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    : 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 $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n096.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 18:37:54 CST 2018
4.21/4.42	% done 1306 iterations in 4.224s
4.21/4.42	% SZS status Theorem for 'stdin'
4.21/4.42	% SZS output start Refutation
4.21/4.43	tff(zf_stmt_13, axiom,
4.21/4.43	  (![A:$tType,A0:app_encode_fun(A,$o),A1:app_encode_fun(A,$o)]:
4.21/4.43	     (app_encode_app(app_encode_fun(A,$o),$o,
4.21/4.43	                     app_encode_app(app_encode_fun(A,$o),
4.21/4.43	                                    app_encode_fun(app_encode_fun(A,$o),$o),
4.21/4.43	                                    'const/sets/SUBSET'(A),A0),
4.21/4.43	                     A1) <=>
4.21/4.43	      (![A2:A]:
4.21/4.43	         (app_encode_app(app_encode_fun(A,$o),$o,
4.21/4.43	                         app_encode_app(A,
4.21/4.43	                                        app_encode_fun(app_encode_fun(A,$o),
4.21/4.43	                                                       $o),
4.21/4.43	                                        'const/sets/IN'(A),A2),
4.21/4.43	                         A0) =>
4.21/4.43	          app_encode_app(app_encode_fun(A,$o),$o,
4.21/4.43	                         app_encode_app(A,
4.21/4.43	                                        app_encode_fun(app_encode_fun(A,$o),
4.21/4.43	                                                       $o),
4.21/4.43	                                        'const/sets/IN'(A),A2),
4.21/4.43	                         A1)))))).
4.21/4.43	tff('0', plain,
4.21/4.43	    ![X7 : $tType, X9 : app_encode_fun(X7, $o), X11 : app_encode_fun(X7, $o)]:
4.21/4.43	      (app_encode_app(app_encode_fun(X7, $o), $o, 
4.21/4.43	         app_encode_app(app_encode_fun(X7, $o), 
4.21/4.43	           app_encode_fun(app_encode_fun(X7, $o), $o), 
4.21/4.43	           'const/sets/SUBSET'(X7), X9), X11)
4.21/4.43	       | app_encode_app(app_encode_fun(X7, $o), $o, 
4.21/4.43	           app_encode_app(X7, app_encode_fun(app_encode_fun(X7, $o), $o), 
4.21/4.43	             'const/sets/IN'(X7), sk_A2(X7, X11, X9)), X9)),
4.21/4.43	    inference('cnf', [status(esa)], [zf_stmt_13])).
4.21/4.43	tff(zf_stmt_14, axiom,
4.21/4.43	  (![A:$tType,A0:app_encode_fun(A,$o),A1:app_encode_fun(A,$o),A2:A]:
4.21/4.43	     (app_encode_app(app_encode_fun(A,$o),$o,
4.21/4.43	                     app_encode_app(A,
4.21/4.43	                                    app_encode_fun(app_encode_fun(A,$o),$o),
4.21/4.43	                                    'const/sets/IN'(A),A2),
4.21/4.43	                     app_encode_app(app_encode_fun(A,$o),
4.21/4.43	                                    app_encode_fun(A,$o),
4.21/4.43	                                    app_encode_app(app_encode_fun(A,$o),
4.21/4.43	                                                   app_encode_fun(app_encode_fun(
4.21/4.43	                                                                  A,$o),
4.21/4.43	                                                                  app_encode_fun(
4.21/4.43	                                                                  A,$o)),
4.21/4.43	                                                   'const/sets/DIFF'(A),A0),
4.21/4.43	                                    A1)) <=>
4.21/4.43	      (app_encode_app(app_encode_fun(A,$o),$o,
4.21/4.43	                      app_encode_app(A,
4.21/4.43	                                     app_encode_fun(app_encode_fun(A,$o),$o),
4.21/4.43	                                     'const/sets/IN'(A),A2),
4.21/4.43	                      A0) & 
4.21/4.43	       (~
4.21/4.43	         app_encode_app(app_encode_fun(A,$o),$o,
4.21/4.43	                        app_encode_app(A,
4.21/4.43	                                       app_encode_fun(app_encode_fun(A,$o),$o),
4.21/4.43	                                       'const/sets/IN'(A),A2),
4.21/4.43	                        A1)))))).
4.21/4.43	tff('1', plain,
4.21/4.43	    ![X12 : $tType, X13 : X12, X14 : app_encode_fun(X12, $o), 
4.21/4.43	      X15 : app_encode_fun(X12, $o)]:
4.21/4.43	      (app_encode_app(app_encode_fun(X12, $o), $o, 
4.21/4.43	         app_encode_app(X12, app_encode_fun(app_encode_fun(X12, $o), $o), 
4.21/4.43	           'const/sets/IN'(X12), X13), X14)
4.21/4.43	       | ~ app_encode_app(app_encode_fun(X12, $o), $o, 
4.21/4.43	             app_encode_app(X12, 
4.21/4.43	               app_encode_fun(app_encode_fun(X12, $o), $o), 
4.21/4.43	               'const/sets/IN'(X12), X13), 
4.21/4.43	             app_encode_app(app_encode_fun(X12, $o), 
4.21/4.43	               app_encode_fun(X12, $o), 
4.21/4.43	               app_encode_app(app_encode_fun(X12, $o), 
4.21/4.43	                 app_encode_fun(app_encode_fun(X12, $o), 
4.21/4.43	                   app_encode_fun(X12, $o)), 'const/sets/DIFF'(X12), X14), 
4.21/4.43	               X15))),
4.21/4.43	    inference('cnf', [status(esa)], [zf_stmt_14])).
4.21/4.43	tff('2', plain,
4.21/4.43	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : app_encode_fun(X0, $o), 
4.21/4.43	      X3 : app_encode_fun(X0, $o)]:
4.21/4.43	      (~ $true
4.21/4.43	       | app_encode_app(app_encode_fun(X0, $o), $o, 
4.21/4.43	           app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	             app_encode_fun(app_encode_fun(X0, $o), $o), 
4.21/4.43	             'const/sets/SUBSET'(X0), 
4.21/4.43	             app_encode_app(app_encode_fun(X0, $o), app_encode_fun(X0, $o), 
4.21/4.43	               app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	                 app_encode_fun(app_encode_fun(X0, $o), 
4.21/4.43	                   app_encode_fun(X0, $o)), 'const/sets/DIFF'(X0), X2), X1)), 
4.21/4.43	           X3)
4.21/4.43	       | app_encode_app(app_encode_fun(X0, $o), $o, 
4.21/4.43	           app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
4.21/4.43	             'const/sets/IN'(X0), 
4.21/4.43	             sk_A2(X0, X3, 
4.21/4.43	               app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	                 app_encode_fun(X0, $o), 
4.21/4.43	                 app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	                   app_encode_fun(app_encode_fun(X0, $o), 
4.21/4.43	                     app_encode_fun(X0, $o)), 'const/sets/DIFF'(X0), X2), X1))), 
4.21/4.43	           X2)),
4.21/4.43	    inference('sup-', [status(thm)], ['0', '1'])).
