0.00/0.00	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : appext
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : rpo6
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.20	% Computer   : n037.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 18:39:09 CST 2018
11.03/11.24	% done 2542 iterations in 11.038s
11.03/11.24	% SZS status Theorem for 'stdin'
11.03/11.24	% SZS output start Refutation
11.03/11.24	tff(zf_stmt_14, axiom,
11.03/11.24	  (![A:$tType,A0:app_encode_fun(A,$o),A1:app_encode_fun(A,$o)]:
11.03/11.24	     (app_encode_app(app_encode_fun(A,$o),$o,
11.03/11.24	                     app_encode_app(app_encode_fun(A,$o),
11.03/11.24	                                    app_encode_fun(app_encode_fun(A,$o),$o),
11.03/11.24	                                    'const/sets/SUBSET'(A),A0),
11.03/11.24	                     A1) <=>
11.03/11.24	      (![A2:A]:
11.03/11.24	         (app_encode_app(app_encode_fun(A,$o),$o,
11.03/11.24	                         app_encode_app(A,
11.03/11.24	                                        app_encode_fun(app_encode_fun(A,$o),
11.03/11.24	                                                       $o),
11.03/11.24	                                        'const/sets/IN'(A),A2),
11.03/11.24	                         A0) =>
11.03/11.24	          app_encode_app(app_encode_fun(A,$o),$o,
11.03/11.24	                         app_encode_app(A,
11.03/11.24	                                        app_encode_fun(app_encode_fun(A,$o),
11.03/11.24	                                                       $o),
11.03/11.24	                                        'const/sets/IN'(A),A2),
11.03/11.24	                         A1)))))).
11.03/11.24	tff('0', plain,
11.03/11.24	    ![X11 : $tType, X13 : app_encode_fun(X11, $o), 
11.03/11.24	      X15 : app_encode_fun(X11, $o)]:
11.03/11.24	      (app_encode_app(app_encode_fun(X11, $o), $o, 
11.03/11.24	         app_encode_app(app_encode_fun(X11, $o), 
11.03/11.24	           app_encode_fun(app_encode_fun(X11, $o), $o), 
11.03/11.24	           'const/sets/SUBSET'(X11), X13), X15)
11.03/11.24	       | app_encode_app(app_encode_fun(X11, $o), $o, 
11.03/11.24	           app_encode_app(X11, app_encode_fun(app_encode_fun(X11, $o), $o), 
11.03/11.24	             'const/sets/IN'(X11), sk_A2(X11, X15, X13)), X13)),
11.03/11.24	    inference('cnf', [status(esa)], [zf_stmt_14])).
11.03/11.24	tff(zf_stmt_15, axiom,
11.03/11.24	  (![A:$tType,A0:app_encode_fun(A,$o),A1:app_encode_fun(A,$o),A2:A]:
11.03/11.24	     (app_encode_app(app_encode_fun(A,$o),$o,
11.03/11.24	                     app_encode_app(A,
11.03/11.24	                                    app_encode_fun(app_encode_fun(A,$o),$o),
11.03/11.24	                                    'const/sets/IN'(A),A2),
11.03/11.24	                     app_encode_app(app_encode_fun(A,$o),
11.03/11.24	                                    app_encode_fun(A,$o),
11.03/11.24	                                    app_encode_app(app_encode_fun(A,$o),
11.03/11.24	                                                   app_encode_fun(app_encode_fun(
11.03/11.24	                                                                  A,$o),
11.03/11.24	                                                                  app_encode_fun(
11.03/11.24	                                                                  A,$o)),
11.03/11.24	                                                   'const/sets/DIFF'(A),A0),
11.03/11.24	                                    A1)) <=>
11.03/11.24	      (app_encode_app(app_encode_fun(A,$o),$o,
11.03/11.24	                      app_encode_app(A,
11.03/11.24	                                     app_encode_fun(app_encode_fun(A,$o),$o),
11.03/11.24	                                     'const/sets/IN'(A),A2),
11.03/11.24	                      A0) & 
11.03/11.24	       (~
11.03/11.24	         app_encode_app(app_encode_fun(A,$o),$o,
11.03/11.24	                        app_encode_app(A,
11.03/11.24	                                       app_encode_fun(app_encode_fun(A,$o),$o),
11.03/11.24	                                       'const/sets/IN'(A),A2),
11.03/11.24	                        A1)))))).
11.03/11.24	tff('1', plain,
11.03/11.24	    ![X16 : $tType, X17 : X16, X18 : app_encode_fun(X16, $o), 
11.03/11.24	      X19 : app_encode_fun(X16, $o)]:
11.03/11.24	      (app_encode_app(app_encode_fun(X16, $o), $o, 
11.03/11.24	         app_encode_app(X16, app_encode_fun(app_encode_fun(X16, $o), $o), 
11.03/11.24	           'const/sets/IN'(X16), X17), X18)
11.03/11.24	       | ~ app_encode_app(app_encode_fun(X16, $o), $o, 
11.03/11.24	             app_encode_app(X16, 
11.03/11.24	               app_encode_fun(app_encode_fun(X16, $o), $o), 
11.03/11.24	               'const/sets/IN'(X16), X17), 
11.03/11.24	             app_encode_app(app_encode_fun(X16, $o), 
11.03/11.24	               app_encode_fun(X16, $o), 
11.03/11.24	               app_encode_app(app_encode_fun(X16, $o), 
11.03/11.24	                 app_encode_fun(app_encode_fun(X16, $o), 
11.03/11.24	                   app_encode_fun(X16, $o)), 'const/sets/DIFF'(X16), X18), 
11.03/11.24	               X19))),
11.03/11.24	    inference('cnf', [status(esa)], [zf_stmt_15])).
11.03/11.24	tff('2', plain,
11.03/11.24	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : app_encode_fun(X0, $o), 
11.03/11.24	      X3 : app_encode_fun(X0, $o)]:
11.03/11.24	      (~ $true
11.03/11.24	       | app_encode_app(app_encode_fun(X0, $o), $o, 
11.03/11.24	           app_encode_app(app_encode_fun(X0, $o), 
11.03/11.24	             app_encode_fun(app_encode_fun(X0, $o), $o), 
11.03/11.24	             'const/sets/SUBSET'(X0), 
11.03/11.24	             app_encode_app(app_encode_fun(X0, $o), app_encode_fun(X0, $o), 
11.03/11.24	               app_encode_app(app_encode_fun(X0, $o), 
11.03/11.24	                 app_encode_fun(app_encode_fun(X0, $o), 
11.03/11.24	                   app_encode_fun(X0, $o)), 'const/sets/DIFF'(X0), X2), X1)), 
11.03/11.24	           X3)
11.03/11.24	       | app_encode_app(app_encode_fun(X0, $o), $o, 
11.03/11.24	           app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
11.03/11.24	             'const/sets/IN'(X0), 
11.03/11.24	             sk_A2(X0, X3, 
11.03/11.24	               app_encode_app(app_encode_fun(X0, $o), 
11.03/11.24	                 app_encode_fun(X0, $o), 
11.03/11.24	                 app_encode_app(app_encode_fun(X0, $o), 
11.03/11.24	                   app_encode_fun(app_encode_fun(X0, $o), 
11.03/11.24	                     app_encode_fun(X0, $o)), 'const/sets/DIFF'(X0), X2), X1))), 
11.03/11.24	           X2)),
11.03/11.24	    inference('sup-', [status(thm)], ['0', '1'])).
