_Xp(X0)))),
0.72/0.89	    inference('sup-', [status(thm)], ['103', '35'])).
0.72/0.89	tff('105', plain,
0.72/0.89	    ![X0 : a]: (~ $true | ~ $true | sk_Xp(X0) = sk_Xp(sk_Xz1(sk_Xp(X0)))),
0.72/0.89	    inference('demod', [status(thm)], ['104', '1'])).
0.72/0.89	tff('106', plain, ![X0 : a]: sk_Xp(X0) = sk_Xp(sk_Xz1(sk_Xp(X0))),
0.72/0.89	    inference('simplify', [status(thm)], ['105'])).
0.72/0.89	tff('107', plain,
0.72/0.89	    (sk_Xp(sk_Xx2) = sk_Xp(sk_Xz1(sk_S1)) | sk_S = sk_Xp(sk_Xx1)),
0.72/0.89	    inference('sup+', [status(thm)], ['101', '106'])).
0.72/0.89	tff('108', plain,
0.72/0.89	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.72/0.89	     | sk_S = sk_Xp(sk_Xx1)),
0.72/0.89	    inference('sup+', [status(thm)], ['101', '1'])).
0.72/0.89	tff('109', plain,
0.72/0.89	    ![X7 : app_encode_fun(a, $o)]:
0.72/0.89	      (~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.89	       | ~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.89	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	       | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.72/0.89	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.72/0.89	tff('110', plain,
0.72/0.89	    ![X7 : app_encode_fun(a, $o)]:
0.72/0.89	      (app_encode_app(a, $o, sk_S1, sk_Xy1)
0.72/0.89	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.89	       | ~ app_encode_app(a, $o, X7, sk_Xx)),
0.72/0.89	    inference('simplify', [status(thm)], ['109'])).
0.72/0.89	tff('111', plain,
0.72/0.89	    ![X0 : a]:
0.72/0.89	      (~ $true
0.72/0.89	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.72/0.89	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	       | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.72/0.89	    inference('sup-', [status(thm)], ['1', '110'])).
0.72/0.89	tff('112', plain,
0.72/0.89	    ![X0 : a]:
0.72/0.89	      (app_encode_app(a, $o, sk_S1, sk_Xy1)
0.72/0.89	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.72/0.89	    inference('simplify', [status(thm)], ['111'])).
0.72/0.89	tff('113', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	     | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.72/0.89	    inference('sup-', [status(thm)], ['0', '112'])).
0.72/0.89	tff('114', plain,
0.72/0.89	    (app_encode_app(a, $o, sk_S1, sk_Xy1)
0.72/0.89	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.72/0.89	    inference('simplify', [status(thm)], ['113'])).
0.72/0.89	tff('115', plain,
0.72/0.89	    ![X7 : app_encode_fun(a, $o)]:
0.72/0.89	      (~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.89	       | ~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.89	       | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.72/0.89	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.72/0.89	tff('116', plain,
0.72/0.89	    ![X7 : app_encode_fun(a, $o)]:
0.72/0.89	      (app_encode_app(a, $o, sk_S1, sk_Xy1)
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.89	       | ~ app_encode_app(a, $o, X7, sk_Xx)),
0.72/0.89	    inference('simplify', [status(thm)], ['115'])).
0.72/0.89	tff('117', plain,
0.72/0.89	    ![X0 : a]:
0.72/0.89	      (~ $true
0.72/0.89	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.89	       | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.72/0.89	    inference('sup-', [status(thm)], ['1', '116'])).
0.72/0.89	tff('118', plain,
0.72/0.89	    ![X0 : a]:
0.72/0.89	      (app_encode_app(a, $o, sk_S1, sk_Xy1)
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.89	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.72/0.89	    inference('simplify', [status(thm)], ['117'])).
0.72/0.89	tff('119', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.89	     | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.72/0.89	    inference('sup-', [status(thm)], ['0', '118'])).
0.72/0.89	tff('120', plain,
0.72/0.89	    (app_encode_app(a, $o, sk_S1, sk_Xy1)
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.72/0.89	    inference('simplify', [status(thm)], ['119'])).
0.72/0.89	tff('121', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.89	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.72/0.89	     | sk_S1 = sk_Xp(sk_Xy1)),
0.72/0.89	    inference('sup-', [status(thm)], ['120', '35'])).
0.72/0.89	tff('122', plain,
0.72/0.89	    (sk_S1 = sk_Xp(sk_Xy1)
0.72/0.89	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.72/0.89	    inference('simplify', [status(thm)], ['121'])).
0.72/0.89	tff('123', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.89	     | sk_S1 = sk_Xp(sk_Xy1)),
0.72/0.89	    inference('sup-', [status(thm)], ['82', '122'])).
0.72/0.89	tff('124', plain,
0.72/0.89	    (sk_S1 = sk_Xp(sk_Xy1) | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.72/0.89	    inference('simplify', [status(thm)], ['123'])).
0.72/0.89	tff('125', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | sk_S1 = sk_Xp(sk_Xy1)
0.72/0.89	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	     | sk_S = sk_Xp(sk_Xx1)),
0.72/0.89	    inference('sup-', [status(thm)], ['124', '35'])).
0.72/0.89	tff('126', plain,
0.72/0.89	    (sk_S = sk_Xp(sk_Xx1)
0.72/0.89	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	     | sk_S1 = sk_Xp(sk_Xy1)),
0.72/0.89	    inference('simplify', [status(thm)], ['125'])).
0.72/0.89	tff('127', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | app_encode_app(a, $o, sk_S1, sk_Xy1)
0.72/0.89	     | sk_S1 = sk_Xp(sk_Xy1)
0.72/0.89	     | sk_S = sk_Xp(sk_Xx1)),
0.72/0.89	    inference('sup-', [status(thm)], ['114', '126'])).
0.72/0.89	tff('128', plain,
0.72/0.89	    (sk_S = sk_Xp(sk_Xx1)
0.72/0.89	     | sk_S1 = sk_Xp(sk_Xy1)
0.72/0.89	     | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.72/0.89	    inference('simplify', [status(thm)], ['127'])).
0.72/0.89	tff('129', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | sk_S1 = sk_Xp(sk_Xy1)
0.72/0.89	     | sk_S = sk_Xp(sk_Xx1)
0.72/0.89	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.72/0.89	     | sk_S1 = sk_Xp(sk_Xy1)),
0.72/0.89	    inference('sup-', [status(thm)], ['128', '35'])).
0.72/0.89	tff('130', plain,
0.72/0.89	    (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.72/0.89	     | sk_S = sk_Xp(sk_Xx1)
0.72/0.89	     | sk_S1 = sk_Xp(sk_Xy1)),
0.72/0.89	    inference('simplify', [status(thm)], ['129'])).
0.72/0.89	tff('131', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | sk_S = sk_Xp(sk_Xx1)
0.72/0.89	     | sk_S1 = sk_Xp(sk_Xy1)
0.72/0.89	     | sk_S = sk_Xp(sk_Xx1)),
0.72/0.89	    inference('sup-', [status(thm)], ['108', '130'])).
0.72/0.89	tff('132', plain, (sk_S1 = sk_Xp(sk_Xy1) | sk_S = sk_Xp(sk_Xx1)),
0.72/0.89	    inference('simplify', [status(thm)], ['131'])).
0.72/0.89	tff('133', plain,
0.72/0.89	    (sk_Xp(sk_Xy1) = sk_Xp(sk_Xz1(sk_S1)) | sk_S = sk_Xp(sk_Xx1)),
0.72/0.89	    inference('sup+', [status(thm)], ['132', '106'])).
0.72/0.89	tff('134', plain,
0.72/0.89	    (sk_Xp(sk_Xy1) = sk_Xp(sk_Xx2)
0.72/0.89	     | sk_S = sk_Xp(sk_Xx1)
0.72/0.89	     | sk_S = sk_Xp(sk_Xx1)),
0.72/0.89	    inference('sup+', [status(thm)], ['107', '133'])).
0.72/0.89	tff('135', plain, (sk_S = sk_Xp(sk_Xx1) | sk_Xp(sk_Xy1) = sk_Xp(sk_Xx2)),
0.72/0.89	    inference('simplify', [status(thm)], ['134'])).
0.72/0.89	tff('136', plain,
0.72/0.89	    (sk_S2 = sk_Xp(sk_Xx2) | sk_S = sk_Xp(sk_Xx1) | sk_S = sk_Xp(sk_Xx1)),
0.72/0.89	    inference('sup+', [status(thm)], ['64', '135'])).
0.72/0.89	tff('137', plain, (sk_S = sk_Xp(sk_Xx1) | sk_S2 = sk_Xp(sk_Xx2)),
0.72/0.89	    inference('simplify', [status(thm)], ['136'])).
0.72/0.89	tff('138', plain,
0.72/0.89	    (app_encode_app(a, $o, sk_S2, sk_Xx2) | sk_S = sk_Xp(sk_Xx1)),
0.72/0.89	    inference('sup+', [status(thm)], ['137', '0'])).
0.72/0.89	tff('139', plain,
0.72/0.89	    ![X7 : app_encode_fun(a, $o), X8 : app_encode_fun(a, $o)]:
0.72/0.89	      (~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.89	       | ~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X8)
0.72/0.89	       | ~ app_encode_app(a, $o, X8, sk_Xx2)
0.72/0.89	       | ~ app_encode_app(a, $o, X8, sk_Xz)),
0.72/0.89	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.72/0.89	tff('140', plain,
0.72/0.89	    ![X7 : app_encode_fun(a, $o), X8 : app_encode_fun(a, $o)]:
0.72/0.89	      (~ app_encode_app(a, $o, X8, sk_Xz)
0.72/0.89	       | ~ app_encode_app(a, $o, X8, sk_Xx2)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X8)
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.89	       | ~ app_encode_app(a, $o, X7, sk_Xx)),
0.72/0.89	    inference('simplify', [status(thm)], ['139'])).