4.21/4.43	tff('3', plain,
4.21/4.43	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : app_encode_fun(X0, $o), 
4.21/4.43	      X3 : app_encode_fun(X0, $o)]:
4.21/4.43	      (app_encode_app(app_encode_fun(X0, $o), $o, 
4.21/4.43	         app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
4.21/4.43	           'const/sets/IN'(X0), 
4.21/4.43	           sk_A2(X0, X3, 
4.21/4.43	             app_encode_app(app_encode_fun(X0, $o), app_encode_fun(X0, $o), 
4.21/4.43	               app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	                 app_encode_fun(app_encode_fun(X0, $o), 
4.21/4.43	                   app_encode_fun(X0, $o)), 'const/sets/DIFF'(X0), X2), X1))), 
4.21/4.43	         X2)
4.21/4.43	       | app_encode_app(app_encode_fun(X0, $o), $o, 
4.21/4.43	           app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	             app_encode_fun(app_encode_fun(X0, $o), $o), 
4.21/4.43	             'const/sets/SUBSET'(X0), 
4.21/4.43	             app_encode_app(app_encode_fun(X0, $o), app_encode_fun(X0, $o), 
4.21/4.43	               app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	                 app_encode_fun(app_encode_fun(X0, $o), 
4.21/4.43	                   app_encode_fun(X0, $o)), 'const/sets/DIFF'(X0), X2), X1)), 
4.21/4.43	           X3)),
4.21/4.43	    inference('simplify', [status(thm)], ['2'])).
4.21/4.43	tff('4', plain,
4.21/4.43	    ![X7 : $tType, X9 : app_encode_fun(X7, $o), X11 : app_encode_fun(X7, $o)]:
4.21/4.43	      (app_encode_app(app_encode_fun(X7, $o), $o, 
4.21/4.43	         app_encode_app(app_encode_fun(X7, $o), 
4.21/4.43	           app_encode_fun(app_encode_fun(X7, $o), $o), 
4.21/4.43	           'const/sets/SUBSET'(X7), X9), X11)
4.21/4.43	       | ~ app_encode_app(app_encode_fun(X7, $o), $o, 
4.21/4.43	             app_encode_app(X7, app_encode_fun(app_encode_fun(X7, $o), $o), 
4.21/4.43	               'const/sets/IN'(X7), sk_A2(X7, X11, X9)), X11)),
4.21/4.43	    inference('cnf', [status(esa)], [zf_stmt_13])).
4.21/4.43	tff('5', plain,
4.21/4.43	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : app_encode_fun(X0, $o)]:
4.21/4.43	      (~ $true
4.21/4.43	       | app_encode_app(app_encode_fun(X0, $o), $o, 
4.21/4.43	           app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	             app_encode_fun(app_encode_fun(X0, $o), $o), 
4.21/4.43	             'const/sets/SUBSET'(X0), 
4.21/4.43	             app_encode_app(app_encode_fun(X0, $o), app_encode_fun(X0, $o), 
4.21/4.43	               app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	                 app_encode_fun(app_encode_fun(X0, $o), 
4.21/4.43	                   app_encode_fun(X0, $o)), 'const/sets/DIFF'(X0), X1), X2)), 
4.21/4.43	           X1)
4.21/4.43	       | app_encode_app(app_encode_fun(X0, $o), $o, 
4.21/4.43	           app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	             app_encode_fun(app_encode_fun(X0, $o), $o), 
4.21/4.43	             'const/sets/SUBSET'(X0), 
4.21/4.43	             app_encode_app(app_encode_fun(X0, $o), app_encode_fun(X0, $o), 
4.21/4.43	               app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	                 app_encode_fun(app_encode_fun(X0, $o), 
4.21/4.43	                   app_encode_fun(X0, $o)), 'const/sets/DIFF'(X0), X1), X2)), 
4.21/4.43	           X1)),
4.21/4.43	    inference('sup-', [status(thm)], ['3', '4'])).
4.21/4.43	tff('6', plain,
4.21/4.43	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : app_encode_fun(X0, $o)]:
4.21/4.43	      app_encode_app(app_encode_fun(X0, $o), $o, 
4.21/4.43	        app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	          app_encode_fun(app_encode_fun(X0, $o), $o), 
4.21/4.43	          'const/sets/SUBSET'(X0), 
4.21/4.43	          app_encode_app(app_encode_fun(X0, $o), app_encode_fun(X0, $o), 
4.21/4.43	            app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	              app_encode_fun(app_encode_fun(X0, $o), app_encode_fun(X0, $o)), 
4.21/4.43	              'const/sets/DIFF'(X0), X1), X2)), X1),
4.21/4.43	    inference('simplify', [status(thm)], ['5'])).
4.21/4.43	tff(zf_stmt_15, conjecture,
4.21/4.43	  (![A:$tType,A0:app_encode_fun(A,$o),A1:app_encode_fun(A,$o),
4.21/4.43	     A2:app_encode_fun(A,'type/nums/num')]:
4.21/4.43	     ((app_encode_app(app_encode_fun(A,$o),$o,'const/sets/FINITE'(A),A1) & 
4.21/4.43	       app_encode_app(app_encode_fun(A,$o),$o,
4.21/4.43	                      app_encode_app(app_encode_fun(A,$o),
4.21/4.43	                                     app_encode_fun(app_encode_fun(A,$o),$o),
4.21/4.43	                                     'const/sets/SUBSET'(A),A0),
4.21/4.43	                      A1)) =>
4.21/4.43	      app_encode_app('type/nums/num',$o,
4.21/4.43	                     app_encode_app('type/nums/num',
4.21/4.43	                                    app_encode_fun('type/nums/num',$o),
4.21/4.43	                                    'const/arith/<=',
4.21/4.43	                                    app_encode_app(app_encode_fun(A,
4.21/4.43	                                                                  'type/nums/num'),
4.21/4.43	                                                   'type/nums/num',
4.21/4.43	                                                   app_encode_app(app_encode_fun(
4.21/4.43	                                                                  A,$o),
4.21/4.43	                                                                  app_encode_fun(
4.21/4.43	                                                                  app_encode_fun(
4.21/4.43	                                                                  A,
4.21/4.43	                                                                  'type/nums/num'),
4.21/4.43	                                                                  'type/nums/num'),
4.21/4.43	                                                                  'const/iterate/nsum'(
4.21/4.43	                                                                  A),A0),
4.21/4.43	                                                   A2)),
4.21/4.43	                     app_encode_app(app_encode_fun(A,'type/nums/num'),
4.21/4.43	                                    'type/nums/num',
4.21/4.43	                                    app_encode_app(app_encode_fun(A,$o),
4.21/4.43	                                                   app_encode_fun(app_encode_fun(
4.21/4.43	                                                                  A,
4.21/4.43	                                                                  'type/nums/num'),
4.21/4.43	                                                                  'type/nums/num'),
4.21/4.43	                                                   'const/iterate/nsum'(A),A1),
4.21/4.43	                                    A2))))).
