0.00/0.00	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : appext
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : rpo6
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n145.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 18:34:09 CST 2018
130.02/130.28	% done 9925 iterations in 130.078s
130.02/130.28	% SZS status Theorem for 'stdin'
130.02/130.28	% SZS output start Refutation
130.02/130.28	tff(zf_stmt_10, axiom,
130.02/130.28	  (![A:$tType,A0:app_encode_fun(A,$o),A1:app_encode_fun(A,$o)]:
130.02/130.28	     (app_encode_app(app_encode_fun(A,$o),$o,
130.02/130.28	                     app_encode_app(app_encode_fun(A,$o),
130.02/130.28	                                    app_encode_fun(app_encode_fun(A,$o),$o),
130.02/130.28	                                    'const/sets/SUBSET'(A),A0),
130.02/130.28	                     A1) <=>
130.02/130.28	      (![A2:A]:
130.02/130.28	         (app_encode_app(app_encode_fun(A,$o),$o,
130.02/130.28	                         app_encode_app(A,
130.02/130.28	                                        app_encode_fun(app_encode_fun(A,$o),
130.02/130.28	                                                       $o),
130.02/130.28	                                        'const/sets/IN'(A),A2),
130.02/130.28	                         A0) =>
130.02/130.28	          app_encode_app(app_encode_fun(A,$o),$o,
130.02/130.28	                         app_encode_app(A,
130.02/130.28	                                        app_encode_fun(app_encode_fun(A,$o),
130.02/130.28	                                                       $o),
130.02/130.28	                                        'const/sets/IN'(A),A2),
130.02/130.28	                         A1)))))).
130.02/130.28	tff('0', plain,
130.02/130.28	    ![X15 : $tType, X17 : app_encode_fun(X15, $o), 
130.02/130.28	      X19 : app_encode_fun(X15, $o)]:
130.02/130.28	      (app_encode_app(app_encode_fun(X15, $o), $o, 
130.02/130.28	         app_encode_app(app_encode_fun(X15, $o), 
130.02/130.28	           app_encode_fun(app_encode_fun(X15, $o), $o), 
130.02/130.28	           'const/sets/SUBSET'(X15), X17), X19)
130.02/130.28	       | app_encode_app(app_encode_fun(X15, $o), $o, 
130.02/130.28	           app_encode_app(X15, app_encode_fun(app_encode_fun(X15, $o), $o), 
130.02/130.28	             'const/sets/IN'(X15), sk_A21(X15, X19, X17)), X17)),
130.02/130.28	    inference('cnf', [status(esa)], [zf_stmt_10])).
130.02/130.28	tff(zf_stmt_8, axiom,
130.02/130.28	  (![A:$tType,P:app_encode_fun(A,$o),A0:A]:
130.02/130.28	     (app_encode_app(app_encode_fun(A,$o),$o,
130.02/130.28	                     app_encode_app(A,
130.02/130.28	                                    app_encode_fun(app_encode_fun(A,$o),$o),
130.02/130.28	                                    'const/sets/IN'(A),A0),
130.02/130.28	                     P) <=>
130.02/130.28	      app_encode_app(A,$o,P,A0)))).
130.02/130.28	tff('1', plain,
130.02/130.28	    ![X6 : $tType, X7 : app_encode_fun(X6, $o), X8 : X6]:
130.02/130.28	      (app_encode_app(X6, $o, X7, X8)
130.02/130.28	       | ~ app_encode_app(app_encode_fun(X6, $o), $o, 
130.02/130.28	             app_encode_app(X6, app_encode_fun(app_encode_fun(X6, $o), $o), 
130.02/130.28	               'const/sets/IN'(X6), X8), X7)),
130.02/130.28	    inference('cnf', [status(esa)], [zf_stmt_8])).
130.02/130.28	tff('2', plain,
130.02/130.28	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : app_encode_fun(X0, $o)]:
130.02/130.28	      (~ $true
130.02/130.28	       | app_encode_app(app_encode_fun(X0, $o), $o, 
130.02/130.28	           app_encode_app(app_encode_fun(X0, $o), 
130.02/130.28	             app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.28	             'const/sets/SUBSET'(X0), X1), X2)
130.02/130.28	       | app_encode_app(X0, $o, X1, sk_A21(X0, X2, X1))),
130.02/130.28	    inference('sup-', [status(thm)], ['0', '1'])).
130.02/130.28	tff('3', plain,
130.02/130.28	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : app_encode_fun(X0, $o)]:
130.02/130.28	      (app_encode_app(X0, $o, X1, sk_A21(X0, X2, X1))
130.02/130.28	       | app_encode_app(app_encode_fun(X0, $o), $o, 
130.02/130.28	           app_encode_app(app_encode_fun(X0, $o), 
130.02/130.28	             app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.28	             'const/sets/SUBSET'(X0), X1), X2)),
130.02/130.28	    inference('simplify', [status(thm)], ['2'])).
130.02/130.28	tff(zf_stmt_9, axiom,
130.02/130.28	  (![A:$tType,A0:app_encode_fun(app_encode_fun(A,$o),$o),A1:A]:
130.02/130.28	     (app_encode_app(app_encode_fun(A,$o),$o,
130.02/130.28	                     app_encode_app(A,
130.02/130.28	                                    app_encode_fun(app_encode_fun(A,$o),$o),
130.02/130.28	                                    'const/sets/IN'(A),A1),
130.02/130.28	                     app_encode_app(app_encode_fun(app_encode_fun(A,$o),$o),
130.02/130.28	                                    app_encode_fun(A,$o),
130.02/130.28	                                    'const/sets/INTERS'(A),A0)) <=>
130.02/130.28	      (![A2:app_encode_fun(A,$o)]:
130.02/130.28	         (app_encode_app(app_encode_fun(app_encode_fun(A,$o),$o),$o,
130.02/130.28	                         app_encode_app(app_encode_fun(A,$o),
130.02/130.28	                                        app_encode_fun(app_encode_fun(
130.02/130.28	                                                       app_encode_fun(A,$o),
130.02/130.28	                                                       $o),$o),
130.02/130.28	                                        'const/sets/IN'(app_encode_fun(A,$o)),
130.02/130.28	                                        A2),
130.02/130.28	                         A0) =>
130.02/130.28	          app_encode_app(app_encode_fun(A,$o),$o,
130.02/130.28	                         app_encode_app(A,
130.02/130.28	                                        app_encode_fun(app_encode_fun(A,$o),
130.02/130.28	                                                       $o),
130.02/130.28	                                        'const/sets/IN'(A),A1),
130.02/130.28	                         A2)))))).
