0.00/0.00	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : app
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : kbo
0.00/0.00	% Command    : 
0.00/0.00	#!/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 $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n047.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 18:39:09 CST 2018
0.00/0.31	% done 13 iterations in 0.114s
0.00/0.31	% SZS status Theorem for 'stdin'
0.00/0.31	% SZS output start Refutation
0.00/0.31	tff(zf_stmt_16, axiom,
0.00/0.31	  (![A:$tType]:
0.00/0.31	     ('const/iterate/nsum'(A) =
0.00/0.31	      app_encode_app(app_encode_fun('type/nums/num',
0.00/0.31	                                    app_encode_fun('type/nums/num',
0.00/0.31	                                                   'type/nums/num')),
0.00/0.31	                     app_encode_fun(app_encode_fun(A,$o),
0.00/0.31	                                    app_encode_fun(app_encode_fun(A,
0.00/0.31	                                                                  'type/nums/num'),
0.00/0.31	                                                   'type/nums/num')),
0.00/0.31	                     'const/iterate/iterate'(A,'type/nums/num'),
0.00/0.31	                     'const/arith/+')))).
0.00/0.31	tff('0', plain,
0.00/0.31	    ![X6 : $tType]:
0.00/0.31	      'const/iterate/nsum'(X6)
0.00/0.31	       = app_encode_app(
0.00/0.31	           app_encode_fun('type/nums/num', 
0.00/0.31	             app_encode_fun('type/nums/num', 'type/nums/num')), 
0.00/0.31	           app_encode_fun(app_encode_fun(X6, $o), 
0.00/0.31	             app_encode_fun(app_encode_fun(X6, 'type/nums/num'), 
0.00/0.31	               'type/nums/num')), 
0.00/0.31	           'const/iterate/iterate'(X6, 'type/nums/num'), 'const/arith/+'),
0.00/0.31	    inference('cnf', [status(esa)], [zf_stmt_16])).
0.00/0.31	tff(zf_stmt_14, axiom,
0.00/0.31	  (![A:$tType,B:$tType,A0:app_encode_fun(B,app_encode_fun(B,B))]:
0.00/0.31	     (app_encode_app(app_encode_fun(B,app_encode_fun(B,B)),$o,
0.00/0.31	                     'const/iterate/monoidal'(B),A0) =>
0.00/0.31	      (![A1:app_encode_fun(A,B),A2:app_encode_fun(A,$o),
0.00/0.31	         A3:app_encode_fun(A,$o)]:
0.00/0.31	         ((app_encode_app(app_encode_fun(A,$o),$o,'const/sets/FINITE'(A),A2) & 
0.00/0.31	           app_encode_app(app_encode_fun(A,$o),$o,'const/sets/FINITE'(A),A3) & 
0.00/0.31	           (![A4:A]:
0.00/0.31	              (app_encode_app(app_encode_fun(A,$o),$o,
0.00/0.31	                              app_encode_app(A,
0.00/0.31	                                             app_encode_fun(app_encode_fun(
0.00/0.31	                                                            A,$o),$o),
0.00/0.31	                                             'const/sets/IN'(A),A4),
0.00/0.31	                              app_encode_app(app_encode_fun(A,$o),
0.00/0.31	                                             app_encode_fun(A,$o),
0.00/0.31	                                             app_encode_app(app_encode_fun(
0.00/0.31	                                                            A,$o),
0.00/0.31	                                                            app_encode_fun(
0.00/0.31	                                                            app_encode_fun(
0.00/0.31	                                                            A,$o),
0.00/0.31	                                                            app_encode_fun(
0.00/0.31	                                                            A,$o)),
0.00/0.31	                                                            'const/sets/INTER'(
0.00/0.31	                                                            A),A2),
0.00/0.31	                                             A3)) =>
0.00/0.31	               (app_encode_app(A,B,A1,A4) =
0.00/0.31	                app_encode_app(app_encode_fun(B,app_encode_fun(B,B)),B,
0.00/0.31	                               'const/iterate/neutral'(B),A0))))) =>
0.00/0.31	          (app_encode_app(app_encode_fun(A,B),B,
0.00/0.31	                          app_encode_app(app_encode_fun(A,$o),
0.00/0.31	                                         app_encode_fun(app_encode_fun(A,B),B),
0.00/0.31	                                         app_encode_app(app_encode_fun(
0.00/0.31	                                                        B,app_encode_fun(B,B)),
0.00/0.31	                                                        app_encode_fun(
0.00/0.31	                                                        app_encode_fun(A,$o),
0.00/0.31	                                                        app_encode_fun(
0.00/0.31	                                                        app_encode_fun(A,B),B)),
0.00/0.31	                                                        'const/iterate/iterate'(
0.00/0.31	                                                        A,B),A0),
0.00/0.31	                                         app_encode_app(app_encode_fun(A,$o),
0.00/0.31	                                                        app_encode_fun(A,$o),
0.00/0.31	                                                        app_encode_app(
0.00/0.31	                                                        app_encode_fun(A,$o),
0.00/0.31	                                                        app_encode_fun(
0.00/0.31	                                                        app_encode_fun(A,$o),
0.00/0.31	                                                        app_encode_fun(A,$o)),
0.00/0.31	                                                        'const/sets/UNION'(A),
0.00/0.31	                                                        A2),A3)),
0.00/0.31	                          A1) =
0.00/0.31	           app_encode_app(B,B,
0.00/0.31	                          app_encode_app(B,app_encode_fun(B,B),A0,
0.00/0.31	                                         app_encode_app(app_encode_fun(A,B),
0.00/0.31	                                                        B,
0.00/0.31	                                                        app_encode_app(
0.00/0.31	                                                        app_encode_fun(A,$o),
0.00/0.31	                                                        app_encode_fun(
0.00/0.31	                                                        app_encode_fun(A,B),B),
0.00/0.31	                                                        app_encode_app(
0.00/0.31	                                                        app_encode_fun(
0.00/0.31	                                                        B,app_encode_fun(B,B)),
0.00/0.31	                                                        app_encode_fun(
0.00/0.31	                                                        app_encode_fun(A,$o),
0.00/0.31	                                                        app_encode_fun(
0.00/0.31	                                                        app_encode_fun(A,B),B)),
0.00/0.31	                                                        'const/iterate/iterate'(
0.00/0.31	                                                        A,B),A0),A2),A1)),
0.00/0.31	                          app_encode_app(app_encode_fun(A,B),B,
0.00/0.31	                                         app_encode_app(app_encode_fun(A,$o),
0.00/0.31	                                                        app_encode_fun(
0.00/0.31	                                                        app_encode_fun(A,B),B),
0.00/0.31	                                                        app_encode_app(
0.00/0.31	                                                        app_encode_fun(
0.00/0.31	                                                        B,app_encode_fun(B,B)),
0.00/0.31	                                                        app_encode_fun(
0.00/0.31	                                                        app_encode_fun(A,$o),
0.00/0.31	                                                        app_encode_fun(
0.00/0.31	                                                        app_encode_fun(A,B),B)),
0.00/0.31	                                                        'const/iterate/iterate'(
0.00/0.31	                                                        A,B),A0),A3),
0.00/0.31	                                         A1)))))))).