0.72/0.89	tff('141', plain,
0.72/0.89	    ![X0 : app_encode_fun(a, $o)]:
0.72/0.89	      (~ $true
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.89	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.89	       | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)
0.72/0.89	       | ~ app_encode_app(a, $o, sk_S2, sk_Xz)),
0.72/0.89	    inference('sup-', [status(thm)], ['28', '140'])).
0.72/0.89	tff('142', plain,
0.72/0.89	    ![X0 : app_encode_fun(a, $o)]:
0.72/0.89	      (~ app_encode_app(a, $o, sk_S2, sk_Xz)
0.72/0.89	       | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.72/0.89	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.72/0.89	    inference('simplify', [status(thm)], ['141'])).
0.72/0.89	tff('143', plain,
0.72/0.89	    ![X7 : app_encode_fun(a, $o)]:
0.72/0.89	      (~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.89	       | ~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.89	       | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.72/0.89	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.72/0.89	tff('144', plain,
0.72/0.89	    ![X7 : app_encode_fun(a, $o)]:
0.72/0.89	      (app_encode_app(a, $o, sk_S2, sk_Xz)
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.89	       | ~ app_encode_app(a, $o, X7, sk_Xx)),
0.72/0.89	    inference('simplify', [status(thm)], ['143'])).
0.72/0.89	tff('145', plain,
0.72/0.89	    ![X0 : a]:
0.72/0.89	      (~ $true
0.72/0.89	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.89	       | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.72/0.89	    inference('sup-', [status(thm)], ['1', '144'])).
0.72/0.89	tff('146', plain,
0.72/0.89	    ![X0 : a]:
0.72/0.89	      (app_encode_app(a, $o, sk_S2, sk_Xz)
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.89	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.72/0.89	    inference('simplify', [status(thm)], ['145'])).
0.72/0.89	tff('147', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.89	     | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.72/0.89	    inference('sup-', [status(thm)], ['0', '146'])).
0.72/0.89	tff('148', plain,
0.72/0.89	    (app_encode_app(a, $o, sk_S2, sk_Xz)
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.72/0.89	    inference('simplify', [status(thm)], ['147'])).
0.72/0.89	tff('149', plain,
0.72/0.89	    ![X0 : app_encode_fun(a, $o)]:
0.72/0.89	      (app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.89	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.72/0.89	       | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)),
0.72/0.89	    inference('clc', [status(thm)], ['142', '148'])).
0.72/0.89	tff('150', plain,
0.72/0.89	    ![X0 : a]:
0.72/0.89	      (~ $true
0.72/0.89	       | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)
0.72/0.89	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.72/0.89	    inference('sup-', [status(thm)], ['1', '149'])).
0.72/0.89	tff('151', plain,
0.72/0.89	    ![X0 : a]:
0.72/0.89	      (app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.89	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.72/0.89	       | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)),
0.72/0.89	    inference('simplify', [status(thm)], ['150'])).
0.72/0.89	tff('152', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.72/0.89	    inference('sup-', [status(thm)], ['0', '151'])).
0.72/0.89	tff('153', plain,
0.72/0.89	    (app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.89	     | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)),
0.72/0.89	    inference('simplify', [status(thm)], ['152'])).
0.72/0.89	tff('154', plain,
0.72/0.89	    (~ $true | sk_S = sk_Xp(sk_Xx1) | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.72/0.89	    inference('sup-', [status(thm)], ['138', '153'])).
0.72/0.89	tff('155', plain,
0.72/0.89	    (app_encode_app(a, $o, sk_S, sk_Xx1) | sk_S = sk_Xp(sk_Xx1)),
0.72/0.89	    inference('simplify', [status(thm)], ['154'])).
0.72/0.89	tff('156', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | sk_S = sk_Xp(sk_Xx1)
0.72/0.89	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	     | sk_S = sk_Xp(sk_Xx1)),
0.72/0.89	    inference('sup-', [status(thm)], ['155', '35'])).
0.72/0.89	tff('157', plain,
0.72/0.89	    (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	     | sk_S = sk_Xp(sk_Xx1)),
0.72/0.89	    inference('simplify', [status(thm)], ['156'])).
0.72/0.89	tff('158', plain,
0.72/0.89	    (~ $true | ~ app_encode_app(a, $o, sk_S2, sk_Xx2) | sk_S = sk_Xp(sk_Xx1)),
0.72/0.89	    inference('sup-', [status(thm)], ['22', '157'])).
0.72/0.89	tff('159', plain,
0.72/0.89	    (sk_S = sk_Xp(sk_Xx1) | ~ app_encode_app(a, $o, sk_S2, sk_Xx2)),
0.72/0.89	    inference('simplify', [status(thm)], ['158'])).
0.72/0.89	tff('160', plain, sk_S = sk_Xp(sk_Xx1),
0.72/0.89	    inference('clc', [status(thm)], ['159', '138'])).
0.72/0.89	tff('161', plain, app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S),
0.72/0.89	    inference('sup+', [status(thm)], ['160', '1'])).
0.72/0.89	tff('162', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | app_encode_app(a, $o, sk_S2, sk_Xz)
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xz1(sk_S))),
0.72/0.89	    inference('sup-', [status(thm)], ['17', '48'])).
0.72/0.89	tff('163', plain,
0.72/0.89	    (app_encode_app(a, $o, sk_S, sk_Xz1(sk_S))
0.72/0.89	     | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.72/0.89	    inference('simplify', [status(thm)], ['162'])).
0.72/0.89	tff('164', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | app_encode_app(a, $o, sk_S2, sk_Xz)
0.72/0.89	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	     | sk_S = sk_Xp(sk_Xz1(sk_S))),
0.72/0.89	    inference('sup-', [status(thm)], ['163', '35'])).
0.72/0.89	tff('165', plain,
0.72/0.89	    (sk_S = sk_Xp(sk_Xz1(sk_S))
0.72/0.89	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	     | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.72/0.89	    inference('simplify', [status(thm)], ['164'])).
0.72/0.89	tff('166', plain,
0.72/0.89	    (app_encode_app(a, $o, sk_S2, sk_Xz) | sk_S = sk_Xp(sk_Xz1(sk_S))),
0.72/0.89	    inference('clc', [status(thm)], ['165', '17'])).
0.72/0.89	tff('167', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | sk_S = sk_Xp(sk_Xz1(sk_S))
0.72/0.89	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.72/0.89	     | sk_S2 = sk_Xp(sk_Xz)),
0.72/0.89	    inference('sup-', [status(thm)], ['166', '35'])).
0.72/0.89	tff('168', plain,
0.72/0.89	    (sk_S2 = sk_Xp(sk_Xz)
0.72/0.89	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.72/0.89	     | sk_S = sk_Xp(sk_Xz1(sk_S))),
0.72/0.89	    inference('simplify', [status(thm)], ['167'])).
0.72/0.89	tff('169', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	     | sk_S = sk_Xp(sk_Xz1(sk_S))
0.72/0.89	     | sk_S2 = sk_Xp(sk_Xz)),
0.72/0.89	    inference('sup-', [status(thm)], ['7', '168'])).
0.72/0.89	tff('170', plain,
0.72/0.89	    (sk_S2 = sk_Xp(sk_Xz)
0.72/0.89	     | sk_S = sk_Xp(sk_Xz1(sk_S))
0.72/0.89	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.72/0.89	    inference('simplify', [status(thm)], ['169'])).
0.72/0.89	tff('171', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | sk_S = sk_Xp(sk_Xz1(sk_S))
0.72/0.89	     | sk_S2 = sk_Xp(sk_Xz)
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xz1(sk_S))),
0.72/0.89	    inference('sup-', [status(thm)], ['170', '48'])).
0.72/0.89	tff('172', plain,
0.72/0.89	    (app_encode_app(a, $o, sk_S, sk_Xz1(sk_S))
0.72/0.89	     | sk_S2 = sk_Xp(sk_Xz)
0.72/0.89	     | sk_S = sk_Xp(sk_Xz1(sk_S))),
0.72/0.89	    inference('simplify', [status(thm)], ['171'])).
0.72/0.89	tff('173', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | sk_S = sk_Xp(sk_Xz1(sk_S))
0.72/0.89	     | sk_S2 = sk_Xp(sk_Xz)
0.72/0.89	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	     | sk_S = sk_Xp(sk_Xz1(sk_S))),
0.72/0.89	    inference('sup-', [status(thm)], ['172', '35'])).
0.72/0.89	tff('174', plain,
0.72/0.89	    (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	     | sk_S2 = sk_Xp(sk_Xz)
0.72/0.89	     | sk_S = sk_Xp(sk_Xz1(sk_S))),
0.72/0.89	    inference('simplify', [status(thm)], ['173'])).
0.72/0.89	tff('175', plain, (sk_S = sk_Xp(sk_Xz1(sk_S)) | sk_S2 = sk_Xp(sk_Xz)),
0.72/0.89	    inference('clc', [status(thm)], ['174', '170'])).
0.72/0.89	tff('176', plain,
0.72/0.89	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	     | sk_S2 = sk_Xp(sk_Xz)),
0.72/0.89	    inference('sup+', [status(thm)], ['175', '1'])).