4.21/4.43	tff(zf_stmt_0, negated_conjecture,
4.21/4.43	  (~
4.21/4.43	    (![A:$tType,A0:app_encode_fun(A,$o),A1:app_encode_fun(A,$o),
4.21/4.43	       A2:app_encode_fun(A,'type/nums/num')]:
4.21/4.43	       ((app_encode_app(app_encode_fun(A,$o),$o,'const/sets/FINITE'(A),A1) & 
4.21/4.43	         app_encode_app(app_encode_fun(A,$o),$o,
4.21/4.43	                        app_encode_app(app_encode_fun(A,$o),
4.21/4.43	                                       app_encode_fun(app_encode_fun(A,$o),$o),
4.21/4.43	                                       'const/sets/SUBSET'(A),A0),
4.21/4.43	                        A1)) =>
4.21/4.43	        app_encode_app('type/nums/num',$o,
4.21/4.43	                       app_encode_app('type/nums/num',
4.21/4.43	                                      app_encode_fun('type/nums/num',$o),
4.21/4.43	                                      'const/arith/<=',
4.21/4.43	                                      app_encode_app(app_encode_fun(A,
4.21/4.43	                                                                    'type/nums/num'),
4.21/4.43	                                                     'type/nums/num',
4.21/4.43	                                                     app_encode_app(app_encode_fun(
4.21/4.43	                                                                    A,$o),
4.21/4.43	                                                                    app_encode_fun(
4.21/4.43	                                                                    app_encode_fun(
4.21/4.43	                                                                    A,
4.21/4.43	                                                                    'type/nums/num'),
4.21/4.43	                                                                    'type/nums/num'),
4.21/4.43	                                                                    'const/iterate/nsum'(
4.21/4.43	                                                                    A),A0),
4.21/4.43	                                                     A2)),
4.21/4.43	                       app_encode_app(app_encode_fun(A,'type/nums/num'),
4.21/4.43	                                      'type/nums/num',
4.21/4.43	                                      app_encode_app(app_encode_fun(A,$o),
4.21/4.43	                                                     app_encode_fun(app_encode_fun(
4.21/4.43	                                                                    A,
4.21/4.43	                                                                    'type/nums/num'),
4.21/4.43	                                                                    'type/nums/num'),
4.21/4.43	                                                     'const/iterate/nsum'(A),
4.21/4.43	                                                     A1),
4.21/4.43	                                      A2)))))).
4.21/4.43	tff('7', plain,
4.21/4.43	    app_encode_app(app_encode_fun(sk_A, $o), $o, 
4.21/4.43	      app_encode_app(app_encode_fun(sk_A, $o), 
4.21/4.43	        app_encode_fun(app_encode_fun(sk_A, $o), $o), 
4.21/4.43	        'const/sets/SUBSET'(sk_A), sk_A0), sk_A1),
4.21/4.43	    inference('cnf', [status(esa)], [zf_stmt_0])).
4.21/4.43	tff('8', plain,
4.21/4.43	    ![X7 : $tType, X8 : X7, X9 : app_encode_fun(X7, $o), 
4.21/4.43	      X10 : app_encode_fun(X7, $o)]:
4.21/4.43	      (~ app_encode_app(app_encode_fun(X7, $o), $o, 
4.21/4.43	           app_encode_app(X7, app_encode_fun(app_encode_fun(X7, $o), $o), 
4.21/4.43	             'const/sets/IN'(X7), X8), X9)
4.21/4.43	       | app_encode_app(app_encode_fun(X7, $o), $o, 
4.21/4.43	           app_encode_app(X7, app_encode_fun(app_encode_fun(X7, $o), $o), 
4.21/4.43	             'const/sets/IN'(X7), X8), X10)
4.21/4.43	       | ~ app_encode_app(app_encode_fun(X7, $o), $o, 
4.21/4.43	             app_encode_app(app_encode_fun(X7, $o), 
4.21/4.43	               app_encode_fun(app_encode_fun(X7, $o), $o), 
4.21/4.43	               'const/sets/SUBSET'(X7), X9), X10)),
4.21/4.43	    inference('cnf', [status(esa)], [zf_stmt_13])).
4.21/4.43	tff('9', plain,
4.21/4.43	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : app_encode_fun(X0, $o), 
4.21/4.43	      X3 : app_encode_fun(X0, $o)]:
4.21/4.43	      (~ $true
4.21/4.43	       | app_encode_app(app_encode_fun(X0, $o), $o, 
4.21/4.43	           app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	             app_encode_fun(app_encode_fun(X0, $o), $o), 
4.21/4.43	             'const/sets/SUBSET'(X0), X1), X2)
4.21/4.43	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
4.21/4.43	             app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	               app_encode_fun(app_encode_fun(X0, $o), $o), 
4.21/4.43	               'const/sets/SUBSET'(X0), X1), X3)
4.21/4.43	       | app_encode_app(app_encode_fun(X0, $o), $o, 
4.21/4.43	           app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
4.21/4.43	             'const/sets/IN'(X0), sk_A2(X0, X2, X1)), X3)),
4.21/4.43	    inference('sup-', [status(thm)], ['0', '8'])).
4.21/4.43	tff('10', plain,
4.21/4.43	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : app_encode_fun(X0, $o), 
4.21/4.43	      X3 : app_encode_fun(X0, $o)]:
4.21/4.43	      (app_encode_app(app_encode_fun(X0, $o), $o, 
4.21/4.43	         app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
4.21/4.43	           'const/sets/IN'(X0), sk_A2(X0, X2, X1)), X3)
4.21/4.43	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
4.21/4.43	             app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	               app_encode_fun(app_encode_fun(X0, $o), $o), 
4.21/4.43	               'const/sets/SUBSET'(X0), X1), X3)
4.21/4.43	       | app_encode_app(app_encode_fun(X0, $o), $o, 
4.21/4.43	           app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	             app_encode_fun(app_encode_fun(X0, $o), $o), 
4.21/4.43	             'const/sets/SUBSET'(X0), X1), X2)),
4.21/4.43	    inference('simplify', [status(thm)], ['9'])).
4.21/4.43	tff('11', plain,
4.21/4.43	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : app_encode_fun(X0, $o), 
4.21/4.43	      X3 : app_encode_fun(X0, $o), X4 : app_encode_fun(X0, $o)]:
4.21/4.43	      (~ $true
4.21/4.43	       | app_encode_app(app_encode_fun(X0, $o), $o, 
4.21/4.43	           app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	             app_encode_fun(app_encode_fun(X0, $o), $o), 
4.21/4.43	             'const/sets/SUBSET'(X0), X2), X3)
4.21/4.43	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
4.21/4.43	             app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	               app_encode_fun(app_encode_fun(X0, $o), $o), 
4.21/4.43	               'const/sets/SUBSET'(X0), X2), X1)
4.21/4.43	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
4.21/4.43	             app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	               app_encode_fun(app_encode_fun(X0, $o), $o), 
4.21/4.43	               'const/sets/SUBSET'(X0), X1), X4)
4.21/4.43	       | app_encode_app(app_encode_fun(X0, $o), $o, 
4.21/4.43	           app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
4.21/4.43	             'const/sets/IN'(X0), sk_A2(X0, X3, X2)), X4)),
4.21/4.43	    inference('sup-', [status(thm)], ['10', '8'])).