0.00/0.31	tff('1', plain,
0.00/0.31	    ![X0 : $tType, X1 : app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.31	      X2 : $tType, X3 : app_encode_fun(X2, $o), X4 : app_encode_fun(X2, X0), 
0.00/0.31	      X5 : app_encode_fun(X2, $o)]:
0.00/0.31	      (app_encode_app(app_encode_fun(X2, X0), X0, 
0.00/0.31	         app_encode_app(app_encode_fun(X2, $o), 
0.00/0.31	           app_encode_fun(app_encode_fun(X2, X0), X0), 
0.00/0.31	           app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.31	             app_encode_fun(app_encode_fun(X2, $o), 
0.00/0.31	               app_encode_fun(app_encode_fun(X2, X0), X0)), 
0.00/0.31	             'const/iterate/iterate'(X2, X0), X1), 
0.00/0.31	           app_encode_app(app_encode_fun(X2, $o), app_encode_fun(X2, $o), 
0.00/0.31	             app_encode_app(app_encode_fun(X2, $o), 
0.00/0.31	               app_encode_fun(app_encode_fun(X2, $o), app_encode_fun(X2, $o)), 
0.00/0.31	               'const/sets/UNION'(X2), X3), X5)), X4)
0.00/0.31	        = app_encode_app(X0, X0, 
0.00/0.31	            app_encode_app(X0, app_encode_fun(X0, X0), X1, 
0.00/0.31	              app_encode_app(app_encode_fun(X2, X0), X0, 
0.00/0.31	                app_encode_app(app_encode_fun(X2, $o), 
0.00/0.31	                  app_encode_fun(app_encode_fun(X2, X0), X0), 
0.00/0.31	                  app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.31	                    app_encode_fun(app_encode_fun(X2, $o), 
0.00/0.31	                      app_encode_fun(app_encode_fun(X2, X0), X0)), 
0.00/0.31	                    'const/iterate/iterate'(X2, X0), X1), X3), X4)), 
0.00/0.31	            app_encode_app(app_encode_fun(X2, X0), X0, 
0.00/0.31	              app_encode_app(app_encode_fun(X2, $o), 
0.00/0.31	                app_encode_fun(app_encode_fun(X2, X0), X0), 
0.00/0.31	                app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.31	                  app_encode_fun(app_encode_fun(X2, $o), 
0.00/0.31	                    app_encode_fun(app_encode_fun(X2, X0), X0)), 
0.00/0.31	                  'const/iterate/iterate'(X2, X0), X1), X5), X4))
0.00/0.31	       | app_encode_app(X2, X0, X4, sk_A4(X0, X2, X5, X3, X4, X1))
0.00/0.31	          != app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), X0, 
0.00/0.31	               'const/iterate/neutral'(X0), X1)
0.00/0.31	       | ~ app_encode_app(app_encode_fun(X2, $o), $o, 
0.00/0.31	             'const/sets/FINITE'(X2), X5)
0.00/0.31	       | ~ app_encode_app(app_encode_fun(X2, $o), $o, 
0.00/0.31	             'const/sets/FINITE'(X2), X3)
0.00/0.31	       | ~ app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), $o, 
0.00/0.31	             'const/iterate/monoidal'(X0), X1)),
0.00/0.31	    inference('cnf', [status(esa)], [zf_stmt_14])).
0.00/0.31	tff('2', plain,
0.00/0.31	    ![X0 : $tType, X1 : app_encode_fun(X0, 'type/nums/num'), 
0.00/0.31	      X2 : app_encode_fun(X0, $o), X3 : app_encode_fun(X0, $o)]:
0.00/0.31	      (app_encode_app(app_encode_fun(X0, 'type/nums/num'), 'type/nums/num', 
0.00/0.31	         app_encode_app(app_encode_fun(X0, $o), 
0.00/0.31	           app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
0.00/0.31	             'type/nums/num'), 
0.00/0.31	           app_encode_app(
0.00/0.31	             app_encode_fun('type/nums/num', 
0.00/0.31	               app_encode_fun('type/nums/num', 'type/nums/num')), 
0.00/0.31	             app_encode_fun(app_encode_fun(X0, $o), 
0.00/0.31	               app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
0.00/0.31	                 'type/nums/num')), 
0.00/0.31	             'const/iterate/iterate'(X0, 'type/nums/num'), 'const/arith/+'), 
0.00/0.31	           app_encode_app(app_encode_fun(X0, $o), app_encode_fun(X0, $o), 
0.00/0.31	             app_encode_app(app_encode_fun(X0, $o), 
0.00/0.31	               app_encode_fun(app_encode_fun(X0, $o), app_encode_fun(X0, $o)), 
0.00/0.31	               'const/sets/UNION'(X0), X3), X2)), X1)
0.00/0.31	        = app_encode_app('type/nums/num', 'type/nums/num', 
0.00/0.31	            app_encode_app('type/nums/num', 
0.00/0.31	              app_encode_fun('type/nums/num', 'type/nums/num'), 
0.00/0.31	              'const/arith/+', 
0.00/0.31	              app_encode_app(app_encode_fun(X0, 'type/nums/num'), 
0.00/0.31	                'type/nums/num', 
0.00/0.31	                app_encode_app(app_encode_fun(X0, $o), 
0.00/0.31	                  app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
0.00/0.31	                    'type/nums/num'), 'const/iterate/nsum'(X0), X3), X1)), 
0.00/0.31	            app_encode_app(app_encode_fun(X0, 'type/nums/num'), 
0.00/0.31	              'type/nums/num', 
0.00/0.31	              app_encode_app(app_encode_fun(X0, $o), 
0.00/0.31	                app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
0.00/0.31	                  'type/nums/num'), 
0.00/0.31	                app_encode_app(
0.00/0.31	                  app_encode_fun('type/nums/num', 
0.00/0.31	                    app_encode_fun('type/nums/num', 'type/nums/num')), 
0.00/0.31	                  app_encode_fun(app_encode_fun(X0, $o), 
0.00/0.31	                    app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
0.00/0.31	                      'type/nums/num')), 
0.00/0.31	                  'const/iterate/iterate'(X0, 'type/nums/num'), 
0.00/0.31	                  'const/arith/+'), X2), X1))
0.00/0.31	       | ~ app_encode_app(
0.00/0.31	             app_encode_fun('type/nums/num', 
0.00/0.31	               app_encode_fun('type/nums/num', 'type/nums/num')), $o, 
0.00/0.31	             'const/iterate/monoidal'('type/nums/num'), 'const/arith/+')
0.00/0.31	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
0.00/0.31	             'const/sets/FINITE'(X0), X3)
0.00/0.31	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
0.00/0.31	             'const/sets/FINITE'(X0), X2)
0.00/0.31	       | app_encode_app(X0, 'type/nums/num', X1, 
0.00/0.31	           sk_A4('type/nums/num', X0, X2, X3, X1, 'const/arith/+'))
0.00/0.31	          != app_encode_app(
0.00/0.31	               app_encode_fun('type/nums/num', 
0.00/0.31	                 app_encode_fun('type/nums/num', 'type/nums/num')), 
0.00/0.31	               'type/nums/num', 'const/iterate/neutral'('type/nums/num'), 
0.00/0.31	               'const/arith/+')),
0.00/0.31	    inference('sup+', [status(thm)], ['0', '1'])).