0.72/0.89	tff('177', plain,
0.72/0.89	    ![X7 : app_encode_fun(a, $o), X9 : app_encode_fun(a, $o)]:
0.72/0.89	      (~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.89	       | ~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.89	       | ~ app_encode_app(a, $o, X9, sk_Xx1)
0.72/0.89	       | ~ app_encode_app(a, $o, X9, sk_Xy)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X9)
0.72/0.89	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.72/0.89	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.72/0.89	tff('178', plain,
0.72/0.89	    ![X7 : app_encode_fun(a, $o), X9 : app_encode_fun(a, $o)]:
0.72/0.89	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X9)
0.72/0.89	       | ~ app_encode_app(a, $o, X9, sk_Xy)
0.72/0.89	       | ~ app_encode_app(a, $o, X9, sk_Xx1)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.89	       | ~ app_encode_app(a, $o, X7, sk_Xx)),
0.72/0.89	    inference('simplify', [status(thm)], ['177'])).
0.72/0.89	tff('179', plain,
0.72/0.89	    ![X0 : app_encode_fun(a, $o)]:
0.72/0.89	      (~ $true
0.72/0.89	       | sk_S2 = sk_Xp(sk_Xz)
0.72/0.89	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.72/0.89	       | ~ app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.89	       | ~ app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.89	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.72/0.89	    inference('sup-', [status(thm)], ['176', '178'])).
0.72/0.89	tff('180', plain,
0.72/0.89	    ![X0 : app_encode_fun(a, $o)]:
0.72/0.89	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.72/0.89	       | ~ app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.89	       | ~ app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.72/0.89	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.72/0.89	       | sk_S2 = sk_Xp(sk_Xz)),
0.72/0.89	    inference('simplify', [status(thm)], ['179'])).
0.72/0.89	tff('181', plain,
0.72/0.89	    ![X7 : app_encode_fun(a, $o)]:
0.72/0.89	      (~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.89	       | ~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.89	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.72/0.89	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.72/0.89	tff('182', plain,
0.72/0.89	    ![X7 : app_encode_fun(a, $o)]:
0.72/0.89	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.89	       | ~ app_encode_app(a, $o, X7, sk_Xx)),
0.72/0.89	    inference('simplify', [status(thm)], ['181'])).
0.72/0.89	tff('183', plain,
0.72/0.89	    ![X0 : a]:
0.72/0.89	      (~ $true
0.72/0.89	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.89	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.72/0.89	    inference('sup-', [status(thm)], ['1', '182'])).
0.72/0.89	tff('184', plain,
0.72/0.89	    ![X0 : a]:
0.72/0.89	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.89	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.72/0.89	    inference('simplify', [status(thm)], ['183'])).
0.72/0.89	tff('185', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.89	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.72/0.89	    inference('sup-', [status(thm)], ['0', '184'])).
0.72/0.89	tff('186', plain,
0.72/0.89	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xy)),
0.72/0.89	    inference('simplify', [status(thm)], ['185'])).
0.72/0.89	tff('187', plain,
0.72/0.89	    ![X7 : app_encode_fun(a, $o)]:
0.72/0.89	      (~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.89	       | ~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.89	       | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.72/0.89	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.72/0.89	tff('188', plain,
0.72/0.89	    ![X7 : app_encode_fun(a, $o)]:
0.72/0.89	      (app_encode_app(a, $o, sk_S2, sk_Xz)
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.89	       | ~ app_encode_app(a, $o, X7, sk_Xx)),
0.72/0.89	    inference('simplify', [status(thm)], ['187'])).
0.72/0.89	tff('189', plain,
0.72/0.89	    ![X0 : a]:
0.72/0.89	      (~ $true
0.72/0.89	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.89	       | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.72/0.89	    inference('sup-', [status(thm)], ['1', '188'])).
0.72/0.89	tff('190', plain,
0.72/0.89	    ![X0 : a]:
0.72/0.89	      (app_encode_app(a, $o, sk_S2, sk_Xz)
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.89	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.72/0.89	    inference('simplify', [status(thm)], ['189'])).
0.72/0.89	tff('191', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.89	     | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.72/0.89	    inference('sup-', [status(thm)], ['0', '190'])).
0.72/0.89	tff('192', plain,
0.72/0.89	    (app_encode_app(a, $o, sk_S2, sk_Xz) | app_encode_app(a, $o, sk_S, sk_Xy)),
0.72/0.89	    inference('simplify', [status(thm)], ['191'])).
0.72/0.89	tff('193', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.89	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.72/0.89	     | sk_S2 = sk_Xp(sk_Xz)),
0.72/0.89	    inference('sup-', [status(thm)], ['192', '35'])).
0.72/0.89	tff('194', plain,
0.72/0.89	    (sk_S2 = sk_Xp(sk_Xz)
0.72/0.89	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xy)),
0.72/0.89	    inference('simplify', [status(thm)], ['193'])).
0.72/0.89	tff('195', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.89	     | sk_S2 = sk_Xp(sk_Xz)),
0.72/0.89	    inference('sup-', [status(thm)], ['186', '194'])).
0.72/0.89	tff('196', plain,
0.72/0.89	    (sk_S2 = sk_Xp(sk_Xz) | app_encode_app(a, $o, sk_S, sk_Xy)),
0.72/0.89	    inference('simplify', [status(thm)], ['195'])).
0.72/0.89	tff('197', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | sk_S2 = sk_Xp(sk_Xz)
0.72/0.89	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	     | sk_S = sk_Xp(sk_Xy)),
0.72/0.89	    inference('sup-', [status(thm)], ['196', '35'])).
0.72/0.89	tff('198', plain,
0.72/0.89	    (sk_S = sk_Xp(sk_Xy)
0.72/0.89	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	     | sk_S2 = sk_Xp(sk_Xz)),
0.72/0.89	    inference('simplify', [status(thm)], ['197'])).
0.72/0.89	tff('199', plain, (sk_S2 = sk_Xp(sk_Xz) | sk_S = sk_Xp(sk_Xy)),
0.72/0.89	    inference('clc', [status(thm)], ['198', '176'])).
0.72/0.89	tff('200', plain,
0.72/0.89	    (sk_Xp(sk_Xz) = sk_Xp(sk_Xz1(sk_S2)) | sk_S = sk_Xp(sk_Xy)),
0.72/0.89	    inference('sup+', [status(thm)], ['199', '106'])).
0.72/0.89	tff('201', plain,
0.72/0.89	    ![X7 : app_encode_fun(a, $o)]:
0.72/0.89	      (~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.89	       | ~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.89	       | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.72/0.89	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.72/0.89	tff('202', plain,
0.72/0.89	    ![X7 : app_encode_fun(a, $o)]:
0.72/0.89	      (app_encode_app(a, $o, sk_S2, sk_Xy1)
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.89	       | ~ app_encode_app(a, $o, X7, sk_Xx)),
0.72/0.89	    inference('simplify', [status(thm)], ['201'])).
0.72/0.89	tff('203', plain,
0.72/0.89	    ![X0 : a]:
0.72/0.89	      (~ $true
0.72/0.89	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.89	       | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.72/0.89	    inference('sup-', [status(thm)], ['1', '202'])).
0.72/0.89	tff('204', plain,
0.72/0.89	    ![X0 : a]:
0.72/0.89	      (app_encode_app(a, $o, sk_S2, sk_Xy1)
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.89	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.72/0.89	    inference('simplify', [status(thm)], ['203'])).
0.72/0.89	tff('205', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.89	     | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.72/0.89	    inference('sup-', [status(thm)], ['0', '204'])).
0.72/0.89	tff('206', plain,
0.72/0.89	    (app_encode_app(a, $o, sk_S2, sk_Xy1)
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xy)),
0.72/0.89	    inference('simplify', [status(thm)], ['205'])).
0.72/0.89	tff('207', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.89	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.72/0.89	     | sk_S2 = sk_Xp(sk_Xy1)),
0.72/0.89	    inference('sup-', [status(thm)], ['206', '35'])).
0.72/0.89	tff('208', plain,
0.72/0.89	    (sk_S2 = sk_Xp(sk_Xy1)
0.72/0.89	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xy)),
0.72/0.89	    inference('simplify', [status(thm)], ['207'])).
0.72/0.89	tff('209', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.89	     | sk_S2 = sk_Xp(sk_Xy1)),
0.72/0.89	    inference('sup-', [status(thm)], ['186', '208'])).
0.72/0.89	tff('210', plain,
0.72/0.89	    (sk_S2 = sk_Xp(sk_Xy1) | app_encode_app(a, $o, sk_S, sk_Xy)),
0.72/0.89	    inference('simplify', [status(thm)], ['209'])).
0.72/0.89	tff('211', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | sk_S2 = sk_Xp(sk_Xy1)
0.72/0.89	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	     | sk_S = sk_Xp(sk_Xy)),
0.72/0.89	    inference('sup-', [status(thm)], ['210', '35'])).
0.72/0.89	tff('212', plain,
0.72/0.89	    (sk_S = sk_Xp(sk_Xy)
0.72/0.89	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	     | sk_S2 = sk_Xp(sk_Xy1)),
0.72/0.89	    inference('simplify', [status(thm)], ['211'])).
0.72/0.89	tff('213', plain, (sk_S2 = sk_Xp(sk_Xy1) | sk_S = sk_Xp(sk_Xy)),
0.72/0.89	    inference('clc', [status(thm)], ['212', '63'])).
0.72/0.89	tff('214', plain,
0.72/0.89	    ![X7 : app_encode_fun(a, $o)]:
0.72/0.89	      (~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.89	       | ~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.89	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.72/0.89	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.72/0.89	tff('215', plain,
0.72/0.89	    ![X7 : app_encode_fun(a, $o)]:
0.72/0.89	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.89	       | ~ app_encode_app(a, $o, X7, sk_Xx)),
0.72/0.89	    inference('simplify', [status(thm)], ['214'])).