11.03/11.24	tff('3', plain,
11.03/11.24	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : app_encode_fun(X0, $o), 
11.03/11.24	      X3 : app_encode_fun(X0, $o)]:
11.03/11.24	      (app_encode_app(app_encode_fun(X0, $o), $o, 
11.03/11.24	         app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
11.03/11.24	           'const/sets/IN'(X0), 
11.03/11.24	           sk_A2(X0, X3, 
11.03/11.24	             app_encode_app(app_encode_fun(X0, $o), app_encode_fun(X0, $o), 
11.03/11.24	               app_encode_app(app_encode_fun(X0, $o), 
11.03/11.24	                 app_encode_fun(app_encode_fun(X0, $o), 
11.03/11.24	                   app_encode_fun(X0, $o)), 'const/sets/DIFF'(X0), X2), X1))), 
11.03/11.24	         X2)
11.03/11.24	       | app_encode_app(app_encode_fun(X0, $o), $o, 
11.03/11.24	           app_encode_app(app_encode_fun(X0, $o), 
11.03/11.24	             app_encode_fun(app_encode_fun(X0, $o), $o), 
11.03/11.24	             'const/sets/SUBSET'(X0), 
11.03/11.24	             app_encode_app(app_encode_fun(X0, $o), app_encode_fun(X0, $o), 
11.03/11.24	               app_encode_app(app_encode_fun(X0, $o), 
11.03/11.24	                 app_encode_fun(app_encode_fun(X0, $o), 
11.03/11.24	                   app_encode_fun(X0, $o)), 'const/sets/DIFF'(X0), X2), X1)), 
11.03/11.24	           X3)),
11.03/11.24	    inference('simplify', [status(thm)], ['2'])).
11.03/11.24	tff('4', plain,
11.03/11.24	    ![X11 : $tType, X13 : app_encode_fun(X11, $o), 
11.03/11.24	      X15 : app_encode_fun(X11, $o)]:
11.03/11.24	      (app_encode_app(app_encode_fun(X11, $o), $o, 
11.03/11.24	         app_encode_app(app_encode_fun(X11, $o), 
11.03/11.24	           app_encode_fun(app_encode_fun(X11, $o), $o), 
11.03/11.24	           'const/sets/SUBSET'(X11), X13), X15)
11.03/11.24	       | ~ app_encode_app(app_encode_fun(X11, $o), $o, 
11.03/11.24	             app_encode_app(X11, 
11.03/11.24	               app_encode_fun(app_encode_fun(X11, $o), $o), 
11.03/11.24	               'const/sets/IN'(X11), sk_A2(X11, X15, X13)), X15)),
11.03/11.24	    inference('cnf', [status(esa)], [zf_stmt_14])).
11.03/11.24	tff('5', plain,
11.03/11.24	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : app_encode_fun(X0, $o)]:
11.03/11.24	      (~ $true
11.03/11.24	       | app_encode_app(app_encode_fun(X0, $o), $o, 
11.03/11.24	           app_encode_app(app_encode_fun(X0, $o), 
11.03/11.24	             app_encode_fun(app_encode_fun(X0, $o), $o), 
11.03/11.24	             'const/sets/SUBSET'(X0), 
11.03/11.24	             app_encode_app(app_encode_fun(X0, $o), app_encode_fun(X0, $o), 
11.03/11.24	               app_encode_app(app_encode_fun(X0, $o), 
11.03/11.24	                 app_encode_fun(app_encode_fun(X0, $o), 
11.03/11.24	                   app_encode_fun(X0, $o)), 'const/sets/DIFF'(X0), X1), X2)), 
11.03/11.24	           X1)
11.03/11.24	       | app_encode_app(app_encode_fun(X0, $o), $o, 
11.03/11.24	           app_encode_app(app_encode_fun(X0, $o), 
11.03/11.24	             app_encode_fun(app_encode_fun(X0, $o), $o), 
11.03/11.24	             'const/sets/SUBSET'(X0), 
11.03/11.24	             app_encode_app(app_encode_fun(X0, $o), app_encode_fun(X0, $o), 
11.03/11.24	               app_encode_app(app_encode_fun(X0, $o), 
11.03/11.24	                 app_encode_fun(app_encode_fun(X0, $o), 
11.03/11.24	                   app_encode_fun(X0, $o)), 'const/sets/DIFF'(X0), X1), X2)), 
11.03/11.24	           X1)),
11.03/11.24	    inference('sup-', [status(thm)], ['3', '4'])).
11.03/11.24	tff('6', plain,
11.03/11.24	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : app_encode_fun(X0, $o)]:
11.03/11.24	      app_encode_app(app_encode_fun(X0, $o), $o, 
11.03/11.24	        app_encode_app(app_encode_fun(X0, $o), 
11.03/11.24	          app_encode_fun(app_encode_fun(X0, $o), $o), 
11.03/11.24	          'const/sets/SUBSET'(X0), 
11.03/11.24	          app_encode_app(app_encode_fun(X0, $o), app_encode_fun(X0, $o), 
11.03/11.24	            app_encode_app(app_encode_fun(X0, $o), 
11.03/11.24	              app_encode_fun(app_encode_fun(X0, $o), app_encode_fun(X0, $o)), 
11.03/11.24	              'const/sets/DIFF'(X0), X1), X2)), X1),
11.03/11.24	    inference('simplify', [status(thm)], ['5'])).
11.03/11.24	tff(zf_stmt_16, conjecture,
11.03/11.24	  (![A:$tType,A0:app_encode_fun(A,$o),A1:app_encode_fun(A,$o),
11.03/11.24	     A2:app_encode_fun(A,'type/nums/num')]:
11.03/11.24	     ((app_encode_app(app_encode_fun(A,$o),$o,'const/sets/FINITE'(A),A1) & 
11.03/11.24	       app_encode_app(app_encode_fun(A,$o),$o,
11.03/11.24	                      app_encode_app(app_encode_fun(A,$o),
11.03/11.24	                                     app_encode_fun(app_encode_fun(A,$o),$o),
11.03/11.24	                                     'const/sets/SUBSET'(A),A0),
11.03/11.24	                      A1)) =>
11.03/11.24	      app_encode_app('type/nums/num',$o,
11.03/11.24	                     app_encode_app('type/nums/num',
11.03/11.24	                                    app_encode_fun('type/nums/num',$o),
11.03/11.24	                                    'const/arith/<=',
11.03/11.24	                                    app_encode_app(app_encode_fun(A,
11.03/11.24	                                                                  'type/nums/num'),
11.03/11.24	                                                   'type/nums/num',
11.03/11.24	                                                   app_encode_app(app_encode_fun(
11.03/11.24	                                                                  A,$o),
11.03/11.24	                                                                  app_encode_fun(
11.03/11.24	                                                                  app_encode_fun(
11.03/11.24	                                                                  A,
11.03/11.24	                                                                  'type/nums/num'),
11.03/11.24	                                                                  'type/nums/num'),
11.03/11.24	                                                                  'const/iterate/nsum'(
11.03/11.24	                                                                  A),A0),
11.03/11.24	                                                   A2)),
11.03/11.24	                     app_encode_app(app_encode_fun(A,'type/nums/num'),
11.03/11.24	                                    'type/nums/num',
11.03/11.24	                                    app_encode_app(app_encode_fun(A,$o),
11.03/11.24	                                                   app_encode_fun(app_encode_fun(
11.03/11.24	                                                                  A,
11.03/11.24	                                                                  'type/nums/num'),
11.03/11.24	                                                                  'type/nums/num'),
11.03/11.24	                                                   'const/iterate/nsum'(A),A1),
11.03/11.24	                                    A2))))).