0.00/0.31	tff(zf_stmt_15, axiom,
0.00/0.31	  (app_encode_app(app_encode_fun('type/nums/num',
0.00/0.31	                                 app_encode_fun('type/nums/num',
0.00/0.31	                                                'type/nums/num')),
0.00/0.31	                  $o,'const/iterate/monoidal'('type/nums/num'),
0.00/0.31	                  'const/arith/+'))).
0.00/0.31	tff('3', plain,
0.00/0.31	    app_encode_app(
0.00/0.31	      app_encode_fun('type/nums/num', 
0.00/0.31	        app_encode_fun('type/nums/num', 'type/nums/num')), $o, 
0.00/0.31	      'const/iterate/monoidal'('type/nums/num'), 'const/arith/+'),
0.00/0.31	    inference('cnf', [status(esa)], [zf_stmt_15])).
0.00/0.31	tff(zf_stmt_17, axiom,
0.00/0.31	  (app_encode_app(app_encode_fun('type/nums/num',
0.00/0.31	                                 app_encode_fun('type/nums/num',
0.00/0.31	                                                'type/nums/num')),
0.00/0.31	                  'type/nums/num','const/iterate/neutral'('type/nums/num'),
0.00/0.31	                  'const/arith/+') =
0.00/0.31	   app_encode_app('type/nums/num','type/nums/num','const/nums/NUMERAL',
0.00/0.31	                  'const/nums/_0'))).
0.00/0.31	tff('4', plain,
0.00/0.31	    app_encode_app(
0.00/0.31	      app_encode_fun('type/nums/num', 
0.00/0.31	        app_encode_fun('type/nums/num', 'type/nums/num')), 'type/nums/num', 
0.00/0.31	      'const/iterate/neutral'('type/nums/num'), 'const/arith/+')
0.00/0.31	     = app_encode_app('type/nums/num', 'type/nums/num', 
0.00/0.31	         'const/nums/NUMERAL', 'const/nums/_0'),
0.00/0.31	    inference('cnf', [status(esa)], [zf_stmt_17])).
0.00/0.31	tff('5', plain,
0.00/0.31	    ![X0 : $tType, X1 : app_encode_fun(X0, 'type/nums/num'), 
0.00/0.31	      X2 : app_encode_fun(X0, $o), X3 : app_encode_fun(X0, $o)]:
0.00/0.31	      (app_encode_app(app_encode_fun(X0, 'type/nums/num'), 'type/nums/num', 
0.00/0.31	         app_encode_app(app_encode_fun(X0, $o), 
0.00/0.31	           app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
0.00/0.31	             'type/nums/num'), 'const/iterate/nsum'(X0), 
0.00/0.31	           app_encode_app(app_encode_fun(X0, $o), app_encode_fun(X0, $o), 
0.00/0.31	             app_encode_app(app_encode_fun(X0, $o), 
0.00/0.31	               app_encode_fun(app_encode_fun(X0, $o), app_encode_fun(X0, $o)), 
0.00/0.31	               'const/sets/UNION'(X0), X3), X2)), X1)
0.00/0.31	        = app_encode_app('type/nums/num', 'type/nums/num', 
0.00/0.31	            app_encode_app('type/nums/num', 
0.00/0.31	              app_encode_fun('type/nums/num', 'type/nums/num'), 
0.00/0.31	              'const/arith/+', 
0.00/0.31	              app_encode_app(app_encode_fun(X0, 'type/nums/num'), 
0.00/0.31	                'type/nums/num', 
0.00/0.31	                app_encode_app(app_encode_fun(X0, $o), 
0.00/0.31	                  app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
0.00/0.31	                    'type/nums/num'), 'const/iterate/nsum'(X0), X3), X1)), 
0.00/0.31	            app_encode_app(app_encode_fun(X0, 'type/nums/num'), 
0.00/0.31	              'type/nums/num', 
0.00/0.31	              app_encode_app(app_encode_fun(X0, $o), 
0.00/0.31	                app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
0.00/0.31	                  'type/nums/num'), 'const/iterate/nsum'(X0), X2), X1))
0.00/0.31	       | ~ $true
0.00/0.31	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
0.00/0.31	             'const/sets/FINITE'(X0), X3)
0.00/0.31	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
0.00/0.31	             'const/sets/FINITE'(X0), X2)
0.00/0.31	       | app_encode_app(X0, 'type/nums/num', X1, 
0.00/0.31	           sk_A4('type/nums/num', X0, X2, X3, X1, 'const/arith/+'))
0.00/0.31	          != app_encode_app('type/nums/num', 'type/nums/num', 
0.00/0.31	               'const/nums/NUMERAL', 'const/nums/_0')),
0.00/0.32	    inference('demod', [status(thm)], ['2', '0', '0', '3', '4'])).
0.00/0.32	tff('6', plain,
0.00/0.32	    ![X0 : $tType, X1 : app_encode_fun(X0, 'type/nums/num'), 
0.00/0.32	      X2 : app_encode_fun(X0, $o), X3 : app_encode_fun(X0, $o)]:
0.00/0.32	      (app_encode_app(X0, 'type/nums/num', X1, 
0.00/0.32	         sk_A4('type/nums/num', X0, X2, X3, X1, 'const/arith/+'))
0.00/0.32	        != app_encode_app('type/nums/num', 'type/nums/num', 
0.00/0.32	             'const/nums/NUMERAL', 'const/nums/_0')
0.00/0.32	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
0.00/0.32	             'const/sets/FINITE'(X0), X2)
0.00/0.32	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
0.00/0.32	             'const/sets/FINITE'(X0), X3)
0.00/0.32	       | app_encode_app(app_encode_fun(X0, 'type/nums/num'), 
0.00/0.32	           'type/nums/num', 
0.00/0.32	           app_encode_app(app_encode_fun(X0, $o), 
0.00/0.32	             app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
0.00/0.32	               'type/nums/num'), 'const/iterate/nsum'(X0), 
0.00/0.32	             app_encode_app(app_encode_fun(X0, $o), app_encode_fun(X0, $o), 
0.00/0.32	               app_encode_app(app_encode_fun(X0, $o), 
0.00/0.32	                 app_encode_fun(app_encode_fun(X0, $o), 
0.00/0.32	                   app_encode_fun(X0, $o)), 'const/sets/UNION'(X0), X3), X2)), 
0.00/0.32	           X1)
0.00/0.32	          = app_encode_app('type/nums/num', 'type/nums/num', 
0.00/0.32	              app_encode_app('type/nums/num', 
0.00/0.32	                app_encode_fun('type/nums/num', 'type/nums/num'), 
0.00/0.32	                'const/arith/+', 
0.00/0.32	                app_encode_app(app_encode_fun(X0, 'type/nums/num'), 
0.00/0.32	                  'type/nums/num', 
0.00/0.32	                  app_encode_app(app_encode_fun(X0, $o), 
0.00/0.32	                    app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
0.00/0.32	                      'type/nums/num'), 'const/iterate/nsum'(X0), X3), X1)), 
0.00/0.32	              app_encode_app(app_encode_fun(X0, 'type/nums/num'), 
0.00/0.32	                'type/nums/num', 
0.00/0.32	                app_encode_app(app_encode_fun(X0, $o), 
0.00/0.32	                  app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
0.00/0.32	                    'type/nums/num'), 'const/iterate/nsum'(X0), X2), X1))),
0.00/0.32	    inference('simplify', [status(thm)], ['5'])).