0.72/0.89	tff('216', plain,
0.72/0.89	    ![X0 : a]:
0.72/0.89	      (~ $true
0.72/0.89	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.89	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.72/0.89	    inference('sup-', [status(thm)], ['1', '215'])).
0.72/0.89	tff('217', plain,
0.72/0.89	    ![X0 : a]:
0.72/0.89	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.89	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.72/0.89	    inference('simplify', [status(thm)], ['216'])).
0.72/0.89	tff('218', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.89	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.72/0.89	    inference('sup-', [status(thm)], ['0', '217'])).
0.72/0.89	tff('219', plain,
0.72/0.89	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xy)),
0.72/0.89	    inference('simplify', [status(thm)], ['218'])).
0.72/0.89	tff('220', plain,
0.72/0.89	    ![X7 : app_encode_fun(a, $o)]:
0.72/0.89	      (~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.89	       | ~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.89	       | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.72/0.89	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.72/0.89	tff('221', plain,
0.72/0.89	    ![X7 : app_encode_fun(a, $o)]:
0.72/0.89	      (app_encode_app(a, $o, sk_S1, sk_Xx2)
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.89	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.89	       | ~ app_encode_app(a, $o, X7, sk_Xx)),
0.72/0.89	    inference('simplify', [status(thm)], ['220'])).
0.72/0.89	tff('222', plain,
0.72/0.89	    ![X0 : a]:
0.72/0.89	      (~ $true
0.72/0.89	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.89	       | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.72/0.89	    inference('sup-', [status(thm)], ['1', '221'])).
0.72/0.89	tff('223', plain,
0.72/0.89	    ![X0 : a]:
0.72/0.89	      (app_encode_app(a, $o, sk_S1, sk_Xx2)
0.72/0.89	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.89	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.72/0.89	    inference('simplify', [status(thm)], ['222'])).
0.72/0.89	tff('224', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.89	     | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.72/0.89	    inference('sup-', [status(thm)], ['0', '223'])).
0.72/0.89	tff('225', plain,
0.72/0.89	    (app_encode_app(a, $o, sk_S1, sk_Xx2)
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xy)),
0.72/0.89	    inference('simplify', [status(thm)], ['224'])).
0.72/0.89	tff('226', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.89	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.72/0.89	     | sk_S1 = sk_Xp(sk_Xx2)),
0.72/0.89	    inference('sup-', [status(thm)], ['225', '35'])).
0.72/0.89	tff('227', plain,
0.72/0.89	    (sk_S1 = sk_Xp(sk_Xx2)
0.72/0.89	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xy)),
0.72/0.89	    inference('simplify', [status(thm)], ['226'])).
0.72/0.89	tff('228', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.89	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.89	     | sk_S1 = sk_Xp(sk_Xx2)),
0.72/0.89	    inference('sup-', [status(thm)], ['219', '227'])).
0.72/0.89	tff('229', plain,
0.72/0.89	    (sk_S1 = sk_Xp(sk_Xx2) | app_encode_app(a, $o, sk_S, sk_Xy)),
0.72/0.89	    inference('simplify', [status(thm)], ['228'])).
0.72/0.89	tff('230', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | sk_S1 = sk_Xp(sk_Xx2)
0.72/0.89	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	     | sk_S = sk_Xp(sk_Xy)),
0.72/0.89	    inference('sup-', [status(thm)], ['229', '35'])).
0.72/0.89	tff('231', plain,
0.72/0.89	    (sk_S = sk_Xp(sk_Xy)
0.72/0.89	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	     | sk_S1 = sk_Xp(sk_Xx2)),
0.72/0.89	    inference('simplify', [status(thm)], ['230'])).
0.72/0.89	tff('232', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | app_encode_app(a, $o, sk_S1, sk_Xx2)
0.72/0.89	     | sk_S1 = sk_Xp(sk_Xx2)
0.72/0.89	     | sk_S = sk_Xp(sk_Xy)),
0.72/0.89	    inference('sup-', [status(thm)], ['76', '231'])).
0.72/0.89	tff('233', plain,
0.72/0.89	    (sk_S = sk_Xp(sk_Xy)
0.72/0.89	     | sk_S1 = sk_Xp(sk_Xx2)
0.72/0.89	     | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.72/0.89	    inference('simplify', [status(thm)], ['232'])).
0.72/0.89	tff('234', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | sk_S1 = sk_Xp(sk_Xx2)
0.72/0.89	     | sk_S = sk_Xp(sk_Xy)
0.72/0.89	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.72/0.89	     | sk_S1 = sk_Xp(sk_Xx2)),
0.72/0.89	    inference('sup-', [status(thm)], ['233', '35'])).
0.72/0.89	tff('235', plain,
0.72/0.89	    (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.72/0.89	     | sk_S = sk_Xp(sk_Xy)
0.72/0.89	     | sk_S1 = sk_Xp(sk_Xx2)),
0.72/0.89	    inference('simplify', [status(thm)], ['234'])).
0.72/0.89	tff('236', plain,
0.72/0.89	    (~ $true
0.72/0.89	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.89	     | sk_S1 = sk_Xp(sk_Xx2)
0.72/0.89	     | sk_S = sk_Xp(sk_Xy)),
0.72/0.89	    inference('sup-', [status(thm)], ['70', '235'])).
0.72/0.89	tff('237', plain,
0.72/0.89	    (sk_S = sk_Xp(sk_Xy)
0.72/0.89	     | sk_S1 = sk_Xp(sk_Xx2)
0.72/0.89	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.72/0.89	    inference('simplify', [status(thm)], ['236'])).
0.72/0.89	tff('238', plain, (sk_S1 = sk_Xp(sk_Xx2) | sk_S = sk_Xp(sk_Xy)),
0.72/0.89	    inference('clc', [status(thm)], ['237', '231'])).
0.72/0.90	tff('239', plain,
0.72/0.90	    (sk_Xp(sk_Xx2) = sk_Xp(sk_Xz1(sk_S1)) | sk_S = sk_Xp(sk_Xy)),
0.72/0.90	    inference('sup+', [status(thm)], ['238', '106'])).
0.72/0.90	tff('240', plain,
0.72/0.90	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.72/0.90	     | sk_S = sk_Xp(sk_Xy)),
0.72/0.90	    inference('sup+', [status(thm)], ['238', '1'])).
0.72/0.90	tff('241', plain,
0.72/0.90	    ![X7 : app_encode_fun(a, $o)]:
0.72/0.90	      (~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.90	       | ~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.90	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.90	       | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.72/0.90	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.72/0.90	tff('242', plain,
0.72/0.90	    ![X7 : app_encode_fun(a, $o)]:
0.72/0.90	      (app_encode_app(a, $o, sk_S1, sk_Xy1)
0.72/0.90	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.90	       | ~ app_encode_app(a, $o, X7, sk_Xx)),
0.72/0.90	    inference('simplify', [status(thm)], ['241'])).
0.72/0.90	tff('243', plain,
0.72/0.90	    ![X0 : a]:
0.72/0.90	      (~ $true
0.72/0.90	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.72/0.90	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.90	       | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.72/0.90	    inference('sup-', [status(thm)], ['1', '242'])).
0.72/0.90	tff('244', plain,
0.72/0.90	    ![X0 : a]:
0.72/0.90	      (app_encode_app(a, $o, sk_S1, sk_Xy1)
0.72/0.90	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.90	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.72/0.90	    inference('simplify', [status(thm)], ['243'])).
0.72/0.90	tff('245', plain,
0.72/0.90	    (~ $true
0.72/0.90	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.90	     | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.72/0.90	    inference('sup-', [status(thm)], ['0', '244'])).
0.72/0.90	tff('246', plain,
0.72/0.90	    (app_encode_app(a, $o, sk_S1, sk_Xy1)
0.72/0.90	     | app_encode_app(a, $o, sk_S, sk_Xy)),
0.72/0.90	    inference('simplify', [status(thm)], ['245'])).
0.72/0.90	tff('247', plain,
0.72/0.90	    (~ $true
0.72/0.90	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.90	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.72/0.90	     | sk_S1 = sk_Xp(sk_Xy1)),
0.72/0.90	    inference('sup-', [status(thm)], ['246', '35'])).
0.72/0.90	tff('248', plain,
0.72/0.90	    (sk_S1 = sk_Xp(sk_Xy1)
0.72/0.90	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.72/0.90	     | app_encode_app(a, $o, sk_S, sk_Xy)),
0.72/0.90	    inference('simplify', [status(thm)], ['247'])).
0.72/0.90	tff('249', plain,
0.72/0.90	    (~ $true
0.72/0.90	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.90	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.90	     | sk_S1 = sk_Xp(sk_Xy1)),
0.72/0.90	    inference('sup-', [status(thm)], ['219', '248'])).
0.72/0.90	tff('250', plain,
0.72/0.90	    (sk_S1 = sk_Xp(sk_Xy1) | app_encode_app(a, $o, sk_S, sk_Xy)),
0.72/0.90	    inference('simplify', [status(thm)], ['249'])).
0.72/0.90	tff('251', plain,
0.72/0.90	    (~ $true
0.72/0.90	     | sk_S1 = sk_Xp(sk_Xy1)
0.72/0.90	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.90	     | sk_S = sk_Xp(sk_Xy)),
0.72/0.90	    inference('sup-', [status(thm)], ['250', '35'])).