130.02/130.28	tff('4', plain,
130.02/130.28	    ![X10 : $tType, X12 : app_encode_fun(app_encode_fun(X10, $o), $o), 
130.02/130.28	      X14 : X10]:
130.02/130.28	      (app_encode_app(app_encode_fun(X10, $o), $o, 
130.02/130.28	         app_encode_app(X10, app_encode_fun(app_encode_fun(X10, $o), $o), 
130.02/130.28	           'const/sets/IN'(X10), X14), 
130.02/130.28	         app_encode_app(app_encode_fun(app_encode_fun(X10, $o), $o), 
130.02/130.28	           app_encode_fun(X10, $o), 'const/sets/INTERS'(X10), X12))
130.02/130.28	       | app_encode_app(app_encode_fun(app_encode_fun(X10, $o), $o), $o, 
130.02/130.28	           app_encode_app(app_encode_fun(X10, $o), 
130.02/130.28	             app_encode_fun(app_encode_fun(app_encode_fun(X10, $o), $o), $o), 
130.02/130.28	             'const/sets/IN'(app_encode_fun(X10, $o)), sk_A2(X10, X14, X12)), 
130.02/130.28	           X12)),
130.02/130.28	    inference('cnf', [status(esa)], [zf_stmt_9])).
130.02/130.28	tff('5', plain,
130.02/130.28	    ![X0 : $tType, X1 : app_encode_fun(app_encode_fun(X0, $o), $o), X2 : X0]:
130.02/130.28	      (~ $true
130.02/130.28	       | app_encode_app(app_encode_fun(X0, $o), $o, 
130.02/130.28	           app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.28	             'const/sets/IN'(X0), X2), 
130.02/130.28	           app_encode_app(app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.28	             app_encode_fun(X0, $o), 'const/sets/INTERS'(X0), X1))
130.02/130.28	       | app_encode_app(app_encode_fun(X0, $o), $o, X1, sk_A2(X0, X2, X1))),
130.02/130.28	    inference('sup-', [status(thm)], ['4', '1'])).
130.02/130.28	tff('6', plain,
130.02/130.28	    ![X0 : $tType, X1 : app_encode_fun(app_encode_fun(X0, $o), $o), X2 : X0]:
130.02/130.28	      (app_encode_app(app_encode_fun(X0, $o), $o, X1, sk_A2(X0, X2, X1))
130.02/130.28	       | app_encode_app(app_encode_fun(X0, $o), $o, 
130.02/130.28	           app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.28	             'const/sets/IN'(X0), X2), 
130.02/130.28	           app_encode_app(app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.28	             app_encode_fun(X0, $o), 'const/sets/INTERS'(X0), X1))),
130.02/130.28	    inference('simplify', [status(thm)], ['5'])).
130.02/130.28	tff('7', plain,
130.02/130.28	    ![X6 : $tType, X7 : app_encode_fun(X6, $o), X9 : X6]:
130.02/130.28	      (app_encode_app(app_encode_fun(X6, $o), $o, 
130.02/130.28	         app_encode_app(X6, app_encode_fun(app_encode_fun(X6, $o), $o), 
130.02/130.28	           'const/sets/IN'(X6), X9), X7)
130.02/130.28	       | ~ app_encode_app(X6, $o, X7, X9)),
130.02/130.28	    inference('cnf', [status(esa)], [zf_stmt_8])).
130.02/130.28	tff('8', plain,
130.02/130.28	    ![X15 : $tType, X16 : X15, X17 : app_encode_fun(X15, $o), 
130.02/130.28	      X18 : app_encode_fun(X15, $o)]:
130.02/130.28	      (~ app_encode_app(app_encode_fun(X15, $o), $o, 
130.02/130.28	           app_encode_app(X15, app_encode_fun(app_encode_fun(X15, $o), $o), 
130.02/130.28	             'const/sets/IN'(X15), X16), X17)
130.02/130.28	       | app_encode_app(app_encode_fun(X15, $o), $o, 
130.02/130.28	           app_encode_app(X15, app_encode_fun(app_encode_fun(X15, $o), $o), 
130.02/130.28	             'const/sets/IN'(X15), X16), X18)
130.02/130.28	       | ~ app_encode_app(app_encode_fun(X15, $o), $o, 
130.02/130.28	             app_encode_app(app_encode_fun(X15, $o), 
130.02/130.28	               app_encode_fun(app_encode_fun(X15, $o), $o), 
130.02/130.28	               'const/sets/SUBSET'(X15), X17), X18)),
130.02/130.28	    inference('cnf', [status(esa)], [zf_stmt_10])).
130.02/130.28	tff('9', plain,
130.02/130.28	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : X0, 
130.02/130.28	      X3 : app_encode_fun(X0, $o)]:
130.02/130.28	      (~ $true
130.02/130.28	       | ~ app_encode_app(X0, $o, X1, X2)
130.02/130.28	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
130.02/130.28	             app_encode_app(app_encode_fun(X0, $o), 
130.02/130.28	               app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.28	               'const/sets/SUBSET'(X0), X1), X3)
130.02/130.28	       | app_encode_app(app_encode_fun(X0, $o), $o, 
130.02/130.28	           app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.28	             'const/sets/IN'(X0), X2), X3)),
130.02/130.28	    inference('sup-', [status(thm)], ['7', '8'])).
130.02/130.28	tff('10', plain,
130.02/130.28	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : X0, 
130.02/130.28	      X3 : app_encode_fun(X0, $o)]:
130.02/130.28	      (app_encode_app(app_encode_fun(X0, $o), $o, 
130.02/130.28	         app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.28	           'const/sets/IN'(X0), X2), X3)
130.02/130.28	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
130.02/130.28	             app_encode_app(app_encode_fun(X0, $o), 
130.02/130.28	               app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.28	               'const/sets/SUBSET'(X0), X1), X3)
130.02/130.28	       | ~ app_encode_app(X0, $o, X1, X2)),
130.02/130.28	    inference('simplify', [status(thm)], ['9'])).
130.02/130.28	tff('11', plain,
130.02/130.28	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : X0, X3 : X0]:
130.02/130.28	      (~ $true
130.02/130.28	       | app_encode_app(app_encode_fun(X0, $o), $o, 
130.02/130.28	           app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.28	             'const/sets/IN'(X0), X2), 
130.02/130.28	           app_encode_app(app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.28	             app_encode_fun(X0, $o), 'const/sets/INTERS'(X0), 
130.02/130.28	             app_encode_app(app_encode_fun(X0, $o), 
130.02/130.28	               app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.28	               'const/sets/SUBSET'(X0), X1)))
130.02/130.28	       | ~ app_encode_app(X0, $o, X1, X3)
130.02/130.28	       | app_encode_app(app_encode_fun(X0, $o), $o, 
130.02/130.28	           app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.28	             'const/sets/IN'(X0), X3), 
130.02/130.28	           sk_A2(X0, X2, 
130.02/130.28	             app_encode_app(app_encode_fun(X0, $o), 
130.02/130.28	               app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.28	               'const/sets/SUBSET'(X0), X1)))),
130.02/130.28	    inference('sup-', [status(thm)], ['6', '10'])).