11.03/11.24	tff(zf_stmt_0, negated_conjecture,
11.03/11.24	  (~
11.03/11.24	    (![A:$tType,A0:app_encode_fun(A,$o),A1:app_encode_fun(A,$o),
11.03/11.24	       A2:app_encode_fun(A,'type/nums/num')]:
11.03/11.24	       ((app_encode_app(app_encode_fun(A,$o),$o,'const/sets/FINITE'(A),A1) & 
11.03/11.24	         app_encode_app(app_encode_fun(A,$o),$o,
11.03/11.24	                        app_encode_app(app_encode_fun(A,$o),
11.03/11.24	                                       app_encode_fun(app_encode_fun(A,$o),$o),
11.03/11.24	                                       'const/sets/SUBSET'(A),A0),
11.03/11.24	                        A1)) =>
11.03/11.24	        app_encode_app('type/nums/num',$o,
11.03/11.24	                       app_encode_app('type/nums/num',
11.03/11.24	                                      app_encode_fun('type/nums/num',$o),
11.03/11.24	                                      'const/arith/<=',
11.03/11.24	                                      app_encode_app(app_encode_fun(A,
11.03/11.24	                                                                    'type/nums/num'),
11.03/11.24	                                                     'type/nums/num',
11.03/11.24	                                                     app_encode_app(app_encode_fun(
11.03/11.24	                                                                    A,$o),
11.03/11.24	                                                                    app_encode_fun(
11.03/11.24	                                                                    app_encode_fun(
11.03/11.24	                                                                    A,
11.03/11.24	                                                                    'type/nums/num'),
11.03/11.24	                                                                    'type/nums/num'),
11.03/11.24	                                                                    'const/iterate/nsum'(
11.03/11.24	                                                                    A),A0),
11.03/11.24	                                                     A2)),
11.03/11.24	                       app_encode_app(app_encode_fun(A,'type/nums/num'),
11.03/11.24	                                      'type/nums/num',
11.03/11.24	                                      app_encode_app(app_encode_fun(A,$o),
11.03/11.24	                                                     app_encode_fun(app_encode_fun(
11.03/11.24	                                                                    A,
11.03/11.24	                                                                    'type/nums/num'),
11.03/11.24	                                                                    'type/nums/num'),
11.03/11.24	                                                     'const/iterate/nsum'(A),
11.03/11.24	                                                     A1),
11.03/11.24	                                      A2)))))).
11.03/11.24	tff('7', plain,
11.03/11.24	    app_encode_app(app_encode_fun(sk_A, $o), $o, 
11.03/11.24	      app_encode_app(app_encode_fun(sk_A, $o), 
11.03/11.24	        app_encode_fun(app_encode_fun(sk_A, $o), $o), 
11.03/11.24	        'const/sets/SUBSET'(sk_A), sk_A0), sk_A1),
11.03/11.24	    inference('cnf', [status(esa)], [zf_stmt_0])).
11.03/11.24	tff('8', plain,
11.03/11.24	    ![X11 : $tType, X12 : X11, X13 : app_encode_fun(X11, $o), 
11.03/11.24	      X14 : app_encode_fun(X11, $o)]:
11.03/11.24	      (~ app_encode_app(app_encode_fun(X11, $o), $o, 
11.03/11.24	           app_encode_app(X11, app_encode_fun(app_encode_fun(X11, $o), $o), 
11.03/11.24	             'const/sets/IN'(X11), X12), X13)
11.03/11.24	       | app_encode_app(app_encode_fun(X11, $o), $o, 
11.03/11.24	           app_encode_app(X11, app_encode_fun(app_encode_fun(X11, $o), $o), 
11.03/11.24	             'const/sets/IN'(X11), X12), X14)
11.03/11.24	       | ~ app_encode_app(app_encode_fun(X11, $o), $o, 
11.03/11.24	             app_encode_app(app_encode_fun(X11, $o), 
11.03/11.24	               app_encode_fun(app_encode_fun(X11, $o), $o), 
11.03/11.24	               'const/sets/SUBSET'(X11), X13), X14)),
11.03/11.24	    inference('cnf', [status(esa)], [zf_stmt_14])).
11.03/11.24	tff('9', plain,
11.03/11.24	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : app_encode_fun(X0, $o), 
11.03/11.24	      X3 : app_encode_fun(X0, $o)]:
11.03/11.24	      (~ $true
11.03/11.24	       | app_encode_app(app_encode_fun(X0, $o), $o, 
11.03/11.24	           app_encode_app(app_encode_fun(X0, $o), 
11.03/11.24	             app_encode_fun(app_encode_fun(X0, $o), $o), 
11.03/11.24	             'const/sets/SUBSET'(X0), X1), X2)
11.03/11.24	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
11.03/11.24	             app_encode_app(app_encode_fun(X0, $o), 
11.03/11.24	               app_encode_fun(app_encode_fun(X0, $o), $o), 
11.03/11.24	               'const/sets/SUBSET'(X0), X1), X3)
11.03/11.24	       | app_encode_app(app_encode_fun(X0, $o), $o, 
11.03/11.24	           app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
11.03/11.24	             'const/sets/IN'(X0), sk_A2(X0, X2, X1)), X3)),
11.03/11.24	    inference('sup-', [status(thm)], ['0', '8'])).
11.03/11.24	tff('10', plain,
11.03/11.24	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : app_encode_fun(X0, $o), 
11.03/11.24	      X3 : app_encode_fun(X0, $o)]:
11.03/11.24	      (app_encode_app(app_encode_fun(X0, $o), $o, 
11.03/11.24	         app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
11.03/11.24	           'const/sets/IN'(X0), sk_A2(X0, X2, X1)), X3)
11.03/11.24	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
11.03/11.24	             app_encode_app(app_encode_fun(X0, $o), 
11.03/11.24	               app_encode_fun(app_encode_fun(X0, $o), $o), 
11.03/11.24	               'const/sets/SUBSET'(X0), X1), X3)
11.03/11.24	       | app_encode_app(app_encode_fun(X0, $o), $o, 
11.03/11.24	           app_encode_app(app_encode_fun(X0, $o), 
11.03/11.24	             app_encode_fun(app_encode_fun(X0, $o), $o), 
11.03/11.24	             'const/sets/SUBSET'(X0), X1), X2)),
11.03/11.24	    inference('simplify', [status(thm)], ['9'])).
11.03/11.24	tff('11', plain,
11.03/11.24	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : app_encode_fun(X0, $o), 
11.03/11.24	      X3 : app_encode_fun(X0, $o), X4 : app_encode_fun(X0, $o)]:
11.03/11.24	      (~ $true
11.03/11.24	       | app_encode_app(app_encode_fun(X0, $o), $o, 
11.03/11.24	           app_encode_app(app_encode_fun(X0, $o), 
11.03/11.24	             app_encode_fun(app_encode_fun(X0, $o), $o), 
11.03/11.24	             'const/sets/SUBSET'(X0), X2), X3)
11.03/11.24	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
11.03/11.25	             app_encode_app(app_encode_fun(X0, $o), 
11.03/11.25	               app_encode_fun(app_encode_fun(X0, $o), $o), 
11.03/11.25	               'const/sets/SUBSET'(X0), X2), X1)
11.03/11.25	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
11.03/11.25	             app_encode_app(app_encode_fun(X0, $o), 
11.03/11.25	               app_encode_fun(app_encode_fun(X0, $o), $o), 
11.03/11.25	               'const/sets/SUBSET'(X0), X1), X4)
11.03/11.25	       | app_encode_app(app_encode_fun(X0, $o), $o, 
11.03/11.25	           app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
11.03/11.25	             'const/sets/IN'(X0), sk_A2(X0, X3, X2)), X4)),
11.03/11.25	    inference('sup-', [status(thm)], ['10', '8'])).