0.72/0.90	tff('252', plain,
0.72/0.90	    (sk_S = sk_Xp(sk_Xy)
0.72/0.90	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.90	     | sk_S1 = sk_Xp(sk_Xy1)),
0.72/0.90	    inference('simplify', [status(thm)], ['251'])).
0.72/0.90	tff('253', plain,
0.72/0.90	    (~ $true
0.72/0.90	     | app_encode_app(a, $o, sk_S1, sk_Xy1)
0.72/0.90	     | sk_S1 = sk_Xp(sk_Xy1)
0.72/0.90	     | sk_S = sk_Xp(sk_Xy)),
0.72/0.90	    inference('sup-', [status(thm)], ['114', '252'])).
0.72/0.90	tff('254', plain,
0.72/0.90	    (sk_S = sk_Xp(sk_Xy)
0.72/0.90	     | sk_S1 = sk_Xp(sk_Xy1)
0.72/0.90	     | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.72/0.90	    inference('simplify', [status(thm)], ['253'])).
0.72/0.90	tff('255', plain,
0.72/0.90	    (~ $true
0.72/0.90	     | sk_S1 = sk_Xp(sk_Xy1)
0.72/0.90	     | sk_S = sk_Xp(sk_Xy)
0.72/0.90	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.72/0.90	     | sk_S1 = sk_Xp(sk_Xy1)),
0.72/0.90	    inference('sup-', [status(thm)], ['254', '35'])).
0.72/0.90	tff('256', plain,
0.72/0.90	    (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.72/0.90	     | sk_S = sk_Xp(sk_Xy)
0.72/0.90	     | sk_S1 = sk_Xp(sk_Xy1)),
0.72/0.90	    inference('simplify', [status(thm)], ['255'])).
0.72/0.90	tff('257', plain,
0.72/0.90	    (~ $true
0.72/0.90	     | sk_S = sk_Xp(sk_Xy)
0.72/0.90	     | sk_S1 = sk_Xp(sk_Xy1)
0.72/0.90	     | sk_S = sk_Xp(sk_Xy)),
0.72/0.90	    inference('sup-', [status(thm)], ['240', '256'])).
0.72/0.90	tff('258', plain, (sk_S1 = sk_Xp(sk_Xy1) | sk_S = sk_Xp(sk_Xy)),
0.72/0.90	    inference('simplify', [status(thm)], ['257'])).
0.72/0.90	tff('259', plain,
0.72/0.90	    (sk_Xp(sk_Xy1) = sk_Xp(sk_Xz1(sk_S1)) | sk_S = sk_Xp(sk_Xy)),
0.72/0.90	    inference('sup+', [status(thm)], ['258', '106'])).
0.72/0.90	tff('260', plain,
0.72/0.90	    (sk_Xp(sk_Xy1) = sk_Xp(sk_Xx2)
0.72/0.90	     | sk_S = sk_Xp(sk_Xy)
0.72/0.90	     | sk_S = sk_Xp(sk_Xy)),
0.72/0.90	    inference('sup+', [status(thm)], ['239', '259'])).
0.72/0.90	tff('261', plain, (sk_S = sk_Xp(sk_Xy) | sk_Xp(sk_Xy1) = sk_Xp(sk_Xx2)),
0.72/0.90	    inference('simplify', [status(thm)], ['260'])).
0.72/0.90	tff('262', plain,
0.72/0.90	    (sk_S2 = sk_Xp(sk_Xx2) | sk_S = sk_Xp(sk_Xy) | sk_S = sk_Xp(sk_Xy)),
0.72/0.90	    inference('sup+', [status(thm)], ['213', '261'])).
0.72/0.90	tff('263', plain, (sk_S = sk_Xp(sk_Xy) | sk_S2 = sk_Xp(sk_Xx2)),
0.72/0.90	    inference('simplify', [status(thm)], ['262'])).
0.72/0.90	tff('264', plain,
0.72/0.90	    (sk_Xp(sk_Xx2) = sk_Xp(sk_Xz1(sk_S2)) | sk_S = sk_Xp(sk_Xy)),
0.72/0.90	    inference('sup+', [status(thm)], ['263', '106'])).
0.72/0.90	tff('265', plain,
0.72/0.90	    (sk_Xp(sk_Xx2) = sk_Xp(sk_Xz) | sk_S = sk_Xp(sk_Xy) | sk_S = sk_Xp(sk_Xy)),
0.72/0.90	    inference('sup+', [status(thm)], ['200', '264'])).
0.72/0.90	tff('266', plain, (sk_S = sk_Xp(sk_Xy) | sk_Xp(sk_Xx2) = sk_Xp(sk_Xz)),
0.72/0.90	    inference('simplify', [status(thm)], ['265'])).
0.72/0.90	tff('267', plain,
0.72/0.90	    (app_encode_app(a, $o, sk_Xp(sk_Xx2), sk_Xz) | sk_S = sk_Xp(sk_Xy)),
0.72/0.90	    inference('sup+', [status(thm)], ['266', '0'])).
0.72/0.90	tff('268', plain,
0.72/0.90	    ![X7 : app_encode_fun(a, $o), X8 : app_encode_fun(a, $o)]:
0.72/0.90	      (~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.90	       | ~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.90	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X8)
0.72/0.90	       | ~ app_encode_app(a, $o, X8, sk_Xx2)
0.72/0.90	       | ~ app_encode_app(a, $o, X8, sk_Xz)),
0.72/0.90	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.72/0.90	tff('269', plain,
0.72/0.90	    ![X7 : app_encode_fun(a, $o), X8 : app_encode_fun(a, $o)]:
0.72/0.90	      (~ app_encode_app(a, $o, X8, sk_Xz)
0.72/0.90	       | ~ app_encode_app(a, $o, X8, sk_Xx2)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X8)
0.72/0.90	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.90	       | ~ app_encode_app(a, $o, X7, sk_Xx)),
0.72/0.90	    inference('simplify', [status(thm)], ['268'])).
0.72/0.90	tff('270', plain,
0.72/0.90	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
0.72/0.90	      (~ $true
0.72/0.90	       | ~ app_encode_app(a, $o, X1, sk_Xx)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X1)
0.72/0.90	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.90	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx2)
0.72/0.90	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xz)),
0.72/0.90	    inference('sup-', [status(thm)], ['1', '269'])).
0.72/0.90	tff('271', plain,
0.72/0.90	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
0.72/0.90	      (~ app_encode_app(a, $o, sk_Xp(X0), sk_Xz)
0.72/0.90	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx2)
0.72/0.90	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X1)
0.72/0.90	       | ~ app_encode_app(a, $o, X1, sk_Xx)),
0.72/0.90	    inference('simplify', [status(thm)], ['270'])).
0.72/0.90	tff('272', plain,
0.72/0.90	    ![X0 : app_encode_fun(a, $o)]:
0.72/0.90	      (~ $true
0.72/0.90	       | sk_S = sk_Xp(sk_Xy)
0.72/0.90	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.72/0.90	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.90	       | ~ app_encode_app(a, $o, sk_Xp(sk_Xx2), sk_Xx2)),
0.72/0.90	    inference('sup-', [status(thm)], ['267', '271'])).
0.72/0.90	tff('273', plain,
0.72/0.90	    ![X0 : app_encode_fun(a, $o)]:
0.72/0.90	      (~ $true
0.72/0.90	       | sk_S = sk_Xp(sk_Xy)
0.72/0.90	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.72/0.90	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.90	       | ~ $true),
0.72/0.90	    inference('demod', [status(thm)], ['272', '0'])).
0.72/0.90	tff('274', plain,
0.72/0.90	    ![X0 : app_encode_fun(a, $o)]:
0.72/0.90	      (app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.72/0.90	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.72/0.90	       | sk_S = sk_Xp(sk_Xy)),
0.72/0.90	    inference('simplify', [status(thm)], ['273'])).
0.72/0.90	tff('275', plain,
0.72/0.90	    ![X0 : a]:
0.72/0.90	      (~ $true
0.72/0.90	       | sk_S = sk_Xp(sk_Xy)
0.72/0.90	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.72/0.90	       | app_encode_app(a, $o, sk_S, sk_Xy)),
0.72/0.90	    inference('sup-', [status(thm)], ['1', '274'])).
0.72/0.90	tff('276', plain,
0.72/0.90	    ![X0 : a]:
0.72/0.90	      (app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.90	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.72/0.90	       | sk_S = sk_Xp(sk_Xy)),
0.72/0.90	    inference('simplify', [status(thm)], ['275'])).
0.72/0.90	tff('277', plain,
0.72/0.90	    (~ $true | sk_S = sk_Xp(sk_Xy) | app_encode_app(a, $o, sk_S, sk_Xy)),
0.72/0.90	    inference('sup-', [status(thm)], ['0', '276'])).
0.72/0.90	tff('278', plain, (app_encode_app(a, $o, sk_S, sk_Xy) | sk_S = sk_Xp(sk_Xy)),
0.72/0.90	    inference('simplify', [status(thm)], ['277'])).
0.72/0.90	tff('279', plain,
0.72/0.90	    (~ $true
0.72/0.90	     | sk_S = sk_Xp(sk_Xy)
0.72/0.90	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.72/0.90	     | sk_S = sk_Xp(sk_Xy)),
0.72/0.90	    inference('sup-', [status(thm)], ['278', '35'])).
0.72/0.90	tff('280', plain,
0.72/0.90	    (~ $true | sk_S = sk_Xp(sk_Xy) | ~ $true | sk_S = sk_Xp(sk_Xy)),
0.72/0.90	    inference('demod', [status(thm)], ['279', '161'])).
