0.00/0.00	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : app
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : kbo
0.00/0.00	% Command    : 
0.00/0.01	#!/bin/sh
0.00/0.01	
0.00/0.01	./zipperposition.native ${1:+"$1"} \
0.00/0.01	  -i tptp \
0.00/0.01	  -o tptp \
0.00/0.01	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.01	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.01	  --no-ho \
0.00/0.01	  --no-avatar \
0.00/0.01	  --no-induction \
0.00/0.01	  --no-unif-pattern \
0.00/0.01	  --ord $2 \
0.00/0.01	  --simultaneous-sup false \
0.00/0.01	  --no-max-vars \
0.00/0.01	  --no-fool
0.00/0.19	% Computer   : n189.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 18:33:09 CST 2018
8.94/9.19	% done 935 iterations in 8.991s
8.94/9.19	% SZS status Theorem for 'stdin'
8.94/9.19	% SZS output start Refutation
8.94/9.20	tff(zf_stmt_5, conjecture,
8.94/9.20	  (![A:$tType,A0:$tType,P:app_encode_fun(A,$o),A1:app_encode_fun(A0,A),
8.94/9.20	     A2:app_encode_fun(A0,$o)]:
8.94/9.20	     ((![A3:A]:
8.94/9.20	         (app_encode_app(app_encode_fun(A,$o),$o,
8.94/9.20	                         app_encode_app(A,
8.94/9.20	                                        app_encode_fun(app_encode_fun(A,$o),
8.94/9.20	                                                       $o),
8.94/9.20	                                        'const/sets/IN'(A),A3),
8.94/9.20	                         app_encode_app(app_encode_fun(A0,$o),
8.94/9.20	                                        app_encode_fun(A,$o),
8.94/9.20	                                        app_encode_app(app_encode_fun(A0,A),
8.94/9.20	                                                       app_encode_fun(
8.94/9.20	                                                       app_encode_fun(A0,$o),
8.94/9.20	                                                       app_encode_fun(A,$o)),
8.94/9.20	                                                       'const/sets/IMAGE'(
8.94/9.20	                                                       A0,A),A1),
8.94/9.20	                                        A2)) =>
8.94/9.20	          app_encode_app(A,$o,P,A3))) <=>
8.94/9.20	      (![A3:A0]:
8.94/9.20	         (app_encode_app(app_encode_fun(A0,$o),$o,
8.94/9.20	                         app_encode_app(A0,
8.94/9.20	                                        app_encode_fun(app_encode_fun(A0,$o),
8.94/9.20	                                                       $o),
8.94/9.20	                                        'const/sets/IN'(A0),A3),
8.94/9.20	                         A2) =>
8.94/9.20	          app_encode_app(A,$o,P,app_encode_app(A0,A,A1,A3))))))).
8.94/9.20	tff(zf_stmt_0, negated_conjecture,
8.94/9.20	  (~
8.94/9.20	    (![A:$tType,A0:$tType,P:app_encode_fun(A,$o),A1:app_encode_fun(A0,A),
8.94/9.20	       A2:app_encode_fun(A0,$o)]:
8.94/9.20	       ((![A3:A]:
8.94/9.20	           (app_encode_app(app_encode_fun(A,$o),$o,
8.94/9.20	                           app_encode_app(A,
8.94/9.20	                                          app_encode_fun(app_encode_fun(A,$o),
8.94/9.20	                                                         $o),
8.94/9.20	                                          'const/sets/IN'(A),A3),
8.94/9.20	                           app_encode_app(app_encode_fun(A0,$o),
8.94/9.20	                                          app_encode_fun(A,$o),
8.94/9.20	                                          app_encode_app(app_encode_fun(A0,A),
8.94/9.20	                                                         app_encode_fun(
8.94/9.20	                                                         app_encode_fun(
8.94/9.20	                                                         A0,$o),
8.94/9.20	                                                         app_encode_fun(A,$o)),
8.94/9.20	                                                         'const/sets/IMAGE'(
8.94/9.20	                                                         A0,A),A1),
8.94/9.20	                                          A2)) =>
8.94/9.20	            app_encode_app(A,$o,P,A3))) <=>
8.94/9.20	        (![A3:A0]:
8.94/9.20	           (app_encode_app(app_encode_fun(A0,$o),$o,
8.94/9.20	                           app_encode_app(A0,
8.94/9.20	                                          app_encode_fun(app_encode_fun(
8.94/9.20	                                                         A0,$o),$o),
8.94/9.20	                                          'const/sets/IN'(A0),A3),
8.94/9.20	                           A2) =>
8.94/9.20	            app_encode_app(A,$o,P,app_encode_app(A0,A,A1,A3)))))))).
8.94/9.20	tff('0', plain,
8.94/9.20	    (app_encode_app(app_encode_fun(sk_A0, $o), $o, 
8.94/9.20	       app_encode_app(sk_A0, app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
8.94/9.20	         'const/sets/IN'(sk_A0), sk_A31), sk_A2)
8.94/9.20	     | app_encode_app(app_encode_fun(sk_A, $o), $o, 
8.94/9.20	         app_encode_app(sk_A, app_encode_fun(app_encode_fun(sk_A, $o), $o), 
8.94/9.20	           'const/sets/IN'(sk_A), sk_A32), 
8.94/9.20	         app_encode_app(app_encode_fun(sk_A0, $o), app_encode_fun(sk_A, $o), 
8.94/9.20	           app_encode_app(app_encode_fun(sk_A0, sk_A), 
8.94/9.20	             app_encode_fun(app_encode_fun(sk_A0, $o), 
8.94/9.20	               app_encode_fun(sk_A, $o)), 'const/sets/IMAGE'(sk_A0, sk_A), 
8.94/9.20	             sk_A1), sk_A2))),
8.94/9.20	    inference('cnf', [status(esa)], [zf_stmt_0])).
8.94/9.20	tff(zf_stmt_4, axiom,
8.94/9.20	  (![B:$tType,A:$tType,A0:B,A1:app_encode_fun(A,$o),A2:app_encode_fun(A,B)]:
8.94/9.20	     (app_encode_app(app_encode_fun(B,$o),$o,
8.94/9.20	                     app_encode_app(B,
8.94/9.20	                                    app_encode_fun(app_encode_fun(B,$o),$o),
8.94/9.20	                                    'const/sets/IN'(B),A0),
8.94/9.20	                     app_encode_app(app_encode_fun(A,$o),
8.94/9.20	                                    app_encode_fun(B,$o),
8.94/9.20	                                    app_encode_app(app_encode_fun(A,B),
8.94/9.20	                                                   app_encode_fun(app_encode_fun(
8.94/9.20	                                                                  A,$o),
8.94/9.20	                                                                  app_encode_fun(
8.94/9.20	                                                                  B,$o)),
8.94/9.20	                                                   'const/sets/IMAGE'(A,B),A2),
8.94/9.20	                                    A1)) <=>
8.94/9.20	      (?[A3:A]:
8.94/9.20	         ((A0 = app_encode_app(A,B,A2,A3)) & 
8.94/9.20	          app_encode_app(app_encode_fun(A,$o),$o,
8.94/9.20	                         app_encode_app(A,
8.94/9.20	                                        app_encode_fun(app_encode_fun(A,$o),
8.94/9.20	                                                       $o),
8.94/9.20	                                        'const/sets/IN'(A),A3),
8.94/9.20	                         A1)))))).
8.94/9.20	tff('1', plain,
8.94/9.20	    ![X0 : $tType, X1 : $tType, X2 : app_encode_fun(X0, X1), 
8.94/9.20	      X3 : app_encode_fun(X0, $o), X4 : X1]:
8.94/9.20	      (app_encode_app(app_encode_fun(X0, $o), $o, 
8.94/9.20	         app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
8.94/9.20	           'const/sets/IN'(X0), sk_A3(X0, X1, X2, X3, X4)), X3)
8.94/9.20	       | ~ app_encode_app(app_encode_fun(X1, $o), $o, 
8.94/9.20	             app_encode_app(X1, app_encode_fun(app_encode_fun(X1, $o), $o), 
8.94/9.20	               'const/sets/IN'(X1), X4), 
8.94/9.20	             app_encode_app(app_encode_fun(X0, $o), app_encode_fun(X1, $o), 
8.94/9.20	               app_encode_app(app_encode_fun(X0, X1), 
8.94/9.20	                 app_encode_fun(app_encode_fun(X0, $o), 
8.94/9.20	                   app_encode_fun(X1, $o)), 'const/sets/IMAGE'(X0, X1), X2), 
8.94/9.20	               X3))),
8.94/9.20	    inference('cnf', [status(esa)], [zf_stmt_4])).