11.03/11.25	tff('12', plain,
11.03/11.25	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : app_encode_fun(X0, $o), 
11.03/11.25	      X3 : app_encode_fun(X0, $o), X4 : app_encode_fun(X0, $o)]:
11.03/11.25	      (app_encode_app(app_encode_fun(X0, $o), $o, 
11.03/11.25	         app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
11.03/11.25	           'const/sets/IN'(X0), sk_A2(X0, X3, X2)), X4)
11.03/11.25	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
11.03/11.25	             app_encode_app(app_encode_fun(X0, $o), 
11.03/11.25	               app_encode_fun(app_encode_fun(X0, $o), $o), 
11.03/11.25	               'const/sets/SUBSET'(X0), X1), X4)
11.03/11.25	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
11.03/11.25	             app_encode_app(app_encode_fun(X0, $o), 
11.03/11.25	               app_encode_fun(app_encode_fun(X0, $o), $o), 
11.03/11.25	               'const/sets/SUBSET'(X0), X2), X1)
11.03/11.25	       | app_encode_app(app_encode_fun(X0, $o), $o, 
11.03/11.25	           app_encode_app(app_encode_fun(X0, $o), 
11.03/11.25	             app_encode_fun(app_encode_fun(X0, $o), $o), 
11.03/11.25	             'const/sets/SUBSET'(X0), X2), X3)),
11.03/11.25	    inference('simplify', [status(thm)], ['11'])).
11.03/11.25	tff('13', plain,
11.03/11.25	    ![X0 : app_encode_fun(sk_A, $o), X1 : app_encode_fun(sk_A, $o)]:
11.03/11.25	      (~ $true
11.03/11.25	       | app_encode_app(app_encode_fun(sk_A, $o), $o, 
11.03/11.25	           app_encode_app(app_encode_fun(sk_A, $o), 
11.03/11.25	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
11.03/11.25	             'const/sets/SUBSET'(sk_A), X1), X0)
11.03/11.25	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
11.03/11.25	             app_encode_app(app_encode_fun(sk_A, $o), 
11.03/11.25	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
11.03/11.25	               'const/sets/SUBSET'(sk_A), X1), sk_A0)
11.03/11.25	       | app_encode_app(app_encode_fun(sk_A, $o), $o, 
11.03/11.25	           app_encode_app(sk_A, 
11.03/11.25	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
11.03/11.25	             'const/sets/IN'(sk_A), sk_A2(sk_A, X0, X1)), sk_A1)),
11.03/11.25	    inference('sup-', [status(thm)], ['7', '12'])).
11.03/11.25	tff('14', plain,
11.03/11.25	    ![X0 : app_encode_fun(sk_A, $o), X1 : app_encode_fun(sk_A, $o)]:
11.03/11.25	      (app_encode_app(app_encode_fun(sk_A, $o), $o, 
11.03/11.25	         app_encode_app(sk_A, app_encode_fun(app_encode_fun(sk_A, $o), $o), 
11.03/11.25	           'const/sets/IN'(sk_A), sk_A2(sk_A, X0, X1)), sk_A1)
11.03/11.25	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
11.03/11.25	             app_encode_app(app_encode_fun(sk_A, $o), 
11.03/11.25	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
11.03/11.25	               'const/sets/SUBSET'(sk_A), X1), sk_A0)
11.03/11.25	       | app_encode_app(app_encode_fun(sk_A, $o), $o, 
11.03/11.25	           app_encode_app(app_encode_fun(sk_A, $o), 
11.03/11.25	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
11.03/11.25	             'const/sets/SUBSET'(sk_A), X1), X0)),
11.03/11.25	    inference('simplify', [status(thm)], ['13'])).
11.03/11.25	tff('15', plain,
11.03/11.25	    ![X0 : app_encode_fun(sk_A, $o)]:
11.03/11.25	      (~ $true
11.03/11.25	       | app_encode_app(app_encode_fun(sk_A, $o), $o, 
11.03/11.25	           app_encode_app(app_encode_fun(sk_A, $o), 
11.03/11.25	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
11.03/11.25	             'const/sets/SUBSET'(sk_A), X0), sk_A1)
11.03/11.25	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
11.03/11.25	             app_encode_app(app_encode_fun(sk_A, $o), 
11.03/11.25	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
11.03/11.25	               'const/sets/SUBSET'(sk_A), X0), sk_A0)
11.03/11.25	       | app_encode_app(app_encode_fun(sk_A, $o), $o, 
11.03/11.25	           app_encode_app(app_encode_fun(sk_A, $o), 
11.03/11.25	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
11.03/11.25	             'const/sets/SUBSET'(sk_A), X0), sk_A1)),
11.03/11.25	    inference('sup-', [status(thm)], ['14', '4'])).
11.03/11.25	tff('16', plain,
11.03/11.25	    ![X0 : app_encode_fun(sk_A, $o)]:
11.03/11.25	      (~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
11.03/11.25	           app_encode_app(app_encode_fun(sk_A, $o), 
11.03/11.25	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
11.03/11.25	             'const/sets/SUBSET'(sk_A), X0), sk_A0)
11.03/11.25	       | app_encode_app(app_encode_fun(sk_A, $o), $o, 
11.03/11.25	           app_encode_app(app_encode_fun(sk_A, $o), 
11.03/11.25	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
11.03/11.25	             'const/sets/SUBSET'(sk_A), X0), sk_A1)),
11.03/11.25	    inference('simplify', [status(thm)], ['15'])).
11.03/11.25	tff('17', plain,
11.03/11.25	    ![X0 : app_encode_fun(sk_A, $o)]:
11.03/11.25	      (~ $true
11.03/11.25	       | app_encode_app(app_encode_fun(sk_A, $o), $o, 
11.03/11.25	           app_encode_app(app_encode_fun(sk_A, $o), 
11.03/11.25	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
11.03/11.25	             'const/sets/SUBSET'(sk_A), 
11.03/11.25	             app_encode_app(app_encode_fun(sk_A, $o), 
11.03/11.25	               app_encode_fun(sk_A, $o), 
11.03/11.25	               app_encode_app(app_encode_fun(sk_A, $o), 
11.03/11.25	                 app_encode_fun(app_encode_fun(sk_A, $o), 
11.03/11.25	                   app_encode_fun(sk_A, $o)), 'const/sets/DIFF'(sk_A), sk_A0), 
11.03/11.25	               X0)), sk_A1)),
11.03/11.25	    inference('sup-', [status(thm)], ['6', '16'])).