0.72/0.90	tff('281', plain, sk_S = sk_Xp(sk_Xy),
0.72/0.90	    inference('simplify', [status(thm)], ['280'])).
0.72/0.90	tff('282', plain, app_encode_app(a, $o, sk_S, sk_Xy),
0.72/0.90	    inference('sup+', [status(thm)], ['281', '0'])).
0.72/0.90	tff('283', plain, app_encode_app(a, $o, sk_S, sk_Xx1),
0.72/0.90	    inference('sup+', [status(thm)], ['160', '0'])).
0.72/0.90	tff('284', plain,
0.72/0.90	    ![X0 : app_encode_fun(a, $o)]:
0.72/0.90	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.72/0.90	       | ~ $true
0.72/0.90	       | ~ $true
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.72/0.90	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.72/0.90	       | sk_S2 = sk_Xp(sk_Xz)),
0.72/0.90	    inference('demod', [status(thm)], ['180', '282', '283'])).
0.72/0.90	tff('285', plain,
0.72/0.90	    ![X0 : app_encode_fun(a, $o)]:
0.72/0.90	      (sk_S2 = sk_Xp(sk_Xz)
0.72/0.90	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.72/0.90	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.72/0.90	    inference('simplify', [status(thm)], ['284'])).
0.72/0.90	tff('286', plain,
0.72/0.90	    ![X7 : app_encode_fun(a, $o), X9 : app_encode_fun(a, $o)]:
0.72/0.90	      (~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.90	       | ~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.90	       | ~ app_encode_app(a, $o, X9, sk_Xx1)
0.72/0.90	       | ~ app_encode_app(a, $o, X9, sk_Xy)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X9)
0.72/0.90	       | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.72/0.90	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.72/0.90	tff('287', plain,
0.72/0.90	    ![X7 : app_encode_fun(a, $o), X9 : app_encode_fun(a, $o)]:
0.72/0.90	      (app_encode_app(a, $o, sk_S2, sk_Xz)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X9)
0.72/0.90	       | ~ app_encode_app(a, $o, X9, sk_Xy)
0.72/0.90	       | ~ app_encode_app(a, $o, X9, sk_Xx1)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.90	       | ~ app_encode_app(a, $o, X7, sk_Xx)),
0.72/0.90	    inference('simplify', [status(thm)], ['286'])).
0.72/0.90	tff('288', plain,
0.72/0.90	    ![X0 : app_encode_fun(a, $o)]:
0.72/0.90	      (~ $true
0.72/0.90	       | app_encode_app(a, $o, sk_S2, sk_Xz)
0.72/0.90	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.72/0.90	       | ~ app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.90	       | ~ app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.90	       | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.72/0.90	    inference('sup-', [status(thm)], ['17', '287'])).
0.72/0.90	tff('289', plain,
0.72/0.90	    ![X0 : app_encode_fun(a, $o)]:
0.72/0.90	      (~ app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.90	       | ~ app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.72/0.90	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.72/0.90	       | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.72/0.90	    inference('simplify', [status(thm)], ['288'])).
0.72/0.90	tff('290', plain,
0.72/0.90	    ![X0 : app_encode_fun(a, $o)]:
0.72/0.90	      (~ $true
0.72/0.90	       | ~ $true
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.72/0.90	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.72/0.90	       | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.72/0.90	    inference('demod', [status(thm)], ['289', '282', '283'])).
0.72/0.90	tff('291', plain,
0.72/0.90	    ![X0 : app_encode_fun(a, $o)]:
0.72/0.90	      (app_encode_app(a, $o, sk_S2, sk_Xz)
0.72/0.90	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)),
0.72/0.90	    inference('simplify', [status(thm)], ['290'])).
0.72/0.90	tff('292', plain,
0.72/0.90	    ![X0 : a]:
0.72/0.90	      (~ $true
0.72/0.90	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.72/0.90	       | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.72/0.90	    inference('sup-', [status(thm)], ['1', '291'])).
0.72/0.90	tff('293', plain,
0.72/0.90	    ![X0 : a]:
0.72/0.90	      (app_encode_app(a, $o, sk_S2, sk_Xz)
0.72/0.90	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.72/0.90	    inference('simplify', [status(thm)], ['292'])).
0.72/0.90	tff('294', plain, (~ $true | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.72/0.90	    inference('sup-', [status(thm)], ['0', '293'])).
0.72/0.90	tff('295', plain, app_encode_app(a, $o, sk_S2, sk_Xz),
0.72/0.90	    inference('simplify', [status(thm)], ['294'])).
0.72/0.90	tff('296', plain,
0.72/0.90	    (~ $true
0.72/0.90	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.72/0.90	     | sk_S2 = sk_Xp(sk_Xz)),
0.72/0.90	    inference('sup-', [status(thm)], ['295', '35'])).
0.72/0.90	tff('297', plain,
0.72/0.90	    (sk_S2 = sk_Xp(sk_Xz)
0.72/0.90	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.72/0.90	    inference('simplify', [status(thm)], ['296'])).
0.72/0.90	tff('298', plain,
0.72/0.90	    ![X0 : app_encode_fun(a, $o)]:
0.72/0.90	      (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.72/0.90	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.72/0.90	       | sk_S2 = sk_Xp(sk_Xz)),
0.72/0.90	    inference('clc', [status(thm)], ['285', '297'])).
0.72/0.90	tff('299', plain,
0.72/0.90	    ![X0 : a]:
0.72/0.90	      (~ $true
0.72/0.90	       | sk_S2 = sk_Xp(sk_Xz)
0.72/0.90	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.72/0.90	    inference('sup-', [status(thm)], ['1', '298'])).
0.72/0.90	tff('300', plain,
0.72/0.90	    ![X0 : a]:
0.72/0.90	      (~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx) | sk_S2 = sk_Xp(sk_Xz)),
0.72/0.90	    inference('simplify', [status(thm)], ['299'])).
0.72/0.90	tff('301', plain, (~ $true | sk_S2 = sk_Xp(sk_Xz)),
0.72/0.90	    inference('sup-', [status(thm)], ['0', '300'])).
0.72/0.90	tff('302', plain, sk_S2 = sk_Xp(sk_Xz),
0.72/0.90	    inference('simplify', [status(thm)], ['301'])).
0.72/0.90	tff('303', plain, sk_Xp(sk_Xz) = sk_Xp(sk_Xz1(sk_S2)),
0.72/0.90	    inference('sup+', [status(thm)], ['302', '106'])).
0.72/0.90	tff('304', plain, sk_S2 = sk_Xp(sk_Xz1(sk_S2)),
0.72/0.90	    inference('demod', [status(thm)], ['303', '302'])).
0.72/0.90	tff('305', plain,
0.72/0.90	    ![X7 : app_encode_fun(a, $o), X9 : app_encode_fun(a, $o)]:
0.72/0.90	      (~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.90	       | ~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.90	       | ~ app_encode_app(a, $o, X9, sk_Xx1)
0.72/0.90	       | ~ app_encode_app(a, $o, X9, sk_Xy)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X9)
0.72/0.90	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.72/0.90	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.72/0.90	tff('306', plain,
0.72/0.90	    ![X7 : app_encode_fun(a, $o), X9 : app_encode_fun(a, $o)]:
0.72/0.90	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X9)
0.72/0.90	       | ~ app_encode_app(a, $o, X9, sk_Xy)
0.72/0.90	       | ~ app_encode_app(a, $o, X9, sk_Xx1)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.90	       | ~ app_encode_app(a, $o, X7, sk_Xx)),
0.72/0.90	    inference('simplify', [status(thm)], ['305'])).
0.72/0.90	tff('307', plain,
0.72/0.90	    ![X0 : app_encode_fun(a, $o)]:
0.72/0.90	      (~ $true
0.72/0.90	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.72/0.90	       | ~ app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.90	       | ~ app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.90	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.72/0.90	    inference('sup-', [status(thm)], ['161', '306'])).
0.72/0.90	tff('308', plain,
0.72/0.90	    ![X0 : app_encode_fun(a, $o)]:
0.72/0.90	      (~ $true
0.72/0.90	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.72/0.90	       | ~ $true
0.72/0.90	       | ~ app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.90	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.72/0.90	    inference('demod', [status(thm)], ['307', '283'])).
0.72/0.90	tff('309', plain,
0.72/0.90	    ![X0 : app_encode_fun(a, $o)]:
0.72/0.90	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.72/0.90	       | ~ app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.72/0.90	       | ~ app_encode_app(a, $o, X0, sk_Xx)),
0.72/0.90	    inference('simplify', [status(thm)], ['308'])).
0.72/0.90	tff('310', plain,
0.72/0.90	    ![X0 : app_encode_fun(a, $o)]:
0.72/0.90	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.72/0.90	       | ~ $true
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.72/0.90	       | ~ app_encode_app(a, $o, X0, sk_Xx)),
0.72/0.90	    inference('demod', [status(thm)], ['309', '282'])).
0.72/0.90	tff('311', plain,
0.72/0.90	    ![X0 : app_encode_fun(a, $o)]:
0.72/0.90	      (~ app_encode_app(a, $o, X0, sk_Xx)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.72/0.90	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.72/0.90	    inference('simplify', [status(thm)], ['310'])).
0.72/0.90	tff('312', plain,
0.72/0.90	    ![X0 : a]:
0.72/0.90	      (~ $true
0.72/0.90	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.72/0.90	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.72/0.90	    inference('sup-', [status(thm)], ['1', '311'])).
0.72/0.90	tff('313', plain,
0.72/0.90	    ![X0 : a]:
0.72/0.90	      (~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.72/0.90	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.72/0.90	    inference('simplify', [status(thm)], ['312'])).