130.02/130.28	tff('12', plain,
130.02/130.28	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : X0, X3 : X0]:
130.02/130.28	      (app_encode_app(app_encode_fun(X0, $o), $o, 
130.02/130.28	         app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.28	           'const/sets/IN'(X0), X3), 
130.02/130.28	         sk_A2(X0, X2, 
130.02/130.28	           app_encode_app(app_encode_fun(X0, $o), 
130.02/130.28	             app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.28	             'const/sets/SUBSET'(X0), X1)))
130.02/130.28	       | ~ app_encode_app(X0, $o, X1, X3)
130.02/130.28	       | app_encode_app(app_encode_fun(X0, $o), $o, 
130.02/130.28	           app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.28	             'const/sets/IN'(X0), X2), 
130.02/130.28	           app_encode_app(app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.28	             app_encode_fun(X0, $o), 'const/sets/INTERS'(X0), 
130.02/130.28	             app_encode_app(app_encode_fun(X0, $o), 
130.02/130.28	               app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.28	               'const/sets/SUBSET'(X0), X1)))),
130.02/130.28	    inference('simplify', [status(thm)], ['11'])).
130.02/130.28	tff('13', plain,
130.02/130.28	    ![X10 : $tType, X12 : app_encode_fun(app_encode_fun(X10, $o), $o), 
130.02/130.28	      X14 : X10]:
130.02/130.28	      (app_encode_app(app_encode_fun(X10, $o), $o, 
130.02/130.28	         app_encode_app(X10, app_encode_fun(app_encode_fun(X10, $o), $o), 
130.02/130.28	           'const/sets/IN'(X10), X14), 
130.02/130.28	         app_encode_app(app_encode_fun(app_encode_fun(X10, $o), $o), 
130.02/130.28	           app_encode_fun(X10, $o), 'const/sets/INTERS'(X10), X12))
130.02/130.28	       | ~ app_encode_app(app_encode_fun(X10, $o), $o, 
130.02/130.28	             app_encode_app(X10, 
130.02/130.28	               app_encode_fun(app_encode_fun(X10, $o), $o), 
130.02/130.28	               'const/sets/IN'(X10), X14), sk_A2(X10, X14, X12))),
130.02/130.28	    inference('cnf', [status(esa)], [zf_stmt_9])).
130.02/130.29	tff('14', plain,
130.02/130.29	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : X0]:
130.02/130.29	      (~ $true
130.02/130.29	       | app_encode_app(app_encode_fun(X0, $o), $o, 
130.02/130.29	           app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	             'const/sets/IN'(X0), X2), 
130.02/130.29	           app_encode_app(app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	             app_encode_fun(X0, $o), 'const/sets/INTERS'(X0), 
130.02/130.29	             app_encode_app(app_encode_fun(X0, $o), 
130.02/130.29	               app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	               'const/sets/SUBSET'(X0), X1)))
130.02/130.29	       | ~ app_encode_app(X0, $o, X1, X2)
130.02/130.29	       | app_encode_app(app_encode_fun(X0, $o), $o, 
130.02/130.29	           app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	             'const/sets/IN'(X0), X2), 
130.02/130.29	           app_encode_app(app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	             app_encode_fun(X0, $o), 'const/sets/INTERS'(X0), 
130.02/130.29	             app_encode_app(app_encode_fun(X0, $o), 
130.02/130.29	               app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	               'const/sets/SUBSET'(X0), X1)))),
130.02/130.29	    inference('sup-', [status(thm)], ['12', '13'])).
130.02/130.29	tff('15', plain,
130.02/130.29	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : X0]:
130.02/130.29	      (~ app_encode_app(X0, $o, X1, X2)
130.02/130.29	       | app_encode_app(app_encode_fun(X0, $o), $o, 
130.02/130.29	           app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	             'const/sets/IN'(X0), X2), 
130.02/130.29	           app_encode_app(app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	             app_encode_fun(X0, $o), 'const/sets/INTERS'(X0), 
130.02/130.29	             app_encode_app(app_encode_fun(X0, $o), 
130.02/130.29	               app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	               'const/sets/SUBSET'(X0), X1)))),
130.02/130.29	    inference('simplify', [status(thm)], ['14'])).
130.02/130.29	tff('16', plain,
130.02/130.29	    ![X15 : $tType, X17 : app_encode_fun(X15, $o), 
130.02/130.29	      X19 : app_encode_fun(X15, $o)]:
130.02/130.29	      (app_encode_app(app_encode_fun(X15, $o), $o, 
130.02/130.29	         app_encode_app(app_encode_fun(X15, $o), 
130.02/130.29	           app_encode_fun(app_encode_fun(X15, $o), $o), 
130.02/130.29	           'const/sets/SUBSET'(X15), X17), X19)
130.02/130.29	       | ~ app_encode_app(app_encode_fun(X15, $o), $o, 
130.02/130.29	             app_encode_app(X15, 
130.02/130.29	               app_encode_fun(app_encode_fun(X15, $o), $o), 
130.02/130.29	               'const/sets/IN'(X15), sk_A21(X15, X19, X17)), X19)),
130.02/130.29	    inference('cnf', [status(esa)], [zf_stmt_10])).
130.02/130.29	tff('17', plain,
130.02/130.29	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : app_encode_fun(X0, $o)]:
130.02/130.29	      (~ $true
130.02/130.29	       | ~ app_encode_app(X0, $o, X1, 
130.02/130.29	             sk_A21(X0, 
130.02/130.29	               app_encode_app(app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	                 app_encode_fun(X0, $o), 'const/sets/INTERS'(X0), 
130.02/130.29	                 app_encode_app(app_encode_fun(X0, $o), 
130.02/130.29	                   app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	                   'const/sets/SUBSET'(X0), X1)), X2))
130.02/130.29	       | app_encode_app(app_encode_fun(X0, $o), $o, 
130.02/130.29	           app_encode_app(app_encode_fun(X0, $o), 
130.02/130.29	             app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	             'const/sets/SUBSET'(X0), X2), 
130.02/130.29	           app_encode_app(app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	             app_encode_fun(X0, $o), 'const/sets/INTERS'(X0), 
130.02/130.29	             app_encode_app(app_encode_fun(X0, $o), 
130.02/130.29	               app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	               'const/sets/SUBSET'(X0), X1)))),
130.02/130.29	    inference('sup-', [status(thm)], ['15', '16'])).
