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    : rpo6
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 $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.20	% Computer   : n132.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 17:30:08 CST 2018
0.00/0.34	% done 499 iterations in 0.142s
0.00/0.34	% SZS status Theorem for 'stdin'
0.00/0.34	% SZS output start Refutation
0.00/0.35	tff(zf_stmt_4, conjecture,
0.00/0.35	  (![P:app_encode_fun(app_encode_fun(a,$o),$o)]:
0.00/0.35	     ((![Xx:a]:
0.00/0.35	         (?[Xp:app_encode_fun(a,$o)]:
0.00/0.35	            (app_encode_app(app_encode_fun(a,$o),$o,P,Xp) & 
0.00/0.35	             app_encode_app(a,$o,Xp,Xx) & 
0.00/0.35	             (![Xq:app_encode_fun(a,$o)]:
0.00/0.35	                ((app_encode_app(app_encode_fun(a,$o),$o,P,Xq) & 
0.00/0.35	                  app_encode_app(a,$o,Xq,Xx)) =>
0.00/0.35	                 (Xq = Xp)))))) =>
0.00/0.35	      ((![Xx:a]:
0.00/0.35	          (?[S:app_encode_fun(a,$o)]:
0.00/0.35	             (app_encode_app(app_encode_fun(a,$o),$o,P,S) & 
0.00/0.35	              app_encode_app(a,$o,S,Xx) & app_encode_app(a,$o,S,Xx)))) & 
0.00/0.35	       (![Xx:a,Xy:a]:
0.00/0.35	          ((?[S:app_encode_fun(a,$o)]:
0.00/0.35	              (app_encode_app(app_encode_fun(a,$o),$o,P,S) & 
0.00/0.35	               app_encode_app(a,$o,S,Xx) & app_encode_app(a,$o,S,Xy))) =>
0.00/0.35	           (?[S:app_encode_fun(a,$o)]:
0.00/0.35	              (app_encode_app(app_encode_fun(a,$o),$o,P,S) & 
0.00/0.35	               app_encode_app(a,$o,S,Xy) & app_encode_app(a,$o,S,Xx))))) & 
0.00/0.35	       (![Xx:a,Xy:a,Xz:a]:
0.00/0.35	          (((?[S:app_encode_fun(a,$o)]:
0.00/0.35	               (app_encode_app(app_encode_fun(a,$o),$o,P,S) & 
0.00/0.35	                app_encode_app(a,$o,S,Xx) & app_encode_app(a,$o,S,Xy))) & 
0.00/0.35	            (?[S:app_encode_fun(a,$o)]:
0.00/0.35	               (app_encode_app(app_encode_fun(a,$o),$o,P,S) & 
0.00/0.35	                app_encode_app(a,$o,S,Xy) & app_encode_app(a,$o,S,Xz)))) =>
0.00/0.35	           (?[S:app_encode_fun(a,$o)]:
0.00/0.35	              (app_encode_app(app_encode_fun(a,$o),$o,P,S) & 
0.00/0.35	               app_encode_app(a,$o,S,Xx) & app_encode_app(a,$o,S,Xz))))))))).
0.00/0.35	tff(zf_stmt_0, negated_conjecture,
0.00/0.35	  (~
0.00/0.35	    (![P:app_encode_fun(app_encode_fun(a,$o),$o)]:
0.00/0.35	       ((![Xx:a]:
0.00/0.35	           (?[Xp:app_encode_fun(a,$o)]:
0.00/0.35	              (app_encode_app(app_encode_fun(a,$o),$o,P,Xp) & 
0.00/0.35	               app_encode_app(a,$o,Xp,Xx) & 
0.00/0.35	               (![Xq:app_encode_fun(a,$o)]:
0.00/0.35	                  ((app_encode_app(app_encode_fun(a,$o),$o,P,Xq) & 
0.00/0.35	                    app_encode_app(a,$o,Xq,Xx)) =>
0.00/0.35	                   (Xq = Xp)))))) =>
0.00/0.35	        ((![Xx:a]:
0.00/0.35	            (?[S:app_encode_fun(a,$o)]:
0.00/0.35	               (app_encode_app(app_encode_fun(a,$o),$o,P,S) & 
0.00/0.35	                app_encode_app(a,$o,S,Xx) & app_encode_app(a,$o,S,Xx)))) & 
0.00/0.35	         (![Xx:a,Xy:a]:
0.00/0.35	            ((?[S:app_encode_fun(a,$o)]:
0.00/0.35	                (app_encode_app(app_encode_fun(a,$o),$o,P,S) & 
0.00/0.35	                 app_encode_app(a,$o,S,Xx) & app_encode_app(a,$o,S,Xy))) =>
0.00/0.35	             (?[S:app_encode_fun(a,$o)]:
0.00/0.35	                (app_encode_app(app_encode_fun(a,$o),$o,P,S) & 
0.00/0.35	                 app_encode_app(a,$o,S,Xy) & app_encode_app(a,$o,S,Xx))))) & 
0.00/0.35	         (![Xx:a,Xy:a,Xz:a]:
0.00/0.35	            (((?[S:app_encode_fun(a,$o)]:
0.00/0.35	                 (app_encode_app(app_encode_fun(a,$o),$o,P,S) & 
0.00/0.35	                  app_encode_app(a,$o,S,Xx) & app_encode_app(a,$o,S,Xy))) & 
0.00/0.35	              (?[S:app_encode_fun(a,$o)]:
0.00/0.35	                 (app_encode_app(app_encode_fun(a,$o),$o,P,S) & 
0.00/0.35	                  app_encode_app(a,$o,S,Xy) & app_encode_app(a,$o,S,Xz)))) =>
0.00/0.35	             (?[S:app_encode_fun(a,$o)]:
0.00/0.35	                (app_encode_app(app_encode_fun(a,$o),$o,P,S) & 
0.00/0.35	                 app_encode_app(a,$o,S,Xx) & app_encode_app(a,$o,S,Xz)))))))))).
0.00/0.35	tff('0', plain, ![X4 : a]: app_encode_app(a, $o, sk_Xp(X4), X4),
0.00/0.35	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.35	tff('1', plain,
0.00/0.35	    ![X4 : a]: app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_Xp(X4)),
0.00/0.35	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.35	tff('2', plain,
0.00/0.35	    ![X6 : app_encode_fun(a, $o)]:
0.00/0.35	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.35	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.35	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.35	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.00/0.35	       | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.00/0.35	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.35	tff('3', plain,
0.00/0.35	    ![X6 : app_encode_fun(a, $o)]:
0.00/0.35	      (app_encode_app(a, $o, sk_S2, sk_Xy1)
0.00/0.35	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.00/0.35	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.35	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.00/0.35	    inference('simplify', [status(thm)], ['2'])).
0.00/0.35	tff('4', plain,
0.00/0.35	    ![X0 : a]:
0.00/0.35	      (~ $true
0.00/0.35	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.00/0.35	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.00/0.35	       | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.00/0.35	    inference('sup-', [status(thm)], ['1', '3'])).
0.00/0.35	tff('5', plain,
0.00/0.35	    ![X0 : a]:
0.00/0.35	      (app_encode_app(a, $o, sk_S2, sk_Xy1)
0.00/0.35	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.00/0.35	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.00/0.35	    inference('simplify', [status(thm)], ['4'])).
0.00/0.35	tff('6', plain,
0.00/0.35	    (~ $true
0.00/0.35	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.00/0.35	     | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.00/0.35	    inference('sup-', [status(thm)], ['0', '5'])).
0.00/0.35	tff('7', plain,
0.00/0.35	    (app_encode_app(a, $o, sk_S2, sk_Xy1)
0.00/0.35	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.00/0.35	    inference('simplify', [status(thm)], ['6'])).
0.00/0.35	tff('8', plain,
0.00/0.35	    ![X4 : a, X5 : app_encode_fun(a, $o)]:
0.00/0.35	      (X5 = sk_Xp(X4)
0.00/0.35	       | ~ app_encode_app(a, $o, X5, X4)
0.00/0.35	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X5)),
0.00/0.35	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.35	tff('9', plain,
0.00/0.35	    (~ $true
0.00/0.35	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.00/0.35	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.00/0.35	     | sk_S2 = sk_Xp(sk_Xy1)),
0.00/0.35	    inference('sup-', [status(thm)], ['7', '8'])).
0.00/0.35	tff('10', plain,
0.00/0.35	    (sk_S2 = sk_Xp(sk_Xy1)
0.00/0.35	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.00/0.35	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.00/0.35	    inference('simplify', [status(thm)], ['9'])).
0.00/0.35	tff('11', plain,
0.00/0.35	    ![X6 : app_encode_fun(a, $o)]:
0.00/0.35	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.35	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.35	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.35	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.00/0.35	       | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.00/0.35	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.35	tff('12', plain,
0.00/0.35	    ![X6 : app_encode_fun(a, $o)]:
0.00/0.35	      (app_encode_app(a, $o, sk_S1, sk_Xy1)
0.00/0.35	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.00/0.35	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.35	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.00/0.35	    inference('simplify', [status(thm)], ['11'])).
0.00/0.35	tff('13', plain,
0.00/0.35	    ![X0 : a]:
0.00/0.35	      (~ $true
0.00/0.35	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.00/0.35	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.00/0.35	       | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.00/0.35	    inference('sup-', [status(thm)], ['1', '12'])).
0.00/0.35	tff('14', plain,
0.00/0.35	    ![X0 : a]:
0.00/0.35	      (app_encode_app(a, $o, sk_S1, sk_Xy1)
0.00/0.35	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.00/0.35	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.00/0.35	    inference('simplify', [status(thm)], ['13'])).
0.00/0.35	tff('15', plain,
0.00/0.35	    (~ $true
0.00/0.35	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.00/0.35	     | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.00/0.35	    inference('sup-', [status(thm)], ['0', '14'])).