0.72/0.90	tff('314', plain,
0.72/0.90	    (~ $true | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.72/0.90	    inference('sup-', [status(thm)], ['0', '313'])).
0.72/0.90	tff('315', plain, app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1),
0.72/0.90	    inference('simplify', [status(thm)], ['314'])).
0.72/0.90	tff('316', plain,
0.72/0.90	    ![X7 : app_encode_fun(a, $o), X9 : app_encode_fun(a, $o)]:
0.72/0.90	      (~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.90	       | ~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.90	       | ~ app_encode_app(a, $o, X9, sk_Xx1)
0.72/0.90	       | ~ app_encode_app(a, $o, X9, sk_Xy)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X9)
0.72/0.90	       | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.72/0.90	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.72/0.90	tff('317', plain,
0.72/0.90	    ![X7 : app_encode_fun(a, $o), X9 : app_encode_fun(a, $o)]:
0.72/0.90	      (app_encode_app(a, $o, sk_S1, sk_Xy1)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X9)
0.72/0.90	       | ~ app_encode_app(a, $o, X9, sk_Xy)
0.72/0.90	       | ~ app_encode_app(a, $o, X9, sk_Xx1)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.90	       | ~ app_encode_app(a, $o, X7, sk_Xx)),
0.72/0.90	    inference('simplify', [status(thm)], ['316'])).
0.72/0.90	tff('318', plain,
0.72/0.90	    ![X0 : app_encode_fun(a, $o)]:
0.72/0.90	      (~ $true
0.72/0.90	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.72/0.90	       | ~ app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.90	       | ~ app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.90	       | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.72/0.90	    inference('sup-', [status(thm)], ['161', '317'])).
0.72/0.90	tff('319', plain,
0.72/0.90	    ![X0 : app_encode_fun(a, $o)]:
0.72/0.90	      (~ $true
0.72/0.90	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.72/0.90	       | ~ $true
0.72/0.90	       | ~ app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.90	       | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.72/0.90	    inference('demod', [status(thm)], ['318', '283'])).
0.72/0.90	tff('320', plain,
0.72/0.90	    ![X0 : app_encode_fun(a, $o)]:
0.72/0.90	      (app_encode_app(a, $o, sk_S1, sk_Xy1)
0.72/0.90	       | ~ app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.72/0.90	       | ~ app_encode_app(a, $o, X0, sk_Xx)),
0.72/0.90	    inference('simplify', [status(thm)], ['319'])).
0.72/0.90	tff('321', plain,
0.72/0.90	    ![X0 : app_encode_fun(a, $o)]:
0.72/0.90	      (app_encode_app(a, $o, sk_S1, sk_Xy1)
0.72/0.90	       | ~ $true
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.72/0.90	       | ~ app_encode_app(a, $o, X0, sk_Xx)),
0.72/0.90	    inference('demod', [status(thm)], ['320', '282'])).
0.72/0.90	tff('322', plain,
0.72/0.90	    ![X0 : app_encode_fun(a, $o)]:
0.72/0.90	      (~ app_encode_app(a, $o, X0, sk_Xx)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.72/0.90	       | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.72/0.90	    inference('simplify', [status(thm)], ['321'])).
0.72/0.90	tff('323', plain,
0.72/0.90	    ![X0 : a]:
0.72/0.90	      (~ $true
0.72/0.90	       | app_encode_app(a, $o, sk_S1, sk_Xy1)
0.72/0.90	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.72/0.90	    inference('sup-', [status(thm)], ['1', '322'])).
0.72/0.90	tff('324', plain,
0.72/0.90	    ![X0 : a]:
0.72/0.90	      (~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.72/0.90	       | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.72/0.90	    inference('simplify', [status(thm)], ['323'])).
0.72/0.90	tff('325', plain, (~ $true | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.72/0.90	    inference('sup-', [status(thm)], ['0', '324'])).
0.72/0.90	tff('326', plain, app_encode_app(a, $o, sk_S1, sk_Xy1),
0.72/0.90	    inference('simplify', [status(thm)], ['325'])).
0.72/0.90	tff('327', plain,
0.72/0.90	    (~ $true
0.72/0.90	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.72/0.90	     | sk_S1 = sk_Xp(sk_Xy1)),
0.72/0.90	    inference('sup-', [status(thm)], ['326', '35'])).
0.72/0.90	tff('328', plain,
0.72/0.90	    (sk_S1 = sk_Xp(sk_Xy1)
0.72/0.90	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.72/0.90	    inference('simplify', [status(thm)], ['327'])).
0.72/0.90	tff('329', plain, app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2),
0.72/0.90	    inference('sup+', [status(thm)], ['302', '1'])).
0.72/0.90	tff('330', plain,
0.72/0.90	    ![X7 : app_encode_fun(a, $o), X9 : app_encode_fun(a, $o)]:
0.72/0.90	      (~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.90	       | ~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.90	       | ~ app_encode_app(a, $o, X9, sk_Xx1)
0.72/0.90	       | ~ app_encode_app(a, $o, X9, sk_Xy)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X9)
0.72/0.90	       | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.72/0.90	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.72/0.90	tff('331', plain,
0.72/0.90	    ![X7 : app_encode_fun(a, $o), X9 : app_encode_fun(a, $o)]:
0.72/0.90	      (app_encode_app(a, $o, sk_S2, sk_Xy1)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X9)
0.72/0.90	       | ~ app_encode_app(a, $o, X9, sk_Xy)
0.72/0.90	       | ~ app_encode_app(a, $o, X9, sk_Xx1)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.90	       | ~ app_encode_app(a, $o, X7, sk_Xx)),
0.72/0.90	    inference('simplify', [status(thm)], ['330'])).
0.72/0.90	tff('332', plain,
0.72/0.90	    ![X0 : app_encode_fun(a, $o)]:
0.72/0.90	      (~ $true
0.72/0.90	       | app_encode_app(a, $o, sk_S2, sk_Xy1)
0.72/0.90	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.72/0.90	       | ~ app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.90	       | ~ app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.90	       | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.72/0.90	    inference('sup-', [status(thm)], ['47', '331'])).
0.72/0.90	tff('333', plain,
0.72/0.90	    ![X0 : app_encode_fun(a, $o)]:
0.72/0.90	      (~ app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.90	       | ~ app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.72/0.90	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.72/0.90	       | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.72/0.90	    inference('simplify', [status(thm)], ['332'])).
0.72/0.90	tff('334', plain,
0.72/0.90	    ![X0 : app_encode_fun(a, $o)]:
0.72/0.90	      (~ $true
0.72/0.90	       | ~ $true
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.72/0.90	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.72/0.90	       | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.72/0.90	    inference('demod', [status(thm)], ['333', '282', '283'])).
0.72/0.90	tff('335', plain,
0.72/0.90	    ![X0 : app_encode_fun(a, $o)]:
0.72/0.90	      (app_encode_app(a, $o, sk_S2, sk_Xy1)
0.72/0.90	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)),
0.72/0.90	    inference('simplify', [status(thm)], ['334'])).
0.72/0.90	tff('336', plain,
0.72/0.90	    ![X0 : a]:
0.72/0.90	      (~ $true
0.72/0.90	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.72/0.90	       | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.72/0.90	    inference('sup-', [status(thm)], ['1', '335'])).
0.72/0.90	tff('337', plain,
0.72/0.90	    ![X0 : a]:
0.72/0.90	      (app_encode_app(a, $o, sk_S2, sk_Xy1)
0.72/0.90	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.72/0.90	    inference('simplify', [status(thm)], ['336'])).
0.72/0.90	tff('338', plain, (~ $true | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.72/0.90	    inference('sup-', [status(thm)], ['0', '337'])).
0.72/0.90	tff('339', plain, app_encode_app(a, $o, sk_S2, sk_Xy1),
0.72/0.90	    inference('simplify', [status(thm)], ['338'])).
0.72/0.90	tff('340', plain,
0.72/0.90	    (~ $true
0.72/0.90	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.72/0.90	     | sk_S2 = sk_Xp(sk_Xy1)),
0.72/0.90	    inference('sup-', [status(thm)], ['339', '35'])).
0.72/0.90	tff('341', plain,
0.72/0.90	    (sk_S2 = sk_Xp(sk_Xy1)
0.72/0.90	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.72/0.90	    inference('simplify', [status(thm)], ['340'])).
0.72/0.90	tff('342', plain, (~ $true | sk_S2 = sk_Xp(sk_Xy1)),
0.72/0.90	    inference('sup-', [status(thm)], ['329', '341'])).
0.72/0.90	tff('343', plain, sk_S2 = sk_Xp(sk_Xy1),
0.72/0.90	    inference('simplify', [status(thm)], ['342'])).
0.72/0.90	tff('344', plain,
0.72/0.90	    (sk_S1 = sk_S2 | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.72/0.90	    inference('demod', [status(thm)], ['328', '343'])).
0.72/0.90	tff('345', plain, (~ $true | sk_S1 = sk_S2),
0.72/0.90	    inference('sup-', [status(thm)], ['315', '344'])).
0.72/0.90	tff('346', plain, sk_S1 = sk_S2,
0.72/0.90	    inference('simplify', [status(thm)], ['345'])).
0.72/0.90	tff('347', plain, sk_S1 = sk_Xp(sk_Xz1(sk_S1)),
0.72/0.90	    inference('demod', [status(thm)], ['304', '346', '346'])).