0.00/0.32	tff(zf_stmt_18, conjecture,
0.00/0.32	  (![A:$tType,A0:app_encode_fun(A,'type/nums/num'),A1:app_encode_fun(A,$o),
0.00/0.32	     A2:app_encode_fun(A,$o)]:
0.00/0.32	     ((app_encode_app(app_encode_fun(A,$o),$o,'const/sets/FINITE'(A),A1) & 
0.00/0.32	       app_encode_app(app_encode_fun(A,$o),$o,'const/sets/FINITE'(A),A2) & 
0.00/0.32	       (![A3:A]:
0.00/0.32	          (app_encode_app(app_encode_fun(A,$o),$o,
0.00/0.32	                          app_encode_app(A,
0.00/0.32	                                         app_encode_fun(app_encode_fun(A,$o),
0.00/0.32	                                                        $o),
0.00/0.32	                                         'const/sets/IN'(A),A3),
0.00/0.32	                          app_encode_app(app_encode_fun(A,$o),
0.00/0.32	                                         app_encode_fun(A,$o),
0.00/0.32	                                         app_encode_app(app_encode_fun(A,$o),
0.00/0.32	                                                        app_encode_fun(
0.00/0.32	                                                        app_encode_fun(A,$o),
0.00/0.32	                                                        app_encode_fun(A,$o)),
0.00/0.32	                                                        'const/sets/INTER'(A),
0.00/0.32	                                                        A1),
0.00/0.32	                                         A2)) =>
0.00/0.32	           (app_encode_app(A,'type/nums/num',A0,A3) =
0.00/0.32	            app_encode_app('type/nums/num','type/nums/num',
0.00/0.32	                           'const/nums/NUMERAL','const/nums/_0'))))) =>
0.00/0.32	      (app_encode_app(app_encode_fun(A,'type/nums/num'),'type/nums/num',
0.00/0.32	                      app_encode_app(app_encode_fun(A,$o),
0.00/0.32	                                     app_encode_fun(app_encode_fun(A,
0.00/0.32	                                                                   'type/nums/num'),
0.00/0.32	                                                    'type/nums/num'),
0.00/0.32	                                     'const/iterate/nsum'(A),
0.00/0.32	                                     app_encode_app(app_encode_fun(A,$o),
0.00/0.32	                                                    app_encode_fun(A,$o),
0.00/0.32	                                                    app_encode_app(app_encode_fun(
0.00/0.32	                                                                   A,$o),
0.00/0.32	                                                                   app_encode_fun(
0.00/0.32	                                                                   app_encode_fun(
0.00/0.32	                                                                   A,$o),
0.00/0.32	                                                                   app_encode_fun(
0.00/0.32	                                                                   A,$o)),
0.00/0.32	                                                                   'const/sets/UNION'(
0.00/0.32	                                                                   A),A1),
0.00/0.32	                                                    A2)),
0.00/0.32	                      A0) =
0.00/0.32	       app_encode_app('type/nums/num','type/nums/num',
0.00/0.32	                      app_encode_app('type/nums/num',
0.00/0.32	                                     app_encode_fun('type/nums/num',
0.00/0.32	                                                    'type/nums/num'),
0.00/0.32	                                     'const/arith/+',
0.00/0.32	                                     app_encode_app(app_encode_fun(A,
0.00/0.32	                                                                   'type/nums/num'),
0.00/0.32	                                                    'type/nums/num',
0.00/0.32	                                                    app_encode_app(app_encode_fun(
0.00/0.32	                                                                   A,$o),
0.00/0.32	                                                                   app_encode_fun(
0.00/0.32	                                                                   app_encode_fun(
0.00/0.32	                                                                   A,
0.00/0.32	                                                                   'type/nums/num'),
0.00/0.32	                                                                   'type/nums/num'),
0.00/0.32	                                                                   'const/iterate/nsum'(
0.00/0.32	                                                                   A),A1),
0.00/0.32	                                                    A0)),
0.00/0.32	                      app_encode_app(app_encode_fun(A,'type/nums/num'),
0.00/0.32	                                     'type/nums/num',
0.00/0.32	                                     app_encode_app(app_encode_fun(A,$o),
0.00/0.32	                                                    app_encode_fun(app_encode_fun(
0.00/0.32	                                                                   A,
0.00/0.32	                                                                   'type/nums/num'),
0.00/0.32	                                                                   'type/nums/num'),
0.00/0.32	                                                    'const/iterate/nsum'(A),
0.00/0.32	                                                    A2),
0.00/0.32	                                     A0)))))).