8.94/9.20	tff('2', plain,
8.94/9.20	    (~ $true
8.94/9.20	     | app_encode_app(app_encode_fun(sk_A0, $o), $o, 
8.94/9.20	         app_encode_app(sk_A0, 
8.94/9.20	           app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
8.94/9.20	           'const/sets/IN'(sk_A0), sk_A31), sk_A2)
8.94/9.20	     | app_encode_app(app_encode_fun(sk_A0, $o), $o, 
8.94/9.20	         app_encode_app(sk_A0, 
8.94/9.20	           app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
8.94/9.20	           'const/sets/IN'(sk_A0), sk_A3(sk_A0, sk_A, sk_A1, sk_A2, sk_A32)), 
8.94/9.20	         sk_A2)),
8.94/9.20	    inference('sup-', [status(thm)], ['0', '1'])).
8.94/9.20	tff('3', plain,
8.94/9.20	    (app_encode_app(app_encode_fun(sk_A0, $o), $o, 
8.94/9.20	       app_encode_app(sk_A0, app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
8.94/9.20	         'const/sets/IN'(sk_A0), sk_A3(sk_A0, sk_A, sk_A1, sk_A2, sk_A32)), 
8.94/9.20	       sk_A2)
8.94/9.20	     | app_encode_app(app_encode_fun(sk_A0, $o), $o, 
8.94/9.20	         app_encode_app(sk_A0, 
8.94/9.20	           app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
8.94/9.20	           'const/sets/IN'(sk_A0), sk_A31), sk_A2)),
8.94/9.20	    inference('simplify', [status(thm)], ['2'])).
8.94/9.20	tff('4', plain,
8.94/9.20	    ![X7 : sk_A0, X8 : sk_A]:
8.94/9.20	      (~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
8.94/9.20	           app_encode_app(sk_A0, 
8.94/9.20	             app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
8.94/9.20	             'const/sets/IN'(sk_A0), X7), sk_A2)
8.94/9.20	       | app_encode_app(sk_A, $o, sk_P, 
8.94/9.20	           app_encode_app(sk_A0, sk_A, sk_A1, X7))
8.94/9.20	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
8.94/9.20	             app_encode_app(sk_A, 
8.94/9.20	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
8.94/9.20	               'const/sets/IN'(sk_A), X8), 
8.94/9.20	             app_encode_app(app_encode_fun(sk_A0, $o), 
8.94/9.20	               app_encode_fun(sk_A, $o), 
8.94/9.20	               app_encode_app(app_encode_fun(sk_A0, sk_A), 
8.94/9.20	                 app_encode_fun(app_encode_fun(sk_A0, $o), 
8.94/9.20	                   app_encode_fun(sk_A, $o)), 
8.94/9.20	                 'const/sets/IMAGE'(sk_A0, sk_A), sk_A1), sk_A2))
8.94/9.20	       | app_encode_app(sk_A, $o, sk_P, X8)),
8.94/9.20	    inference('cnf', [status(esa)], [zf_stmt_0])).
8.94/9.20	tff('5', plain,
8.94/9.20	    ![X0 : sk_A]:
8.94/9.20	      (~ $true
8.94/9.20	       | app_encode_app(app_encode_fun(sk_A0, $o), $o, 
8.94/9.20	           app_encode_app(sk_A0, 
8.94/9.20	             app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
8.94/9.20	             'const/sets/IN'(sk_A0), sk_A31), sk_A2)
8.94/9.20	       | app_encode_app(sk_A, $o, sk_P, X0)
8.94/9.20	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
8.94/9.20	             app_encode_app(sk_A, 
8.94/9.20	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
8.94/9.20	               'const/sets/IN'(sk_A), X0), 
8.94/9.20	             app_encode_app(app_encode_fun(sk_A0, $o), 
8.94/9.20	               app_encode_fun(sk_A, $o), 
8.94/9.20	               app_encode_app(app_encode_fun(sk_A0, sk_A), 
8.94/9.20	                 app_encode_fun(app_encode_fun(sk_A0, $o), 
8.94/9.20	                   app_encode_fun(sk_A, $o)), 
8.94/9.20	                 'const/sets/IMAGE'(sk_A0, sk_A), sk_A1), sk_A2))
8.94/9.20	       | app_encode_app(sk_A, $o, sk_P, 
8.94/9.20	           app_encode_app(sk_A0, sk_A, sk_A1, 
8.94/9.20	             sk_A3(sk_A0, sk_A, sk_A1, sk_A2, sk_A32)))),
8.94/9.20	    inference('sup-', [status(thm)], ['3', '4'])).
8.94/9.20	tff('6', plain,
8.94/9.20	    ![X0 : sk_A]:
8.94/9.20	      (app_encode_app(sk_A, $o, sk_P, 
8.94/9.20	         app_encode_app(sk_A0, sk_A, sk_A1, 
8.94/9.20	           sk_A3(sk_A0, sk_A, sk_A1, sk_A2, sk_A32)))
8.94/9.20	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
8.94/9.20	             app_encode_app(sk_A, 
8.94/9.20	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
8.94/9.20	               'const/sets/IN'(sk_A), X0), 
8.94/9.20	             app_encode_app(app_encode_fun(sk_A0, $o), 
8.94/9.20	               app_encode_fun(sk_A, $o), 
8.94/9.20	               app_encode_app(app_encode_fun(sk_A0, sk_A), 
8.94/9.20	                 app_encode_fun(app_encode_fun(sk_A0, $o), 
8.94/9.20	                   app_encode_fun(sk_A, $o)), 
8.94/9.20	                 'const/sets/IMAGE'(sk_A0, sk_A), sk_A1), sk_A2))
8.94/9.20	       | app_encode_app(sk_A, $o, sk_P, X0)
8.94/9.20	       | app_encode_app(app_encode_fun(sk_A0, $o), $o, 
8.94/9.20	           app_encode_app(sk_A0, 
8.94/9.20	             app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
8.94/9.20	             'const/sets/IN'(sk_A0), sk_A31), sk_A2)),
8.94/9.20	    inference('simplify', [status(thm)], ['5'])).
8.94/9.20	tff('7', plain,
8.94/9.20	    ![X0 : $tType, X1 : $tType, X2 : app_encode_fun(X0, X1), 
8.94/9.20	      X3 : app_encode_fun(X0, $o), X4 : X1]:
8.94/9.20	      (X4 = app_encode_app(X0, X1, X2, sk_A3(X0, X1, X2, X3, X4))
8.94/9.20	       | ~ app_encode_app(app_encode_fun(X1, $o), $o, 
8.94/9.20	             app_encode_app(X1, app_encode_fun(app_encode_fun(X1, $o), $o), 
8.94/9.20	               'const/sets/IN'(X1), X4), 
8.94/9.20	             app_encode_app(app_encode_fun(X0, $o), app_encode_fun(X1, $o), 
8.94/9.20	               app_encode_app(app_encode_fun(X0, X1), 
8.94/9.20	                 app_encode_fun(app_encode_fun(X0, $o), 
8.94/9.20	                   app_encode_fun(X1, $o)), 'const/sets/IMAGE'(X0, X1), X2), 
8.94/9.20	               X3))),
8.94/9.20	    inference('cnf', [status(esa)], [zf_stmt_4])).
8.94/9.20	tff('8', plain,
8.94/9.20	    (~ $true
8.94/9.20	     | app_encode_app(app_encode_fun(sk_A0, $o), $o, 
8.94/9.20	         app_encode_app(sk_A0, 
8.94/9.20	           app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
8.94/9.20	           'const/sets/IN'(sk_A0), sk_A31), sk_A2)
8.94/9.20	     | sk_A32
8.94/9.20	        = app_encode_app(sk_A0, sk_A, sk_A1, 
8.94/9.20	            sk_A3(sk_A0, sk_A, sk_A1, sk_A2, sk_A32))),
8.94/9.20	    inference('sup-', [status(thm)], ['0', '7'])).