0.00/0.35	tff('16', plain,
0.00/0.35	    (app_encode_app(a, $o, sk_S1, sk_Xy1)
0.00/0.35	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.00/0.35	    inference('simplify', [status(thm)], ['15'])).
0.00/0.35	tff('17', plain,
0.00/0.35	    (~ $true
0.00/0.35	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.00/0.35	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.00/0.35	     | sk_S1 = sk_Xp(sk_Xy1)),
0.00/0.35	    inference('sup-', [status(thm)], ['16', '8'])).
0.00/0.35	tff('18', plain,
0.00/0.35	    (sk_S1 = sk_Xp(sk_Xy1)
0.00/0.35	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.00/0.35	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.00/0.35	    inference('simplify', [status(thm)], ['17'])).
0.00/0.35	tff('19', plain,
0.00/0.35	    ![X6 : app_encode_fun(a, $o)]:
0.00/0.35	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.35	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.35	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.35	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.00/0.35	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.00/0.35	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.35	tff('20', plain,
0.00/0.35	    ![X6 : app_encode_fun(a, $o)]:
0.00/0.35	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.00/0.35	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.00/0.35	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.35	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.00/0.35	    inference('simplify', [status(thm)], ['19'])).
0.00/0.35	tff('21', plain,
0.00/0.35	    ![X0 : a]:
0.00/0.35	      (~ $true
0.00/0.35	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.00/0.35	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.00/0.35	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.00/0.35	    inference('sup-', [status(thm)], ['1', '20'])).
0.00/0.35	tff('22', plain,
0.00/0.35	    ![X0 : a]:
0.00/0.35	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.00/0.35	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.00/0.35	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.00/0.35	    inference('simplify', [status(thm)], ['21'])).
0.00/0.35	tff('23', plain,
0.00/0.35	    (~ $true
0.00/0.35	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.00/0.35	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.00/0.35	    inference('sup-', [status(thm)], ['0', '22'])).
0.00/0.35	tff('24', plain,
0.00/0.35	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.00/0.35	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.00/0.35	    inference('simplify', [status(thm)], ['23'])).
0.00/0.35	tff('25', plain,
0.00/0.35	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.00/0.35	     | sk_S1 = sk_Xp(sk_Xy1)),
0.00/0.35	    inference('clc', [status(thm)], ['18', '24'])).
0.00/0.35	tff('26', plain,
0.00/0.35	    (sk_S1 = sk_S2
0.00/0.35	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.00/0.35	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.00/0.35	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.00/0.35	    inference('sup+', [status(thm)], ['10', '25'])).
0.00/0.35	tff('27', plain,
0.00/0.35	    (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.00/0.35	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.00/0.35	     | sk_S1 = sk_S2),
0.00/0.35	    inference('simplify', [status(thm)], ['26'])).
0.00/0.35	tff('28', plain,
0.00/0.35	    ![X6 : app_encode_fun(a, $o)]:
0.00/0.35	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.35	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.35	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.35	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.00/0.35	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.00/0.35	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.35	tff('29', plain,
0.00/0.35	    ![X6 : app_encode_fun(a, $o)]:
0.00/0.35	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.00/0.35	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.00/0.35	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.35	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.00/0.35	    inference('simplify', [status(thm)], ['28'])).
0.00/0.35	tff('30', plain,
0.00/0.35	    ![X0 : a]:
0.00/0.35	      (~ $true
0.00/0.35	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.00/0.35	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.00/0.35	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.00/0.35	    inference('sup-', [status(thm)], ['1', '29'])).
0.00/0.35	tff('31', plain,
0.00/0.35	    ![X0 : a]:
0.00/0.35	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.00/0.35	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.00/0.35	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.00/0.35	    inference('simplify', [status(thm)], ['30'])).
0.00/0.35	tff('32', plain,
0.00/0.35	    (~ $true
0.00/0.35	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.00/0.35	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.00/0.35	    inference('sup-', [status(thm)], ['0', '31'])).
0.00/0.35	tff('33', plain,
0.00/0.35	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.00/0.35	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.00/0.35	    inference('simplify', [status(thm)], ['32'])).
0.00/0.35	tff('34', plain,
0.00/0.35	    (sk_S1 = sk_S2 | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.00/0.35	    inference('clc', [status(thm)], ['27', '33'])).
0.00/0.35	tff('35', plain,
0.00/0.35	    ![X6 : app_encode_fun(a, $o)]:
0.00/0.35	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.35	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.35	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.35	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.00/0.35	       | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.00/0.35	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.35	tff('36', plain,
0.00/0.35	    ![X6 : app_encode_fun(a, $o)]:
0.00/0.35	      (app_encode_app(a, $o, sk_S2, sk_Xz)
0.00/0.35	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.00/0.35	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.35	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.00/0.35	    inference('simplify', [status(thm)], ['35'])).
0.00/0.35	tff('37', plain,
0.00/0.35	    ![X0 : a]:
0.00/0.35	      (~ $true
0.00/0.35	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.00/0.35	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.00/0.35	       | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.00/0.35	    inference('sup-', [status(thm)], ['1', '36'])).
0.00/0.35	tff('38', plain,
0.00/0.35	    ![X0 : a]:
0.00/0.35	      (app_encode_app(a, $o, sk_S2, sk_Xz)
0.00/0.35	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.00/0.35	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.00/0.35	    inference('simplify', [status(thm)], ['37'])).
0.00/0.35	tff('39', plain,
0.00/0.35	    (~ $true
0.00/0.35	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.00/0.35	     | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.00/0.35	    inference('sup-', [status(thm)], ['0', '38'])).
0.00/0.35	tff('40', plain,
0.00/0.35	    (app_encode_app(a, $o, sk_S2, sk_Xz)
0.00/0.35	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.00/0.35	    inference('simplify', [status(thm)], ['39'])).
0.00/0.35	tff('41', plain,
0.00/0.35	    (app_encode_app(a, $o, sk_S1, sk_Xz)
0.00/0.35	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.00/0.35	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.00/0.35	    inference('sup+', [status(thm)], ['34', '40'])).
0.00/0.35	tff('42', plain,
0.00/0.35	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.00/0.35	     | app_encode_app(a, $o, sk_S1, sk_Xz)),
0.00/0.35	    inference('simplify', [status(thm)], ['41'])).
0.00/0.35	tff('43', plain,
0.00/0.35	    (~ $true
0.00/0.35	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.00/0.35	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.00/0.35	     | sk_S1 = sk_Xp(sk_Xz)),
0.00/0.35	    inference('sup-', [status(thm)], ['42', '8'])).
0.00/0.35	tff('44', plain,
0.00/0.35	    (sk_S1 = sk_Xp(sk_Xz)
0.00/0.35	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.00/0.35	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.00/0.35	    inference('simplify', [status(thm)], ['43'])).
0.00/0.35	tff('45', plain,
0.00/0.35	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.00/0.35	     | sk_S1 = sk_Xp(sk_Xz)),
0.00/0.35	    inference('clc', [status(thm)], ['44', '24'])).
0.00/0.35	tff('46', plain,
0.00/0.35	    ![X6 : app_encode_fun(a, $o), X7 : app_encode_fun(a, $o)]:
0.00/0.35	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.35	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.35	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.35	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.00/0.35	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.00/0.35	       | ~ app_encode_app(a, $o, X7, sk_Xx2)
0.00/0.35	       | ~ app_encode_app(a, $o, X7, sk_Xz)),
0.00/0.35	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.35	tff('47', plain,
0.00/0.35	    ![X6 : app_encode_fun(a, $o), X7 : app_encode_fun(a, $o)]:
0.00/0.35	      (~ app_encode_app(a, $o, X7, sk_Xz)
0.00/0.35	       | ~ app_encode_app(a, $o, X7, sk_Xx2)
0.00/0.35	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.00/0.35	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.00/0.35	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.35	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.00/0.35	    inference('simplify', [status(thm)], ['46'])).
0.00/0.35	tff('48', plain,
0.00/0.35	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.35	      (~ $true
0.00/0.35	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.00/0.35	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.00/0.35	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.00/0.35	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_Xp(sk_Xz))
0.00/0.35	       | ~ app_encode_app(a, $o, sk_Xp(sk_Xz), sk_Xx2)),
0.00/0.35	    inference('sup-', [status(thm)], ['0', '47'])).
0.00/0.35	tff('49', plain,
0.00/0.35	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.35	      (~ $true
0.00/0.35	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.00/0.35	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.00/0.35	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.00/0.35	       | ~ $true
0.00/0.35	       | ~ app_encode_app(a, $o, sk_Xp(sk_Xz), sk_Xx2)),
0.00/0.35	    inference('demod', [status(thm)], ['48', '1'])).
0.00/0.35	tff('50', plain,
0.00/0.35	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.35	      (~ app_encode_app(a, $o, sk_Xp(sk_Xz), sk_Xx2)
0.00/0.35	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.00/0.35	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.00/0.35	       | ~ app_encode_app(a, $o, X0, sk_Xx)),
0.00/0.35	    inference('simplify', [status(thm)], ['49'])).
0.00/0.35	tff('51', plain,
0.00/0.35	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.35	      (~ app_encode_app(a, $o, sk_S1, sk_Xx2)
0.00/0.35	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.00/0.35	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.00/0.35	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.00/0.35	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.00/0.35	    inference('sup-', [status(thm)], ['45', '50'])).
0.00/0.35	tff('52', plain,
0.00/0.35	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.35	      (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.00/0.35	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.00/0.35	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.00/0.35	       | ~ app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.00/0.35	    inference('simplify', [status(thm)], ['51'])).
0.00/0.35	tff('53', plain,
0.00/0.35	    ![X6 : app_encode_fun(a, $o)]:
0.00/0.35	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.35	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.35	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.35	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.00/0.35	       | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.00/0.35	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.35	tff('54', plain,
0.00/0.35	    ![X6 : app_encode_fun(a, $o)]:
0.00/0.35	      (app_encode_app(a, $o, sk_S1, sk_Xx2)
0.00/0.35	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.00/0.35	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.35	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.00/0.35	    inference('simplify', [status(thm)], ['53'])).