11.03/11.25	tff('18', plain,
11.03/11.25	    ![X0 : app_encode_fun(sk_A, $o)]:
11.03/11.25	      app_encode_app(app_encode_fun(sk_A, $o), $o, 
11.03/11.25	        app_encode_app(app_encode_fun(sk_A, $o), 
11.03/11.25	          app_encode_fun(app_encode_fun(sk_A, $o), $o), 
11.03/11.25	          'const/sets/SUBSET'(sk_A), 
11.03/11.25	          app_encode_app(app_encode_fun(sk_A, $o), app_encode_fun(sk_A, $o), 
11.03/11.25	            app_encode_app(app_encode_fun(sk_A, $o), 
11.03/11.25	              app_encode_fun(app_encode_fun(sk_A, $o), 
11.03/11.25	                app_encode_fun(sk_A, $o)), 'const/sets/DIFF'(sk_A), sk_A0), 
11.03/11.25	            X0)), sk_A1),
11.03/11.25	    inference('simplify', [status(thm)], ['17'])).
11.03/11.25	tff(zf_stmt_12, axiom,
11.03/11.25	  (![A:$tType,A0:app_encode_fun(A,$o),A1:app_encode_fun(A,$o),
11.03/11.25	     A2:app_encode_fun(A,'type/nums/num')]:
11.03/11.25	     ((app_encode_app(app_encode_fun(A,$o),$o,'const/sets/FINITE'(A),A0) & 
11.03/11.25	       app_encode_app(app_encode_fun(A,$o),$o,'const/sets/FINITE'(A),A1) & 
11.03/11.25	       (![A3:A]:
11.03/11.25	          (app_encode_app(app_encode_fun(A,$o),$o,
11.03/11.25	                          app_encode_app(A,
11.03/11.25	                                         app_encode_fun(app_encode_fun(A,$o),
11.03/11.25	                                                        $o),
11.03/11.25	                                         'const/sets/IN'(A),A3),
11.03/11.25	                          app_encode_app(app_encode_fun(A,$o),
11.03/11.25	                                         app_encode_fun(A,$o),
11.03/11.25	                                         app_encode_app(app_encode_fun(A,$o),
11.03/11.25	                                                        app_encode_fun(
11.03/11.25	                                                        app_encode_fun(A,$o),
11.03/11.25	                                                        app_encode_fun(A,$o)),
11.03/11.25	                                                        'const/sets/DIFF'(A),
11.03/11.25	                                                        A0),
11.03/11.25	                                         A1)) =>
11.03/11.25	           (app_encode_app(A,'type/nums/num',A2,A3) =
11.03/11.25	            app_encode_app('type/nums/num','type/nums/num',
11.03/11.25	                           'const/nums/NUMERAL','const/nums/_0'))))) =>
11.03/11.25	      app_encode_app('type/nums/num',$o,
11.03/11.25	                     app_encode_app('type/nums/num',
11.03/11.25	                                    app_encode_fun('type/nums/num',$o),
11.03/11.25	                                    'const/arith/<=',
11.03/11.25	                                    app_encode_app(app_encode_fun(A,
11.03/11.25	                                                                  'type/nums/num'),
11.03/11.25	                                                   'type/nums/num',
11.03/11.25	                                                   app_encode_app(app_encode_fun(
11.03/11.25	                                                                  A,$o),
11.03/11.25	                                                                  app_encode_fun(
11.03/11.25	                                                                  app_encode_fun(
11.03/11.25	                                                                  A,
11.03/11.25	                                                                  'type/nums/num'),
11.03/11.25	                                                                  'type/nums/num'),
11.03/11.25	                                                                  'const/iterate/nsum'(
11.03/11.25	                                                                  A),A0),
11.03/11.25	                                                   A2)),
11.03/11.25	                     app_encode_app(app_encode_fun(A,'type/nums/num'),
11.03/11.25	                                    'type/nums/num',
11.03/11.25	                                    app_encode_app(app_encode_fun(A,$o),
11.03/11.25	                                                   app_encode_fun(app_encode_fun(
11.03/11.25	                                                                  A,
11.03/11.25	                                                                  'type/nums/num'),
11.03/11.25	                                                                  'type/nums/num'),
11.03/11.25	                                                   'const/iterate/nsum'(A),A1),
11.03/11.25	                                    A2))))).
11.03/11.25	tff('19', plain,
11.03/11.25	    ![X4 : $tType, X5 : app_encode_fun(X4, $o), X6 : app_encode_fun(X4, $o), 
11.03/11.25	      X7 : app_encode_fun(X4, 'type/nums/num')]:
11.03/11.25	      (~ app_encode_app(app_encode_fun(X4, $o), $o, 'const/sets/FINITE'(X4), 
11.03/11.25	           X5)
11.03/11.25	       | ~ app_encode_app(app_encode_fun(X4, $o), $o, 
11.03/11.25	             'const/sets/FINITE'(X4), X6)
11.03/11.25	       | app_encode_app(app_encode_fun(X4, $o), $o, 
11.03/11.25	           app_encode_app(X4, app_encode_fun(app_encode_fun(X4, $o), $o), 
11.03/11.25	             'const/sets/IN'(X4), sk_A3(X4, X7, X5, X6)), 
11.03/11.25	           app_encode_app(app_encode_fun(X4, $o), app_encode_fun(X4, $o), 
11.03/11.25	             app_encode_app(app_encode_fun(X4, $o), 
11.03/11.25	               app_encode_fun(app_encode_fun(X4, $o), app_encode_fun(X4, $o)), 
11.03/11.25	               'const/sets/DIFF'(X4), X6), X5))
11.03/11.25	       | app_encode_app('type/nums/num', $o, 
11.03/11.25	           app_encode_app('type/nums/num', 
11.03/11.25	             app_encode_fun('type/nums/num', $o), 'const/arith/<=', 
11.03/11.25	             app_encode_app(app_encode_fun(X4, 'type/nums/num'), 
11.03/11.25	               'type/nums/num', 
11.03/11.25	               app_encode_app(app_encode_fun(X4, $o), 
11.03/11.25	                 app_encode_fun(app_encode_fun(X4, 'type/nums/num'), 
11.03/11.25	                   'type/nums/num'), 'const/iterate/nsum'(X4), X6), X7)), 
11.03/11.25	           app_encode_app(app_encode_fun(X4, 'type/nums/num'), 
11.03/11.25	             'type/nums/num', 
11.03/11.25	             app_encode_app(app_encode_fun(X4, $o), 
11.03/11.25	               app_encode_fun(app_encode_fun(X4, 'type/nums/num'), 
11.03/11.25	                 'type/nums/num'), 'const/iterate/nsum'(X4), X5), X7))),
11.03/11.25	    inference('cnf', [status(esa)], [zf_stmt_12])).