4.21/4.43	tff('12', plain,
4.21/4.43	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : app_encode_fun(X0, $o), 
4.21/4.43	      X3 : app_encode_fun(X0, $o), X4 : app_encode_fun(X0, $o)]:
4.21/4.43	      (app_encode_app(app_encode_fun(X0, $o), $o, 
4.21/4.43	         app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
4.21/4.43	           'const/sets/IN'(X0), sk_A2(X0, X3, X2)), X4)
4.21/4.43	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
4.21/4.43	             app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	               app_encode_fun(app_encode_fun(X0, $o), $o), 
4.21/4.43	               'const/sets/SUBSET'(X0), X1), X4)
4.21/4.43	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
4.21/4.43	             app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	               app_encode_fun(app_encode_fun(X0, $o), $o), 
4.21/4.43	               'const/sets/SUBSET'(X0), X2), X1)
4.21/4.43	       | app_encode_app(app_encode_fun(X0, $o), $o, 
4.21/4.43	           app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	             app_encode_fun(app_encode_fun(X0, $o), $o), 
4.21/4.43	             'const/sets/SUBSET'(X0), X2), X3)),
4.21/4.43	    inference('simplify', [status(thm)], ['11'])).
4.21/4.43	tff('13', plain,
4.21/4.43	    ![X0 : app_encode_fun(sk_A, $o), X1 : app_encode_fun(sk_A, $o)]:
4.21/4.43	      (~ $true
4.21/4.43	       | app_encode_app(app_encode_fun(sk_A, $o), $o, 
4.21/4.43	           app_encode_app(app_encode_fun(sk_A, $o), 
4.21/4.43	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
4.21/4.43	             'const/sets/SUBSET'(sk_A), X1), X0)
4.21/4.43	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
4.21/4.43	             app_encode_app(app_encode_fun(sk_A, $o), 
4.21/4.43	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
4.21/4.43	               'const/sets/SUBSET'(sk_A), X1), sk_A0)
4.21/4.43	       | app_encode_app(app_encode_fun(sk_A, $o), $o, 
4.21/4.43	           app_encode_app(sk_A, 
4.21/4.43	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
4.21/4.43	             'const/sets/IN'(sk_A), sk_A2(sk_A, X0, X1)), sk_A1)),
4.21/4.43	    inference('sup-', [status(thm)], ['7', '12'])).
4.21/4.43	tff('14', plain,
4.21/4.43	    ![X0 : app_encode_fun(sk_A, $o), X1 : app_encode_fun(sk_A, $o)]:
4.21/4.43	      (app_encode_app(app_encode_fun(sk_A, $o), $o, 
4.21/4.43	         app_encode_app(sk_A, app_encode_fun(app_encode_fun(sk_A, $o), $o), 
4.21/4.43	           'const/sets/IN'(sk_A), sk_A2(sk_A, X0, X1)), sk_A1)
4.21/4.43	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
4.21/4.43	             app_encode_app(app_encode_fun(sk_A, $o), 
4.21/4.43	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
4.21/4.43	               'const/sets/SUBSET'(sk_A), X1), sk_A0)
4.21/4.43	       | app_encode_app(app_encode_fun(sk_A, $o), $o, 
4.21/4.43	           app_encode_app(app_encode_fun(sk_A, $o), 
4.21/4.43	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
4.21/4.43	             'const/sets/SUBSET'(sk_A), X1), X0)),
4.21/4.43	    inference('simplify', [status(thm)], ['13'])).
4.21/4.43	tff('15', plain,
4.21/4.43	    ![X0 : app_encode_fun(sk_A, $o)]:
4.21/4.43	      (~ $true
4.21/4.43	       | app_encode_app(app_encode_fun(sk_A, $o), $o, 
4.21/4.43	           app_encode_app(app_encode_fun(sk_A, $o), 
4.21/4.43	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
4.21/4.43	             'const/sets/SUBSET'(sk_A), X0), sk_A1)
4.21/4.43	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
4.21/4.43	             app_encode_app(app_encode_fun(sk_A, $o), 
4.21/4.43	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
4.21/4.43	               'const/sets/SUBSET'(sk_A), X0), sk_A0)
4.21/4.43	       | app_encode_app(app_encode_fun(sk_A, $o), $o, 
4.21/4.43	           app_encode_app(app_encode_fun(sk_A, $o), 
4.21/4.43	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
4.21/4.43	             'const/sets/SUBSET'(sk_A), X0), sk_A1)),
4.21/4.43	    inference('sup-', [status(thm)], ['14', '4'])).
4.21/4.43	tff('16', plain,
4.21/4.43	    ![X0 : app_encode_fun(sk_A, $o)]:
4.21/4.43	      (~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
4.21/4.43	           app_encode_app(app_encode_fun(sk_A, $o), 
4.21/4.43	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
4.21/4.43	             'const/sets/SUBSET'(sk_A), X0), sk_A0)
4.21/4.43	       | app_encode_app(app_encode_fun(sk_A, $o), $o, 
4.21/4.43	           app_encode_app(app_encode_fun(sk_A, $o), 
4.21/4.43	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
4.21/4.43	             'const/sets/SUBSET'(sk_A), X0), sk_A1)),
4.21/4.43	    inference('simplify', [status(thm)], ['15'])).
4.21/4.43	tff('17', plain,
4.21/4.43	    ![X0 : app_encode_fun(sk_A, $o)]:
4.21/4.43	      (~ $true
4.21/4.43	       | app_encode_app(app_encode_fun(sk_A, $o), $o, 
4.21/4.43	           app_encode_app(app_encode_fun(sk_A, $o), 
4.21/4.43	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
4.21/4.43	             'const/sets/SUBSET'(sk_A), 
4.21/4.43	             app_encode_app(app_encode_fun(sk_A, $o), 
4.21/4.43	               app_encode_fun(sk_A, $o), 
4.21/4.43	               app_encode_app(app_encode_fun(sk_A, $o), 
4.21/4.43	                 app_encode_fun(app_encode_fun(sk_A, $o), 
4.21/4.43	                   app_encode_fun(sk_A, $o)), 'const/sets/DIFF'(sk_A), sk_A0), 
4.21/4.43	               X0)), sk_A1)),
4.21/4.43	    inference('sup-', [status(thm)], ['6', '16'])).