0.00/0.32	tff(zf_stmt_0, negated_conjecture,
0.00/0.32	  (~
0.00/0.32	    (![A:$tType,A0:app_encode_fun(A,'type/nums/num'),A1:app_encode_fun(A,$o),
0.00/0.32	       A2:app_encode_fun(A,$o)]:
0.00/0.32	       ((app_encode_app(app_encode_fun(A,$o),$o,'const/sets/FINITE'(A),A1) & 
0.00/0.32	         app_encode_app(app_encode_fun(A,$o),$o,'const/sets/FINITE'(A),A2) & 
0.00/0.32	         (![A3:A]:
0.00/0.32	            (app_encode_app(app_encode_fun(A,$o),$o,
0.00/0.32	                            app_encode_app(A,
0.00/0.32	                                           app_encode_fun(app_encode_fun(
0.00/0.32	                                                          A,$o),$o),
0.00/0.32	                                           'const/sets/IN'(A),A3),
0.00/0.32	                            app_encode_app(app_encode_fun(A,$o),
0.00/0.32	                                           app_encode_fun(A,$o),
0.00/0.32	                                           app_encode_app(app_encode_fun(
0.00/0.32	                                                          A,$o),
0.00/0.32	                                                          app_encode_fun(
0.00/0.32	                                                          app_encode_fun(
0.00/0.32	                                                          A,$o),
0.00/0.32	                                                          app_encode_fun(
0.00/0.32	                                                          A,$o)),
0.00/0.32	                                                          'const/sets/INTER'(
0.00/0.32	                                                          A),A1),
0.00/0.32	                                           A2)) =>
0.00/0.32	             (app_encode_app(A,'type/nums/num',A0,A3) =
0.00/0.32	              app_encode_app('type/nums/num','type/nums/num',
0.00/0.32	                             'const/nums/NUMERAL','const/nums/_0'))))) =>
0.00/0.32	        (app_encode_app(app_encode_fun(A,'type/nums/num'),'type/nums/num',
0.00/0.32	                        app_encode_app(app_encode_fun(A,$o),
0.00/0.32	                                       app_encode_fun(app_encode_fun(
0.00/0.32	                                                      A,'type/nums/num'),
0.00/0.32	                                                      'type/nums/num'),
0.00/0.32	                                       'const/iterate/nsum'(A),
0.00/0.32	                                       app_encode_app(app_encode_fun(A,$o),
0.00/0.32	                                                      app_encode_fun(A,$o),
0.00/0.32	                                                      app_encode_app(
0.00/0.32	                                                      app_encode_fun(A,$o),
0.00/0.32	                                                      app_encode_fun(
0.00/0.32	                                                      app_encode_fun(A,$o),
0.00/0.32	                                                      app_encode_fun(A,$o)),
0.00/0.32	                                                      'const/sets/UNION'(A),
0.00/0.32	                                                      A1),A2)),
0.00/0.32	                        A0) =
0.00/0.32	         app_encode_app('type/nums/num','type/nums/num',
0.00/0.32	                        app_encode_app('type/nums/num',
0.00/0.32	                                       app_encode_fun('type/nums/num',
0.00/0.32	                                                      'type/nums/num'),
0.00/0.32	                                       'const/arith/+',
0.00/0.32	                                       app_encode_app(app_encode_fun(
0.00/0.32	                                                      A,'type/nums/num'),
0.00/0.32	                                                      'type/nums/num',
0.00/0.32	                                                      app_encode_app(
0.00/0.32	                                                      app_encode_fun(A,$o),
0.00/0.32	                                                      app_encode_fun(
0.00/0.32	                                                      app_encode_fun(
0.00/0.32	                                                      A,'type/nums/num'),
0.00/0.32	                                                      'type/nums/num'),
0.00/0.32	                                                      'const/iterate/nsum'(A),
0.00/0.32	                                                      A1),A0)),
0.00/0.32	                        app_encode_app(app_encode_fun(A,'type/nums/num'),
0.00/0.32	                                       'type/nums/num',
0.00/0.32	                                       app_encode_app(app_encode_fun(A,$o),
0.00/0.32	                                                      app_encode_fun(
0.00/0.32	                                                      app_encode_fun(
0.00/0.32	                                                      A,'type/nums/num'),
0.00/0.32	                                                      'type/nums/num'),
0.00/0.32	                                                      'const/iterate/nsum'(A),
0.00/0.32	                                                      A2),
0.00/0.32	                                       A0))))))).
0.00/0.32	tff('7', plain,
0.00/0.32	    app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 'type/nums/num', 
0.00/0.32	      app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.32	        app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.32	          'type/nums/num'), 'const/iterate/nsum'(sk_A), 
0.00/0.32	        app_encode_app(app_encode_fun(sk_A, $o), app_encode_fun(sk_A, $o), 
0.00/0.32	          app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.32	            app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.32	              app_encode_fun(sk_A, $o)), 'const/sets/UNION'(sk_A), sk_A1), 
0.00/0.32	          sk_A2)), sk_A0)
0.00/0.32	     != app_encode_app('type/nums/num', 'type/nums/num', 
0.00/0.32	          app_encode_app('type/nums/num', 
0.00/0.32	            app_encode_fun('type/nums/num', 'type/nums/num'), 
0.00/0.32	            'const/arith/+', 
0.00/0.32	            app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.32	              'type/nums/num', 
0.00/0.32	              app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.32	                app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.32	                  'type/nums/num'), 'const/iterate/nsum'(sk_A), sk_A1), 
0.00/0.32	              sk_A0)), 
0.00/0.32	          app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.32	            'type/nums/num', 
0.00/0.32	            app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.32	              app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.32	                'type/nums/num'), 'const/iterate/nsum'(sk_A), sk_A2), sk_A0)),
0.00/0.32	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.32	tff('8', plain,
0.00/0.32	    (app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 'type/nums/num', 
0.00/0.32	       app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.32	         app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.32	           'type/nums/num'), 'const/iterate/nsum'(sk_A), 
0.00/0.32	         app_encode_app(app_encode_fun(sk_A, $o), app_encode_fun(sk_A, $o), 
0.00/0.32	           app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.32	             app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.32	               app_encode_fun(sk_A, $o)), 'const/sets/UNION'(sk_A), sk_A1), 
0.00/0.32	           sk_A2)), sk_A0)
0.00/0.32	      != app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.32	           'type/nums/num', 
0.00/0.32	           app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.32	             app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.32	               'type/nums/num'), 'const/iterate/nsum'(sk_A), 
0.00/0.32	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.32	               app_encode_fun(sk_A, $o), 
0.00/0.32	               app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.32	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.32	                   app_encode_fun(sk_A, $o)), 'const/sets/UNION'(sk_A), 
0.00/0.32	                 sk_A1), sk_A2)), sk_A0)
0.00/0.32	     | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.32	           'const/sets/FINITE'(sk_A), sk_A1)
0.00/0.32	     | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.32	           'const/sets/FINITE'(sk_A), sk_A2)
0.00/0.32	     | app_encode_app(sk_A, 'type/nums/num', sk_A0, 
0.00/0.32	         sk_A4('type/nums/num', sk_A, sk_A2, sk_A1, sk_A0, 'const/arith/+'))
0.00/0.32	        != app_encode_app('type/nums/num', 'type/nums/num', 
0.00/0.32	             'const/nums/NUMERAL', 'const/nums/_0')),
0.00/0.32	    inference('sup-', [status(thm)], ['6', '7'])).