8.94/9.20	tff('9', plain,
8.94/9.20	    (sk_A32
8.94/9.20	      = app_encode_app(sk_A0, sk_A, sk_A1, 
8.94/9.20	          sk_A3(sk_A0, sk_A, sk_A1, sk_A2, sk_A32))
8.94/9.20	     | app_encode_app(app_encode_fun(sk_A0, $o), $o, 
8.94/9.20	         app_encode_app(sk_A0, 
8.94/9.20	           app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
8.94/9.20	           'const/sets/IN'(sk_A0), sk_A31), sk_A2)),
8.94/9.20	    inference('simplify', [status(thm)], ['8'])).
8.94/9.20	tff('10', plain,
8.94/9.20	    ![X0 : $tType, X1 : $tType, X3 : app_encode_fun(X0, $o), X4 : X1, 
8.94/9.20	      X5 : app_encode_fun(X0, X1), X6 : X0]:
8.94/9.20	      (app_encode_app(app_encode_fun(X1, $o), $o, 
8.94/9.20	         app_encode_app(X1, app_encode_fun(app_encode_fun(X1, $o), $o), 
8.94/9.20	           'const/sets/IN'(X1), X4), 
8.94/9.20	         app_encode_app(app_encode_fun(X0, $o), app_encode_fun(X1, $o), 
8.94/9.20	           app_encode_app(app_encode_fun(X0, X1), 
8.94/9.20	             app_encode_fun(app_encode_fun(X0, $o), app_encode_fun(X1, $o)), 
8.94/9.20	             'const/sets/IMAGE'(X0, X1), X5), X3))
8.94/9.20	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
8.94/9.20	             app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
8.94/9.20	               'const/sets/IN'(X0), X6), X3)
8.94/9.20	       | X4 != app_encode_app(X0, X1, X5, X6)),
8.94/9.20	    inference('cnf', [status(esa)], [zf_stmt_4])).
8.94/9.20	tff('11', plain,
8.94/9.20	    ![X0 : $tType, X1 : $tType, X3 : app_encode_fun(X0, $o), 
8.94/9.20	      X5 : app_encode_fun(X0, X1), X6 : X0]:
8.94/9.20	      (~ app_encode_app(app_encode_fun(X0, $o), $o, 
8.94/9.20	           app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
8.94/9.20	             'const/sets/IN'(X0), X6), X3)
8.94/9.20	       | app_encode_app(app_encode_fun(X1, $o), $o, 
8.94/9.20	           app_encode_app(X1, app_encode_fun(app_encode_fun(X1, $o), $o), 
8.94/9.20	             'const/sets/IN'(X1), app_encode_app(X0, X1, X5, X6)), 
8.94/9.20	           app_encode_app(app_encode_fun(X0, $o), app_encode_fun(X1, $o), 
8.94/9.20	             app_encode_app(app_encode_fun(X0, X1), 
8.94/9.20	               app_encode_fun(app_encode_fun(X0, $o), app_encode_fun(X1, $o)), 
8.94/9.20	               'const/sets/IMAGE'(X0, X1), X5), X3))),
8.94/9.20	    inference('simplify', [status(thm)], ['10'])).
8.94/9.20	tff('12', plain,
8.94/9.20	    ![X0 : sk_A]:
8.94/9.20	      (~ $true
8.94/9.20	       | sk_A32
8.94/9.20	          = app_encode_app(sk_A0, sk_A, sk_A1, 
8.94/9.20	              sk_A3(sk_A0, sk_A, sk_A1, sk_A2, sk_A32))
8.94/9.20	       | app_encode_app(sk_A, $o, sk_P, X0)
8.94/9.20	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
8.94/9.20	             app_encode_app(sk_A, 
8.94/9.20	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
8.94/9.20	               'const/sets/IN'(sk_A), X0), 
8.94/9.20	             app_encode_app(app_encode_fun(sk_A0, $o), 
8.94/9.20	               app_encode_fun(sk_A, $o), 
8.94/9.20	               app_encode_app(app_encode_fun(sk_A0, sk_A), 
8.94/9.20	                 app_encode_fun(app_encode_fun(sk_A0, $o), 
8.94/9.20	                   app_encode_fun(sk_A, $o)), 
8.94/9.20	                 'const/sets/IMAGE'(sk_A0, sk_A), sk_A1), sk_A2))
8.94/9.20	       | app_encode_app(sk_A, $o, sk_P, 
8.94/9.20	           app_encode_app(sk_A0, sk_A, sk_A1, sk_A31))),
8.94/9.20	    inference('sup-', [status(thm)], ['9', '4'])).
8.94/9.20	tff('13', plain,
8.94/9.20	    ![X0 : sk_A]:
8.94/9.20	      (app_encode_app(sk_A, $o, sk_P, 
8.94/9.20	         app_encode_app(sk_A0, sk_A, sk_A1, sk_A31))
8.94/9.20	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
8.94/9.20	             app_encode_app(sk_A, 
8.94/9.20	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
8.94/9.20	               'const/sets/IN'(sk_A), X0), 
8.94/9.20	             app_encode_app(app_encode_fun(sk_A0, $o), 
8.94/9.20	               app_encode_fun(sk_A, $o), 
8.94/9.20	               app_encode_app(app_encode_fun(sk_A0, sk_A), 
8.94/9.20	                 app_encode_fun(app_encode_fun(sk_A0, $o), 
8.94/9.20	                   app_encode_fun(sk_A, $o)), 
8.94/9.20	                 'const/sets/IMAGE'(sk_A0, sk_A), sk_A1), sk_A2))
8.94/9.20	       | app_encode_app(sk_A, $o, sk_P, X0)
8.94/9.20	       | sk_A32
8.94/9.20	          = app_encode_app(sk_A0, sk_A, sk_A1, 
8.94/9.20	              sk_A3(sk_A0, sk_A, sk_A1, sk_A2, sk_A32))),
8.94/9.20	    inference('simplify', [status(thm)], ['12'])).
8.94/9.20	tff('14', plain,
8.94/9.20	    (~ app_encode_app(sk_A, $o, sk_P, 
8.94/9.20	         app_encode_app(sk_A0, sk_A, sk_A1, sk_A31))
8.94/9.20	     | app_encode_app(app_encode_fun(sk_A, $o), $o, 
8.94/9.20	         app_encode_app(sk_A, app_encode_fun(app_encode_fun(sk_A, $o), $o), 
8.94/9.20	           'const/sets/IN'(sk_A), sk_A32), 
8.94/9.20	         app_encode_app(app_encode_fun(sk_A0, $o), app_encode_fun(sk_A, $o), 
8.94/9.20	           app_encode_app(app_encode_fun(sk_A0, sk_A), 
8.94/9.20	             app_encode_fun(app_encode_fun(sk_A0, $o), 
8.94/9.20	               app_encode_fun(sk_A, $o)), 'const/sets/IMAGE'(sk_A0, sk_A), 
8.94/9.20	             sk_A1), sk_A2))),
8.94/9.20	    inference('cnf', [status(esa)], [zf_stmt_0])).
8.94/9.20	tff('15', plain,
8.94/9.20	    (~ $true
8.94/9.20	     | ~ app_encode_app(sk_A, $o, sk_P, 
8.94/9.20	           app_encode_app(sk_A0, sk_A, sk_A1, sk_A31))
8.94/9.20	     | sk_A32
8.94/9.20	        = app_encode_app(sk_A0, sk_A, sk_A1, 
8.94/9.20	            sk_A3(sk_A0, sk_A, sk_A1, sk_A2, sk_A32))),
8.94/9.20	    inference('sup-', [status(thm)], ['14', '7'])).
8.94/9.20	tff('16', plain,
8.94/9.20	    (sk_A32
8.94/9.20	      = app_encode_app(sk_A0, sk_A, sk_A1, 
8.94/9.20	          sk_A3(sk_A0, sk_A, sk_A1, sk_A2, sk_A32))
8.94/9.20	     | ~ app_encode_app(sk_A, $o, sk_P, 
8.94/9.20	           app_encode_app(sk_A0, sk_A, sk_A1, sk_A31))),
8.94/9.20	    inference('simplify', [status(thm)], ['15'])).