0.00/0.35	tff('55', plain,
0.00/0.35	    ![X0 : a]:
0.00/0.35	      (~ $true
0.00/0.35	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.00/0.35	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.00/0.35	       | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.00/0.35	    inference('sup-', [status(thm)], ['1', '54'])).
0.00/0.35	tff('56', plain,
0.00/0.35	    ![X0 : a]:
0.00/0.35	      (app_encode_app(a, $o, sk_S1, sk_Xx2)
0.00/0.35	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.00/0.35	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.00/0.35	    inference('simplify', [status(thm)], ['55'])).
0.00/0.35	tff('57', plain,
0.00/0.35	    (~ $true
0.00/0.35	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.00/0.35	     | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.00/0.35	    inference('sup-', [status(thm)], ['0', '56'])).
0.00/0.35	tff('58', plain,
0.00/0.35	    (app_encode_app(a, $o, sk_S1, sk_Xx2)
0.00/0.35	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.00/0.35	    inference('simplify', [status(thm)], ['57'])).
0.00/0.35	tff('59', plain,
0.00/0.35	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.35	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)
0.00/0.35	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.00/0.35	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)),
0.00/0.35	    inference('clc', [status(thm)], ['52', '58'])).
0.00/0.35	tff('60', plain,
0.00/0.35	    (~ $true
0.00/0.35	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_Xp(sk_Xx))
0.00/0.35	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.00/0.35	    inference('sup-', [status(thm)], ['0', '59'])).
0.00/0.35	tff('61', plain,
0.00/0.35	    (~ $true
0.00/0.35	     | ~ $true
0.00/0.35	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S)),
0.00/0.35	    inference('demod', [status(thm)], ['60', '1'])).
0.00/0.35	tff('62', plain, app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S),
0.00/0.35	    inference('simplify', [status(thm)], ['61'])).
0.00/0.35	tff('63', plain,
0.00/0.35	    ![X6 : app_encode_fun(a, $o), X8 : app_encode_fun(a, $o)]:
0.00/0.35	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.35	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.35	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.35	       | ~ app_encode_app(a, $o, X8, sk_Xx1)
0.00/0.35	       | ~ app_encode_app(a, $o, X8, sk_Xy)
0.00/0.35	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X8)
0.00/0.35	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.00/0.35	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.35	tff('64', plain,
0.00/0.35	    ![X6 : app_encode_fun(a, $o), X8 : app_encode_fun(a, $o)]:
0.00/0.35	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.00/0.35	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X8)
0.00/0.35	       | ~ app_encode_app(a, $o, X8, sk_Xy)
0.00/0.35	       | ~ app_encode_app(a, $o, X8, sk_Xx1)
0.00/0.35	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.35	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.00/0.35	    inference('simplify', [status(thm)], ['63'])).
0.00/0.35	tff('65', plain,
0.00/0.35	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.35	      (~ $true
0.00/0.35	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.00/0.35	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.00/0.35	       | ~ app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.35	       | ~ app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.35	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.00/0.35	    inference('sup-', [status(thm)], ['62', '64'])).
0.00/0.35	tff('66', plain,
0.00/0.35	    ![X6 : app_encode_fun(a, $o)]:
0.00/0.35	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.35	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.35	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.35	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.35	       | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.00/0.35	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.35	tff('67', plain,
0.00/0.35	    ![X6 : app_encode_fun(a, $o)]:
0.00/0.35	      (app_encode_app(a, $o, sk_S2, sk_Xz)
0.00/0.35	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.35	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.35	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.00/0.35	    inference('simplify', [status(thm)], ['66'])).
0.00/0.35	tff('68', plain,
0.00/0.35	    ![X0 : a]:
0.00/0.35	      (~ $true
0.00/0.35	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.00/0.35	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.35	       | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.00/0.35	    inference('sup-', [status(thm)], ['1', '67'])).
0.00/0.35	tff('69', plain,
0.00/0.35	    ![X0 : a]:
0.00/0.35	      (app_encode_app(a, $o, sk_S2, sk_Xz)
0.00/0.35	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.35	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.00/0.35	    inference('simplify', [status(thm)], ['68'])).
0.00/0.35	tff('70', plain,
0.00/0.35	    (~ $true
0.00/0.35	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.35	     | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.00/0.35	    inference('sup-', [status(thm)], ['0', '69'])).
0.00/0.35	tff('71', plain,
0.00/0.35	    (app_encode_app(a, $o, sk_S2, sk_Xz)
0.00/0.35	     | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.00/0.35	    inference('simplify', [status(thm)], ['70'])).
0.00/0.35	tff('72', plain,
0.00/0.35	    (~ $true
0.00/0.35	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.35	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.00/0.35	     | sk_S2 = sk_Xp(sk_Xz)),
0.00/0.35	    inference('sup-', [status(thm)], ['71', '8'])).
0.00/0.35	tff('73', plain,
0.00/0.35	    (sk_S2 = sk_Xp(sk_Xz)
0.00/0.35	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.00/0.35	     | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.00/0.35	    inference('simplify', [status(thm)], ['72'])).
0.00/0.35	tff('74', plain,
0.00/0.35	    ![X6 : app_encode_fun(a, $o)]:
0.00/0.35	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.35	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.35	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.35	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.35	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.00/0.35	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.35	tff('75', plain,
0.00/0.35	    ![X6 : app_encode_fun(a, $o)]:
0.00/0.35	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.00/0.35	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.35	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.35	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.00/0.35	    inference('simplify', [status(thm)], ['74'])).
0.00/0.35	tff('76', plain,
0.00/0.35	    ![X0 : a]:
0.00/0.35	      (~ $true
0.00/0.35	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.00/0.35	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.35	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.00/0.35	    inference('sup-', [status(thm)], ['1', '75'])).
0.00/0.35	tff('77', plain,
0.00/0.35	    ![X0 : a]:
0.00/0.35	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.00/0.35	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.35	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.00/0.35	    inference('simplify', [status(thm)], ['76'])).
0.00/0.35	tff('78', plain,
0.00/0.35	    (~ $true
0.00/0.35	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.35	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.00/0.35	    inference('sup-', [status(thm)], ['0', '77'])).
0.00/0.35	tff('79', plain,
0.00/0.35	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.00/0.35	     | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.00/0.35	    inference('simplify', [status(thm)], ['78'])).
0.00/0.35	tff('80', plain,
0.00/0.35	    ![X6 : app_encode_fun(a, $o)]:
0.00/0.35	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.35	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.35	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.35	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.35	       | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.00/0.35	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.35	tff('81', plain,
0.00/0.35	    ![X6 : app_encode_fun(a, $o)]:
0.00/0.35	      (app_encode_app(a, $o, sk_S2, sk_Xy1)
0.00/0.35	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.35	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.35	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.00/0.35	    inference('simplify', [status(thm)], ['80'])).
0.00/0.35	tff('82', plain,
0.00/0.35	    ![X0 : a]:
0.00/0.35	      (~ $true
0.00/0.35	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.00/0.35	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.35	       | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.00/0.35	    inference('sup-', [status(thm)], ['1', '81'])).
0.00/0.35	tff('83', plain,
0.00/0.35	    ![X0 : a]:
0.00/0.35	      (app_encode_app(a, $o, sk_S2, sk_Xy1)
0.00/0.35	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.35	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.00/0.35	    inference('simplify', [status(thm)], ['82'])).
0.00/0.35	tff('84', plain,
0.00/0.35	    (~ $true
0.00/0.35	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.35	     | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.00/0.35	    inference('sup-', [status(thm)], ['0', '83'])).
0.00/0.35	tff('85', plain,
0.00/0.35	    (app_encode_app(a, $o, sk_S2, sk_Xy1)
0.00/0.35	     | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.00/0.35	    inference('simplify', [status(thm)], ['84'])).
0.00/0.35	tff('86', plain,
0.00/0.35	    (~ $true
0.00/0.35	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.35	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.00/0.35	     | sk_S2 = sk_Xp(sk_Xy1)),
0.00/0.35	    inference('sup-', [status(thm)], ['85', '8'])).
0.00/0.35	tff('87', plain,
0.00/0.35	    (sk_S2 = sk_Xp(sk_Xy1)
0.00/0.35	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.00/0.35	     | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.00/0.35	    inference('simplify', [status(thm)], ['86'])).
0.00/0.35	tff('88', plain,
0.00/0.35	    ![X6 : app_encode_fun(a, $o)]:
0.00/0.35	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.35	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.35	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.35	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.35	       | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.00/0.35	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.35	tff('89', plain,
0.00/0.35	    ![X6 : app_encode_fun(a, $o)]:
0.00/0.35	      (app_encode_app(a, $o, sk_S1, sk_Xy1)
0.00/0.35	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.35	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.35	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.00/0.35	    inference('simplify', [status(thm)], ['88'])).
0.00/0.35	tff('90', plain,
0.00/0.35	    ![X0 : a]:
0.00/0.35	      (~ $true
0.00/0.35	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.00/0.35	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.35	       | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.00/0.35	    inference('sup-', [status(thm)], ['1', '89'])).
0.00/0.35	tff('91', plain,
0.00/0.35	    ![X0 : a]:
0.00/0.35	      (app_encode_app(a, $o, sk_S1, sk_Xy1)
0.00/0.35	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.35	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.00/0.35	    inference('simplify', [status(thm)], ['90'])).
0.00/0.35	tff('92', plain,
0.00/0.35	    (~ $true
0.00/0.35	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.35	     | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.00/0.35	    inference('sup-', [status(thm)], ['0', '91'])).
0.00/0.35	tff('93', plain,
0.00/0.35	    (app_encode_app(a, $o, sk_S1, sk_Xy1)
0.00/0.35	     | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.00/0.35	    inference('simplify', [status(thm)], ['92'])).