0.00/0.32	tff('9', plain,
0.00/0.32	    app_encode_app(app_encode_fun(sk_A, $o), $o, 'const/sets/FINITE'(sk_A), 
0.00/0.32	      sk_A1),
0.00/0.32	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.32	tff('10', plain,
0.00/0.32	    app_encode_app(app_encode_fun(sk_A, $o), $o, 'const/sets/FINITE'(sk_A), 
0.00/0.32	      sk_A2),
0.00/0.32	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.32	tff('11', plain,
0.00/0.32	    ![X0 : $tType, X1 : app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.32	      X2 : $tType, X3 : app_encode_fun(X2, $o), X4 : app_encode_fun(X2, X0), 
0.00/0.32	      X5 : app_encode_fun(X2, $o)]:
0.00/0.32	      (app_encode_app(app_encode_fun(X2, X0), X0, 
0.00/0.32	         app_encode_app(app_encode_fun(X2, $o), 
0.00/0.32	           app_encode_fun(app_encode_fun(X2, X0), X0), 
0.00/0.32	           app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.32	             app_encode_fun(app_encode_fun(X2, $o), 
0.00/0.32	               app_encode_fun(app_encode_fun(X2, X0), X0)), 
0.00/0.32	             'const/iterate/iterate'(X2, X0), X1), 
0.00/0.32	           app_encode_app(app_encode_fun(X2, $o), app_encode_fun(X2, $o), 
0.00/0.32	             app_encode_app(app_encode_fun(X2, $o), 
0.00/0.32	               app_encode_fun(app_encode_fun(X2, $o), app_encode_fun(X2, $o)), 
0.00/0.32	               'const/sets/UNION'(X2), X3), X5)), X4)
0.00/0.32	        = app_encode_app(X0, X0, 
0.00/0.32	            app_encode_app(X0, app_encode_fun(X0, X0), X1, 
0.00/0.32	              app_encode_app(app_encode_fun(X2, X0), X0, 
0.00/0.32	                app_encode_app(app_encode_fun(X2, $o), 
0.00/0.32	                  app_encode_fun(app_encode_fun(X2, X0), X0), 
0.00/0.32	                  app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.32	                    app_encode_fun(app_encode_fun(X2, $o), 
0.00/0.32	                      app_encode_fun(app_encode_fun(X2, X0), X0)), 
0.00/0.32	                    'const/iterate/iterate'(X2, X0), X1), X3), X4)), 
0.00/0.32	            app_encode_app(app_encode_fun(X2, X0), X0, 
0.00/0.32	              app_encode_app(app_encode_fun(X2, $o), 
0.00/0.32	                app_encode_fun(app_encode_fun(X2, X0), X0), 
0.00/0.32	                app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.32	                  app_encode_fun(app_encode_fun(X2, $o), 
0.00/0.32	                    app_encode_fun(app_encode_fun(X2, X0), X0)), 
0.00/0.32	                  'const/iterate/iterate'(X2, X0), X1), X5), X4))
0.00/0.32	       | app_encode_app(app_encode_fun(X2, $o), $o, 
0.00/0.32	           app_encode_app(X2, app_encode_fun(app_encode_fun(X2, $o), $o), 
0.00/0.32	             'const/sets/IN'(X2), sk_A4(X0, X2, X5, X3, X4, X1)), 
0.00/0.32	           app_encode_app(app_encode_fun(X2, $o), app_encode_fun(X2, $o), 
0.00/0.32	             app_encode_app(app_encode_fun(X2, $o), 
0.00/0.32	               app_encode_fun(app_encode_fun(X2, $o), app_encode_fun(X2, $o)), 
0.00/0.32	               'const/sets/INTER'(X2), X3), X5))
0.00/0.32	       | ~ app_encode_app(app_encode_fun(X2, $o), $o, 
0.00/0.32	             'const/sets/FINITE'(X2), X5)
0.00/0.32	       | ~ app_encode_app(app_encode_fun(X2, $o), $o, 
0.00/0.32	             'const/sets/FINITE'(X2), X3)
0.00/0.32	       | ~ app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), $o, 
0.00/0.32	             'const/iterate/monoidal'(X0), X1)),
0.00/0.32	    inference('cnf', [status(esa)], [zf_stmt_14])).
0.00/0.32	tff('12', plain,
0.00/0.32	    ![X0 : $tType, X1 : app_encode_fun(X0, 'type/nums/num'), 
0.00/0.32	      X2 : app_encode_fun(X0, $o), X3 : app_encode_fun(X0, $o)]:
0.00/0.32	      (app_encode_app(app_encode_fun(X0, 'type/nums/num'), 'type/nums/num', 
0.00/0.32	         app_encode_app(app_encode_fun(X0, $o), 
0.00/0.32	           app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
0.00/0.32	             'type/nums/num'), 
0.00/0.32	           app_encode_app(
0.00/0.32	             app_encode_fun('type/nums/num', 
0.00/0.32	               app_encode_fun('type/nums/num', 'type/nums/num')), 
0.00/0.32	             app_encode_fun(app_encode_fun(X0, $o), 
0.00/0.32	               app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
0.00/0.32	                 'type/nums/num')), 
0.00/0.32	             'const/iterate/iterate'(X0, 'type/nums/num'), 'const/arith/+'), 
0.00/0.32	           app_encode_app(app_encode_fun(X0, $o), app_encode_fun(X0, $o), 
0.00/0.32	             app_encode_app(app_encode_fun(X0, $o), 
0.00/0.32	               app_encode_fun(app_encode_fun(X0, $o), app_encode_fun(X0, $o)), 
0.00/0.32	               'const/sets/UNION'(X0), X3), X2)), X1)
0.00/0.32	        = app_encode_app('type/nums/num', 'type/nums/num', 
0.00/0.32	            app_encode_app('type/nums/num', 
0.00/0.32	              app_encode_fun('type/nums/num', 'type/nums/num'), 
0.00/0.32	              'const/arith/+', 
0.00/0.32	              app_encode_app(app_encode_fun(X0, 'type/nums/num'), 
0.00/0.32	                'type/nums/num', 
0.00/0.32	                app_encode_app(app_encode_fun(X0, $o), 
0.00/0.32	                  app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
0.00/0.32	                    'type/nums/num'), 'const/iterate/nsum'(X0), X3), X1)), 
0.00/0.32	            app_encode_app(app_encode_fun(X0, 'type/nums/num'), 
0.00/0.32	              'type/nums/num', 
0.00/0.32	              app_encode_app(app_encode_fun(X0, $o), 
0.00/0.32	                app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
0.00/0.32	                  'type/nums/num'), 
0.00/0.32	                app_encode_app(
0.00/0.32	                  app_encode_fun('type/nums/num', 
0.00/0.32	                    app_encode_fun('type/nums/num', 'type/nums/num')), 
0.00/0.32	                  app_encode_fun(app_encode_fun(X0, $o), 
0.00/0.32	                    app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
0.00/0.32	                      'type/nums/num')), 
0.00/0.32	                  'const/iterate/iterate'(X0, 'type/nums/num'), 
0.00/0.32	                  'const/arith/+'), X2), X1))
0.00/0.32	       | ~ app_encode_app(
0.00/0.32	             app_encode_fun('type/nums/num', 
0.00/0.32	               app_encode_fun('type/nums/num', 'type/nums/num')), $o, 
0.00/0.32	             'const/iterate/monoidal'('type/nums/num'), 'const/arith/+')
0.00/0.32	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
0.00/0.32	             'const/sets/FINITE'(X0), X3)
0.00/0.32	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
0.00/0.32	             'const/sets/FINITE'(X0), X2)
0.00/0.32	       | app_encode_app(app_encode_fun(X0, $o), $o, 
0.00/0.32	           app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
0.00/0.32	             'const/sets/IN'(X0), 
0.00/0.32	             sk_A4('type/nums/num', X0, X2, X3, X1, 'const/arith/+')), 
0.00/0.32	           app_encode_app(app_encode_fun(X0, $o), app_encode_fun(X0, $o), 
0.00/0.32	             app_encode_app(app_encode_fun(X0, $o), 
0.00/0.32	               app_encode_fun(app_encode_fun(X0, $o), app_encode_fun(X0, $o)), 
0.00/0.32	               'const/sets/INTER'(X0), X3), X2))),
0.00/0.32	    inference('sup+', [status(thm)], ['0', '11'])).