8.94/9.20	tff('17', plain,
8.94/9.20	    ![X0 : sk_A]:
8.94/9.20	      (sk_A32
8.94/9.20	        = app_encode_app(sk_A0, sk_A, sk_A1, 
8.94/9.20	            sk_A3(sk_A0, sk_A, sk_A1, sk_A2, sk_A32))
8.94/9.20	       | app_encode_app(sk_A, $o, sk_P, X0)
8.94/9.20	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
8.94/9.20	             app_encode_app(sk_A, 
8.94/9.20	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
8.94/9.20	               'const/sets/IN'(sk_A), X0), 
8.94/9.20	             app_encode_app(app_encode_fun(sk_A0, $o), 
8.94/9.20	               app_encode_fun(sk_A, $o), 
8.94/9.20	               app_encode_app(app_encode_fun(sk_A0, sk_A), 
8.94/9.20	                 app_encode_fun(app_encode_fun(sk_A0, $o), 
8.94/9.20	                   app_encode_fun(sk_A, $o)), 
8.94/9.20	                 'const/sets/IMAGE'(sk_A0, sk_A), sk_A1), sk_A2))),
8.94/9.20	    inference('clc', [status(thm)], ['13', '16'])).
8.94/9.20	tff('18', plain,
8.94/9.20	    ![X0 : sk_A0]:
8.94/9.20	      (~ $true
8.94/9.20	       | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
8.94/9.20	             app_encode_app(sk_A0, 
8.94/9.20	               app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
8.94/9.20	               'const/sets/IN'(sk_A0), X0), sk_A2)
8.94/9.20	       | app_encode_app(sk_A, $o, sk_P, 
8.94/9.20	           app_encode_app(sk_A0, sk_A, sk_A1, X0))
8.94/9.20	       | sk_A32
8.94/9.20	          = app_encode_app(sk_A0, sk_A, sk_A1, 
8.94/9.20	              sk_A3(sk_A0, sk_A, sk_A1, sk_A2, sk_A32))),
8.94/9.20	    inference('sup-', [status(thm)], ['11', '17'])).
8.94/9.20	tff('19', plain,
8.94/9.20	    ![X0 : sk_A0]:
8.94/9.20	      (sk_A32
8.94/9.20	        = app_encode_app(sk_A0, sk_A, sk_A1, 
8.94/9.20	            sk_A3(sk_A0, sk_A, sk_A1, sk_A2, sk_A32))
8.94/9.20	       | app_encode_app(sk_A, $o, sk_P, 
8.94/9.20	           app_encode_app(sk_A0, sk_A, sk_A1, X0))
8.94/9.20	       | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
8.94/9.20	             app_encode_app(sk_A0, 
8.94/9.20	               app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
8.94/9.20	               'const/sets/IN'(sk_A0), X0), sk_A2)),
8.94/9.20	    inference('simplify', [status(thm)], ['18'])).
8.94/9.20	tff('20', plain,
8.94/9.20	    (~ $true
8.94/9.20	     | sk_A32
8.94/9.20	        = app_encode_app(sk_A0, sk_A, sk_A1, 
8.94/9.20	            sk_A3(sk_A0, sk_A, sk_A1, sk_A2, sk_A32))
8.94/9.20	     | app_encode_app(sk_A, $o, sk_P, 
8.94/9.20	         app_encode_app(sk_A0, sk_A, sk_A1, sk_A31))
8.94/9.20	     | sk_A32
8.94/9.20	        = app_encode_app(sk_A0, sk_A, sk_A1, 
8.94/9.20	            sk_A3(sk_A0, sk_A, sk_A1, sk_A2, sk_A32))),
8.94/9.20	    inference('sup-', [status(thm)], ['9', '19'])).
8.94/9.20	tff('21', plain,
8.94/9.20	    (app_encode_app(sk_A, $o, sk_P, 
8.94/9.20	       app_encode_app(sk_A0, sk_A, sk_A1, sk_A31))
8.94/9.20	     | sk_A32
8.94/9.20	        = app_encode_app(sk_A0, sk_A, sk_A1, 
8.94/9.20	            sk_A3(sk_A0, sk_A, sk_A1, sk_A2, sk_A32))),
8.94/9.20	    inference('simplify', [status(thm)], ['20'])).
8.94/9.20	tff('22', plain,
8.94/9.20	    sk_A32
8.94/9.20	     = app_encode_app(sk_A0, sk_A, sk_A1, 
8.94/9.20	         sk_A3(sk_A0, sk_A, sk_A1, sk_A2, sk_A32)),
8.94/9.20	    inference('clc', [status(thm)], ['21', '16'])).
8.94/9.20	tff('23', plain,
8.94/9.20	    ![X0 : sk_A]:
8.94/9.20	      (app_encode_app(sk_A, $o, sk_P, sk_A32)
8.94/9.20	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
8.94/9.20	             app_encode_app(sk_A, 
8.94/9.20	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
8.94/9.20	               'const/sets/IN'(sk_A), X0), 
8.94/9.20	             app_encode_app(app_encode_fun(sk_A0, $o), 
8.94/9.20	               app_encode_fun(sk_A, $o), 
8.94/9.20	               app_encode_app(app_encode_fun(sk_A0, sk_A), 
8.94/9.20	                 app_encode_fun(app_encode_fun(sk_A0, $o), 
8.94/9.20	                   app_encode_fun(sk_A, $o)), 
8.94/9.20	                 'const/sets/IMAGE'(sk_A0, sk_A), sk_A1), sk_A2))
8.94/9.20	       | app_encode_app(sk_A, $o, sk_P, X0)
8.94/9.20	       | app_encode_app(app_encode_fun(sk_A0, $o), $o, 
8.94/9.20	           app_encode_app(sk_A0, 
8.94/9.20	             app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
8.94/9.20	             'const/sets/IN'(sk_A0), sk_A31), sk_A2)),
8.94/9.20	    inference('demod', [status(thm)], ['6', '22'])).
8.94/9.20	tff('24', plain,
8.94/9.20	    (app_encode_app(app_encode_fun(sk_A0, $o), $o, 
8.94/9.20	       app_encode_app(sk_A0, app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
8.94/9.20	         'const/sets/IN'(sk_A0), sk_A31), sk_A2)
8.94/9.20	     | ~ app_encode_app(sk_A, $o, sk_P, sk_A32)),
8.94/9.20	    inference('cnf', [status(esa)], [zf_stmt_0])).
8.94/9.20	tff('25', plain,
8.94/9.20	    ![X0 : sk_A]:
8.94/9.20	      (~ $true
8.94/9.20	       | ~ app_encode_app(sk_A, $o, sk_P, sk_A32)
8.94/9.20	       | app_encode_app(sk_A, $o, sk_P, X0)
8.94/9.20	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
8.94/9.20	             app_encode_app(sk_A, 
8.94/9.20	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
8.94/9.20	               'const/sets/IN'(sk_A), X0), 
8.94/9.20	             app_encode_app(app_encode_fun(sk_A0, $o), 
8.94/9.20	               app_encode_fun(sk_A, $o), 
8.94/9.20	               app_encode_app(app_encode_fun(sk_A0, sk_A), 
8.94/9.20	                 app_encode_fun(app_encode_fun(sk_A0, $o), 
8.94/9.20	                   app_encode_fun(sk_A, $o)), 
8.94/9.20	                 'const/sets/IMAGE'(sk_A0, sk_A), sk_A1), sk_A2))
8.94/9.20	       | app_encode_app(sk_A, $o, sk_P, 
8.94/9.20	           app_encode_app(sk_A0, sk_A, sk_A1, sk_A31))),
8.94/9.20	    inference('sup-', [status(thm)], ['24', '4'])).
8.94/9.20	tff('26', plain,
8.94/9.20	    ![X0 : sk_A]:
8.94/9.20	      (app_encode_app(sk_A, $o, sk_P, 
8.94/9.20	         app_encode_app(sk_A0, sk_A, sk_A1, sk_A31))
8.94/9.20	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
8.94/9.20	             app_encode_app(sk_A, 
8.94/9.20	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
8.94/9.20	               'const/sets/IN'(sk_A), X0), 
8.94/9.20	             app_encode_app(app_encode_fun(sk_A0, $o), 
8.94/9.20	               app_encode_fun(sk_A, $o), 
8.94/9.20	               app_encode_app(app_encode_fun(sk_A0, sk_A), 
8.94/9.20	                 app_encode_fun(app_encode_fun(sk_A0, $o), 
8.94/9.20	                   app_encode_fun(sk_A, $o)), 
8.94/9.20	                 'const/sets/IMAGE'(sk_A0, sk_A), sk_A1), sk_A2))
8.94/9.20	       | app_encode_app(sk_A, $o, sk_P, X0)
8.94/9.20	       | ~ app_encode_app(sk_A, $o, sk_P, sk_A32)),
8.94/9.20	    inference('simplify', [status(thm)], ['25'])).