130.02/130.29	tff('18', plain,
130.02/130.29	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : app_encode_fun(X0, $o)]:
130.02/130.29	      (app_encode_app(app_encode_fun(X0, $o), $o, 
130.02/130.29	         app_encode_app(app_encode_fun(X0, $o), 
130.02/130.29	           app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	           'const/sets/SUBSET'(X0), X2), 
130.02/130.29	         app_encode_app(app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	           app_encode_fun(X0, $o), 'const/sets/INTERS'(X0), 
130.02/130.29	           app_encode_app(app_encode_fun(X0, $o), 
130.02/130.29	             app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	             'const/sets/SUBSET'(X0), X1)))
130.02/130.29	       | ~ app_encode_app(X0, $o, X1, 
130.02/130.29	             sk_A21(X0, 
130.02/130.29	               app_encode_app(app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	                 app_encode_fun(X0, $o), 'const/sets/INTERS'(X0), 
130.02/130.29	                 app_encode_app(app_encode_fun(X0, $o), 
130.02/130.29	                   app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	                   'const/sets/SUBSET'(X0), X1)), X2))),
130.02/130.29	    inference('simplify', [status(thm)], ['17'])).
130.02/130.29	tff('19', plain,
130.02/130.29	    ![X0 : $tType, X1 : app_encode_fun(X0, $o)]:
130.02/130.29	      (~ $true
130.02/130.29	       | app_encode_app(app_encode_fun(X0, $o), $o, 
130.02/130.29	           app_encode_app(app_encode_fun(X0, $o), 
130.02/130.29	             app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	             'const/sets/SUBSET'(X0), X1), 
130.02/130.29	           app_encode_app(app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	             app_encode_fun(X0, $o), 'const/sets/INTERS'(X0), 
130.02/130.29	             app_encode_app(app_encode_fun(X0, $o), 
130.02/130.29	               app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	               'const/sets/SUBSET'(X0), X1)))
130.02/130.29	       | app_encode_app(app_encode_fun(X0, $o), $o, 
130.02/130.29	           app_encode_app(app_encode_fun(X0, $o), 
130.02/130.29	             app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	             'const/sets/SUBSET'(X0), X1), 
130.02/130.29	           app_encode_app(app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	             app_encode_fun(X0, $o), 'const/sets/INTERS'(X0), 
130.02/130.29	             app_encode_app(app_encode_fun(X0, $o), 
130.02/130.29	               app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	               'const/sets/SUBSET'(X0), X1)))),
130.02/130.29	    inference('sup-', [status(thm)], ['3', '18'])).
130.02/130.29	tff('20', plain,
130.02/130.29	    ![X0 : $tType, X1 : app_encode_fun(X0, $o)]:
130.02/130.29	      app_encode_app(app_encode_fun(X0, $o), $o, 
130.02/130.29	        app_encode_app(app_encode_fun(X0, $o), 
130.02/130.29	          app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	          'const/sets/SUBSET'(X0), X1), 
130.02/130.29	        app_encode_app(app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	          app_encode_fun(X0, $o), 'const/sets/INTERS'(X0), 
130.02/130.29	          app_encode_app(app_encode_fun(X0, $o), 
130.02/130.29	            app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	            'const/sets/SUBSET'(X0), X1))),
130.02/130.29	    inference('simplify', [status(thm)], ['19'])).
130.02/130.29	tff('21', plain,
130.02/130.29	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : app_encode_fun(X0, $o), 
130.02/130.29	      X3 : app_encode_fun(X0, $o)]:
130.02/130.29	      (~ $true
130.02/130.29	       | app_encode_app(app_encode_fun(X0, $o), $o, 
130.02/130.29	           app_encode_app(app_encode_fun(X0, $o), 
130.02/130.29	             app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	             'const/sets/SUBSET'(X0), X1), X2)
130.02/130.29	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
130.02/130.29	             app_encode_app(app_encode_fun(X0, $o), 
130.02/130.29	               app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	               'const/sets/SUBSET'(X0), X1), X3)
130.02/130.29	       | app_encode_app(app_encode_fun(X0, $o), $o, 
130.02/130.29	           app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	             'const/sets/IN'(X0), sk_A21(X0, X2, X1)), X3)),
130.02/130.29	    inference('sup-', [status(thm)], ['0', '8'])).
130.02/130.29	tff('22', plain,
130.02/130.29	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : app_encode_fun(X0, $o), 
130.02/130.29	      X3 : app_encode_fun(X0, $o)]:
130.02/130.29	      (app_encode_app(app_encode_fun(X0, $o), $o, 
130.02/130.29	         app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	           'const/sets/IN'(X0), sk_A21(X0, X2, X1)), X3)
130.02/130.29	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
130.02/130.29	             app_encode_app(app_encode_fun(X0, $o), 
130.02/130.29	               app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	               'const/sets/SUBSET'(X0), X1), X3)
130.02/130.29	       | app_encode_app(app_encode_fun(X0, $o), $o, 
130.02/130.29	           app_encode_app(app_encode_fun(X0, $o), 
130.02/130.29	             app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	             'const/sets/SUBSET'(X0), X1), X2)),
130.02/130.29	    inference('simplify', [status(thm)], ['21'])).
130.02/130.29	tff('23', plain,
130.02/130.29	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : app_encode_fun(X0, $o), 
130.02/130.29	      X3 : app_encode_fun(X0, $o)]:
130.02/130.29	      (~ $true
130.02/130.29	       | app_encode_app(app_encode_fun(X0, $o), $o, 
130.02/130.29	           app_encode_app(app_encode_fun(X0, $o), 
130.02/130.29	             app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	             'const/sets/SUBSET'(X0), X2), X3)
130.02/130.29	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
130.02/130.29	             app_encode_app(app_encode_fun(X0, $o), 
130.02/130.29	               app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	               'const/sets/SUBSET'(X0), X2), X1)
130.02/130.29	       | app_encode_app(X0, $o, X1, sk_A21(X0, X3, X2))),
130.02/130.29	    inference('sup-', [status(thm)], ['22', '1'])).
130.02/130.29	tff('24', plain,
130.02/130.29	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : app_encode_fun(X0, $o), 
130.02/130.29	      X3 : app_encode_fun(X0, $o)]:
130.02/130.29	      (app_encode_app(X0, $o, X1, sk_A21(X0, X3, X2))
130.02/130.29	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
130.02/130.29	             app_encode_app(app_encode_fun(X0, $o), 
130.02/130.29	               app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	               'const/sets/SUBSET'(X0), X2), X1)
130.02/130.29	       | app_encode_app(app_encode_fun(X0, $o), $o, 
130.02/130.29	           app_encode_app(app_encode_fun(X0, $o), 
130.02/130.29	             app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	             'const/sets/SUBSET'(X0), X2), X3)),
130.02/130.29	    inference('simplify', [status(thm)], ['23'])).
130.02/130.29	tff('25', plain,
130.02/130.29	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : app_encode_fun(X0, $o)]:
130.02/130.29	      (~ $true
130.02/130.29	       | app_encode_app(app_encode_fun(X0, $o), $o, 
130.02/130.29	           app_encode_app(app_encode_fun(X0, $o), 
130.02/130.29	             app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	             'const/sets/SUBSET'(X0), X1), X2)
130.02/130.29	       | app_encode_app(X0, $o, 
130.02/130.29	           app_encode_app(app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	             app_encode_fun(X0, $o), 'const/sets/INTERS'(X0), 
130.02/130.29	             app_encode_app(app_encode_fun(X0, $o), 
130.02/130.29	               app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	               'const/sets/SUBSET'(X0), X1)), sk_A21(X0, X2, X1))),
130.02/130.29	    inference('sup-', [status(thm)], ['20', '24'])).