0.00/0.35	tff('94', plain,
0.00/0.35	    (~ $true
0.00/0.35	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.35	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.00/0.35	     | sk_S1 = sk_Xp(sk_Xy1)),
0.00/0.35	    inference('sup-', [status(thm)], ['93', '8'])).
0.00/0.35	tff('95', plain,
0.00/0.35	    (sk_S1 = sk_Xp(sk_Xy1)
0.00/0.35	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.00/0.35	     | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.00/0.35	    inference('simplify', [status(thm)], ['94'])).
0.00/0.35	tff('96', plain,
0.00/0.35	    (sk_S1 = sk_S2
0.00/0.35	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.35	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.00/0.35	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.35	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.00/0.35	    inference('sup+', [status(thm)], ['87', '95'])).
0.00/0.35	tff('97', plain,
0.00/0.35	    (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.00/0.35	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.00/0.35	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.35	     | sk_S1 = sk_S2),
0.00/0.35	    inference('simplify', [status(thm)], ['96'])).
0.00/0.35	tff('98', plain,
0.00/0.35	    (~ $true
0.00/0.35	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.35	     | sk_S1 = sk_S2
0.00/0.35	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.35	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.00/0.35	    inference('sup-', [status(thm)], ['79', '97'])).
0.00/0.35	tff('99', plain,
0.00/0.35	    (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.00/0.35	     | sk_S1 = sk_S2
0.00/0.35	     | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.00/0.35	    inference('simplify', [status(thm)], ['98'])).
0.00/0.35	tff('100', plain,
0.00/0.35	    (app_encode_app(a, $o, sk_S1, sk_Xz)
0.00/0.35	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.35	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.00/0.35	     | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.00/0.35	    inference('sup+', [status(thm)], ['99', '71'])).
0.00/0.35	tff('101', plain,
0.00/0.35	    (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.00/0.35	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.35	     | app_encode_app(a, $o, sk_S1, sk_Xz)),
0.00/0.35	    inference('simplify', [status(thm)], ['100'])).
0.00/0.35	tff('102', plain,
0.00/0.35	    (~ $true
0.00/0.35	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.35	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.00/0.35	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.00/0.35	     | sk_S1 = sk_Xp(sk_Xz)),
0.00/0.35	    inference('sup-', [status(thm)], ['101', '8'])).
0.00/0.35	tff('103', plain,
0.00/0.35	    (sk_S1 = sk_Xp(sk_Xz)
0.00/0.35	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.00/0.35	     | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.00/0.35	    inference('simplify', [status(thm)], ['102'])).
0.00/0.35	tff('104', plain,
0.00/0.35	    (sk_S1 = sk_S2
0.00/0.35	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.35	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.00/0.35	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.35	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.00/0.35	    inference('sup+', [status(thm)], ['73', '103'])).
0.00/0.35	tff('105', plain,
0.00/0.35	    (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.00/0.35	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.00/0.35	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.35	     | sk_S1 = sk_S2),
0.00/0.35	    inference('simplify', [status(thm)], ['104'])).
0.00/0.35	tff('106', plain,
0.00/0.35	    ![X6 : app_encode_fun(a, $o)]:
0.00/0.35	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.35	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.35	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.35	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.35	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.00/0.35	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.35	tff('107', plain,
0.00/0.35	    ![X6 : app_encode_fun(a, $o)]:
0.00/0.35	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.00/0.35	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.35	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.35	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.00/0.35	    inference('simplify', [status(thm)], ['106'])).
0.00/0.35	tff('108', plain,
0.00/0.35	    ![X0 : a]:
0.00/0.35	      (~ $true
0.00/0.35	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.00/0.35	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.35	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.00/0.35	    inference('sup-', [status(thm)], ['1', '107'])).
0.00/0.35	tff('109', plain,
0.00/0.35	    ![X0 : a]:
0.00/0.35	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.00/0.35	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.35	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.00/0.35	    inference('simplify', [status(thm)], ['108'])).
0.00/0.35	tff('110', plain,
0.00/0.35	    (~ $true
0.00/0.35	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.35	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.00/0.35	    inference('sup-', [status(thm)], ['0', '109'])).
0.00/0.35	tff('111', plain,
0.00/0.35	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.00/0.35	     | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.00/0.35	    inference('simplify', [status(thm)], ['110'])).
0.00/0.35	tff('112', plain,
0.00/0.35	    (sk_S1 = sk_S2
0.00/0.35	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.35	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.00/0.35	    inference('clc', [status(thm)], ['105', '111'])).
0.00/0.35	tff('113', plain, (app_encode_app(a, $o, sk_S, sk_Xx1) | sk_S1 = sk_S2),
0.00/0.35	    inference('clc', [status(thm)], ['112', '79'])).
0.00/0.35	tff('114', plain,
0.00/0.35	    (app_encode_app(a, $o, sk_S1, sk_Xz)
0.00/0.35	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.35	     | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.00/0.35	    inference('sup+', [status(thm)], ['113', '71'])).
0.00/0.35	tff('115', plain,
0.00/0.35	    (app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.35	     | app_encode_app(a, $o, sk_S1, sk_Xz)),
0.00/0.35	    inference('simplify', [status(thm)], ['114'])).
0.00/0.35	tff('116', plain,
0.00/0.35	    (~ $true
0.00/0.35	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.35	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.00/0.35	     | sk_S1 = sk_Xp(sk_Xz)),
0.00/0.35	    inference('sup-', [status(thm)], ['115', '8'])).
0.00/0.35	tff('117', plain,
0.00/0.35	    (sk_S1 = sk_Xp(sk_Xz)
0.00/0.35	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.00/0.35	     | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.00/0.35	    inference('simplify', [status(thm)], ['116'])).
0.00/0.35	tff('118', plain,
0.00/0.35	    (app_encode_app(a, $o, sk_S, sk_Xx1) | sk_S1 = sk_Xp(sk_Xz)),
0.00/0.35	    inference('clc', [status(thm)], ['117', '111'])).
0.00/0.35	tff('119', plain,
0.00/0.35	    ![X6 : app_encode_fun(a, $o), X7 : app_encode_fun(a, $o)]:
0.00/0.35	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.35	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.35	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.35	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.35	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.00/0.35	       | ~ app_encode_app(a, $o, X7, sk_Xx2)
0.00/0.35	       | ~ app_encode_app(a, $o, X7, sk_Xz)),
0.00/0.35	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.35	tff('120', plain,
0.00/0.35	    ![X6 : app_encode_fun(a, $o), X7 : app_encode_fun(a, $o)]:
0.00/0.36	      (~ app_encode_app(a, $o, X7, sk_Xz)
0.00/0.36	       | ~ app_encode_app(a, $o, X7, sk_Xx2)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.00/0.36	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.36	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.00/0.36	    inference('simplify', [status(thm)], ['119'])).
0.00/0.36	tff('121', plain,
0.00/0.36	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.36	      (~ $true
0.00/0.36	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.00/0.36	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_Xp(sk_Xz))
0.00/0.36	       | ~ app_encode_app(a, $o, sk_Xp(sk_Xz), sk_Xx2)),
0.00/0.36	    inference('sup-', [status(thm)], ['0', '120'])).
0.00/0.36	tff('122', plain,
0.00/0.36	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.36	      (~ $true
0.00/0.36	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.00/0.36	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.36	       | ~ $true
0.00/0.36	       | ~ app_encode_app(a, $o, sk_Xp(sk_Xz), sk_Xx2)),
0.00/0.36	    inference('demod', [status(thm)], ['121', '1'])).
0.00/0.36	tff('123', plain,
0.00/0.36	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.36	      (~ app_encode_app(a, $o, sk_Xp(sk_Xz), sk_Xx2)
0.00/0.36	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.00/0.36	       | ~ app_encode_app(a, $o, X0, sk_Xx)),
0.00/0.36	    inference('simplify', [status(thm)], ['122'])).
0.00/0.36	tff('124', plain,
0.00/0.36	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.36	      (~ app_encode_app(a, $o, sk_S1, sk_Xx2)
0.00/0.36	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.36	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.00/0.36	       | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.00/0.36	    inference('sup-', [status(thm)], ['118', '123'])).
0.00/0.36	tff('125', plain,
0.00/0.36	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.36	      (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.00/0.36	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.00/0.36	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.36	       | ~ app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.00/0.36	    inference('simplify', [status(thm)], ['124'])).
0.00/0.36	tff('126', plain,
0.00/0.36	    ![X6 : app_encode_fun(a, $o)]:
0.00/0.36	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.36	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.36	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.36	       | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.00/0.36	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.36	tff('127', plain,
0.00/0.36	    ![X6 : app_encode_fun(a, $o)]:
0.00/0.36	      (app_encode_app(a, $o, sk_S1, sk_Xx2)
0.00/0.36	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.36	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.00/0.36	    inference('simplify', [status(thm)], ['126'])).
0.00/0.36	tff('128', plain,
0.00/0.36	    ![X0 : a]:
0.00/0.36	      (~ $true
0.00/0.36	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.00/0.36	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.36	       | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.00/0.36	    inference('sup-', [status(thm)], ['1', '127'])).
0.00/0.36	tff('129', plain,
0.00/0.36	    ![X0 : a]:
0.00/0.36	      (app_encode_app(a, $o, sk_S1, sk_Xx2)
0.00/0.36	       | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.36	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.00/0.36	    inference('simplify', [status(thm)], ['128'])).
0.00/0.36	tff('130', plain,
0.00/0.36	    (~ $true
0.00/0.36	     | app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.36	     | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.00/0.36	    inference('sup-', [status(thm)], ['0', '129'])).
0.00/0.36	tff('131', plain,
0.00/0.36	    (app_encode_app(a, $o, sk_S1, sk_Xx2)
0.00/0.36	     | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.00/0.36	    inference('simplify', [status(thm)], ['130'])).