8.94/9.20	tff('27', plain,
8.94/9.20	    (~ app_encode_app(sk_A, $o, sk_P, 
8.94/9.20	         app_encode_app(sk_A0, sk_A, sk_A1, sk_A31))
8.94/9.20	     | ~ app_encode_app(sk_A, $o, sk_P, sk_A32)),
8.94/9.20	    inference('cnf', [status(esa)], [zf_stmt_0])).
8.94/9.20	tff('28', plain,
8.94/9.20	    ![X0 : sk_A]:
8.94/9.20	      (~ app_encode_app(sk_A, $o, sk_P, sk_A32)
8.94/9.20	       | app_encode_app(sk_A, $o, sk_P, X0)
8.94/9.20	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
8.94/9.20	             app_encode_app(sk_A, 
8.94/9.20	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
8.94/9.20	               'const/sets/IN'(sk_A), X0), 
8.94/9.20	             app_encode_app(app_encode_fun(sk_A0, $o), 
8.94/9.20	               app_encode_fun(sk_A, $o), 
8.94/9.20	               app_encode_app(app_encode_fun(sk_A0, sk_A), 
8.94/9.20	                 app_encode_fun(app_encode_fun(sk_A0, $o), 
8.94/9.20	                   app_encode_fun(sk_A, $o)), 
8.94/9.20	                 'const/sets/IMAGE'(sk_A0, sk_A), sk_A1), sk_A2))),
8.94/9.20	    inference('clc', [status(thm)], ['26', '27'])).
8.94/9.20	tff('29', plain,
8.94/9.20	    ![X0 : sk_A0]:
8.94/9.20	      (~ $true
8.94/9.20	       | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
8.94/9.20	             app_encode_app(sk_A0, 
8.94/9.20	               app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
8.94/9.20	               'const/sets/IN'(sk_A0), X0), sk_A2)
8.94/9.20	       | app_encode_app(sk_A, $o, sk_P, 
8.94/9.20	           app_encode_app(sk_A0, sk_A, sk_A1, X0))
8.94/9.20	       | ~ app_encode_app(sk_A, $o, sk_P, sk_A32)),
8.94/9.20	    inference('sup-', [status(thm)], ['11', '28'])).
8.94/9.20	tff('30', plain,
8.94/9.20	    ![X0 : sk_A0]:
8.94/9.20	      (~ app_encode_app(sk_A, $o, sk_P, sk_A32)
8.94/9.20	       | app_encode_app(sk_A, $o, sk_P, 
8.94/9.20	           app_encode_app(sk_A0, sk_A, sk_A1, X0))
8.94/9.20	       | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
8.94/9.20	             app_encode_app(sk_A0, 
8.94/9.20	               app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
8.94/9.20	               'const/sets/IN'(sk_A0), X0), sk_A2)),
8.94/9.20	    inference('simplify', [status(thm)], ['29'])).
8.94/9.20	tff('31', plain,
8.94/9.20	    (~ $true
8.94/9.20	     | ~ app_encode_app(sk_A, $o, sk_P, sk_A32)
8.94/9.20	     | app_encode_app(sk_A, $o, sk_P, 
8.94/9.20	         app_encode_app(sk_A0, sk_A, sk_A1, sk_A31))
8.94/9.20	     | ~ app_encode_app(sk_A, $o, sk_P, sk_A32)),
8.94/9.20	    inference('sup-', [status(thm)], ['24', '30'])).
8.94/9.20	tff('32', plain,
8.94/9.20	    (app_encode_app(sk_A, $o, sk_P, 
8.94/9.20	       app_encode_app(sk_A0, sk_A, sk_A1, sk_A31))
8.94/9.20	     | ~ app_encode_app(sk_A, $o, sk_P, sk_A32)),
8.94/9.20	    inference('simplify', [status(thm)], ['31'])).
8.94/9.20	tff('33', plain, ~ app_encode_app(sk_A, $o, sk_P, sk_A32),
8.94/9.20	    inference('clc', [status(thm)], ['32', '27'])).
8.94/9.20	tff('34', plain,
8.94/9.20	    ![X0 : sk_A]:
8.94/9.20	      (app_encode_app(app_encode_fun(sk_A0, $o), $o, 
8.94/9.20	         app_encode_app(sk_A0, 
8.94/9.20	           app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
8.94/9.20	           'const/sets/IN'(sk_A0), sk_A31), sk_A2)
8.94/9.20	       | app_encode_app(sk_A, $o, sk_P, X0)
8.94/9.20	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
8.94/9.20	             app_encode_app(sk_A, 
8.94/9.20	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
8.94/9.20	               'const/sets/IN'(sk_A), X0), 
8.94/9.20	             app_encode_app(app_encode_fun(sk_A0, $o), 
8.94/9.20	               app_encode_fun(sk_A, $o), 
8.94/9.20	               app_encode_app(app_encode_fun(sk_A0, sk_A), 
8.94/9.20	                 app_encode_fun(app_encode_fun(sk_A0, $o), 
8.94/9.20	                   app_encode_fun(sk_A, $o)), 
8.94/9.20	                 'const/sets/IMAGE'(sk_A0, sk_A), sk_A1), sk_A2))),
8.94/9.20	    inference('clc', [status(thm)], ['23', '33'])).
8.94/9.20	tff('35', plain,
8.94/9.20	    (~ $true
8.94/9.20	     | app_encode_app(app_encode_fun(sk_A0, $o), $o, 
8.94/9.20	         app_encode_app(sk_A0, 
8.94/9.20	           app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
8.94/9.20	           'const/sets/IN'(sk_A0), sk_A31), sk_A2)
8.94/9.20	     | app_encode_app(sk_A, $o, sk_P, sk_A32)
8.94/9.20	     | app_encode_app(app_encode_fun(sk_A0, $o), $o, 
8.94/9.20	         app_encode_app(sk_A0, 
8.94/9.20	           app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
8.94/9.20	           'const/sets/IN'(sk_A0), sk_A31), sk_A2)),
8.94/9.20	    inference('sup-', [status(thm)], ['0', '34'])).
8.94/9.20	tff('36', plain,
8.94/9.20	    (app_encode_app(sk_A, $o, sk_P, sk_A32)
8.94/9.20	     | app_encode_app(app_encode_fun(sk_A0, $o), $o, 
8.94/9.20	         app_encode_app(sk_A0, 
8.94/9.20	           app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
8.94/9.20	           'const/sets/IN'(sk_A0), sk_A31), sk_A2)),
8.94/9.20	    inference('simplify', [status(thm)], ['35'])).
8.94/9.20	tff('37', plain,
8.94/9.20	    app_encode_app(app_encode_fun(sk_A0, $o), $o, 
8.94/9.20	      app_encode_app(sk_A0, app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
8.94/9.20	        'const/sets/IN'(sk_A0), sk_A31), sk_A2),
8.94/9.20	    inference('clc', [status(thm)], ['36', '33'])).
8.94/9.20	tff('38', plain,
8.94/9.20	    ![X0 : $tType, X1 : $tType, X2 : app_encode_fun(X1, $o), 
8.94/9.20	      X3 : app_encode_fun(X1, X0), X4 : X1]:
8.94/9.20	      (~ $true
8.94/9.20	       | ~ app_encode_app(app_encode_fun(X1, $o), $o, 
8.94/9.20	             app_encode_app(X1, app_encode_fun(app_encode_fun(X1, $o), $o), 
8.94/9.20	               'const/sets/IN'(X1), X4), X2)
8.94/9.20	       | app_encode_app(X1, X0, X3, X4)
8.94/9.20	          = app_encode_app(X1, X0, X3, 
8.94/9.20	              sk_A3(X1, X0, X3, X2, app_encode_app(X1, X0, X3, X4)))),
8.94/9.20	    inference('sup-', [status(thm)], ['11', '7'])).
8.94/9.20	tff('39', plain,
8.94/9.20	    ![X0 : $tType, X1 : $tType, X2 : app_encode_fun(X1, $o), 
8.94/9.20	      X3 : app_encode_fun(X1, X0), X4 : X1]:
8.94/9.20	      (app_encode_app(X1, X0, X3, X4)
8.94/9.20	        = app_encode_app(X1, X0, X3, 
8.94/9.20	            sk_A3(X1, X0, X3, X2, app_encode_app(X1, X0, X3, X4)))
8.94/9.20	       | ~ app_encode_app(app_encode_fun(X1, $o), $o, 
8.94/9.20	             app_encode_app(X1, app_encode_fun(app_encode_fun(X1, $o), $o), 
8.94/9.20	               'const/sets/IN'(X1), X4), X2)),
8.94/9.20	    inference('simplify', [status(thm)], ['38'])).