130.02/130.29	tff('26', plain,
130.02/130.29	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : app_encode_fun(X0, $o)]:
130.02/130.29	      (app_encode_app(X0, $o, 
130.02/130.29	         app_encode_app(app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	           app_encode_fun(X0, $o), 'const/sets/INTERS'(X0), 
130.02/130.29	           app_encode_app(app_encode_fun(X0, $o), 
130.02/130.29	             app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	             'const/sets/SUBSET'(X0), X1)), sk_A21(X0, X2, X1))
130.02/130.29	       | app_encode_app(app_encode_fun(X0, $o), $o, 
130.02/130.29	           app_encode_app(app_encode_fun(X0, $o), 
130.02/130.29	             app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	             'const/sets/SUBSET'(X0), X1), X2)),
130.02/130.29	    inference('simplify', [status(thm)], ['25'])).
130.02/130.29	tff(zf_stmt_11, conjecture,
130.02/130.29	  (![A:$tType,A0:app_encode_fun(A,$o),
130.02/130.29	     A1:app_encode_fun(app_encode_fun(A,$o),$o)]:
130.02/130.29	     (app_encode_app(app_encode_fun(A,$o),$o,
130.02/130.29	                     app_encode_app(app_encode_fun(A,$o),
130.02/130.29	                                    app_encode_fun(app_encode_fun(A,$o),$o),
130.02/130.29	                                    'const/sets/SUBSET'(A),A0),
130.02/130.29	                     app_encode_app(app_encode_fun(app_encode_fun(A,$o),$o),
130.02/130.29	                                    app_encode_fun(A,$o),
130.02/130.29	                                    'const/sets/INTERS'(A),A1)) <=>
130.02/130.29	      (![A2:app_encode_fun(A,$o)]:
130.02/130.29	         (app_encode_app(app_encode_fun(app_encode_fun(A,$o),$o),$o,
130.02/130.29	                         app_encode_app(app_encode_fun(A,$o),
130.02/130.29	                                        app_encode_fun(app_encode_fun(
130.02/130.29	                                                       app_encode_fun(A,$o),
130.02/130.29	                                                       $o),$o),
130.02/130.29	                                        'const/sets/IN'(app_encode_fun(A,$o)),
130.02/130.29	                                        A2),
130.02/130.29	                         A1) =>
130.02/130.29	          app_encode_app(app_encode_fun(A,$o),$o,
130.02/130.29	                         app_encode_app(app_encode_fun(A,$o),
130.02/130.29	                                        app_encode_fun(app_encode_fun(A,$o),
130.02/130.29	                                                       $o),
130.02/130.29	                                        'const/sets/SUBSET'(A),A0),
130.02/130.29	                         A2)))))).
130.02/130.29	tff(zf_stmt_0, negated_conjecture,
130.02/130.29	  (~
130.02/130.29	    (![A:$tType,A0:app_encode_fun(A,$o),
130.02/130.29	       A1:app_encode_fun(app_encode_fun(A,$o),$o)]:
130.02/130.29	       (app_encode_app(app_encode_fun(A,$o),$o,
130.02/130.29	                       app_encode_app(app_encode_fun(A,$o),
130.02/130.29	                                      app_encode_fun(app_encode_fun(A,$o),$o),
130.02/130.29	                                      'const/sets/SUBSET'(A),A0),
130.02/130.29	                       app_encode_app(app_encode_fun(app_encode_fun(A,$o),$o),
130.02/130.29	                                      app_encode_fun(A,$o),
130.02/130.29	                                      'const/sets/INTERS'(A),A1)) <=>
130.02/130.29	        (![A2:app_encode_fun(A,$o)]:
130.02/130.29	           (app_encode_app(app_encode_fun(app_encode_fun(A,$o),$o),$o,
130.02/130.29	                           app_encode_app(app_encode_fun(A,$o),
130.02/130.29	                                          app_encode_fun(app_encode_fun(
130.02/130.29	                                                         app_encode_fun(A,$o),
130.02/130.29	                                                         $o),$o),
130.02/130.29	                                          'const/sets/IN'(app_encode_fun(
130.02/130.29	                                                          A,$o)),
130.02/130.29	                                          A2),
130.02/130.29	                           A1) =>
130.02/130.29	            app_encode_app(app_encode_fun(A,$o),$o,
130.02/130.29	                           app_encode_app(app_encode_fun(A,$o),
130.02/130.29	                                          app_encode_fun(app_encode_fun(A,$o),
130.02/130.29	                                                         $o),
130.02/130.29	                                          'const/sets/SUBSET'(A),A0),
130.02/130.29	                           A2))))))).
130.02/130.29	tff('27', plain,
130.02/130.29	    ![X20 : app_encode_fun(sk_A, $o)]:
130.02/130.29	      (~ app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), $o, 
130.02/130.29	           app_encode_app(app_encode_fun(sk_A, $o), 
130.02/130.29	             app_encode_fun(app_encode_fun(app_encode_fun(sk_A, $o), $o), $o), 
130.02/130.29	             'const/sets/IN'(app_encode_fun(sk_A, $o)), X20), sk_A1)
130.02/130.29	       | app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	           app_encode_app(app_encode_fun(sk_A, $o), 
130.02/130.29	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	             'const/sets/SUBSET'(sk_A), sk_A0), X20)
130.02/130.29	       | app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	           app_encode_app(app_encode_fun(sk_A, $o), 
130.02/130.29	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	             'const/sets/SUBSET'(sk_A), sk_A0), 
130.02/130.29	           app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	             app_encode_fun(sk_A, $o), 'const/sets/INTERS'(sk_A), sk_A1))),
130.02/130.29	    inference('cnf', [status(esa)], [zf_stmt_0])).
130.02/130.29	tff('28', plain,
130.02/130.29	    ![X0 : sk_A]:
130.02/130.29	      (~ $true
130.02/130.29	       | app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	           app_encode_app(sk_A, 
130.02/130.29	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	             'const/sets/IN'(sk_A), X0), 
130.02/130.29	           app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	             app_encode_fun(sk_A, $o), 'const/sets/INTERS'(sk_A), sk_A1))
130.02/130.29	       | app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	           app_encode_app(app_encode_fun(sk_A, $o), 
130.02/130.29	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	             'const/sets/SUBSET'(sk_A), sk_A0), 
130.02/130.29	           app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	             app_encode_fun(sk_A, $o), 'const/sets/INTERS'(sk_A), sk_A1))
130.02/130.29	       | app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	           app_encode_app(app_encode_fun(sk_A, $o), 
130.02/130.29	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	             'const/sets/SUBSET'(sk_A), sk_A0), sk_A2(sk_A, X0, sk_A1))),
130.02/130.29	    inference('sup-', [status(thm)], ['4', '27'])).