0.00/0.36	tff('132', plain,
0.00/0.36	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.36	      (app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.36	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)),
0.00/0.36	    inference('clc', [status(thm)], ['125', '131'])).
0.00/0.36	tff('133', plain,
0.00/0.36	    (~ $true
0.00/0.36	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_Xp(sk_Xx))
0.00/0.36	     | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.00/0.36	    inference('sup-', [status(thm)], ['0', '132'])).
0.00/0.36	tff('134', plain, (~ $true | ~ $true | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.00/0.36	    inference('demod', [status(thm)], ['133', '1'])).
0.00/0.36	tff('135', plain, app_encode_app(a, $o, sk_S, sk_Xx1),
0.00/0.36	    inference('simplify', [status(thm)], ['134'])).
0.00/0.36	tff('136', plain,
0.00/0.36	    ![X6 : app_encode_fun(a, $o)]:
0.00/0.36	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.36	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.36	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.36	       | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.00/0.36	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.36	tff('137', plain,
0.00/0.36	    ![X6 : app_encode_fun(a, $o)]:
0.00/0.36	      (app_encode_app(a, $o, sk_S2, sk_Xy1)
0.00/0.36	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.36	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.00/0.36	    inference('simplify', [status(thm)], ['136'])).
0.00/0.36	tff('138', plain,
0.00/0.36	    ![X0 : a]:
0.00/0.36	      (~ $true
0.00/0.36	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.00/0.36	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.36	       | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.00/0.36	    inference('sup-', [status(thm)], ['1', '137'])).
0.00/0.36	tff('139', plain,
0.00/0.36	    ![X0 : a]:
0.00/0.36	      (app_encode_app(a, $o, sk_S2, sk_Xy1)
0.00/0.36	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.36	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.00/0.36	    inference('simplify', [status(thm)], ['138'])).
0.00/0.36	tff('140', plain,
0.00/0.36	    (~ $true
0.00/0.36	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.36	     | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.00/0.36	    inference('sup-', [status(thm)], ['0', '139'])).
0.00/0.36	tff('141', plain,
0.00/0.36	    (app_encode_app(a, $o, sk_S2, sk_Xy1)
0.00/0.36	     | app_encode_app(a, $o, sk_S, sk_Xy)),
0.00/0.36	    inference('simplify', [status(thm)], ['140'])).
0.00/0.36	tff('142', plain,
0.00/0.36	    (~ $true
0.00/0.36	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.36	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.00/0.36	     | sk_S2 = sk_Xp(sk_Xy1)),
0.00/0.36	    inference('sup-', [status(thm)], ['141', '8'])).
0.00/0.36	tff('143', plain,
0.00/0.36	    (sk_S2 = sk_Xp(sk_Xy1)
0.00/0.36	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.00/0.36	     | app_encode_app(a, $o, sk_S, sk_Xy)),
0.00/0.36	    inference('simplify', [status(thm)], ['142'])).
0.00/0.36	tff('144', plain,
0.00/0.36	    ![X6 : app_encode_fun(a, $o)]:
0.00/0.36	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.36	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.36	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.36	       | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.00/0.36	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.36	tff('145', plain,
0.00/0.36	    ![X6 : app_encode_fun(a, $o)]:
0.00/0.36	      (app_encode_app(a, $o, sk_S1, sk_Xy1)
0.00/0.36	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.36	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.00/0.36	    inference('simplify', [status(thm)], ['144'])).
0.00/0.36	tff('146', plain,
0.00/0.36	    ![X0 : a]:
0.00/0.36	      (~ $true
0.00/0.36	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.00/0.36	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.36	       | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.00/0.36	    inference('sup-', [status(thm)], ['1', '145'])).
0.00/0.36	tff('147', plain,
0.00/0.36	    ![X0 : a]:
0.00/0.36	      (app_encode_app(a, $o, sk_S1, sk_Xy1)
0.00/0.36	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.36	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.00/0.36	    inference('simplify', [status(thm)], ['146'])).
0.00/0.36	tff('148', plain,
0.00/0.36	    (~ $true
0.00/0.36	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.36	     | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.00/0.36	    inference('sup-', [status(thm)], ['0', '147'])).
0.00/0.36	tff('149', plain,
0.00/0.36	    (app_encode_app(a, $o, sk_S1, sk_Xy1)
0.00/0.36	     | app_encode_app(a, $o, sk_S, sk_Xy)),
0.00/0.36	    inference('simplify', [status(thm)], ['148'])).
0.00/0.36	tff('150', plain,
0.00/0.36	    (~ $true
0.00/0.36	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.36	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.00/0.36	     | sk_S1 = sk_Xp(sk_Xy1)),
0.00/0.36	    inference('sup-', [status(thm)], ['149', '8'])).
0.00/0.36	tff('151', plain,
0.00/0.36	    (sk_S1 = sk_Xp(sk_Xy1)
0.00/0.36	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.00/0.36	     | app_encode_app(a, $o, sk_S, sk_Xy)),
0.00/0.36	    inference('simplify', [status(thm)], ['150'])).
0.00/0.36	tff('152', plain,
0.00/0.36	    ![X6 : app_encode_fun(a, $o)]:
0.00/0.36	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.36	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.36	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.36	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.00/0.36	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.36	tff('153', plain,
0.00/0.36	    ![X6 : app_encode_fun(a, $o)]:
0.00/0.36	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.00/0.36	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.36	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.00/0.36	    inference('simplify', [status(thm)], ['152'])).
0.00/0.36	tff('154', plain,
0.00/0.36	    ![X0 : a]:
0.00/0.36	      (~ $true
0.00/0.36	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.00/0.36	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.36	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.00/0.36	    inference('sup-', [status(thm)], ['1', '153'])).
0.00/0.36	tff('155', plain,
0.00/0.36	    ![X0 : a]:
0.00/0.36	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.00/0.36	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.36	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.00/0.36	    inference('simplify', [status(thm)], ['154'])).
0.00/0.36	tff('156', plain,
0.00/0.36	    (~ $true
0.00/0.36	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.36	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.00/0.36	    inference('sup-', [status(thm)], ['0', '155'])).
0.00/0.36	tff('157', plain,
0.00/0.36	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.00/0.36	     | app_encode_app(a, $o, sk_S, sk_Xy)),
0.00/0.36	    inference('simplify', [status(thm)], ['156'])).
0.00/0.36	tff('158', plain,
0.00/0.36	    (app_encode_app(a, $o, sk_S, sk_Xy) | sk_S1 = sk_Xp(sk_Xy1)),
0.00/0.36	    inference('clc', [status(thm)], ['151', '157'])).
0.00/0.36	tff('159', plain,
0.00/0.36	    (sk_S1 = sk_S2
0.00/0.36	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.36	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.00/0.36	     | app_encode_app(a, $o, sk_S, sk_Xy)),
0.00/0.36	    inference('sup+', [status(thm)], ['143', '158'])).
0.00/0.36	tff('160', plain,
0.00/0.36	    (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.00/0.36	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.36	     | sk_S1 = sk_S2),
0.00/0.36	    inference('simplify', [status(thm)], ['159'])).
0.00/0.36	tff('161', plain,
0.00/0.36	    ![X6 : app_encode_fun(a, $o)]:
0.00/0.36	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.36	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.36	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.36	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.00/0.36	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.36	tff('162', plain,
0.00/0.36	    ![X6 : app_encode_fun(a, $o)]:
0.00/0.36	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.00/0.36	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.36	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.00/0.36	    inference('simplify', [status(thm)], ['161'])).
0.00/0.36	tff('163', plain,
0.00/0.36	    ![X0 : a]:
0.00/0.36	      (~ $true
0.00/0.36	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.00/0.36	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.36	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.00/0.36	    inference('sup-', [status(thm)], ['1', '162'])).
0.00/0.36	tff('164', plain,
0.00/0.36	    ![X0 : a]:
0.00/0.36	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.00/0.36	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.36	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.00/0.36	    inference('simplify', [status(thm)], ['163'])).
0.00/0.36	tff('165', plain,
0.00/0.36	    (~ $true
0.00/0.36	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.36	     | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.00/0.36	    inference('sup-', [status(thm)], ['0', '164'])).
0.00/0.36	tff('166', plain,
0.00/0.36	    (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.00/0.36	     | app_encode_app(a, $o, sk_S, sk_Xy)),
0.00/0.36	    inference('simplify', [status(thm)], ['165'])).
0.00/0.36	tff('167', plain, (sk_S1 = sk_S2 | app_encode_app(a, $o, sk_S, sk_Xy)),
0.00/0.36	    inference('clc', [status(thm)], ['160', '166'])).
0.00/0.36	tff('168', plain,
0.00/0.36	    ![X6 : app_encode_fun(a, $o)]:
0.00/0.36	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.36	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.36	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.36	       | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.00/0.36	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.36	tff('169', plain,
0.00/0.36	    ![X6 : app_encode_fun(a, $o)]:
0.00/0.36	      (app_encode_app(a, $o, sk_S2, sk_Xz)
0.00/0.36	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.36	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.00/0.36	    inference('simplify', [status(thm)], ['168'])).
0.00/0.36	tff('170', plain,
0.00/0.36	    ![X0 : a]:
0.00/0.36	      (~ $true
0.00/0.36	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.00/0.36	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.36	       | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.00/0.36	    inference('sup-', [status(thm)], ['1', '169'])).
0.00/0.36	tff('171', plain,
0.00/0.36	    ![X0 : a]:
0.00/0.36	      (app_encode_app(a, $o, sk_S2, sk_Xz)
0.00/0.36	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.36	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.00/0.36	    inference('simplify', [status(thm)], ['170'])).
0.00/0.36	tff('172', plain,
0.00/0.36	    (~ $true
0.00/0.36	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.36	     | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.00/0.36	    inference('sup-', [status(thm)], ['0', '171'])).
0.00/0.36	tff('173', plain,
0.00/0.36	    (app_encode_app(a, $o, sk_S2, sk_Xz) | app_encode_app(a, $o, sk_S, sk_Xy)),
0.00/0.36	    inference('simplify', [status(thm)], ['172'])).