8.94/9.20	tff('40', plain,
8.94/9.20	    ![X0 : $tType, X1 : app_encode_fun(sk_A0, X0)]:
8.94/9.20	      (~ $true
8.94/9.20	       | app_encode_app(sk_A0, X0, X1, sk_A31)
8.94/9.20	          = app_encode_app(sk_A0, X0, X1, 
8.94/9.20	              sk_A3(sk_A0, X0, X1, sk_A2, 
8.94/9.20	                app_encode_app(sk_A0, X0, X1, sk_A31)))),
8.94/9.20	    inference('sup-', [status(thm)], ['37', '39'])).
8.94/9.20	tff('41', plain,
8.94/9.20	    ![X0 : $tType, X1 : app_encode_fun(sk_A0, X0)]:
8.94/9.20	      app_encode_app(sk_A0, X0, X1, sk_A31)
8.94/9.20	       = app_encode_app(sk_A0, X0, X1, 
8.94/9.20	           sk_A3(sk_A0, X0, X1, sk_A2, app_encode_app(sk_A0, X0, X1, sk_A31))),
8.94/9.20	    inference('simplify', [status(thm)], ['40'])).
8.94/9.20	tff('42', plain,
8.94/9.20	    ![X0 : $tType, X1 : app_encode_fun(sk_A0, X0), 
8.94/9.20	      X2 : app_encode_fun(sk_A0, $o)]:
8.94/9.20	      (app_encode_app(app_encode_fun(X0, $o), $o, 
8.94/9.20	         app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
8.94/9.20	           'const/sets/IN'(X0), app_encode_app(sk_A0, X0, X1, sk_A31)), 
8.94/9.20	         app_encode_app(app_encode_fun(sk_A0, $o), app_encode_fun(X0, $o), 
8.94/9.20	           app_encode_app(app_encode_fun(sk_A0, X0), 
8.94/9.20	             app_encode_fun(app_encode_fun(sk_A0, $o), 
8.94/9.20	               app_encode_fun(X0, $o)), 'const/sets/IMAGE'(sk_A0, X0), X1), 
8.94/9.20	           X2))
8.94/9.20	       | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
8.94/9.20	             app_encode_app(sk_A0, 
8.94/9.20	               app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
8.94/9.20	               'const/sets/IN'(sk_A0), 
8.94/9.20	               sk_A3(sk_A0, X0, X1, sk_A2, 
8.94/9.20	                 app_encode_app(sk_A0, X0, X1, sk_A31))), X2)),
8.94/9.20	    inference('sup+', [status(thm)], ['41', '11'])).
8.94/9.20	tff('43', plain,
8.94/9.20	    ![X0 : $tType, X1 : $tType, X2 : app_encode_fun(X1, $o), 
8.94/9.20	      X3 : app_encode_fun(X1, X0), X4 : X1]:
8.94/9.20	      (~ $true
8.94/9.20	       | ~ app_encode_app(app_encode_fun(X1, $o), $o, 
8.94/9.20	             app_encode_app(X1, app_encode_fun(app_encode_fun(X1, $o), $o), 
8.94/9.20	               'const/sets/IN'(X1), X4), X2)
8.94/9.20	       | app_encode_app(app_encode_fun(X1, $o), $o, 
8.94/9.20	           app_encode_app(X1, app_encode_fun(app_encode_fun(X1, $o), $o), 
8.94/9.20	             'const/sets/IN'(X1), 
8.94/9.20	             sk_A3(X1, X0, X3, X2, app_encode_app(X1, X0, X3, X4))), X2)),
8.94/9.20	    inference('sup-', [status(thm)], ['11', '1'])).
8.94/9.20	tff('44', plain,
8.94/9.20	    ![X0 : $tType, X1 : $tType, X2 : app_encode_fun(X1, $o), 
8.94/9.20	      X3 : app_encode_fun(X1, X0), X4 : X1]:
8.94/9.20	      (app_encode_app(app_encode_fun(X1, $o), $o, 
8.94/9.20	         app_encode_app(X1, app_encode_fun(app_encode_fun(X1, $o), $o), 
8.94/9.20	           'const/sets/IN'(X1), 
8.94/9.20	           sk_A3(X1, X0, X3, X2, app_encode_app(X1, X0, X3, X4))), X2)
8.94/9.20	       | ~ app_encode_app(app_encode_fun(X1, $o), $o, 
8.94/9.20	             app_encode_app(X1, app_encode_fun(app_encode_fun(X1, $o), $o), 
8.94/9.20	               'const/sets/IN'(X1), X4), X2)),
8.94/9.20	    inference('simplify', [status(thm)], ['43'])).
8.94/9.20	tff('45', plain,
8.94/9.20	    ![X0 : $tType, X1 : sk_A0, X2 : app_encode_fun(sk_A0, X0), X3 : sk_A]:
8.94/9.20	      (~ $true
8.94/9.20	       | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
8.94/9.20	             app_encode_app(sk_A0, 
8.94/9.20	               app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
8.94/9.20	               'const/sets/IN'(sk_A0), X1), sk_A2)
8.94/9.20	       | app_encode_app(sk_A, $o, sk_P, X3)
8.94/9.20	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
8.94/9.20	             app_encode_app(sk_A, 
8.94/9.20	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
8.94/9.20	               'const/sets/IN'(sk_A), X3), 
8.94/9.20	             app_encode_app(app_encode_fun(sk_A0, $o), 
8.94/9.20	               app_encode_fun(sk_A, $o), 
8.94/9.20	               app_encode_app(app_encode_fun(sk_A0, sk_A), 
8.94/9.20	                 app_encode_fun(app_encode_fun(sk_A0, $o), 
8.94/9.20	                   app_encode_fun(sk_A, $o)), 
8.94/9.20	                 'const/sets/IMAGE'(sk_A0, sk_A), sk_A1), sk_A2))
8.94/9.20	       | app_encode_app(sk_A, $o, sk_P, 
8.94/9.20	           app_encode_app(sk_A0, sk_A, sk_A1, 
8.94/9.20	             sk_A3(sk_A0, X0, X2, sk_A2, app_encode_app(sk_A0, X0, X2, X1))))),
8.94/9.20	    inference('sup-', [status(thm)], ['44', '4'])).
8.94/9.20	tff('46', plain,
8.94/9.20	    ![X0 : $tType, X1 : sk_A0, X2 : app_encode_fun(sk_A0, X0), X3 : sk_A]:
8.94/9.20	      (app_encode_app(sk_A, $o, sk_P, 
8.94/9.20	         app_encode_app(sk_A0, sk_A, sk_A1, 
8.94/9.20	           sk_A3(sk_A0, X0, X2, sk_A2, app_encode_app(sk_A0, X0, X2, X1))))
8.94/9.20	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
8.94/9.20	             app_encode_app(sk_A, 
8.94/9.20	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
8.94/9.20	               'const/sets/IN'(sk_A), X3), 
8.94/9.20	             app_encode_app(app_encode_fun(sk_A0, $o), 
8.94/9.20	               app_encode_fun(sk_A, $o), 
8.94/9.20	               app_encode_app(app_encode_fun(sk_A0, sk_A), 
8.94/9.20	                 app_encode_fun(app_encode_fun(sk_A0, $o), 
8.94/9.20	                   app_encode_fun(sk_A, $o)), 
8.94/9.20	                 'const/sets/IMAGE'(sk_A0, sk_A), sk_A1), sk_A2))
8.94/9.20	       | app_encode_app(sk_A, $o, sk_P, X3)
8.94/9.20	       | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
8.94/9.20	             app_encode_app(sk_A0, 
8.94/9.20	               app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
8.94/9.20	               'const/sets/IN'(sk_A0), X1), sk_A2)),
8.94/9.20	    inference('simplify', [status(thm)], ['45'])).