4.21/4.43	tff('18', plain,
4.21/4.43	    ![X0 : app_encode_fun(sk_A, $o)]:
4.21/4.43	      app_encode_app(app_encode_fun(sk_A, $o), $o, 
4.21/4.43	        app_encode_app(app_encode_fun(sk_A, $o), 
4.21/4.43	          app_encode_fun(app_encode_fun(sk_A, $o), $o), 
4.21/4.43	          'const/sets/SUBSET'(sk_A), 
4.21/4.43	          app_encode_app(app_encode_fun(sk_A, $o), app_encode_fun(sk_A, $o), 
4.21/4.43	            app_encode_app(app_encode_fun(sk_A, $o), 
4.21/4.43	              app_encode_fun(app_encode_fun(sk_A, $o), 
4.21/4.43	                app_encode_fun(sk_A, $o)), 'const/sets/DIFF'(sk_A), sk_A0), 
4.21/4.43	            X0)), sk_A1),
4.21/4.43	    inference('simplify', [status(thm)], ['17'])).
4.21/4.43	tff(zf_stmt_11, axiom,
4.21/4.43	  (![A:$tType,A0:app_encode_fun(A,$o),A1:app_encode_fun(A,$o),
4.21/4.43	     A2:app_encode_fun(A,'type/nums/num')]:
4.21/4.43	     ((app_encode_app(app_encode_fun(A,$o),$o,'const/sets/FINITE'(A),A0) & 
4.21/4.43	       app_encode_app(app_encode_fun(A,$o),$o,'const/sets/FINITE'(A),A1) & 
4.21/4.43	       (![A3:A]:
4.21/4.43	          (app_encode_app(app_encode_fun(A,$o),$o,
4.21/4.43	                          app_encode_app(A,
4.21/4.43	                                         app_encode_fun(app_encode_fun(A,$o),
4.21/4.43	                                                        $o),
4.21/4.43	                                         'const/sets/IN'(A),A3),
4.21/4.43	                          app_encode_app(app_encode_fun(A,$o),
4.21/4.43	                                         app_encode_fun(A,$o),
4.21/4.43	                                         app_encode_app(app_encode_fun(A,$o),
4.21/4.43	                                                        app_encode_fun(
4.21/4.43	                                                        app_encode_fun(A,$o),
4.21/4.43	                                                        app_encode_fun(A,$o)),
4.21/4.43	                                                        'const/sets/DIFF'(A),
4.21/4.43	                                                        A0),
4.21/4.43	                                         A1)) =>
4.21/4.43	           (app_encode_app(A,'type/nums/num',A2,A3) =
4.21/4.43	            app_encode_app('type/nums/num','type/nums/num',
4.21/4.43	                           'const/nums/NUMERAL','const/nums/_0'))))) =>
4.21/4.43	      app_encode_app('type/nums/num',$o,
4.21/4.43	                     app_encode_app('type/nums/num',
4.21/4.43	                                    app_encode_fun('type/nums/num',$o),
4.21/4.43	                                    'const/arith/<=',
4.21/4.43	                                    app_encode_app(app_encode_fun(A,
4.21/4.43	                                                                  'type/nums/num'),
4.21/4.43	                                                   'type/nums/num',
4.21/4.43	                                                   app_encode_app(app_encode_fun(
4.21/4.43	                                                                  A,$o),
4.21/4.43	                                                                  app_encode_fun(
4.21/4.43	                                                                  app_encode_fun(
4.21/4.43	                                                                  A,
4.21/4.43	                                                                  'type/nums/num'),
4.21/4.43	                                                                  'type/nums/num'),
4.21/4.43	                                                                  'const/iterate/nsum'(
4.21/4.43	                                                                  A),A0),
4.21/4.43	                                                   A2)),
4.21/4.43	                     app_encode_app(app_encode_fun(A,'type/nums/num'),
4.21/4.43	                                    'type/nums/num',
4.21/4.43	                                    app_encode_app(app_encode_fun(A,$o),
4.21/4.43	                                                   app_encode_fun(app_encode_fun(
4.21/4.43	                                                                  A,
4.21/4.43	                                                                  'type/nums/num'),
4.21/4.43	                                                                  'type/nums/num'),
4.21/4.43	                                                   'const/iterate/nsum'(A),A1),
4.21/4.43	                                    A2))))).
4.21/4.43	tff('19', plain,
4.21/4.43	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : app_encode_fun(X0, $o), 
4.21/4.43	      X3 : app_encode_fun(X0, 'type/nums/num')]:
4.21/4.43	      (~ app_encode_app(app_encode_fun(X0, $o), $o, 'const/sets/FINITE'(X0), 
4.21/4.43	           X1)
4.21/4.43	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
4.21/4.43	             'const/sets/FINITE'(X0), X2)
4.21/4.43	       | app_encode_app(app_encode_fun(X0, $o), $o, 
4.21/4.43	           app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
4.21/4.43	             'const/sets/IN'(X0), sk_A3(X0, X3, X1, X2)), 
4.21/4.43	           app_encode_app(app_encode_fun(X0, $o), app_encode_fun(X0, $o), 
4.21/4.43	             app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	               app_encode_fun(app_encode_fun(X0, $o), app_encode_fun(X0, $o)), 
4.21/4.43	               'const/sets/DIFF'(X0), X2), X1))
4.21/4.43	       | app_encode_app('type/nums/num', $o, 
4.21/4.43	           app_encode_app('type/nums/num', 
4.21/4.43	             app_encode_fun('type/nums/num', $o), 'const/arith/<=', 
4.21/4.43	             app_encode_app(app_encode_fun(X0, 'type/nums/num'), 
4.21/4.43	               'type/nums/num', 
4.21/4.43	               app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	                 app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
4.21/4.43	                   'type/nums/num'), 'const/iterate/nsum'(X0), X2), X3)), 
4.21/4.43	           app_encode_app(app_encode_fun(X0, 'type/nums/num'), 
4.21/4.43	             'type/nums/num', 
4.21/4.43	             app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	               app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
4.21/4.43	                 'type/nums/num'), 'const/iterate/nsum'(X0), X1), X3))),
4.21/4.43	    inference('cnf', [status(esa)], [zf_stmt_11])).