0.00/0.36	tff('174', plain,
0.00/0.36	    (app_encode_app(a, $o, sk_S1, sk_Xz)
0.00/0.36	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.36	     | app_encode_app(a, $o, sk_S, sk_Xy)),
0.00/0.36	    inference('sup+', [status(thm)], ['167', '173'])).
0.00/0.36	tff('175', plain,
0.00/0.36	    (app_encode_app(a, $o, sk_S, sk_Xy) | app_encode_app(a, $o, sk_S1, sk_Xz)),
0.00/0.36	    inference('simplify', [status(thm)], ['174'])).
0.00/0.36	tff('176', plain,
0.00/0.36	    (~ $true
0.00/0.36	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.36	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.00/0.36	     | sk_S1 = sk_Xp(sk_Xz)),
0.00/0.36	    inference('sup-', [status(thm)], ['175', '8'])).
0.00/0.36	tff('177', plain,
0.00/0.36	    (sk_S1 = sk_Xp(sk_Xz)
0.00/0.36	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.00/0.36	     | app_encode_app(a, $o, sk_S, sk_Xy)),
0.00/0.36	    inference('simplify', [status(thm)], ['176'])).
0.00/0.36	tff('178', plain,
0.00/0.36	    (app_encode_app(a, $o, sk_S, sk_Xy) | sk_S1 = sk_Xp(sk_Xz)),
0.00/0.36	    inference('clc', [status(thm)], ['177', '157'])).
0.00/0.36	tff('179', plain,
0.00/0.36	    ![X6 : app_encode_fun(a, $o), X7 : app_encode_fun(a, $o)]:
0.00/0.36	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.36	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.36	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.00/0.36	       | ~ app_encode_app(a, $o, X7, sk_Xx2)
0.00/0.36	       | ~ app_encode_app(a, $o, X7, sk_Xz)),
0.00/0.36	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.36	tff('180', plain,
0.00/0.36	    ![X6 : app_encode_fun(a, $o), X7 : app_encode_fun(a, $o)]:
0.00/0.36	      (~ app_encode_app(a, $o, X7, sk_Xz)
0.00/0.36	       | ~ app_encode_app(a, $o, X7, sk_Xx2)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.00/0.36	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.36	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.00/0.36	    inference('simplify', [status(thm)], ['179'])).
0.00/0.36	tff('181', plain,
0.00/0.36	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.36	      (~ $true
0.00/0.36	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.00/0.36	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_Xp(sk_Xz))
0.00/0.36	       | ~ app_encode_app(a, $o, sk_Xp(sk_Xz), sk_Xx2)),
0.00/0.36	    inference('sup-', [status(thm)], ['0', '180'])).
0.00/0.36	tff('182', plain,
0.00/0.36	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.36	      (~ $true
0.00/0.36	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.00/0.36	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.36	       | ~ $true
0.00/0.36	       | ~ app_encode_app(a, $o, sk_Xp(sk_Xz), sk_Xx2)),
0.00/0.36	    inference('demod', [status(thm)], ['181', '1'])).
0.00/0.36	tff('183', plain,
0.00/0.36	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.36	      (~ app_encode_app(a, $o, sk_Xp(sk_Xz), sk_Xx2)
0.00/0.36	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.00/0.36	       | ~ app_encode_app(a, $o, X0, sk_Xx)),
0.00/0.36	    inference('simplify', [status(thm)], ['182'])).
0.00/0.36	tff('184', plain,
0.00/0.36	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.36	      (~ app_encode_app(a, $o, sk_S1, sk_Xx2)
0.00/0.36	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.36	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.00/0.36	       | app_encode_app(a, $o, sk_S, sk_Xy)),
0.00/0.36	    inference('sup-', [status(thm)], ['178', '183'])).
0.00/0.36	tff('185', plain,
0.00/0.36	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.36	      (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.00/0.36	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.00/0.36	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.36	       | ~ app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.00/0.36	    inference('simplify', [status(thm)], ['184'])).
0.00/0.36	tff('186', plain,
0.00/0.36	    ![X6 : app_encode_fun(a, $o)]:
0.00/0.36	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.36	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.36	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.36	       | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.00/0.36	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.36	tff('187', plain,
0.00/0.36	    ![X6 : app_encode_fun(a, $o)]:
0.00/0.36	      (app_encode_app(a, $o, sk_S1, sk_Xx2)
0.00/0.36	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.36	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.00/0.36	    inference('simplify', [status(thm)], ['186'])).
0.00/0.36	tff('188', plain,
0.00/0.36	    ![X0 : a]:
0.00/0.36	      (~ $true
0.00/0.36	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.00/0.36	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.36	       | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.00/0.36	    inference('sup-', [status(thm)], ['1', '187'])).
0.00/0.36	tff('189', plain,
0.00/0.36	    ![X0 : a]:
0.00/0.36	      (app_encode_app(a, $o, sk_S1, sk_Xx2)
0.00/0.36	       | app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.36	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.00/0.36	    inference('simplify', [status(thm)], ['188'])).
0.00/0.36	tff('190', plain,
0.00/0.36	    (~ $true
0.00/0.36	     | app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.36	     | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.00/0.36	    inference('sup-', [status(thm)], ['0', '189'])).
0.00/0.36	tff('191', plain,
0.00/0.36	    (app_encode_app(a, $o, sk_S1, sk_Xx2)
0.00/0.36	     | app_encode_app(a, $o, sk_S, sk_Xy)),
0.00/0.36	    inference('simplify', [status(thm)], ['190'])).
0.00/0.36	tff('192', plain,
0.00/0.36	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.36	      (app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.36	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)),
0.00/0.36	    inference('clc', [status(thm)], ['185', '191'])).
0.00/0.36	tff('193', plain,
0.00/0.36	    (~ $true
0.00/0.36	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_Xp(sk_Xx))
0.00/0.36	     | app_encode_app(a, $o, sk_S, sk_Xy)),
0.00/0.36	    inference('sup-', [status(thm)], ['0', '192'])).
0.00/0.36	tff('194', plain, (~ $true | ~ $true | app_encode_app(a, $o, sk_S, sk_Xy)),
0.00/0.36	    inference('demod', [status(thm)], ['193', '1'])).
0.00/0.36	tff('195', plain, app_encode_app(a, $o, sk_S, sk_Xy),
0.00/0.36	    inference('simplify', [status(thm)], ['194'])).
0.00/0.36	tff('196', plain,
0.00/0.36	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.36	      (~ $true
0.00/0.36	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.00/0.36	       | ~ $true
0.00/0.36	       | ~ $true
0.00/0.36	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.00/0.36	    inference('demod', [status(thm)], ['65', '135', '195'])).
0.00/0.36	tff('197', plain,
0.00/0.36	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.36	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.00/0.36	       | ~ app_encode_app(a, $o, X0, sk_Xx)),
0.00/0.36	    inference('simplify', [status(thm)], ['196'])).
0.00/0.36	tff('198', plain,
0.00/0.36	    ![X0 : a]:
0.00/0.36	      (~ $true
0.00/0.36	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.00/0.36	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.00/0.36	    inference('sup-', [status(thm)], ['1', '197'])).
0.00/0.36	tff('199', plain,
0.00/0.36	    ![X0 : a]:
0.00/0.36	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.00/0.36	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.00/0.36	    inference('simplify', [status(thm)], ['198'])).
0.00/0.36	tff('200', plain,
0.00/0.36	    (~ $true | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.00/0.36	    inference('sup-', [status(thm)], ['0', '199'])).
0.00/0.36	tff('201', plain, app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2),
0.00/0.36	    inference('simplify', [status(thm)], ['200'])).
0.00/0.36	tff('202', plain,
0.00/0.36	    ![X6 : app_encode_fun(a, $o), X8 : app_encode_fun(a, $o)]:
0.00/0.36	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.36	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.36	       | ~ app_encode_app(a, $o, X8, sk_Xx1)
0.00/0.36	       | ~ app_encode_app(a, $o, X8, sk_Xy)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X8)
0.00/0.36	       | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.00/0.36	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.36	tff('203', plain,
0.00/0.36	    ![X6 : app_encode_fun(a, $o), X8 : app_encode_fun(a, $o)]:
0.00/0.36	      (app_encode_app(a, $o, sk_S1, sk_Xy1)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X8)
0.00/0.36	       | ~ app_encode_app(a, $o, X8, sk_Xy)
0.00/0.36	       | ~ app_encode_app(a, $o, X8, sk_Xx1)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.36	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.00/0.36	    inference('simplify', [status(thm)], ['202'])).
0.00/0.36	tff('204', plain,
0.00/0.36	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.36	      (~ $true
0.00/0.36	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.00/0.36	       | ~ app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.36	       | ~ app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.36	       | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.00/0.36	    inference('sup-', [status(thm)], ['62', '203'])).
0.00/0.36	tff('205', plain,
0.00/0.36	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.36	      (~ $true
0.00/0.36	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.00/0.36	       | ~ $true
0.00/0.36	       | ~ $true
0.00/0.36	       | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.00/0.36	    inference('demod', [status(thm)], ['204', '135', '195'])).
0.00/0.36	tff('206', plain,
0.00/0.36	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.36	      (app_encode_app(a, $o, sk_S1, sk_Xy1)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.00/0.36	       | ~ app_encode_app(a, $o, X0, sk_Xx)),
0.00/0.36	    inference('simplify', [status(thm)], ['205'])).
0.00/0.36	tff('207', plain,
0.00/0.36	    ![X0 : a]:
0.00/0.36	      (~ $true
0.00/0.36	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.00/0.36	       | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.00/0.36	    inference('sup-', [status(thm)], ['1', '206'])).
0.00/0.36	tff('208', plain,
0.00/0.36	    ![X0 : a]:
0.00/0.36	      (app_encode_app(a, $o, sk_S1, sk_Xy1)
0.00/0.36	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.00/0.36	    inference('simplify', [status(thm)], ['207'])).