8.94/9.20	tff('47', plain,
8.94/9.20	    ![X0 : sk_A0, X1 : $tType, X2 : app_encode_fun(sk_A0, X1)]:
8.94/9.20	      (~ $true
8.94/9.20	       | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
8.94/9.20	             app_encode_app(sk_A0, 
8.94/9.20	               app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
8.94/9.20	               'const/sets/IN'(sk_A0), 
8.94/9.20	               sk_A3(sk_A0, sk_A, sk_A1, sk_A2, 
8.94/9.20	                 app_encode_app(sk_A0, sk_A, sk_A1, sk_A31))), sk_A2)
8.94/9.20	       | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
8.94/9.20	             app_encode_app(sk_A0, 
8.94/9.20	               app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
8.94/9.20	               'const/sets/IN'(sk_A0), X0), sk_A2)
8.94/9.20	       | app_encode_app(sk_A, $o, sk_P, 
8.94/9.20	           app_encode_app(sk_A0, sk_A, sk_A1, sk_A31))
8.94/9.20	       | app_encode_app(sk_A, $o, sk_P, 
8.94/9.20	           app_encode_app(sk_A0, sk_A, sk_A1, 
8.94/9.20	             sk_A3(sk_A0, X1, X2, sk_A2, app_encode_app(sk_A0, X1, X2, X0))))),
8.94/9.20	    inference('sup-', [status(thm)], ['42', '46'])).
8.94/9.20	tff('48', plain,
8.94/9.20	    ![X0 : $tType, X1 : app_encode_fun(sk_A0, X0), 
8.94/9.20	      X2 : app_encode_fun(sk_A0, $o)]:
8.94/9.20	      (app_encode_app(app_encode_fun(sk_A0, $o), $o, 
8.94/9.20	         app_encode_app(sk_A0, 
8.94/9.20	           app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
8.94/9.20	           'const/sets/IN'(sk_A0), 
8.94/9.20	           sk_A3(sk_A0, X0, X1, X2, app_encode_app(sk_A0, X0, X1, sk_A31))), 
8.94/9.20	         X2)
8.94/9.20	       | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
8.94/9.20	             app_encode_app(sk_A0, 
8.94/9.20	               app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
8.94/9.20	               'const/sets/IN'(sk_A0), 
8.94/9.20	               sk_A3(sk_A0, X0, X1, sk_A2, 
8.94/9.20	                 app_encode_app(sk_A0, X0, X1, sk_A31))), X2)),
8.94/9.20	    inference('sup+', [status(thm)], ['41', '44'])).
8.94/9.20	tff('49', plain,
8.94/9.20	    ![X0 : $tType, X1 : app_encode_fun(sk_A0, X0)]:
8.94/9.20	      (~ $true
8.94/9.20	       | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
8.94/9.20	             app_encode_app(sk_A0, 
8.94/9.20	               app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
8.94/9.20	               'const/sets/IN'(sk_A0), sk_A31), sk_A2)
8.94/9.20	       | app_encode_app(app_encode_fun(sk_A0, $o), $o, 
8.94/9.20	           app_encode_app(sk_A0, 
8.94/9.20	             app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
8.94/9.20	             'const/sets/IN'(sk_A0), 
8.94/9.20	             sk_A3(sk_A0, X0, X1, sk_A2, 
8.94/9.20	               app_encode_app(sk_A0, X0, X1, sk_A31))), sk_A2)),
8.94/9.20	    inference('sup-', [status(thm)], ['44', '48'])).
8.94/9.20	tff('50', plain,
8.94/9.20	    ![X0 : $tType, X1 : app_encode_fun(sk_A0, X0)]:
8.94/9.20	      (~ $true
8.94/9.20	       | ~ $true
8.94/9.20	       | app_encode_app(app_encode_fun(sk_A0, $o), $o, 
8.94/9.20	           app_encode_app(sk_A0, 
8.94/9.20	             app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
8.94/9.20	             'const/sets/IN'(sk_A0), 
8.94/9.20	             sk_A3(sk_A0, X0, X1, sk_A2, 
8.94/9.20	               app_encode_app(sk_A0, X0, X1, sk_A31))), sk_A2)),
8.94/9.20	    inference('demod', [status(thm)], ['49', '37'])).
8.94/9.20	tff('51', plain,
8.94/9.20	    ![X0 : $tType, X1 : app_encode_fun(sk_A0, X0)]:
8.94/9.20	      app_encode_app(app_encode_fun(sk_A0, $o), $o, 
8.94/9.20	        app_encode_app(sk_A0, app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
8.94/9.20	          'const/sets/IN'(sk_A0), 
8.94/9.20	          sk_A3(sk_A0, X0, X1, sk_A2, app_encode_app(sk_A0, X0, X1, sk_A31))), 
8.94/9.20	        sk_A2),
8.94/9.20	    inference('simplify', [status(thm)], ['50'])).
8.94/9.20	tff('52', plain,
8.94/9.20	    ![X0 : sk_A0, X1 : $tType, X2 : app_encode_fun(sk_A0, X1)]:
8.94/9.20	      (~ $true
8.94/9.20	       | ~ $true
8.94/9.20	       | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
8.94/9.20	             app_encode_app(sk_A0, 
8.94/9.20	               app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
8.94/9.20	               'const/sets/IN'(sk_A0), X0), sk_A2)
8.94/9.20	       | app_encode_app(sk_A, $o, sk_P, 
8.94/9.20	           app_encode_app(sk_A0, sk_A, sk_A1, sk_A31))
8.94/9.20	       | app_encode_app(sk_A, $o, sk_P, 
8.94/9.20	           app_encode_app(sk_A0, sk_A, sk_A1, 
8.94/9.20	             sk_A3(sk_A0, X1, X2, sk_A2, app_encode_app(sk_A0, X1, X2, X0))))),
8.94/9.20	    inference('demod', [status(thm)], ['47', '51'])).
8.94/9.20	tff('53', plain,
8.94/9.20	    ![X0 : sk_A0, X1 : $tType, X2 : app_encode_fun(sk_A0, X1)]:
8.94/9.20	      (app_encode_app(sk_A, $o, sk_P, 
8.94/9.20	         app_encode_app(sk_A0, sk_A, sk_A1, 
8.94/9.20	           sk_A3(sk_A0, X1, X2, sk_A2, app_encode_app(sk_A0, X1, X2, X0))))
8.94/9.20	       | app_encode_app(sk_A, $o, sk_P, 
8.94/9.20	           app_encode_app(sk_A0, sk_A, sk_A1, sk_A31))
8.94/9.20	       | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
8.94/9.20	             app_encode_app(sk_A0, 
8.94/9.20	               app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
8.94/9.20	               'const/sets/IN'(sk_A0), X0), sk_A2)),
8.94/9.20	    inference('simplify', [status(thm)], ['52'])).
8.94/9.20	tff('54', plain,
8.94/9.20	    (~ $true
8.94/9.20	     | ~ app_encode_app(sk_A, $o, sk_P, 
8.94/9.20	           app_encode_app(sk_A0, sk_A, sk_A1, sk_A31))
8.94/9.20	     | app_encode_app(app_encode_fun(sk_A0, $o), $o, 
8.94/9.20	         app_encode_app(sk_A0, 
8.94/9.20	           app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
8.94/9.20	           'const/sets/IN'(sk_A0), sk_A3(sk_A0, sk_A, sk_A1, sk_A2, sk_A32)), 
8.94/9.20	         sk_A2)),
8.94/9.20	    inference('sup-', [status(thm)], ['14', '1'])).
8.94/9.20	tff('55', plain,
8.94/9.20	    (app_encode_app(app_encode_fun(sk_A0, $o), $o, 
8.94/9.20	       app_encode_app(sk_A0, app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
8.94/9.20	         'const/sets/IN'(sk_A0), sk_A3(sk_A0, sk_A, sk_A1, sk_A2, sk_A32)), 
8.94/9.20	       sk_A2)
8.94/9.20	     | ~ app_encode_app(sk_A, $o, sk_P, 
8.94/9.20	           app_encode_app(sk_A0, sk_A, sk_A1, sk_A31))),
8.94/9.20	    inference('simplify', [status(thm)], ['54'])).