4.21/4.43	tff('20', plain,
4.21/4.43	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : app_encode_fun(X0, $o), 
4.21/4.43	      X3 : app_encode_fun(X0, 'type/nums/num'), X4 : app_encode_fun(X0, $o)]:
4.21/4.43	      (~ $true
4.21/4.43	       | app_encode_app('type/nums/num', $o, 
4.21/4.43	           app_encode_app('type/nums/num', 
4.21/4.43	             app_encode_fun('type/nums/num', $o), 'const/arith/<=', 
4.21/4.43	             app_encode_app(app_encode_fun(X0, 'type/nums/num'), 
4.21/4.43	               'type/nums/num', 
4.21/4.43	               app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	                 app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
4.21/4.43	                   'type/nums/num'), 'const/iterate/nsum'(X0), X2), X3)), 
4.21/4.43	           app_encode_app(app_encode_fun(X0, 'type/nums/num'), 
4.21/4.43	             'type/nums/num', 
4.21/4.43	             app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	               app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
4.21/4.43	                 'type/nums/num'), 'const/iterate/nsum'(X0), X1), X3))
4.21/4.43	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
4.21/4.43	             'const/sets/FINITE'(X0), X2)
4.21/4.43	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
4.21/4.43	             'const/sets/FINITE'(X0), X1)
4.21/4.43	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
4.21/4.43	             app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	               app_encode_fun(app_encode_fun(X0, $o), $o), 
4.21/4.43	               'const/sets/SUBSET'(X0), 
4.21/4.43	               app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	                 app_encode_fun(X0, $o), 
4.21/4.43	                 app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	                   app_encode_fun(app_encode_fun(X0, $o), 
4.21/4.43	                     app_encode_fun(X0, $o)), 'const/sets/DIFF'(X0), X2), X1)), 
4.21/4.43	             X4)
4.21/4.43	       | app_encode_app(app_encode_fun(X0, $o), $o, 
4.21/4.43	           app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
4.21/4.43	             'const/sets/IN'(X0), sk_A3(X0, X3, X1, X2)), X4)),
4.21/4.43	    inference('sup-', [status(thm)], ['19', '8'])).
4.21/4.43	tff('21', plain,
4.21/4.43	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : app_encode_fun(X0, $o), 
4.21/4.43	      X3 : app_encode_fun(X0, 'type/nums/num'), X4 : app_encode_fun(X0, $o)]:
4.21/4.43	      (app_encode_app(app_encode_fun(X0, $o), $o, 
4.21/4.43	         app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
4.21/4.43	           'const/sets/IN'(X0), sk_A3(X0, X3, X1, X2)), X4)
4.21/4.43	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
4.21/4.43	             app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	               app_encode_fun(app_encode_fun(X0, $o), $o), 
4.21/4.43	               'const/sets/SUBSET'(X0), 
4.21/4.43	               app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	                 app_encode_fun(X0, $o), 
4.21/4.43	                 app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	                   app_encode_fun(app_encode_fun(X0, $o), 
4.21/4.43	                     app_encode_fun(X0, $o)), 'const/sets/DIFF'(X0), X2), X1)), 
4.21/4.43	             X4)
4.21/4.43	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
4.21/4.43	             'const/sets/FINITE'(X0), X1)
4.21/4.43	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
4.21/4.43	             'const/sets/FINITE'(X0), X2)
4.21/4.43	       | app_encode_app('type/nums/num', $o, 
4.21/4.43	           app_encode_app('type/nums/num', 
4.21/4.43	             app_encode_fun('type/nums/num', $o), 'const/arith/<=', 
4.21/4.43	             app_encode_app(app_encode_fun(X0, 'type/nums/num'), 
4.21/4.43	               'type/nums/num', 
4.21/4.43	               app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	                 app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
4.21/4.43	                   'type/nums/num'), 'const/iterate/nsum'(X0), X2), X3)), 
4.21/4.43	           app_encode_app(app_encode_fun(X0, 'type/nums/num'), 
4.21/4.43	             'type/nums/num', 
4.21/4.43	             app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	               app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
4.21/4.43	                 'type/nums/num'), 'const/iterate/nsum'(X0), X1), X3))),
4.21/4.43	    inference('simplify', [status(thm)], ['20'])).
4.21/4.43	tff('22', plain,
4.21/4.43	    ![X12 : $tType, X13 : X12, X14 : app_encode_fun(X12, $o), 
4.21/4.43	      X15 : app_encode_fun(X12, $o)]:
4.21/4.43	      (~ app_encode_app(app_encode_fun(X12, $o), $o, 
4.21/4.43	           app_encode_app(X12, app_encode_fun(app_encode_fun(X12, $o), $o), 
4.21/4.43	             'const/sets/IN'(X12), X13), X15)
4.21/4.43	       | ~ app_encode_app(app_encode_fun(X12, $o), $o, 
4.21/4.43	             app_encode_app(X12, 
4.21/4.43	               app_encode_fun(app_encode_fun(X12, $o), $o), 
4.21/4.43	               'const/sets/IN'(X12), X13), 
4.21/4.43	             app_encode_app(app_encode_fun(X12, $o), 
4.21/4.43	               app_encode_fun(X12, $o), 
4.21/4.43	               app_encode_app(app_encode_fun(X12, $o), 
4.21/4.43	                 app_encode_fun(app_encode_fun(X12, $o), 
4.21/4.43	                   app_encode_fun(X12, $o)), 'const/sets/DIFF'(X12), X14), 
4.21/4.43	               X15))),
4.21/4.43	    inference('cnf', [status(esa)], [zf_stmt_14])).
4.21/4.43	tff('23', plain,
4.21/4.43	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : app_encode_fun(X0, $o), 
4.21/4.43	      X3 : app_encode_fun(X0, 'type/nums/num')]:
4.21/4.43	      (~ $true
4.21/4.43	       | app_encode_app('type/nums/num', $o, 
4.21/4.43	           app_encode_app('type/nums/num', 
4.21/4.43	             app_encode_fun('type/nums/num', $o), 'const/arith/<=', 
4.21/4.43	             app_encode_app(app_encode_fun(X0, 'type/nums/num'), 
4.21/4.43	               'type/nums/num', 
4.21/4.43	               app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	                 app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
4.21/4.43	                   'type/nums/num'), 'const/iterate/nsum'(X0), X2), X3)), 
4.21/4.43	           app_encode_app(app_encode_fun(X0, 'type/nums/num'), 
4.21/4.43	             'type/nums/num', 
4.21/4.43	             app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	               app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
4.21/4.43	                 'type/nums/num'), 'const/iterate/nsum'(X0), X1), X3))
4.21/4.43	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
4.21/4.43	             'const/sets/FINITE'(X0), X2)
4.21/4.43	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
4.21/4.43	             'const/sets/FINITE'(X0), X1)
4.21/4.43	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
4.21/4.43	             app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
4.21/4.43	               'const/sets/IN'(X0), sk_A3(X0, X3, X1, X2)), X1)),
4.21/4.43	    inference('sup-', [status(thm)], ['19', '22'])).