0.00/0.32	tff('13', plain,
0.00/0.32	    ![X0 : $tType, X1 : app_encode_fun(X0, 'type/nums/num'), 
0.00/0.32	      X2 : app_encode_fun(X0, $o), X3 : app_encode_fun(X0, $o)]:
0.00/0.32	      (app_encode_app(app_encode_fun(X0, 'type/nums/num'), 'type/nums/num', 
0.00/0.32	         app_encode_app(app_encode_fun(X0, $o), 
0.00/0.32	           app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
0.00/0.32	             'type/nums/num'), 'const/iterate/nsum'(X0), 
0.00/0.32	           app_encode_app(app_encode_fun(X0, $o), app_encode_fun(X0, $o), 
0.00/0.32	             app_encode_app(app_encode_fun(X0, $o), 
0.00/0.32	               app_encode_fun(app_encode_fun(X0, $o), app_encode_fun(X0, $o)), 
0.00/0.32	               'const/sets/UNION'(X0), X3), X2)), X1)
0.00/0.32	        = app_encode_app('type/nums/num', 'type/nums/num', 
0.00/0.32	            app_encode_app('type/nums/num', 
0.00/0.32	              app_encode_fun('type/nums/num', 'type/nums/num'), 
0.00/0.32	              'const/arith/+', 
0.00/0.32	              app_encode_app(app_encode_fun(X0, 'type/nums/num'), 
0.00/0.32	                'type/nums/num', 
0.00/0.32	                app_encode_app(app_encode_fun(X0, $o), 
0.00/0.32	                  app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
0.00/0.32	                    'type/nums/num'), 'const/iterate/nsum'(X0), X3), X1)), 
0.00/0.32	            app_encode_app(app_encode_fun(X0, 'type/nums/num'), 
0.00/0.32	              'type/nums/num', 
0.00/0.32	              app_encode_app(app_encode_fun(X0, $o), 
0.00/0.32	                app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
0.00/0.32	                  'type/nums/num'), 'const/iterate/nsum'(X0), X2), X1))
0.00/0.32	       | ~ $true
0.00/0.32	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
0.00/0.32	             'const/sets/FINITE'(X0), X3)
0.00/0.32	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
0.00/0.32	             'const/sets/FINITE'(X0), X2)
0.00/0.32	       | app_encode_app(app_encode_fun(X0, $o), $o, 
0.00/0.32	           app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
0.00/0.32	             'const/sets/IN'(X0), 
0.00/0.32	             sk_A4('type/nums/num', X0, X2, X3, X1, 'const/arith/+')), 
0.00/0.32	           app_encode_app(app_encode_fun(X0, $o), app_encode_fun(X0, $o), 
0.00/0.32	             app_encode_app(app_encode_fun(X0, $o), 
0.00/0.32	               app_encode_fun(app_encode_fun(X0, $o), app_encode_fun(X0, $o)), 
0.00/0.32	               'const/sets/INTER'(X0), X3), X2))),
0.00/0.32	    inference('demod', [status(thm)], ['12', '0', '0', '3'])).
0.00/0.32	tff('14', plain,
0.00/0.32	    ![X0 : $tType, X1 : app_encode_fun(X0, 'type/nums/num'), 
0.00/0.32	      X2 : app_encode_fun(X0, $o), X3 : app_encode_fun(X0, $o)]:
0.00/0.32	      (app_encode_app(app_encode_fun(X0, $o), $o, 
0.00/0.32	         app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
0.00/0.32	           'const/sets/IN'(X0), 
0.00/0.32	           sk_A4('type/nums/num', X0, X2, X3, X1, 'const/arith/+')), 
0.00/0.32	         app_encode_app(app_encode_fun(X0, $o), app_encode_fun(X0, $o), 
0.00/0.32	           app_encode_app(app_encode_fun(X0, $o), 
0.00/0.32	             app_encode_fun(app_encode_fun(X0, $o), app_encode_fun(X0, $o)), 
0.00/0.32	             'const/sets/INTER'(X0), X3), X2))
0.00/0.32	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
0.00/0.32	             'const/sets/FINITE'(X0), X2)
0.00/0.32	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
0.00/0.32	             'const/sets/FINITE'(X0), X3)
0.00/0.32	       | app_encode_app(app_encode_fun(X0, 'type/nums/num'), 
0.00/0.32	           'type/nums/num', 
0.00/0.32	           app_encode_app(app_encode_fun(X0, $o), 
0.00/0.32	             app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
0.00/0.32	               'type/nums/num'), 'const/iterate/nsum'(X0), 
0.00/0.32	             app_encode_app(app_encode_fun(X0, $o), app_encode_fun(X0, $o), 
0.00/0.32	               app_encode_app(app_encode_fun(X0, $o), 
0.00/0.32	                 app_encode_fun(app_encode_fun(X0, $o), 
0.00/0.32	                   app_encode_fun(X0, $o)), 'const/sets/UNION'(X0), X3), X2)), 
0.00/0.32	           X1)
0.00/0.32	          = app_encode_app('type/nums/num', 'type/nums/num', 
0.00/0.32	              app_encode_app('type/nums/num', 
0.00/0.32	                app_encode_fun('type/nums/num', 'type/nums/num'), 
0.00/0.32	                'const/arith/+', 
0.00/0.32	                app_encode_app(app_encode_fun(X0, 'type/nums/num'), 
0.00/0.32	                  'type/nums/num', 
0.00/0.32	                  app_encode_app(app_encode_fun(X0, $o), 
0.00/0.32	                    app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
0.00/0.32	                      'type/nums/num'), 'const/iterate/nsum'(X0), X3), X1)), 
0.00/0.32	              app_encode_app(app_encode_fun(X0, 'type/nums/num'), 
0.00/0.32	                'type/nums/num', 
0.00/0.32	                app_encode_app(app_encode_fun(X0, $o), 
0.00/0.32	                  app_encode_fun(app_encode_fun(X0, 'type/nums/num'), 
0.00/0.32	                    'type/nums/num'), 'const/iterate/nsum'(X0), X2), X1))),
0.00/0.32	    inference('simplify', [status(thm)], ['13'])).
0.00/0.32	tff('15', plain,
0.00/0.32	    (app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 'type/nums/num', 
0.00/0.32	       app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.32	         app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.32	           'type/nums/num'), 'const/iterate/nsum'(sk_A), 
0.00/0.32	         app_encode_app(app_encode_fun(sk_A, $o), app_encode_fun(sk_A, $o), 
0.00/0.32	           app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.32	             app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.32	               app_encode_fun(sk_A, $o)), 'const/sets/UNION'(sk_A), sk_A1), 
0.00/0.32	           sk_A2)), sk_A0)
0.00/0.32	      != app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.32	           'type/nums/num', 
0.00/0.32	           app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.32	             app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.32	               'type/nums/num'), 'const/iterate/nsum'(sk_A), 
0.00/0.32	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.32	               app_encode_fun(sk_A, $o), 
0.00/0.32	               app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.32	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.32	                   app_encode_fun(sk_A, $o)), 'const/sets/UNION'(sk_A), 
0.00/0.32	                 sk_A1), sk_A2)), sk_A0)
0.00/0.32	     | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.32	           'const/sets/FINITE'(sk_A), sk_A1)
0.00/0.32	     | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.32	           'const/sets/FINITE'(sk_A), sk_A2)
0.00/0.32	     | app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.32	         app_encode_app(sk_A, app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.32	           'const/sets/IN'(sk_A), 
0.00/0.32	           sk_A4('type/nums/num', sk_A, sk_A2, sk_A1, sk_A0, 'const/arith/+')), 
0.00/0.32	         app_encode_app(app_encode_fun(sk_A, $o), app_encode_fun(sk_A, $o), 
0.00/0.32	           app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.32	             app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.32	               app_encode_fun(sk_A, $o)), 'const/sets/INTER'(sk_A), sk_A1), 
0.00/0.32	           sk_A2))),
0.00/0.32	    inference('sup-', [status(thm)], ['14', '7'])).