130.02/130.29	tff('29', plain,
130.02/130.29	    ![X0 : sk_A]:
130.02/130.29	      (app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	         app_encode_app(app_encode_fun(sk_A, $o), 
130.02/130.29	           app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	           'const/sets/SUBSET'(sk_A), sk_A0), sk_A2(sk_A, X0, sk_A1))
130.02/130.29	       | app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	           app_encode_app(app_encode_fun(sk_A, $o), 
130.02/130.29	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	             'const/sets/SUBSET'(sk_A), sk_A0), 
130.02/130.29	           app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	             app_encode_fun(sk_A, $o), 'const/sets/INTERS'(sk_A), sk_A1))
130.02/130.29	       | app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	           app_encode_app(sk_A, 
130.02/130.29	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	             'const/sets/IN'(sk_A), X0), 
130.02/130.29	           app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	             app_encode_fun(sk_A, $o), 'const/sets/INTERS'(sk_A), sk_A1))),
130.02/130.29	    inference('simplify', [status(thm)], ['28'])).
130.02/130.29	tff('30', plain,
130.02/130.29	    ![X0 : sk_A, X1 : sk_A]:
130.02/130.29	      (~ $true
130.02/130.29	       | app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	           app_encode_app(sk_A, 
130.02/130.29	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	             'const/sets/IN'(sk_A), X0), 
130.02/130.29	           app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	             app_encode_fun(sk_A, $o), 'const/sets/INTERS'(sk_A), sk_A1))
130.02/130.29	       | app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	           app_encode_app(app_encode_fun(sk_A, $o), 
130.02/130.29	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	             'const/sets/SUBSET'(sk_A), sk_A0), 
130.02/130.29	           app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	             app_encode_fun(sk_A, $o), 'const/sets/INTERS'(sk_A), sk_A1))
130.02/130.29	       | ~ app_encode_app(sk_A, $o, sk_A0, X1)
130.02/130.29	       | app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	           app_encode_app(sk_A, 
130.02/130.29	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	             'const/sets/IN'(sk_A), X1), sk_A2(sk_A, X0, sk_A1))),
130.02/130.29	    inference('sup-', [status(thm)], ['29', '10'])).
130.02/130.29	tff('31', plain,
130.02/130.29	    ![X0 : sk_A, X1 : sk_A]:
130.02/130.29	      (app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	         app_encode_app(sk_A, app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	           'const/sets/IN'(sk_A), X1), sk_A2(sk_A, X0, sk_A1))
130.02/130.29	       | ~ app_encode_app(sk_A, $o, sk_A0, X1)
130.02/130.29	       | app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	           app_encode_app(app_encode_fun(sk_A, $o), 
130.02/130.29	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	             'const/sets/SUBSET'(sk_A), sk_A0), 
130.02/130.29	           app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	             app_encode_fun(sk_A, $o), 'const/sets/INTERS'(sk_A), sk_A1))
130.02/130.29	       | app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	           app_encode_app(sk_A, 
130.02/130.29	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	             'const/sets/IN'(sk_A), X0), 
130.02/130.29	           app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	             app_encode_fun(sk_A, $o), 'const/sets/INTERS'(sk_A), sk_A1))),
130.02/130.29	    inference('simplify', [status(thm)], ['30'])).
130.02/130.29	tff('32', plain,
130.02/130.29	    ![X0 : sk_A]:
130.02/130.29	      (~ $true
130.02/130.29	       | app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	           app_encode_app(sk_A, 
130.02/130.29	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	             'const/sets/IN'(sk_A), X0), 
130.02/130.29	           app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	             app_encode_fun(sk_A, $o), 'const/sets/INTERS'(sk_A), sk_A1))
130.02/130.29	       | app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	           app_encode_app(app_encode_fun(sk_A, $o), 
130.02/130.29	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	             'const/sets/SUBSET'(sk_A), sk_A0), 
130.02/130.29	           app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	             app_encode_fun(sk_A, $o), 'const/sets/INTERS'(sk_A), sk_A1))
130.02/130.29	       | ~ app_encode_app(sk_A, $o, sk_A0, X0)
130.02/130.29	       | app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	           app_encode_app(sk_A, 
130.02/130.29	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	             'const/sets/IN'(sk_A), X0), 
130.02/130.29	           app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	             app_encode_fun(sk_A, $o), 'const/sets/INTERS'(sk_A), sk_A1))),
130.02/130.29	    inference('sup-', [status(thm)], ['31', '13'])).
130.02/130.29	tff('33', plain,
130.02/130.29	    ![X0 : sk_A]:
130.02/130.29	      (~ app_encode_app(sk_A, $o, sk_A0, X0)
130.02/130.29	       | app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	           app_encode_app(app_encode_fun(sk_A, $o), 
130.02/130.29	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	             'const/sets/SUBSET'(sk_A), sk_A0), 
130.02/130.29	           app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	             app_encode_fun(sk_A, $o), 'const/sets/INTERS'(sk_A), sk_A1))
130.02/130.29	       | app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	           app_encode_app(sk_A, 
130.02/130.29	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	             'const/sets/IN'(sk_A), X0), 
130.02/130.29	           app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	             app_encode_fun(sk_A, $o), 'const/sets/INTERS'(sk_A), sk_A1))),
130.02/130.29	    inference('simplify', [status(thm)], ['32'])).
130.02/130.29	tff('34', plain,
130.02/130.29	    ![X0 : sk_A]:
130.02/130.29	      (app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	         app_encode_app(sk_A, app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	           'const/sets/IN'(sk_A), X0), 
130.02/130.29	         app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	           app_encode_fun(sk_A, $o), 'const/sets/INTERS'(sk_A), sk_A1))
130.02/130.29	       | ~ app_encode_app(sk_A, $o, sk_A0, X0)),
130.02/130.29	    inference('clc', [status(thm)], ['33', '10'])).
130.02/130.29	tff('35', plain,
130.02/130.29	    ![X0 : app_encode_fun(sk_A, $o)]:
130.02/130.29	      (~ $true
130.02/130.29	       | ~ app_encode_app(sk_A, $o, sk_A0, 
130.02/130.29	             sk_A21(sk_A, 
130.02/130.29	               app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	                 app_encode_fun(sk_A, $o), 'const/sets/INTERS'(sk_A), sk_A1), 
130.02/130.29	               X0))
130.02/130.29	       | app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	           app_encode_app(app_encode_fun(sk_A, $o), 
130.02/130.29	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	             'const/sets/SUBSET'(sk_A), X0), 
130.02/130.29	           app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	             app_encode_fun(sk_A, $o), 'const/sets/INTERS'(sk_A), sk_A1))),
130.02/130.29	    inference('sup-', [status(thm)], ['34', '16'])).