8.94/9.20	tff('56', plain,
8.94/9.20	    ![X0 : sk_A]:
8.94/9.20	      (~ $true
8.94/9.20	       | ~ app_encode_app(sk_A, $o, sk_P, 
8.94/9.20	             app_encode_app(sk_A0, sk_A, sk_A1, sk_A31))
8.94/9.20	       | app_encode_app(sk_A, $o, sk_P, X0)
8.94/9.20	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
8.94/9.20	             app_encode_app(sk_A, 
8.94/9.20	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
8.94/9.20	               'const/sets/IN'(sk_A), X0), 
8.94/9.20	             app_encode_app(app_encode_fun(sk_A0, $o), 
8.94/9.20	               app_encode_fun(sk_A, $o), 
8.94/9.20	               app_encode_app(app_encode_fun(sk_A0, sk_A), 
8.94/9.20	                 app_encode_fun(app_encode_fun(sk_A0, $o), 
8.94/9.20	                   app_encode_fun(sk_A, $o)), 
8.94/9.20	                 'const/sets/IMAGE'(sk_A0, sk_A), sk_A1), sk_A2))
8.94/9.20	       | app_encode_app(sk_A, $o, sk_P, 
8.94/9.20	           app_encode_app(sk_A0, sk_A, sk_A1, 
8.94/9.20	             sk_A3(sk_A0, sk_A, sk_A1, sk_A2, sk_A32)))),
8.94/9.20	    inference('sup-', [status(thm)], ['55', '4'])).
8.94/9.20	tff('57', plain,
8.94/9.20	    ![X0 : sk_A]:
8.94/9.20	      (app_encode_app(sk_A, $o, sk_P, 
8.94/9.20	         app_encode_app(sk_A0, sk_A, sk_A1, 
8.94/9.20	           sk_A3(sk_A0, sk_A, sk_A1, sk_A2, sk_A32)))
8.94/9.20	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
8.94/9.20	             app_encode_app(sk_A, 
8.94/9.20	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
8.94/9.20	               'const/sets/IN'(sk_A), X0), 
8.94/9.20	             app_encode_app(app_encode_fun(sk_A0, $o), 
8.94/9.20	               app_encode_fun(sk_A, $o), 
8.94/9.20	               app_encode_app(app_encode_fun(sk_A0, sk_A), 
8.94/9.20	                 app_encode_fun(app_encode_fun(sk_A0, $o), 
8.94/9.20	                   app_encode_fun(sk_A, $o)), 
8.94/9.20	                 'const/sets/IMAGE'(sk_A0, sk_A), sk_A1), sk_A2))
8.94/9.20	       | app_encode_app(sk_A, $o, sk_P, X0)
8.94/9.20	       | ~ app_encode_app(sk_A, $o, sk_P, 
8.94/9.20	             app_encode_app(sk_A0, sk_A, sk_A1, sk_A31))),
8.94/9.20	    inference('simplify', [status(thm)], ['56'])).
8.94/9.20	tff('58', plain,
8.94/9.20	    ![X0 : sk_A]:
8.94/9.20	      (app_encode_app(sk_A, $o, sk_P, sk_A32)
8.94/9.20	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
8.94/9.20	             app_encode_app(sk_A, 
8.94/9.20	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
8.94/9.20	               'const/sets/IN'(sk_A), X0), 
8.94/9.20	             app_encode_app(app_encode_fun(sk_A0, $o), 
8.94/9.20	               app_encode_fun(sk_A, $o), 
8.94/9.20	               app_encode_app(app_encode_fun(sk_A0, sk_A), 
8.94/9.20	                 app_encode_fun(app_encode_fun(sk_A0, $o), 
8.94/9.20	                   app_encode_fun(sk_A, $o)), 
8.94/9.20	                 'const/sets/IMAGE'(sk_A0, sk_A), sk_A1), sk_A2))
8.94/9.20	       | app_encode_app(sk_A, $o, sk_P, X0)
8.94/9.20	       | ~ app_encode_app(sk_A, $o, sk_P, 
8.94/9.20	             app_encode_app(sk_A0, sk_A, sk_A1, sk_A31))),
8.94/9.20	    inference('demod', [status(thm)], ['57', '22'])).
8.94/9.20	tff('59', plain,
8.94/9.20	    ![X0 : sk_A]:
8.94/9.20	      (~ app_encode_app(sk_A, $o, sk_P, 
8.94/9.20	           app_encode_app(sk_A0, sk_A, sk_A1, sk_A31))
8.94/9.20	       | app_encode_app(sk_A, $o, sk_P, X0)
8.94/9.20	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
8.94/9.20	             app_encode_app(sk_A, 
8.94/9.20	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
8.94/9.20	               'const/sets/IN'(sk_A), X0), 
8.94/9.20	             app_encode_app(app_encode_fun(sk_A0, $o), 
8.94/9.20	               app_encode_fun(sk_A, $o), 
8.94/9.20	               app_encode_app(app_encode_fun(sk_A0, sk_A), 
8.94/9.20	                 app_encode_fun(app_encode_fun(sk_A0, $o), 
8.94/9.20	                   app_encode_fun(sk_A, $o)), 
8.94/9.20	                 'const/sets/IMAGE'(sk_A0, sk_A), sk_A1), sk_A2))),
8.94/9.20	    inference('clc', [status(thm)], ['58', '33'])).
8.94/9.20	tff('60', plain,
8.94/9.20	    (~ $true
8.94/9.20	     | ~ app_encode_app(sk_A, $o, sk_P, 
8.94/9.20	           app_encode_app(sk_A0, sk_A, sk_A1, sk_A31))
8.94/9.20	     | app_encode_app(sk_A, $o, sk_P, sk_A32)
8.94/9.20	     | ~ app_encode_app(sk_A, $o, sk_P, 
8.94/9.20	           app_encode_app(sk_A0, sk_A, sk_A1, sk_A31))),
8.94/9.20	    inference('sup-', [status(thm)], ['14', '59'])).
8.94/9.20	tff('61', plain,
8.94/9.20	    (app_encode_app(sk_A, $o, sk_P, sk_A32)
8.94/9.20	     | ~ app_encode_app(sk_A, $o, sk_P, 
8.94/9.20	           app_encode_app(sk_A0, sk_A, sk_A1, sk_A31))),
8.94/9.20	    inference('simplify', [status(thm)], ['60'])).
8.94/9.20	tff('62', plain,
8.94/9.20	    ~ app_encode_app(sk_A, $o, sk_P, 
8.94/9.20	        app_encode_app(sk_A0, sk_A, sk_A1, sk_A31)),
8.94/9.20	    inference('clc', [status(thm)], ['61', '33'])).
8.94/9.20	tff('63', plain,
8.94/9.20	    ![X0 : sk_A0, X1 : $tType, X2 : app_encode_fun(sk_A0, X1)]:
8.94/9.20	      (~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
8.94/9.20	           app_encode_app(sk_A0, 
8.94/9.20	             app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
8.94/9.20	             'const/sets/IN'(sk_A0), X0), sk_A2)
8.94/9.20	       | app_encode_app(sk_A, $o, sk_P, 
8.94/9.20	           app_encode_app(sk_A0, sk_A, sk_A1, 
8.94/9.20	             sk_A3(sk_A0, X1, X2, sk_A2, app_encode_app(sk_A0, X1, X2, X0))))),
8.94/9.20	    inference('clc', [status(thm)], ['53', '62'])).
8.94/9.20	tff('64', plain,
8.94/9.20	    (app_encode_app(sk_A, $o, sk_P, 
8.94/9.20	       app_encode_app(sk_A0, sk_A, sk_A1, sk_A31))
8.94/9.20	     | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
8.94/9.20	           app_encode_app(sk_A0, 
8.94/9.20	             app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
8.94/9.20	             'const/sets/IN'(sk_A0), sk_A31), sk_A2)),
8.94/9.20	    inference('sup+', [status(thm)], ['41', '63'])).
8.94/9.20	tff('65', plain,
8.94/9.20	    (app_encode_app(sk_A, $o, sk_P, 
8.94/9.20	       app_encode_app(sk_A0, sk_A, sk_A1, sk_A31))
8.94/9.20	     | ~ $true),
8.94/9.20	    inference('demod', [status(thm)], ['64', '37'])).
8.94/9.20	tff('66', plain,
8.94/9.20	    app_encode_app(sk_A, $o, sk_P, 
8.94/9.20	      app_encode_app(sk_A0, sk_A, sk_A1, sk_A31)),
8.94/9.20	    inference('simplify', [status(thm)], ['65'])).
8.94/9.20	tff('67', plain, ~ $true, inference('sup-', [status(thm)], ['66', '62'])).
8.94/9.20	tff('68', plain, $false, inference('simplify', [status(thm)], ['67'])).
8.94/9.20	
8.94/9.20	% SZS output end Refutation
8.94/9.20	EOF