0.00/0.32	tff('16', plain,
0.00/0.32	    (app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 'type/nums/num', 
0.00/0.32	       app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.32	         app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.32	           'type/nums/num'), 'const/iterate/nsum'(sk_A), 
0.00/0.32	         app_encode_app(app_encode_fun(sk_A, $o), app_encode_fun(sk_A, $o), 
0.00/0.32	           app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.32	             app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.32	               app_encode_fun(sk_A, $o)), 'const/sets/UNION'(sk_A), sk_A1), 
0.00/0.32	           sk_A2)), sk_A0)
0.00/0.32	      != app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.32	           'type/nums/num', 
0.00/0.32	           app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.32	             app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.32	               'type/nums/num'), 'const/iterate/nsum'(sk_A), 
0.00/0.32	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.32	               app_encode_fun(sk_A, $o), 
0.00/0.32	               app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.32	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.32	                   app_encode_fun(sk_A, $o)), 'const/sets/UNION'(sk_A), 
0.00/0.32	                 sk_A1), sk_A2)), sk_A0)
0.00/0.32	     | ~ $true
0.00/0.32	     | ~ $true
0.00/0.32	     | app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.32	         app_encode_app(sk_A, app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.32	           'const/sets/IN'(sk_A), 
0.00/0.32	           sk_A4('type/nums/num', sk_A, sk_A2, sk_A1, sk_A0, 'const/arith/+')), 
0.00/0.32	         app_encode_app(app_encode_fun(sk_A, $o), app_encode_fun(sk_A, $o), 
0.00/0.32	           app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.32	             app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.32	               app_encode_fun(sk_A, $o)), 'const/sets/INTER'(sk_A), sk_A1), 
0.00/0.32	           sk_A2))),
0.00/0.32	    inference('demod', [status(thm)], ['15', '9', '10'])).
0.00/0.32	tff('17', plain,
0.00/0.32	    app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.32	      app_encode_app(sk_A, app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.32	        'const/sets/IN'(sk_A), 
0.00/0.32	        sk_A4('type/nums/num', sk_A, sk_A2, sk_A1, sk_A0, 'const/arith/+')), 
0.00/0.32	      app_encode_app(app_encode_fun(sk_A, $o), app_encode_fun(sk_A, $o), 
0.00/0.32	        app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.32	          app_encode_fun(app_encode_fun(sk_A, $o), app_encode_fun(sk_A, $o)), 
0.00/0.32	          'const/sets/INTER'(sk_A), sk_A1), sk_A2)),
0.00/0.32	    inference('simplify', [status(thm)], ['16'])).
0.00/0.32	tff('18', plain,
0.00/0.32	    ![X7 : sk_A]:
0.00/0.32	      (app_encode_app(sk_A, 'type/nums/num', sk_A0, X7)
0.00/0.32	        = app_encode_app('type/nums/num', 'type/nums/num', 
0.00/0.32	            'const/nums/NUMERAL', 'const/nums/_0')
0.00/0.32	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.32	             app_encode_app(sk_A, 
0.00/0.32	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.32	               'const/sets/IN'(sk_A), X7), 
0.00/0.32	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.32	               app_encode_fun(sk_A, $o), 
0.00/0.32	               app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.32	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.32	                   app_encode_fun(sk_A, $o)), 'const/sets/INTER'(sk_A), 
0.00/0.32	                 sk_A1), sk_A2))),
0.00/0.32	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.32	tff('19', plain,
0.00/0.32	    (~ $true
0.00/0.32	     | app_encode_app(sk_A, 'type/nums/num', sk_A0, 
0.00/0.32	         sk_A4('type/nums/num', sk_A, sk_A2, sk_A1, sk_A0, 'const/arith/+'))
0.00/0.32	        = app_encode_app('type/nums/num', 'type/nums/num', 
0.00/0.32	            'const/nums/NUMERAL', 'const/nums/_0')),
0.00/0.32	    inference('sup-', [status(thm)], ['17', '18'])).
0.00/0.32	tff('20', plain,
0.00/0.32	    app_encode_app(sk_A, 'type/nums/num', sk_A0, 
0.00/0.32	      sk_A4('type/nums/num', sk_A, sk_A2, sk_A1, sk_A0, 'const/arith/+'))
0.00/0.32	     = app_encode_app('type/nums/num', 'type/nums/num', 
0.00/0.32	         'const/nums/NUMERAL', 'const/nums/_0'),
0.00/0.32	    inference('simplify', [status(thm)], ['19'])).
0.00/0.32	tff('21', plain,
0.00/0.32	    (app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 'type/nums/num', 
0.00/0.32	       app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.32	         app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.32	           'type/nums/num'), 'const/iterate/nsum'(sk_A), 
0.00/0.32	         app_encode_app(app_encode_fun(sk_A, $o), app_encode_fun(sk_A, $o), 
0.00/0.32	           app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.32	             app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.32	               app_encode_fun(sk_A, $o)), 'const/sets/UNION'(sk_A), sk_A1), 
0.00/0.32	           sk_A2)), sk_A0)
0.00/0.32	      != app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.32	           'type/nums/num', 
0.00/0.32	           app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.32	             app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.32	               'type/nums/num'), 'const/iterate/nsum'(sk_A), 
0.00/0.32	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.32	               app_encode_fun(sk_A, $o), 
0.00/0.32	               app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.32	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.32	                   app_encode_fun(sk_A, $o)), 'const/sets/UNION'(sk_A), 
0.00/0.32	                 sk_A1), sk_A2)), sk_A0)
0.00/0.32	     | ~ $true
0.00/0.32	     | ~ $true
0.00/0.32	     | app_encode_app('type/nums/num', 'type/nums/num', 
0.00/0.32	         'const/nums/NUMERAL', 'const/nums/_0')
0.00/0.32	        != app_encode_app('type/nums/num', 'type/nums/num', 
0.00/0.32	             'const/nums/NUMERAL', 'const/nums/_0')),
0.00/0.32	    inference('demod', [status(thm)], ['8', '9', '10', '20'])).
0.00/0.32	tff('22', plain, $false, inference('simplify', [status(thm)], ['21'])).
0.00/0.32	
0.00/0.32	% SZS output end Refutation
0.00/0.32	EOF