130.02/130.29	tff('36', plain,
130.02/130.29	    ![X0 : app_encode_fun(sk_A, $o)]:
130.02/130.29	      (app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	         app_encode_app(app_encode_fun(sk_A, $o), 
130.02/130.29	           app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	           'const/sets/SUBSET'(sk_A), X0), 
130.02/130.29	         app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	           app_encode_fun(sk_A, $o), 'const/sets/INTERS'(sk_A), sk_A1))
130.02/130.29	       | ~ app_encode_app(sk_A, $o, sk_A0, 
130.02/130.29	             sk_A21(sk_A, 
130.02/130.29	               app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	                 app_encode_fun(sk_A, $o), 'const/sets/INTERS'(sk_A), sk_A1), 
130.02/130.29	               X0))),
130.02/130.29	    inference('simplify', [status(thm)], ['35'])).
130.02/130.29	tff('37', plain,
130.02/130.29	    (~ $true
130.02/130.29	     | app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	         app_encode_app(app_encode_fun(sk_A, $o), 
130.02/130.29	           app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	           'const/sets/SUBSET'(sk_A), sk_A0), 
130.02/130.29	         app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	           app_encode_fun(sk_A, $o), 'const/sets/INTERS'(sk_A), sk_A1))
130.02/130.29	     | app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	         app_encode_app(app_encode_fun(sk_A, $o), 
130.02/130.29	           app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	           'const/sets/SUBSET'(sk_A), sk_A0), 
130.02/130.29	         app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	           app_encode_fun(sk_A, $o), 'const/sets/INTERS'(sk_A), sk_A1))),
130.02/130.29	    inference('sup-', [status(thm)], ['3', '36'])).
130.02/130.29	tff('38', plain,
130.02/130.29	    app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	      app_encode_app(app_encode_fun(sk_A, $o), 
130.02/130.29	        app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	        'const/sets/SUBSET'(sk_A), sk_A0), 
130.02/130.29	      app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	        app_encode_fun(sk_A, $o), 'const/sets/INTERS'(sk_A), sk_A1)),
130.02/130.29	    inference('simplify', [status(thm)], ['37'])).
130.02/130.29	tff('39', plain,
130.02/130.29	    ![X10 : $tType, X11 : app_encode_fun(X10, $o), 
130.02/130.29	      X12 : app_encode_fun(app_encode_fun(X10, $o), $o), X13 : X10]:
130.02/130.29	      (~ app_encode_app(app_encode_fun(app_encode_fun(X10, $o), $o), $o, 
130.02/130.29	           app_encode_app(app_encode_fun(X10, $o), 
130.02/130.29	             app_encode_fun(app_encode_fun(app_encode_fun(X10, $o), $o), $o), 
130.02/130.29	             'const/sets/IN'(app_encode_fun(X10, $o)), X11), X12)
130.02/130.29	       | app_encode_app(app_encode_fun(X10, $o), $o, 
130.02/130.29	           app_encode_app(X10, app_encode_fun(app_encode_fun(X10, $o), $o), 
130.02/130.29	             'const/sets/IN'(X10), X13), X11)
130.02/130.29	       | ~ app_encode_app(app_encode_fun(X10, $o), $o, 
130.02/130.29	             app_encode_app(X10, 
130.02/130.29	               app_encode_fun(app_encode_fun(X10, $o), $o), 
130.02/130.29	               'const/sets/IN'(X10), X13), 
130.02/130.29	             app_encode_app(app_encode_fun(app_encode_fun(X10, $o), $o), 
130.02/130.29	               app_encode_fun(X10, $o), 'const/sets/INTERS'(X10), X12))),
130.02/130.29	    inference('cnf', [status(esa)], [zf_stmt_9])).
130.02/130.29	tff('40', plain,
130.02/130.29	    ![X0 : $tType, X1 : app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	      X2 : app_encode_fun(X0, $o), X3 : X0]:
130.02/130.29	      (~ $true
130.02/130.29	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, X1, X2)
130.02/130.29	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
130.02/130.29	             app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	               'const/sets/IN'(X0), X3), 
130.02/130.29	             app_encode_app(app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	               app_encode_fun(X0, $o), 'const/sets/INTERS'(X0), X1))
130.02/130.29	       | app_encode_app(app_encode_fun(X0, $o), $o, 
130.02/130.29	           app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	             'const/sets/IN'(X0), X3), X2)),
130.02/130.29	    inference('sup-', [status(thm)], ['7', '39'])).
130.02/130.29	tff('41', plain,
130.02/130.29	    ![X0 : $tType, X1 : app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	      X2 : app_encode_fun(X0, $o), X3 : X0]:
130.02/130.29	      (app_encode_app(app_encode_fun(X0, $o), $o, 
130.02/130.29	         app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	           'const/sets/IN'(X0), X3), X2)
130.02/130.29	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
130.02/130.29	             app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	               'const/sets/IN'(X0), X3), 
130.02/130.29	             app_encode_app(app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	               app_encode_fun(X0, $o), 'const/sets/INTERS'(X0), X1))
130.02/130.29	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, X1, X2)),
130.02/130.29	    inference('simplify', [status(thm)], ['40'])).
130.02/130.29	tff('42', plain,
130.02/130.29	    ![X0 : $tType, X1 : app_encode_fun(app_encode_fun(X0, $o), $o), X2 : X0, 
130.02/130.29	      X3 : app_encode_fun(X0, $o)]:
130.02/130.29	      (~ $true
130.02/130.29	       | ~ app_encode_app(X0, $o, 
130.02/130.29	             app_encode_app(app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	               app_encode_fun(X0, $o), 'const/sets/INTERS'(X0), X1), X2)
130.02/130.29	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, X1, X3)
130.02/130.29	       | app_encode_app(app_encode_fun(X0, $o), $o, 
130.02/130.29	           app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	             'const/sets/IN'(X0), X2), X3)),
130.02/130.29	    inference('sup-', [status(thm)], ['7', '41'])).
130.02/130.29	tff('43', plain,
130.02/130.29	    ![X0 : $tType, X1 : app_encode_fun(app_encode_fun(X0, $o), $o), X2 : X0, 
130.02/130.29	      X3 : app_encode_fun(X0, $o)]:
130.02/130.29	      (app_encode_app(app_encode_fun(X0, $o), $o, 
130.02/130.29	         app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	           'const/sets/IN'(X0), X2), X3)
130.02/130.29	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, X1, X3)
130.02/130.29	       | ~ app_encode_app(X0, $o, 
130.02/130.29	             app_encode_app(app_encode_fun(app_encode_fun(X0, $o), $o), 
130.02/130.29	               app_encode_fun(X0, $o), 'const/sets/INTERS'(X0), X1), X2)),
130.02/130.29	    inference('simplify', [status(thm)], ['42'])).