11.03/11.25	tff('20', plain,
11.03/11.25	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : app_encode_fun(X0, $o), 
11.03/11.25	      X3 : app_encode_fun(X0, 'type/nums/num'), X4 : app_encode_fun(X0, $o)]:
11.03/11.25	      (~ $true
11.03/11.25	       | app_encode_app('type/nums/num', $o, 
11.03/11.25	           app_encode_app('type/nums/num', 
11.03/11.25	             app_encode_fun('type/nums/num', $o), 'const/arith/<=', 
11.03/11.25	             app_encode_app(app_encode_fun(X0, 'type/nums/num'), 
11.03/11.25	               'type/nums/num', 
11.03/11.25	               app_encode_app(app_encode_fun(X0, $o), 
11.03/11.25	                 app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
11.03/11.25	                   'type/nums/num'), 'const/iterate/nsum'(X0), X2), X3)), 
11.03/11.25	           app_encode_app(app_encode_fun(X0, 'type/nums/num'), 
11.03/11.25	             'type/nums/num', 
11.03/11.25	             app_encode_app(app_encode_fun(X0, $o), 
11.03/11.25	               app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
11.03/11.25	                 'type/nums/num'), 'const/iterate/nsum'(X0), X1), X3))
11.03/11.25	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
11.03/11.25	             'const/sets/FINITE'(X0), X2)
11.03/11.25	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
11.03/11.25	             'const/sets/FINITE'(X0), X1)
11.03/11.25	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
11.03/11.25	             app_encode_app(app_encode_fun(X0, $o), 
11.03/11.25	               app_encode_fun(app_encode_fun(X0, $o), $o), 
11.03/11.25	               'const/sets/SUBSET'(X0), 
11.03/11.25	               app_encode_app(app_encode_fun(X0, $o), 
11.03/11.25	                 app_encode_fun(X0, $o), 
11.03/11.25	                 app_encode_app(app_encode_fun(X0, $o), 
11.03/11.25	                   app_encode_fun(app_encode_fun(X0, $o), 
11.03/11.25	                     app_encode_fun(X0, $o)), 'const/sets/DIFF'(X0), X2), X1)), 
11.03/11.25	             X4)
11.03/11.25	       | app_encode_app(app_encode_fun(X0, $o), $o, 
11.03/11.25	           app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
11.03/11.25	             'const/sets/IN'(X0), sk_A3(X0, X3, X1, X2)), X4)),
11.03/11.25	    inference('sup-', [status(thm)], ['19', '8'])).
11.03/11.25	tff('21', plain,
11.03/11.25	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : app_encode_fun(X0, $o), 
11.03/11.25	      X3 : app_encode_fun(X0, 'type/nums/num'), X4 : app_encode_fun(X0, $o)]:
11.03/11.25	      (app_encode_app(app_encode_fun(X0, $o), $o, 
11.03/11.25	         app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
11.03/11.25	           'const/sets/IN'(X0), sk_A3(X0, X3, X1, X2)), X4)
11.03/11.25	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
11.03/11.25	             app_encode_app(app_encode_fun(X0, $o), 
11.03/11.25	               app_encode_fun(app_encode_fun(X0, $o), $o), 
11.03/11.25	               'const/sets/SUBSET'(X0), 
11.03/11.25	               app_encode_app(app_encode_fun(X0, $o), 
11.03/11.25	                 app_encode_fun(X0, $o), 
11.03/11.25	                 app_encode_app(app_encode_fun(X0, $o), 
11.03/11.25	                   app_encode_fun(app_encode_fun(X0, $o), 
11.03/11.25	                     app_encode_fun(X0, $o)), 'const/sets/DIFF'(X0), X2), X1)), 
11.03/11.25	             X4)
11.03/11.25	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
11.03/11.25	             'const/sets/FINITE'(X0), X1)
11.03/11.25	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
11.03/11.25	             'const/sets/FINITE'(X0), X2)
11.03/11.25	       | app_encode_app('type/nums/num', $o, 
11.03/11.25	           app_encode_app('type/nums/num', 
11.03/11.25	             app_encode_fun('type/nums/num', $o), 'const/arith/<=', 
11.03/11.25	             app_encode_app(app_encode_fun(X0, 'type/nums/num'), 
11.03/11.25	               'type/nums/num', 
11.03/11.25	               app_encode_app(app_encode_fun(X0, $o), 
11.03/11.25	                 app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
11.03/11.25	                   'type/nums/num'), 'const/iterate/nsum'(X0), X2), X3)), 
11.03/11.25	           app_encode_app(app_encode_fun(X0, 'type/nums/num'), 
11.03/11.25	             'type/nums/num', 
11.03/11.25	             app_encode_app(app_encode_fun(X0, $o), 
11.03/11.25	               app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
11.03/11.25	                 'type/nums/num'), 'const/iterate/nsum'(X0), X1), X3))),
11.03/11.25	    inference('simplify', [status(thm)], ['20'])).
11.03/11.25	tff('22', plain,
11.03/11.25	    ![X16 : $tType, X17 : X16, X18 : app_encode_fun(X16, $o), 
11.03/11.25	      X19 : app_encode_fun(X16, $o)]:
11.03/11.25	      (~ app_encode_app(app_encode_fun(X16, $o), $o, 
11.03/11.25	           app_encode_app(X16, app_encode_fun(app_encode_fun(X16, $o), $o), 
11.03/11.25	             'const/sets/IN'(X16), X17), X19)
11.03/11.25	       | ~ app_encode_app(app_encode_fun(X16, $o), $o, 
11.03/11.25	             app_encode_app(X16, 
11.03/11.25	               app_encode_fun(app_encode_fun(X16, $o), $o), 
11.03/11.25	               'const/sets/IN'(X16), X17), 
11.03/11.25	             app_encode_app(app_encode_fun(X16, $o), 
11.03/11.25	               app_encode_fun(X16, $o), 
11.03/11.25	               app_encode_app(app_encode_fun(X16, $o), 
11.03/11.25	                 app_encode_fun(app_encode_fun(X16, $o), 
11.03/11.25	                   app_encode_fun(X16, $o)), 'const/sets/DIFF'(X16), X18), 
11.03/11.25	               X19))),
11.03/11.25	    inference('cnf', [status(esa)], [zf_stmt_15])).
11.03/11.25	tff('23', plain,
11.03/11.25	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : app_encode_fun(X0, $o), 
11.03/11.25	      X3 : app_encode_fun(X0, 'type/nums/num')]:
11.03/11.25	      (~ $true
11.03/11.25	       | app_encode_app('type/nums/num', $o, 
11.03/11.25	           app_encode_app('type/nums/num', 
11.03/11.25	             app_encode_fun('type/nums/num', $o), 'const/arith/<=', 
11.03/11.25	             app_encode_app(app_encode_fun(X0, 'type/nums/num'), 
11.03/11.25	               'type/nums/num', 
11.03/11.25	               app_encode_app(app_encode_fun(X0, $o), 
11.03/11.25	                 app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
11.03/11.25	                   'type/nums/num'), 'const/iterate/nsum'(X0), X2), X3)), 
11.03/11.25	           app_encode_app(app_encode_fun(X0, 'type/nums/num'), 
11.03/11.25	             'type/nums/num', 
11.03/11.25	             app_encode_app(app_encode_fun(X0, $o), 
11.03/11.25	               app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
11.03/11.25	                 'type/nums/num'), 'const/iterate/nsum'(X0), X1), X3))
11.03/11.25	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
11.03/11.25	             'const/sets/FINITE'(X0), X2)
11.03/11.25	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
11.03/11.25	             'const/sets/FINITE'(X0), X1)
11.03/11.25	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
11.03/11.25	             app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
11.03/11.25	               'const/sets/IN'(X0), sk_A3(X0, X3, X1, X2)), X1)),
11.03/11.25	    inference('sup-', [status(thm)], ['19', '22'])).