4.21/4.43	tff('24', plain,
4.21/4.43	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : app_encode_fun(X0, $o), 
4.21/4.43	      X3 : app_encode_fun(X0, 'type/nums/num')]:
4.21/4.43	      (~ app_encode_app(app_encode_fun(X0, $o), $o, 
4.21/4.43	           app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
4.21/4.43	             'const/sets/IN'(X0), sk_A3(X0, X3, X1, X2)), X1)
4.21/4.43	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
4.21/4.43	             'const/sets/FINITE'(X0), X1)
4.21/4.43	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
4.21/4.43	             'const/sets/FINITE'(X0), X2)
4.21/4.43	       | app_encode_app('type/nums/num', $o, 
4.21/4.43	           app_encode_app('type/nums/num', 
4.21/4.43	             app_encode_fun('type/nums/num', $o), 'const/arith/<=', 
4.21/4.43	             app_encode_app(app_encode_fun(X0, 'type/nums/num'), 
4.21/4.43	               'type/nums/num', 
4.21/4.43	               app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	                 app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
4.21/4.43	                   'type/nums/num'), 'const/iterate/nsum'(X0), X2), X3)), 
4.21/4.43	           app_encode_app(app_encode_fun(X0, 'type/nums/num'), 
4.21/4.43	             'type/nums/num', 
4.21/4.43	             app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	               app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
4.21/4.43	                 'type/nums/num'), 'const/iterate/nsum'(X0), X1), X3))),
4.21/4.43	    inference('simplify', [status(thm)], ['23'])).
4.21/4.43	tff('25', plain,
4.21/4.43	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : app_encode_fun(X0, $o), 
4.21/4.43	      X3 : app_encode_fun(X0, 'type/nums/num')]:
4.21/4.43	      (~ $true
4.21/4.43	       | app_encode_app('type/nums/num', $o, 
4.21/4.43	           app_encode_app('type/nums/num', 
4.21/4.43	             app_encode_fun('type/nums/num', $o), 'const/arith/<=', 
4.21/4.43	             app_encode_app(app_encode_fun(X0, 'type/nums/num'), 
4.21/4.43	               'type/nums/num', 
4.21/4.43	               app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	                 app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
4.21/4.43	                   'type/nums/num'), 'const/iterate/nsum'(X0), X2), X3)), 
4.21/4.43	           app_encode_app(app_encode_fun(X0, 'type/nums/num'), 
4.21/4.43	             'type/nums/num', 
4.21/4.43	             app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	               app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
4.21/4.43	                 'type/nums/num'), 'const/iterate/nsum'(X0), X1), X3))
4.21/4.43	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
4.21/4.43	             'const/sets/FINITE'(X0), X2)
4.21/4.43	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
4.21/4.43	             'const/sets/FINITE'(X0), X1)
4.21/4.43	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
4.21/4.43	             app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	               app_encode_fun(app_encode_fun(X0, $o), $o), 
4.21/4.43	               'const/sets/SUBSET'(X0), 
4.21/4.43	               app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	                 app_encode_fun(X0, $o), 
4.21/4.43	                 app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	                   app_encode_fun(app_encode_fun(X0, $o), 
4.21/4.43	                     app_encode_fun(X0, $o)), 'const/sets/DIFF'(X0), X2), X1)), 
4.21/4.43	             X1)
4.21/4.43	       | app_encode_app('type/nums/num', $o, 
4.21/4.43	           app_encode_app('type/nums/num', 
4.21/4.43	             app_encode_fun('type/nums/num', $o), 'const/arith/<=', 
4.21/4.43	             app_encode_app(app_encode_fun(X0, 'type/nums/num'), 
4.21/4.43	               'type/nums/num', 
4.21/4.43	               app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	                 app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
4.21/4.43	                   'type/nums/num'), 'const/iterate/nsum'(X0), X2), X3)), 
4.21/4.43	           app_encode_app(app_encode_fun(X0, 'type/nums/num'), 
4.21/4.43	             'type/nums/num', 
4.21/4.43	             app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	               app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
4.21/4.43	                 'type/nums/num'), 'const/iterate/nsum'(X0), X1), X3))
4.21/4.43	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
4.21/4.43	             'const/sets/FINITE'(X0), X2)
4.21/4.43	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
4.21/4.43	             'const/sets/FINITE'(X0), X1)),
4.21/4.43	    inference('sup-', [status(thm)], ['21', '24'])).
4.21/4.43	tff('26', plain,
4.21/4.43	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : app_encode_fun(X0, $o), 
4.21/4.43	      X3 : app_encode_fun(X0, 'type/nums/num')]:
4.21/4.43	      (~ app_encode_app(app_encode_fun(X0, $o), $o, 
4.21/4.43	           app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	             app_encode_fun(app_encode_fun(X0, $o), $o), 
4.21/4.43	             'const/sets/SUBSET'(X0), 
4.21/4.43	             app_encode_app(app_encode_fun(X0, $o), app_encode_fun(X0, $o), 
4.21/4.43	               app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	                 app_encode_fun(app_encode_fun(X0, $o), 
4.21/4.43	                   app_encode_fun(X0, $o)), 'const/sets/DIFF'(X0), X2), X1)), 
4.21/4.43	           X1)
4.21/4.43	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
4.21/4.43	             'const/sets/FINITE'(X0), X1)
4.21/4.43	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
4.21/4.43	             'const/sets/FINITE'(X0), X2)
4.21/4.43	       | app_encode_app('type/nums/num', $o, 
4.21/4.43	           app_encode_app('type/nums/num', 
4.21/4.43	             app_encode_fun('type/nums/num', $o), 'const/arith/<=', 
4.21/4.43	             app_encode_app(app_encode_fun(X0, 'type/nums/num'), 
4.21/4.43	               'type/nums/num', 
4.21/4.43	               app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	                 app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
4.21/4.43	                   'type/nums/num'), 'const/iterate/nsum'(X0), X2), X3)), 
4.21/4.43	           app_encode_app(app_encode_fun(X0, 'type/nums/num'), 
4.21/4.43	             'type/nums/num', 
4.21/4.43	             app_encode_app(app_encode_fun(X0, $o), 
4.21/4.43	               app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
4.21/4.43	                 'type/nums/num'), 'const/iterate/nsum'(X0), X1), X3))),
4.21/4.43	    inference('simplify', [status(thm)], ['25'])).
4.21/4.43	tff('27', plain,
4.21/4.43	    ![X0 : app_encode_fun(sk_A, 'type/nums/num')]:
4.21/4.43	      (~ $true
4.21/4.43	       | app_encode_app('type/nums/num', $o, 
4.21/4.43	           app_encode_app('type/nums/num', 
4.21/4.43	             app_encode_fun('type/nums/num', $o), 'const/arith/<=', 
4.21/4.43	             app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 
4.21/4.43	               'type/nums/num', 
4.21/4.43	               app_encode_app(app_encode_fun(sk_A, $o), 
4.21/4.43	                 app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
4.21/4.43	                   'type/nums/num'), 'const/iterate/nsum'(sk_A), sk_A0), X0)), 
4.21/4.43	           app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 
4.21/4.43	             'type/nums/num', 
4.21/4.43	             app_encode_app(app_encode_fun(sk_A, $o), 
4.21/4.43	               app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
4.21/4.43	                 'type/nums/num'), 'const/iterate/nsum'(sk_A), sk_A1), X0))
4.21/4.43	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
4.21/4.43	             'const/sets/FINITE'(sk_A), sk_A0)
4.21/4.43	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
4.21/4.43	             'const/sets/FINITE'(sk_A), sk_A1)),
4.21/4.43	    inference('sup-', [status(thm)], ['18', '26'])).