0.00/0.36	tff('209', plain, (~ $true | app_encode_app(a, $o, sk_S1, sk_Xy1)),
0.00/0.36	    inference('sup-', [status(thm)], ['0', '208'])).
0.00/0.36	tff('210', plain, app_encode_app(a, $o, sk_S1, sk_Xy1),
0.00/0.36	    inference('simplify', [status(thm)], ['209'])).
0.00/0.36	tff('211', plain,
0.00/0.36	    (~ $true
0.00/0.36	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.00/0.36	     | sk_S1 = sk_Xp(sk_Xy1)),
0.00/0.36	    inference('sup-', [status(thm)], ['210', '8'])).
0.00/0.36	tff('212', plain,
0.00/0.36	    (sk_S1 = sk_Xp(sk_Xy1)
0.00/0.36	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.00/0.36	    inference('simplify', [status(thm)], ['211'])).
0.00/0.36	tff('213', plain,
0.00/0.36	    ![X6 : app_encode_fun(a, $o), X8 : app_encode_fun(a, $o)]:
0.00/0.36	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.36	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.36	       | ~ app_encode_app(a, $o, X8, sk_Xx1)
0.00/0.36	       | ~ app_encode_app(a, $o, X8, sk_Xy)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X8)
0.00/0.36	       | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.00/0.36	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.36	tff('214', plain,
0.00/0.36	    ![X6 : app_encode_fun(a, $o), X8 : app_encode_fun(a, $o)]:
0.00/0.36	      (app_encode_app(a, $o, sk_S2, sk_Xy1)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X8)
0.00/0.36	       | ~ app_encode_app(a, $o, X8, sk_Xy)
0.00/0.36	       | ~ app_encode_app(a, $o, X8, sk_Xx1)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.36	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.00/0.36	    inference('simplify', [status(thm)], ['213'])).
0.00/0.36	tff('215', plain,
0.00/0.36	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.36	      (~ $true
0.00/0.36	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.00/0.36	       | ~ app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.36	       | ~ app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.36	       | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.00/0.36	    inference('sup-', [status(thm)], ['62', '214'])).
0.00/0.36	tff('216', plain,
0.00/0.36	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.36	      (~ $true
0.00/0.36	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.00/0.36	       | ~ $true
0.00/0.36	       | ~ $true
0.00/0.36	       | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.00/0.36	    inference('demod', [status(thm)], ['215', '135', '195'])).
0.00/0.36	tff('217', plain,
0.00/0.36	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.36	      (app_encode_app(a, $o, sk_S2, sk_Xy1)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.00/0.36	       | ~ app_encode_app(a, $o, X0, sk_Xx)),
0.00/0.36	    inference('simplify', [status(thm)], ['216'])).
0.00/0.36	tff('218', plain,
0.00/0.36	    ![X0 : a]:
0.00/0.36	      (~ $true
0.00/0.36	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.00/0.36	       | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.00/0.36	    inference('sup-', [status(thm)], ['1', '217'])).
0.00/0.36	tff('219', plain,
0.00/0.36	    ![X0 : a]:
0.00/0.36	      (app_encode_app(a, $o, sk_S2, sk_Xy1)
0.00/0.36	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.00/0.36	    inference('simplify', [status(thm)], ['218'])).
0.00/0.36	tff('220', plain, (~ $true | app_encode_app(a, $o, sk_S2, sk_Xy1)),
0.00/0.36	    inference('sup-', [status(thm)], ['0', '219'])).
0.00/0.36	tff('221', plain, app_encode_app(a, $o, sk_S2, sk_Xy1),
0.00/0.36	    inference('simplify', [status(thm)], ['220'])).
0.00/0.36	tff('222', plain,
0.00/0.36	    (~ $true
0.00/0.36	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)
0.00/0.36	     | sk_S2 = sk_Xp(sk_Xy1)),
0.00/0.36	    inference('sup-', [status(thm)], ['221', '8'])).
0.00/0.36	tff('223', plain,
0.00/0.36	    (sk_S2 = sk_Xp(sk_Xy1)
0.00/0.36	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.00/0.36	    inference('simplify', [status(thm)], ['222'])).
0.00/0.36	tff('224', plain,
0.00/0.36	    (sk_S2 = sk_S1
0.00/0.36	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.00/0.36	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S2)),
0.00/0.36	    inference('sup+', [status(thm)], ['212', '223'])).
0.00/0.36	tff('225', plain,
0.00/0.36	    (~ $true
0.00/0.36	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.00/0.36	     | sk_S2 = sk_S1),
0.00/0.36	    inference('sup-', [status(thm)], ['201', '224'])).
0.00/0.36	tff('226', plain,
0.00/0.36	    (sk_S2 = sk_S1 | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.00/0.36	    inference('simplify', [status(thm)], ['225'])).
0.00/0.36	tff('227', plain,
0.00/0.36	    ![X6 : app_encode_fun(a, $o), X8 : app_encode_fun(a, $o)]:
0.00/0.36	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.36	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.36	       | ~ app_encode_app(a, $o, X8, sk_Xx1)
0.00/0.36	       | ~ app_encode_app(a, $o, X8, sk_Xy)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X8)
0.00/0.36	       | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.00/0.36	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.36	tff('228', plain,
0.00/0.36	    ![X6 : app_encode_fun(a, $o), X8 : app_encode_fun(a, $o)]:
0.00/0.36	      (app_encode_app(a, $o, sk_S2, sk_Xz)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X8)
0.00/0.36	       | ~ app_encode_app(a, $o, X8, sk_Xy)
0.00/0.36	       | ~ app_encode_app(a, $o, X8, sk_Xx1)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.36	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.00/0.36	    inference('simplify', [status(thm)], ['227'])).
0.00/0.36	tff('229', plain,
0.00/0.36	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.36	      (~ $true
0.00/0.36	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.00/0.36	       | ~ app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.36	       | ~ app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.36	       | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.00/0.36	    inference('sup-', [status(thm)], ['62', '228'])).
0.00/0.36	tff('230', plain,
0.00/0.36	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.36	      (~ $true
0.00/0.36	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.00/0.36	       | ~ $true
0.00/0.36	       | ~ $true
0.00/0.36	       | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.00/0.36	    inference('demod', [status(thm)], ['229', '135', '195'])).
0.00/0.36	tff('231', plain,
0.00/0.36	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.36	      (app_encode_app(a, $o, sk_S2, sk_Xz)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.00/0.36	       | ~ app_encode_app(a, $o, X0, sk_Xx)),
0.00/0.36	    inference('simplify', [status(thm)], ['230'])).
0.00/0.36	tff('232', plain,
0.00/0.36	    ![X0 : a]:
0.00/0.36	      (~ $true
0.00/0.36	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.00/0.36	       | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.00/0.36	    inference('sup-', [status(thm)], ['1', '231'])).
0.00/0.36	tff('233', plain,
0.00/0.36	    ![X0 : a]:
0.00/0.36	      (app_encode_app(a, $o, sk_S2, sk_Xz)
0.00/0.36	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.00/0.36	    inference('simplify', [status(thm)], ['232'])).
0.00/0.36	tff('234', plain, (~ $true | app_encode_app(a, $o, sk_S2, sk_Xz)),
0.00/0.36	    inference('sup-', [status(thm)], ['0', '233'])).
0.00/0.36	tff('235', plain, app_encode_app(a, $o, sk_S2, sk_Xz),
0.00/0.36	    inference('simplify', [status(thm)], ['234'])).
0.00/0.36	tff('236', plain,
0.00/0.36	    (app_encode_app(a, $o, sk_S1, sk_Xz)
0.00/0.36	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.00/0.36	    inference('sup+', [status(thm)], ['226', '235'])).
0.00/0.36	tff('237', plain,
0.00/0.36	    (~ $true
0.00/0.36	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.00/0.36	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.00/0.36	     | sk_S1 = sk_Xp(sk_Xz)),
0.00/0.36	    inference('sup-', [status(thm)], ['236', '8'])).
0.00/0.36	tff('238', plain,
0.00/0.36	    (sk_S1 = sk_Xp(sk_Xz)
0.00/0.36	     | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.00/0.36	    inference('simplify', [status(thm)], ['237'])).
0.00/0.36	tff('239', plain,
0.00/0.36	    ![X6 : app_encode_fun(a, $o), X7 : app_encode_fun(a, $o), 
0.00/0.36	      X8 : app_encode_fun(a, $o)]:
0.00/0.36	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.36	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.36	       | ~ app_encode_app(a, $o, X8, sk_Xx1)
0.00/0.36	       | ~ app_encode_app(a, $o, X8, sk_Xy)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X8)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.00/0.36	       | ~ app_encode_app(a, $o, X7, sk_Xx2)
0.00/0.36	       | ~ app_encode_app(a, $o, X7, sk_Xz)),
0.00/0.36	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.36	tff('240', plain,
0.00/0.36	    ![X6 : app_encode_fun(a, $o), X7 : app_encode_fun(a, $o), 
0.00/0.36	      X8 : app_encode_fun(a, $o)]:
0.00/0.36	      (~ app_encode_app(a, $o, X7, sk_Xz)
0.00/0.36	       | ~ app_encode_app(a, $o, X7, sk_Xx2)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X7)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X8)
0.00/0.36	       | ~ app_encode_app(a, $o, X8, sk_Xy)
0.00/0.36	       | ~ app_encode_app(a, $o, X8, sk_Xx1)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.36	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.00/0.36	    inference('simplify', [status(thm)], ['239'])).
0.00/0.36	tff('241', plain,
0.00/0.36	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.00/0.36	      (~ $true
0.00/0.36	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.00/0.36	       | ~ app_encode_app(a, $o, X1, sk_Xx1)
0.00/0.36	       | ~ app_encode_app(a, $o, X1, sk_Xy)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X1)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_Xp(sk_Xz))
0.00/0.36	       | ~ app_encode_app(a, $o, sk_Xp(sk_Xz), sk_Xx2)),
0.00/0.36	    inference('sup-', [status(thm)], ['0', '240'])).