11.03/11.25	tff('24', plain,
11.03/11.25	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : app_encode_fun(X0, $o), 
11.03/11.25	      X3 : app_encode_fun(X0, 'type/nums/num')]:
11.03/11.25	      (~ app_encode_app(app_encode_fun(X0, $o), $o, 
11.03/11.25	           app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
11.03/11.25	             'const/sets/IN'(X0), sk_A3(X0, X3, X1, X2)), X1)
11.03/11.25	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
11.03/11.25	             'const/sets/FINITE'(X0), X1)
11.03/11.25	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
11.03/11.25	             'const/sets/FINITE'(X0), X2)
11.03/11.25	       | app_encode_app('type/nums/num', $o, 
11.03/11.25	           app_encode_app('type/nums/num', 
11.03/11.25	             app_encode_fun('type/nums/num', $o), 'const/arith/<=', 
11.03/11.25	             app_encode_app(app_encode_fun(X0, 'type/nums/num'), 
11.03/11.25	               'type/nums/num', 
11.03/11.25	               app_encode_app(app_encode_fun(X0, $o), 
11.03/11.25	                 app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
11.03/11.25	                   'type/nums/num'), 'const/iterate/nsum'(X0), X2), X3)), 
11.03/11.25	           app_encode_app(app_encode_fun(X0, 'type/nums/num'), 
11.03/11.25	             'type/nums/num', 
11.03/11.25	             app_encode_app(app_encode_fun(X0, $o), 
11.03/11.25	               app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
11.03/11.25	                 'type/nums/num'), 'const/iterate/nsum'(X0), X1), X3))),
11.03/11.25	    inference('simplify', [status(thm)], ['23'])).
11.03/11.25	tff('25', plain,
11.03/11.25	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : app_encode_fun(X0, $o), 
11.03/11.25	      X3 : app_encode_fun(X0, 'type/nums/num')]:
11.03/11.25	      (~ $true
11.03/11.25	       | app_encode_app('type/nums/num', $o, 
11.03/11.25	           app_encode_app('type/nums/num', 
11.03/11.25	             app_encode_fun('type/nums/num', $o), 'const/arith/<=', 
11.03/11.25	             app_encode_app(app_encode_fun(X0, 'type/nums/num'), 
11.03/11.25	               'type/nums/num', 
11.03/11.25	               app_encode_app(app_encode_fun(X0, $o), 
11.03/11.25	                 app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
11.03/11.25	                   'type/nums/num'), 'const/iterate/nsum'(X0), X2), X3)), 
11.03/11.25	           app_encode_app(app_encode_fun(X0, 'type/nums/num'), 
11.03/11.25	             'type/nums/num', 
11.03/11.25	             app_encode_app(app_encode_fun(X0, $o), 
11.03/11.25	               app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
11.03/11.25	                 'type/nums/num'), 'const/iterate/nsum'(X0), X1), X3))
11.03/11.25	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
11.03/11.25	             'const/sets/FINITE'(X0), X2)
11.03/11.25	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
11.03/11.25	             'const/sets/FINITE'(X0), X1)
11.03/11.25	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
11.03/11.25	             app_encode_app(app_encode_fun(X0, $o), 
11.03/11.25	               app_encode_fun(app_encode_fun(X0, $o), $o), 
11.03/11.25	               'const/sets/SUBSET'(X0), 
11.03/11.25	               app_encode_app(app_encode_fun(X0, $o), 
11.03/11.25	                 app_encode_fun(X0, $o), 
11.03/11.25	                 app_encode_app(app_encode_fun(X0, $o), 
11.03/11.25	                   app_encode_fun(app_encode_fun(X0, $o), 
11.03/11.25	                     app_encode_fun(X0, $o)), 'const/sets/DIFF'(X0), X2), X1)), 
11.03/11.25	             X1)
11.03/11.25	       | app_encode_app('type/nums/num', $o, 
11.03/11.25	           app_encode_app('type/nums/num', 
11.03/11.25	             app_encode_fun('type/nums/num', $o), 'const/arith/<=', 
11.03/11.25	             app_encode_app(app_encode_fun(X0, 'type/nums/num'), 
11.03/11.25	               'type/nums/num', 
11.03/11.25	               app_encode_app(app_encode_fun(X0, $o), 
11.03/11.25	                 app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
11.03/11.25	                   'type/nums/num'), 'const/iterate/nsum'(X0), X2), X3)), 
11.03/11.25	           app_encode_app(app_encode_fun(X0, 'type/nums/num'), 
11.03/11.25	             'type/nums/num', 
11.03/11.25	             app_encode_app(app_encode_fun(X0, $o), 
11.03/11.25	               app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
11.03/11.25	                 'type/nums/num'), 'const/iterate/nsum'(X0), X1), X3))
11.03/11.25	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
11.03/11.25	             'const/sets/FINITE'(X0), X2)
11.03/11.25	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
11.03/11.25	             'const/sets/FINITE'(X0), X1)),
11.03/11.25	    inference('sup-', [status(thm)], ['21', '24'])).
11.03/11.25	tff('26', plain,
11.03/11.25	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : app_encode_fun(X0, $o), 
11.03/11.25	      X3 : app_encode_fun(X0, 'type/nums/num')]:
11.03/11.25	      (~ app_encode_app(app_encode_fun(X0, $o), $o, 
11.03/11.25	           app_encode_app(app_encode_fun(X0, $o), 
11.03/11.25	             app_encode_fun(app_encode_fun(X0, $o), $o), 
11.03/11.25	             'const/sets/SUBSET'(X0), 
11.03/11.25	             app_encode_app(app_encode_fun(X0, $o), app_encode_fun(X0, $o), 
11.03/11.25	               app_encode_app(app_encode_fun(X0, $o), 
11.03/11.25	                 app_encode_fun(app_encode_fun(X0, $o), 
11.03/11.25	                   app_encode_fun(X0, $o)), 'const/sets/DIFF'(X0), X2), X1)), 
11.03/11.25	           X1)
11.03/11.25	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
11.03/11.25	             'const/sets/FINITE'(X0), X1)
11.03/11.25	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
11.03/11.25	             'const/sets/FINITE'(X0), X2)
11.03/11.25	       | app_encode_app('type/nums/num', $o, 
11.03/11.25	           app_encode_app('type/nums/num', 
11.03/11.25	             app_encode_fun('type/nums/num', $o), 'const/arith/<=', 
11.03/11.25	             app_encode_app(app_encode_fun(X0, 'type/nums/num'), 
11.03/11.25	               'type/nums/num', 
11.03/11.25	               app_encode_app(app_encode_fun(X0, $o), 
11.03/11.25	                 app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
11.03/11.25	                   'type/nums/num'), 'const/iterate/nsum'(X0), X2), X3)), 
11.03/11.25	           app_encode_app(app_encode_fun(X0, 'type/nums/num'), 
11.03/11.25	             'type/nums/num', 
11.03/11.25	             app_encode_app(app_encode_fun(X0, $o), 
11.03/11.25	               app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
11.03/11.25	                 'type/nums/num'), 'const/iterate/nsum'(X0), X1), X3))),
11.03/11.25	    inference('simplify', [status(thm)], ['25'])).
11.03/11.25	tff('27', plain,
11.03/11.25	    ![X0 : app_encode_fun(sk_A, 'type/nums/num')]:
11.03/11.25	      (~ $true
11.03/11.25	       | app_encode_app('type/nums/num', $o, 
11.03/11.25	           app_encode_app('type/nums/num', 
11.03/11.25	             app_encode_fun('type/nums/num', $o), 'const/arith/<=', 
11.03/11.25	             app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 
11.03/11.25	               'type/nums/num', 
11.03/11.25	               app_encode_app(app_encode_fun(sk_A, $o), 
11.03/11.25	                 app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
11.03/11.25	                   'type/nums/num'), 'const/iterate/nsum'(sk_A), sk_A0), X0)), 
11.03/11.25	           app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 
11.03/11.25	             'type/nums/num', 
11.03/11.25	             app_encode_app(app_encode_fun(sk_A, $o), 
11.03/11.25	               app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
11.03/11.25	                 'type/nums/num'), 'const/iterate/nsum'(sk_A), sk_A1), X0))
11.03/11.25	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
11.03/11.25	             'const/sets/FINITE'(sk_A), sk_A0)
11.03/11.25	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
11.03/11.25	             'const/sets/FINITE'(sk_A), sk_A1)),
11.03/11.25	    inference('sup-', [status(thm)], ['18', '26'])).