4.21/4.43	tff(zf_stmt_12, axiom,
4.21/4.43	  (![A:$tType,A0:app_encode_fun(A,$o),A1:app_encode_fun(A,$o)]:
4.21/4.43	     ((app_encode_app(app_encode_fun(A,$o),$o,'const/sets/FINITE'(A),A1) & 
4.21/4.43	       app_encode_app(app_encode_fun(A,$o),$o,
4.21/4.43	                      app_encode_app(app_encode_fun(A,$o),
4.21/4.43	                                     app_encode_fun(app_encode_fun(A,$o),$o),
4.21/4.43	                                     'const/sets/SUBSET'(A),A0),
4.21/4.43	                      A1)) =>
4.21/4.43	      app_encode_app(app_encode_fun(A,$o),$o,'const/sets/FINITE'(A),A0)))).
4.21/4.43	tff('28', plain,
4.21/4.43	    ![X4 : $tType, X5 : app_encode_fun(X4, $o), X6 : app_encode_fun(X4, $o)]:
4.21/4.43	      (app_encode_app(app_encode_fun(X4, $o), $o, 'const/sets/FINITE'(X4), 
4.21/4.43	         X5)
4.21/4.43	       | ~ app_encode_app(app_encode_fun(X4, $o), $o, 
4.21/4.43	             'const/sets/FINITE'(X4), X6)
4.21/4.43	       | ~ app_encode_app(app_encode_fun(X4, $o), $o, 
4.21/4.43	             app_encode_app(app_encode_fun(X4, $o), 
4.21/4.43	               app_encode_fun(app_encode_fun(X4, $o), $o), 
4.21/4.43	               'const/sets/SUBSET'(X4), X5), X6)),
4.21/4.43	    inference('cnf', [status(esa)], [zf_stmt_12])).
4.21/4.43	tff('29', plain,
4.21/4.43	    (~ $true
4.21/4.43	     | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
4.21/4.43	           'const/sets/FINITE'(sk_A), sk_A1)
4.21/4.43	     | app_encode_app(app_encode_fun(sk_A, $o), $o, 
4.21/4.43	         'const/sets/FINITE'(sk_A), sk_A0)),
4.21/4.43	    inference('sup-', [status(thm)], ['7', '28'])).
4.21/4.43	tff('30', plain,
4.21/4.43	    app_encode_app(app_encode_fun(sk_A, $o), $o, 'const/sets/FINITE'(sk_A), 
4.21/4.43	      sk_A1),
4.21/4.43	    inference('cnf', [status(esa)], [zf_stmt_0])).
4.21/4.43	tff('31', plain,
4.21/4.43	    (~ $true
4.21/4.43	     | ~ $true
4.21/4.43	     | app_encode_app(app_encode_fun(sk_A, $o), $o, 
4.21/4.43	         'const/sets/FINITE'(sk_A), sk_A0)),
4.21/4.43	    inference('demod', [status(thm)], ['29', '30'])).
4.21/4.43	tff('32', plain,
4.21/4.43	    app_encode_app(app_encode_fun(sk_A, $o), $o, 'const/sets/FINITE'(sk_A), 
4.21/4.43	      sk_A0),
4.21/4.43	    inference('simplify', [status(thm)], ['31'])).
4.21/4.43	tff('33', plain,
4.21/4.43	    ![X0 : app_encode_fun(sk_A, 'type/nums/num')]:
4.21/4.43	      (~ $true
4.21/4.43	       | app_encode_app('type/nums/num', $o, 
4.21/4.43	           app_encode_app('type/nums/num', 
4.21/4.43	             app_encode_fun('type/nums/num', $o), 'const/arith/<=', 
4.21/4.43	             app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 
4.21/4.43	               'type/nums/num', 
4.21/4.43	               app_encode_app(app_encode_fun(sk_A, $o), 
4.21/4.43	                 app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
4.21/4.43	                   'type/nums/num'), 'const/iterate/nsum'(sk_A), sk_A0), X0)), 
4.21/4.43	           app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 
4.21/4.43	             'type/nums/num', 
4.21/4.43	             app_encode_app(app_encode_fun(sk_A, $o), 
4.21/4.43	               app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
4.21/4.43	                 'type/nums/num'), 'const/iterate/nsum'(sk_A), sk_A1), X0))
4.21/4.43	       | ~ $true
4.21/4.43	       | ~ $true),
4.21/4.43	    inference('demod', [status(thm)], ['27', '32', '30'])).
4.21/4.43	tff('34', plain,
4.21/4.43	    ![X0 : app_encode_fun(sk_A, 'type/nums/num')]:
4.21/4.43	      app_encode_app('type/nums/num', $o, 
4.21/4.43	        app_encode_app('type/nums/num', app_encode_fun('type/nums/num', $o), 
4.21/4.43	          'const/arith/<=', 
4.21/4.43	          app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 
4.21/4.43	            'type/nums/num', 
4.21/4.43	            app_encode_app(app_encode_fun(sk_A, $o), 
4.21/4.43	              app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
4.21/4.43	                'type/nums/num'), 'const/iterate/nsum'(sk_A), sk_A0), X0)), 
4.21/4.43	        app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 
4.21/4.43	          'type/nums/num', 
4.21/4.43	          app_encode_app(app_encode_fun(sk_A, $o), 
4.21/4.43	            app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
4.21/4.43	              'type/nums/num'), 'const/iterate/nsum'(sk_A), sk_A1), X0)),
4.21/4.43	    inference('simplify', [status(thm)], ['33'])).
4.21/4.43	tff('35', plain,
4.21/4.43	    ~ app_encode_app('type/nums/num', $o, 
4.21/4.43	        app_encode_app('type/nums/num', app_encode_fun('type/nums/num', $o), 
4.21/4.43	          'const/arith/<=', 
4.21/4.43	          app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 
4.21/4.43	            'type/nums/num', 
4.21/4.43	            app_encode_app(app_encode_fun(sk_A, $o), 
4.21/4.43	              app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
4.21/4.43	                'type/nums/num'), 'const/iterate/nsum'(sk_A), sk_A0), sk_A21)), 
4.21/4.43	        app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 
4.21/4.43	          'type/nums/num', 
4.21/4.43	          app_encode_app(app_encode_fun(sk_A, $o), 
4.21/4.43	            app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
4.21/4.43	              'type/nums/num'), 'const/iterate/nsum'(sk_A), sk_A1), sk_A21)),
4.21/4.43	    inference('cnf', [status(esa)], [zf_stmt_0])).
4.21/4.43	tff('36', plain, ~ $true, inference('sup-', [status(thm)], ['34', '35'])).
4.21/4.43	tff('37', plain, $false, inference('simplify', [status(thm)], ['36'])).
4.21/4.43	
4.21/4.43	% SZS output end Refutation
4.21/4.43	EOF