0.00/0.36	tff('242', plain,
0.00/0.36	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.00/0.36	      (~ $true
0.00/0.36	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.00/0.36	       | ~ app_encode_app(a, $o, X1, sk_Xx1)
0.00/0.36	       | ~ app_encode_app(a, $o, X1, sk_Xy)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X1)
0.00/0.36	       | ~ $true
0.00/0.36	       | ~ app_encode_app(a, $o, sk_Xp(sk_Xz), sk_Xx2)),
0.00/0.36	    inference('demod', [status(thm)], ['241', '1'])).
0.00/0.36	tff('243', plain,
0.00/0.36	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.00/0.36	      (~ app_encode_app(a, $o, sk_Xp(sk_Xz), sk_Xx2)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X1)
0.00/0.36	       | ~ app_encode_app(a, $o, X1, sk_Xy)
0.00/0.36	       | ~ app_encode_app(a, $o, X1, sk_Xx1)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.00/0.36	       | ~ app_encode_app(a, $o, X0, sk_Xx)),
0.00/0.36	    inference('simplify', [status(thm)], ['242'])).
0.00/0.36	tff('244', plain,
0.00/0.36	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.00/0.36	      (~ app_encode_app(a, $o, sk_S1, sk_Xx2)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.00/0.36	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.00/0.36	       | ~ app_encode_app(a, $o, X1, sk_Xx1)
0.00/0.36	       | ~ app_encode_app(a, $o, X1, sk_Xy)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X1)),
0.00/0.36	    inference('sup-', [status(thm)], ['238', '243'])).
0.00/0.36	tff('245', plain,
0.00/0.36	    ![X6 : app_encode_fun(a, $o), X8 : app_encode_fun(a, $o)]:
0.00/0.36	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.36	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.36	       | ~ app_encode_app(a, $o, X8, sk_Xx1)
0.00/0.36	       | ~ app_encode_app(a, $o, X8, sk_Xy)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X8)
0.00/0.36	       | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.00/0.36	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.36	tff('246', plain,
0.00/0.36	    ![X6 : app_encode_fun(a, $o), X8 : app_encode_fun(a, $o)]:
0.00/0.36	      (app_encode_app(a, $o, sk_S1, sk_Xx2)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X8)
0.00/0.36	       | ~ app_encode_app(a, $o, X8, sk_Xy)
0.00/0.36	       | ~ app_encode_app(a, $o, X8, sk_Xx1)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.36	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.00/0.36	    inference('simplify', [status(thm)], ['245'])).
0.00/0.36	tff('247', plain,
0.00/0.36	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.36	      (~ $true
0.00/0.36	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.00/0.36	       | ~ app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.36	       | ~ app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.36	       | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.00/0.36	    inference('sup-', [status(thm)], ['62', '246'])).
0.00/0.36	tff('248', plain,
0.00/0.36	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.36	      (~ $true
0.00/0.36	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.00/0.36	       | ~ $true
0.00/0.36	       | ~ $true
0.00/0.36	       | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.00/0.36	    inference('demod', [status(thm)], ['247', '135', '195'])).
0.00/0.36	tff('249', plain,
0.00/0.36	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.36	      (app_encode_app(a, $o, sk_S1, sk_Xx2)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.00/0.36	       | ~ app_encode_app(a, $o, X0, sk_Xx)),
0.00/0.36	    inference('simplify', [status(thm)], ['248'])).
0.00/0.36	tff('250', plain,
0.00/0.36	    ![X0 : a]:
0.00/0.36	      (~ $true
0.00/0.36	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.00/0.36	       | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.00/0.36	    inference('sup-', [status(thm)], ['1', '249'])).
0.00/0.36	tff('251', plain,
0.00/0.36	    ![X0 : a]:
0.00/0.36	      (app_encode_app(a, $o, sk_S1, sk_Xx2)
0.00/0.36	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.00/0.36	    inference('simplify', [status(thm)], ['250'])).
0.00/0.36	tff('252', plain, (~ $true | app_encode_app(a, $o, sk_S1, sk_Xx2)),
0.00/0.36	    inference('sup-', [status(thm)], ['0', '251'])).
0.00/0.36	tff('253', plain, app_encode_app(a, $o, sk_S1, sk_Xx2),
0.00/0.36	    inference('simplify', [status(thm)], ['252'])).
0.00/0.36	tff('254', plain,
0.00/0.36	    ![X6 : app_encode_fun(a, $o), X8 : app_encode_fun(a, $o)]:
0.00/0.36	      (~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.36	       | ~ app_encode_app(a, $o, X6, sk_Xx)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.36	       | ~ app_encode_app(a, $o, X8, sk_Xx1)
0.00/0.36	       | ~ app_encode_app(a, $o, X8, sk_Xy)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X8)
0.00/0.36	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.00/0.36	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.36	tff('255', plain,
0.00/0.36	    ![X6 : app_encode_fun(a, $o), X8 : app_encode_fun(a, $o)]:
0.00/0.36	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X8)
0.00/0.36	       | ~ app_encode_app(a, $o, X8, sk_Xy)
0.00/0.36	       | ~ app_encode_app(a, $o, X8, sk_Xx1)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X6)
0.00/0.36	       | ~ app_encode_app(a, $o, X6, sk_Xx)),
0.00/0.36	    inference('simplify', [status(thm)], ['254'])).
0.00/0.36	tff('256', plain,
0.00/0.36	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.36	      (~ $true
0.00/0.36	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.00/0.36	       | ~ app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.36	       | ~ app_encode_app(a, $o, sk_S, sk_Xy)
0.00/0.36	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.00/0.36	    inference('sup-', [status(thm)], ['62', '255'])).
0.00/0.36	tff('257', plain,
0.00/0.36	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.36	      (~ $true
0.00/0.36	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.00/0.36	       | ~ $true
0.00/0.36	       | ~ $true
0.00/0.36	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.00/0.36	    inference('demod', [status(thm)], ['256', '135', '195'])).
0.00/0.36	tff('258', plain,
0.00/0.36	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.36	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.00/0.36	       | ~ app_encode_app(a, $o, X0, sk_Xx)),
0.00/0.36	    inference('simplify', [status(thm)], ['257'])).
0.00/0.36	tff('259', plain,
0.00/0.36	    ![X0 : a]:
0.00/0.36	      (~ $true
0.00/0.36	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)
0.00/0.36	       | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.00/0.36	    inference('sup-', [status(thm)], ['1', '258'])).
0.00/0.36	tff('260', plain,
0.00/0.36	    ![X0 : a]:
0.00/0.36	      (app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)
0.00/0.36	       | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.00/0.36	    inference('simplify', [status(thm)], ['259'])).
0.00/0.36	tff('261', plain,
0.00/0.36	    (~ $true | app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1)),
0.00/0.36	    inference('sup-', [status(thm)], ['0', '260'])).
0.00/0.36	tff('262', plain, app_encode_app(app_encode_fun(a, $o), $o, sk_P, sk_S1),
0.00/0.36	    inference('simplify', [status(thm)], ['261'])).
0.00/0.36	tff('263', plain,
0.00/0.36	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.00/0.36	      (~ $true
0.00/0.36	       | ~ $true
0.00/0.36	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.00/0.36	       | ~ app_encode_app(a, $o, X1, sk_Xx1)
0.00/0.36	       | ~ app_encode_app(a, $o, X1, sk_Xy)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X1)),
0.00/0.36	    inference('demod', [status(thm)], ['244', '253', '262'])).
0.00/0.36	tff('264', plain,
0.00/0.36	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.00/0.36	      (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X1)
0.00/0.36	       | ~ app_encode_app(a, $o, X1, sk_Xy)
0.00/0.36	       | ~ app_encode_app(a, $o, X1, sk_Xx1)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.00/0.36	       | ~ app_encode_app(a, $o, X0, sk_Xx)),
0.00/0.36	    inference('simplify', [status(thm)], ['263'])).
0.00/0.36	tff('265', plain,
0.00/0.36	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.36	      (~ $true
0.00/0.36	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.00/0.36	       | ~ app_encode_app(a, $o, sk_S, sk_Xx1)
0.00/0.36	       | ~ app_encode_app(a, $o, sk_S, sk_Xy)),
0.00/0.36	    inference('sup-', [status(thm)], ['62', '264'])).
0.00/0.36	tff('266', plain,
0.00/0.36	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.36	      (~ $true
0.00/0.36	       | ~ app_encode_app(a, $o, X0, sk_Xx)
0.00/0.36	       | ~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.00/0.36	       | ~ $true
0.00/0.36	       | ~ $true),
0.00/0.36	    inference('demod', [status(thm)], ['265', '135', '195'])).
0.00/0.36	tff('267', plain,
0.00/0.36	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.36	      (~ app_encode_app(app_encode_fun(a, $o), $o, sk_P, X0)
0.00/0.36	       | ~ app_encode_app(a, $o, X0, sk_Xx)),
0.00/0.36	    inference('simplify', [status(thm)], ['266'])).
0.00/0.36	tff('268', plain,
0.00/0.36	    ![X0 : a]: (~ $true | ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx)),
0.00/0.36	    inference('sup-', [status(thm)], ['1', '267'])).
0.00/0.36	tff('269', plain, ![X0 : a]: ~ app_encode_app(a, $o, sk_Xp(X0), sk_Xx),
0.00/0.36	    inference('simplify', [status(thm)], ['268'])).
0.00/0.36	tff('270', plain, ~ $true, inference('sup-', [status(thm)], ['0', '269'])).
0.00/0.36	tff('271', plain, $false, inference('simplify', [status(thm)], ['270'])).
0.00/0.36	
0.00/0.36	% SZS output end Refutation
0.00/0.36	EOF