11.03/11.25	tff(zf_stmt_13, axiom,
11.03/11.25	  (![A:$tType,A0:app_encode_fun(A,$o),A1:app_encode_fun(A,$o)]:
11.03/11.25	     ((app_encode_app(app_encode_fun(A,$o),$o,'const/sets/FINITE'(A),A1) & 
11.03/11.25	       app_encode_app(app_encode_fun(A,$o),$o,
11.03/11.25	                      app_encode_app(app_encode_fun(A,$o),
11.03/11.25	                                     app_encode_fun(app_encode_fun(A,$o),$o),
11.03/11.25	                                     'const/sets/SUBSET'(A),A0),
11.03/11.25	                      A1)) =>
11.03/11.25	      app_encode_app(app_encode_fun(A,$o),$o,'const/sets/FINITE'(A),A0)))).
11.03/11.25	tff('28', plain,
11.03/11.25	    ![X8 : $tType, X9 : app_encode_fun(X8, $o), X10 : app_encode_fun(X8, $o)]:
11.03/11.25	      (app_encode_app(app_encode_fun(X8, $o), $o, 'const/sets/FINITE'(X8), 
11.03/11.25	         X9)
11.03/11.25	       | ~ app_encode_app(app_encode_fun(X8, $o), $o, 
11.03/11.25	             'const/sets/FINITE'(X8), X10)
11.03/11.25	       | ~ app_encode_app(app_encode_fun(X8, $o), $o, 
11.03/11.25	             app_encode_app(app_encode_fun(X8, $o), 
11.03/11.25	               app_encode_fun(app_encode_fun(X8, $o), $o), 
11.03/11.25	               'const/sets/SUBSET'(X8), X9), X10)),
11.03/11.25	    inference('cnf', [status(esa)], [zf_stmt_13])).
11.03/11.25	tff('29', plain,
11.03/11.25	    (~ $true
11.03/11.25	     | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
11.03/11.25	           'const/sets/FINITE'(sk_A), sk_A1)
11.03/11.25	     | app_encode_app(app_encode_fun(sk_A, $o), $o, 
11.03/11.25	         'const/sets/FINITE'(sk_A), sk_A0)),
11.03/11.25	    inference('sup-', [status(thm)], ['7', '28'])).
11.03/11.25	tff('30', plain,
11.03/11.25	    app_encode_app(app_encode_fun(sk_A, $o), $o, 'const/sets/FINITE'(sk_A), 
11.03/11.25	      sk_A1),
11.03/11.25	    inference('cnf', [status(esa)], [zf_stmt_0])).
11.03/11.25	tff('31', plain,
11.03/11.25	    (~ $true
11.03/11.25	     | ~ $true
11.03/11.25	     | app_encode_app(app_encode_fun(sk_A, $o), $o, 
11.03/11.25	         'const/sets/FINITE'(sk_A), sk_A0)),
11.03/11.25	    inference('demod', [status(thm)], ['29', '30'])).
11.03/11.25	tff('32', plain,
11.03/11.25	    app_encode_app(app_encode_fun(sk_A, $o), $o, 'const/sets/FINITE'(sk_A), 
11.03/11.25	      sk_A0),
11.03/11.25	    inference('simplify', [status(thm)], ['31'])).
11.03/11.25	tff('33', plain,
11.03/11.25	    ![X0 : app_encode_fun(sk_A, 'type/nums/num')]:
11.03/11.25	      (~ $true
11.03/11.25	       | app_encode_app('type/nums/num', $o, 
11.03/11.25	           app_encode_app('type/nums/num', 
11.03/11.25	             app_encode_fun('type/nums/num', $o), 'const/arith/<=', 
11.03/11.25	             app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 
11.03/11.25	               'type/nums/num', 
11.03/11.25	               app_encode_app(app_encode_fun(sk_A, $o), 
11.03/11.25	                 app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
11.03/11.25	                   'type/nums/num'), 'const/iterate/nsum'(sk_A), sk_A0), X0)), 
11.03/11.25	           app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 
11.03/11.25	             'type/nums/num', 
11.03/11.25	             app_encode_app(app_encode_fun(sk_A, $o), 
11.03/11.25	               app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
11.03/11.25	                 'type/nums/num'), 'const/iterate/nsum'(sk_A), sk_A1), X0))
11.03/11.25	       | ~ $true
11.03/11.25	       | ~ $true),
11.03/11.25	    inference('demod', [status(thm)], ['27', '32', '30'])).
11.03/11.25	tff('34', plain,
11.03/11.25	    ![X0 : app_encode_fun(sk_A, 'type/nums/num')]:
11.03/11.25	      app_encode_app('type/nums/num', $o, 
11.03/11.25	        app_encode_app('type/nums/num', app_encode_fun('type/nums/num', $o), 
11.03/11.25	          'const/arith/<=', 
11.03/11.25	          app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 
11.03/11.25	            'type/nums/num', 
11.03/11.25	            app_encode_app(app_encode_fun(sk_A, $o), 
11.03/11.25	              app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
11.03/11.25	                'type/nums/num'), 'const/iterate/nsum'(sk_A), sk_A0), X0)), 
11.03/11.25	        app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 
11.03/11.25	          'type/nums/num', 
11.03/11.25	          app_encode_app(app_encode_fun(sk_A, $o), 
11.03/11.25	            app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
11.03/11.25	              'type/nums/num'), 'const/iterate/nsum'(sk_A), sk_A1), X0)),
11.03/11.25	    inference('simplify', [status(thm)], ['33'])).
11.03/11.25	tff('35', plain,
11.03/11.25	    ~ app_encode_app('type/nums/num', $o, 
11.03/11.25	        app_encode_app('type/nums/num', app_encode_fun('type/nums/num', $o), 
11.03/11.25	          'const/arith/<=', 
11.03/11.25	          app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 
11.03/11.25	            'type/nums/num', 
11.03/11.25	            app_encode_app(app_encode_fun(sk_A, $o), 
11.03/11.25	              app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
11.03/11.25	                'type/nums/num'), 'const/iterate/nsum'(sk_A), sk_A0), sk_A21)), 
11.03/11.25	        app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 
11.03/11.25	          'type/nums/num', 
11.03/11.25	          app_encode_app(app_encode_fun(sk_A, $o), 
11.03/11.25	            app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
11.03/11.25	              'type/nums/num'), 'const/iterate/nsum'(sk_A), sk_A1), sk_A21)),
11.03/11.25	    inference('cnf', [status(esa)], [zf_stmt_0])).
11.03/11.25	tff('36', plain, ~ $true, inference('sup-', [status(thm)], ['34', '35'])).
11.03/11.25	tff('37', plain, $false, inference('simplify', [status(thm)], ['36'])).
11.03/11.25	
11.03/11.25	% SZS output end Refutation
11.03/11.25	EOF