0.72/0.90	tff('348', plain,
0.72/0.90	    ![X7 : app_encode_fun(a, $o), X8 : app_encode_fun(a, $o), 
0.72/0.90	      X9 : app_encode_fun(a, $o)]:
0.72/0.90	      (~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.90	       | ~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.90	       | ~ app_encode_app(a, $o, X9, sk_Xx1)
0.72/0.90	       | ~ app_encode_app(a, $o, X9, sk_Xy)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X9)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X8)
0.72/0.90	       | ~ app_encode_app(a, $o, X8, sk_Xx2)
0.72/0.90	       | ~ app_encode_app(a, $o, X8, sk_Xz)),
0.72/0.90	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.72/0.90	tff('349', plain,
0.72/0.90	    ![X7 : app_encode_fun(a, $o), X8 : app_encode_fun(a, $o), 
0.72/0.90	      X9 : app_encode_fun(a, $o)]:
0.72/0.90	      (~ app_encode_app(a, $o, X8, sk_Xz)
0.72/0.90	       | ~ app_encode_app(a, $o, X8, sk_Xx2)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X8)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X9)
0.72/0.90	       | ~ app_encode_app(a, $o, X9, sk_Xy)
0.72/0.90	       | ~ app_encode_app(a, $o, X9, sk_Xx1)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.90	       | ~ app_encode_app(a, $o, X7, sk_Xx)),
0.72/0.90	    inference('simplify', [status(thm)], ['348'])).
0.72/0.90	tff('350', plain,
0.72/0.90	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o)]:
0.72/0.90	      (~ $true
0.72/0.90	       | ~ app_encode_app(a, $o, X1, sk_Xx)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X1)
0.72/0.90	       | ~ app_encode_app(a, $o, X2, sk_Xx1)
0.72/0.90	       | ~ app_encode_app(a, $o, X2, sk_Xy)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.72/0.90	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx2)
0.72/0.90	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xz)),
0.72/0.90	    inference('sup-', [status(thm)], ['1', '349'])).
0.72/0.90	tff('351', plain,
0.72/0.90	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o)]:
0.72/0.90	      (~ app_encode_app(a, $o, sk_Xp(X0), sk_Xz)
0.72/0.90	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx2)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X2)
0.72/0.90	       | ~ app_encode_app(a, $o, X2, sk_Xy)
0.72/0.90	       | ~ app_encode_app(a, $o, X2, sk_Xx1)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X1)
0.72/0.90	       | ~ app_encode_app(a, $o, X1, sk_Xx)),
0.72/0.90	    inference('simplify', [status(thm)], ['350'])).
0.72/0.90	tff('352', plain,
0.72/0.90	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.72/0.90	      (~ app_encode_app(a, $o, sk_S1, sk_Xz)
0.72/0.90	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.72/0.90	       | ~ app_encode_app(a, $o, X1, sk_Xx1)
0.72/0.90	       | ~ app_encode_app(a, $o, X1, sk_Xy)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X1)
0.72/0.90	       | ~ app_encode_app(a, $o, sk_Xp(sk_Xz1(sk_S1)), sk_Xx2)),
0.72/0.90	    inference('sup-', [status(thm)], ['347', '351'])).
0.72/0.90	tff('353', plain, app_encode_app(a, $o, sk_S1, sk_Xz),
0.72/0.90	    inference('demod', [status(thm)], ['295', '346'])).
0.72/0.90	tff('354', plain,
0.72/0.90	    ![X7 : app_encode_fun(a, $o), X9 : app_encode_fun(a, $o)]:
0.72/0.90	      (~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.90	       | ~ app_encode_app(a, $o, X7, sk_Xx)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.90	       | ~ app_encode_app(a, $o, X9, sk_Xx1)
0.72/0.90	       | ~ app_encode_app(a, $o, X9, sk_Xy)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X9)
0.72/0.90	       | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.72/0.90	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.72/0.90	tff('355', plain,
0.72/0.90	    ![X7 : app_encode_fun(a, $o), X9 : app_encode_fun(a, $o)]:
0.72/0.90	      (app_encode_app(a, $o, sk_S1, sk_Xx2)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X9)
0.72/0.90	       | ~ app_encode_app(a, $o, X9, sk_Xy)
0.72/0.90	       | ~ app_encode_app(a, $o, X9, sk_Xx1)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.72/0.90	       | ~ app_encode_app(a, $o, X7, sk_Xx)),
0.72/0.90	    inference('simplify', [status(thm)], ['354'])).
0.72/0.90	tff('356', plain,
0.72/0.90	    ![X0 : app_encode_fun(a, $o)]:
0.72/0.90	      (~ $true
0.72/0.90	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.72/0.90	       | ~ app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.90	       | ~ app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.90	       | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.72/0.90	    inference('sup-', [status(thm)], ['161', '355'])).
0.72/0.90	tff('357', plain,
0.72/0.90	    ![X0 : app_encode_fun(a, $o)]:
0.72/0.90	      (~ $true
0.72/0.90	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.72/0.90	       | ~ $true
0.72/0.90	       | ~ app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.90	       | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.72/0.90	    inference('demod', [status(thm)], ['356', '283'])).
0.72/0.90	tff('358', plain,
0.72/0.90	    ![X0 : app_encode_fun(a, $o)]:
0.72/0.90	      (app_encode_app(a, $o, sk_S1, sk_Xx2)
0.72/0.90	       | ~ app_encode_app(a, $o, sk_S, sk_Xy)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.72/0.90	       | ~ app_encode_app(a, $o, X0, sk_Xx)),
0.72/0.90	    inference('simplify', [status(thm)], ['357'])).
0.72/0.90	tff('359', plain,
0.72/0.90	    ![X0 : app_encode_fun(a, $o)]:
0.72/0.90	      (app_encode_app(a, $o, sk_S1, sk_Xx2)
0.72/0.90	       | ~ $true
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.72/0.90	       | ~ app_encode_app(a, $o, X0, sk_Xx)),
0.72/0.90	    inference('demod', [status(thm)], ['358', '282'])).
0.72/0.90	tff('360', plain,
0.72/0.90	    ![X0 : app_encode_fun(a, $o)]:
0.72/0.90	      (~ app_encode_app(a, $o, X0, sk_Xx)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.72/0.90	       | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.72/0.90	    inference('simplify', [status(thm)], ['359'])).
0.72/0.90	tff('361', plain,
0.72/0.90	    ![X0 : a]:
0.72/0.90	      (~ $true
0.72/0.90	       | app_encode_app(a, $o, sk_S1, sk_Xx2)
0.72/0.90	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.72/0.90	    inference('sup-', [status(thm)], ['1', '360'])).
0.72/0.90	tff('362', plain,
0.72/0.90	    ![X0 : a]:
0.72/0.90	      (~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.72/0.90	       | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.72/0.90	    inference('simplify', [status(thm)], ['361'])).
0.72/0.90	tff('363', plain, (~ $true | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.72/0.90	    inference('sup-', [status(thm)], ['0', '362'])).
0.72/0.90	tff('364', plain, app_encode_app(a, $o, sk_S1, sk_Xx2),
0.72/0.90	    inference('simplify', [status(thm)], ['363'])).
0.72/0.90	tff('365', plain,
0.72/0.90	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.72/0.90	      (~ $true
0.72/0.90	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.72/0.90	       | ~ app_encode_app(a, $o, X1, sk_Xx1)
0.72/0.90	       | ~ app_encode_app(a, $o, X1, sk_Xy)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X1)
0.72/0.90	       | ~ $true),
0.72/0.90	    inference('demod', [status(thm)], ['352', '353', '347', '364'])).
0.72/0.90	tff('366', plain,
0.72/0.90	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.72/0.90	      (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X1)
0.72/0.90	       | ~ app_encode_app(a, $o, X1, sk_Xy)
0.72/0.90	       | ~ app_encode_app(a, $o, X1, sk_Xx1)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.72/0.90	       | ~ app_encode_app(a, $o, X0, sk_Xx)),
0.72/0.90	    inference('simplify', [status(thm)], ['365'])).
0.72/0.90	tff('367', plain,
0.72/0.90	    ![X0 : app_encode_fun(a, $o)]:
0.72/0.90	      (~ $true
0.72/0.90	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.72/0.90	       | ~ app_encode_app(a, $o, sk_S, sk_Xx1)
0.72/0.90	       | ~ app_encode_app(a, $o, sk_S, sk_Xy)),
0.72/0.90	    inference('sup-', [status(thm)], ['161', '366'])).
0.72/0.90	tff('368', plain,
0.72/0.90	    ![X0 : app_encode_fun(a, $o)]:
0.72/0.90	      (~ $true
0.72/0.90	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.72/0.90	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.72/0.90	       | ~ $true
0.72/0.90	       | ~ $true),
0.72/0.90	    inference('demod', [status(thm)], ['367', '283', '282'])).
0.72/0.90	tff('369', plain,
0.72/0.90	    ![X0 : app_encode_fun(a, $o)]:
0.72/0.90	      (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.72/0.90	       | ~ app_encode_app(a, $o, X0, sk_Xx)),
0.72/0.90	    inference('simplify', [status(thm)], ['368'])).
0.72/0.90	tff('370', plain,
0.72/0.90	    ![X0 : a]: (~ $true | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.72/0.90	    inference('sup-', [status(thm)], ['1', '369'])).
0.72/0.90	tff('371', plain, ![X0 : a]: ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx),
0.72/0.90	    inference('simplify', [status(thm)], ['370'])).
0.72/0.90	tff('372', plain, ~ $true, inference('sup-', [status(thm)], ['0', '371'])).
0.72/0.90	tff('373', plain, $false, inference('simplify', [status(thm)], ['372'])).
0.72/0.90	
0.72/0.90	% SZS output end Refutation
0.72/0.90	EOF