130.02/130.29	tff('44', plain,
130.02/130.29	    ![X0 : sk_A]:
130.02/130.29	      (~ $true
130.02/130.29	       | ~ app_encode_app(sk_A, $o, 
130.02/130.29	             app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	               app_encode_fun(sk_A, $o), 'const/sets/INTERS'(sk_A), 
130.02/130.29	               app_encode_app(app_encode_fun(sk_A, $o), 
130.02/130.29	                 app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	                 'const/sets/SUBSET'(sk_A), sk_A0)), X0)
130.02/130.29	       | app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	           app_encode_app(sk_A, 
130.02/130.29	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	             'const/sets/IN'(sk_A), X0), 
130.02/130.29	           app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	             app_encode_fun(sk_A, $o), 'const/sets/INTERS'(sk_A), sk_A1))),
130.02/130.29	    inference('sup-', [status(thm)], ['38', '43'])).
130.02/130.29	tff('45', plain,
130.02/130.29	    ![X0 : sk_A]:
130.02/130.29	      (app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	         app_encode_app(sk_A, app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	           'const/sets/IN'(sk_A), X0), 
130.02/130.29	         app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	           app_encode_fun(sk_A, $o), 'const/sets/INTERS'(sk_A), sk_A1))
130.02/130.29	       | ~ app_encode_app(sk_A, $o, 
130.02/130.29	             app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	               app_encode_fun(sk_A, $o), 'const/sets/INTERS'(sk_A), 
130.02/130.29	               app_encode_app(app_encode_fun(sk_A, $o), 
130.02/130.29	                 app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	                 'const/sets/SUBSET'(sk_A), sk_A0)), X0)),
130.02/130.29	    inference('simplify', [status(thm)], ['44'])).
130.02/130.29	tff('46', plain,
130.02/130.29	    (app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), $o, 
130.02/130.29	       app_encode_app(app_encode_fun(sk_A, $o), 
130.02/130.29	         app_encode_fun(app_encode_fun(app_encode_fun(sk_A, $o), $o), $o), 
130.02/130.29	         'const/sets/IN'(app_encode_fun(sk_A, $o)), sk_A22), sk_A1)
130.02/130.29	     | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	           app_encode_app(app_encode_fun(sk_A, $o), 
130.02/130.29	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	             'const/sets/SUBSET'(sk_A), sk_A0), 
130.02/130.29	           app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	             app_encode_fun(sk_A, $o), 'const/sets/INTERS'(sk_A), sk_A1))),
130.02/130.29	    inference('cnf', [status(esa)], [zf_stmt_0])).
130.02/130.29	tff('47', plain,
130.02/130.29	    ![X0 : sk_A]:
130.02/130.29	      (~ $true
130.02/130.29	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	             app_encode_app(app_encode_fun(sk_A, $o), 
130.02/130.29	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	               'const/sets/SUBSET'(sk_A), sk_A0), 
130.02/130.29	             app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	               app_encode_fun(sk_A, $o), 'const/sets/INTERS'(sk_A), sk_A1))
130.02/130.29	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	             app_encode_app(sk_A, 
130.02/130.29	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	               'const/sets/IN'(sk_A), X0), 
130.02/130.29	             app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	               app_encode_fun(sk_A, $o), 'const/sets/INTERS'(sk_A), sk_A1))
130.02/130.29	       | app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	           app_encode_app(sk_A, 
130.02/130.29	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	             'const/sets/IN'(sk_A), X0), sk_A22)),
130.02/130.29	    inference('sup-', [status(thm)], ['46', '39'])).
130.02/130.29	tff('48', plain,
130.02/130.29	    ![X0 : sk_A]:
130.02/130.29	      (app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	         app_encode_app(sk_A, app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	           'const/sets/IN'(sk_A), X0), sk_A22)
130.02/130.29	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	             app_encode_app(sk_A, 
130.02/130.29	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	               'const/sets/IN'(sk_A), X0), 
130.02/130.29	             app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	               app_encode_fun(sk_A, $o), 'const/sets/INTERS'(sk_A), sk_A1))
130.02/130.29	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	             app_encode_app(app_encode_fun(sk_A, $o), 
130.02/130.29	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	               'const/sets/SUBSET'(sk_A), sk_A0), 
130.02/130.29	             app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	               app_encode_fun(sk_A, $o), 'const/sets/INTERS'(sk_A), sk_A1))),
130.02/130.29	    inference('simplify', [status(thm)], ['47'])).
130.02/130.29	tff('49', plain,
130.02/130.29	    ![X0 : app_encode_fun(sk_A, $o)]:
130.02/130.29	      (~ $true
130.02/130.29	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	             app_encode_app(app_encode_fun(sk_A, $o), 
130.02/130.29	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	               'const/sets/SUBSET'(sk_A), sk_A0), 
130.02/130.29	             app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	               app_encode_fun(sk_A, $o), 'const/sets/INTERS'(sk_A), sk_A1))
130.02/130.29	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	             app_encode_app(sk_A, 
130.02/130.29	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	               'const/sets/IN'(sk_A), sk_A21(sk_A, sk_A22, X0)), 
130.02/130.29	             app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	               app_encode_fun(sk_A, $o), 'const/sets/INTERS'(sk_A), sk_A1))
130.02/130.29	       | app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	           app_encode_app(app_encode_fun(sk_A, $o), 
130.02/130.29	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	             'const/sets/SUBSET'(sk_A), X0), sk_A22)),
130.02/130.29	    inference('sup-', [status(thm)], ['48', '16'])).
130.02/130.29	tff('50', plain,
130.02/130.29	    ![X0 : app_encode_fun(sk_A, $o)]:
130.02/130.29	      (app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	         app_encode_app(app_encode_fun(sk_A, $o), 
130.02/130.29	           app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	           'const/sets/SUBSET'(sk_A), X0), sk_A22)
130.02/130.29	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	             app_encode_app(sk_A, 
130.02/130.29	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	               'const/sets/IN'(sk_A), sk_A21(sk_A, sk_A22, X0)), 
130.02/130.29	             app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	               app_encode_fun(sk_A, $o), 'const/sets/INTERS'(sk_A), sk_A1))
130.02/130.29	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	             app_encode_app(app_encode_fun(sk_A, $o), 
130.02/130.29	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	               'const/sets/SUBSET'(sk_A), sk_A0), 
130.02/130.29	             app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	               app_encode_fun(sk_A, $o), 'const/sets/INTERS'(sk_A), sk_A1))),
130.02/130.29	    inference('simplify', [status(thm)], ['49'])).
130.02/130.29	tff('51', plain,
130.02/130.29	    ![X0 : app_encode_fun(sk_A, $o)]:
130.02/130.29	      (~ $true
130.02/130.29	       | ~ app_encode_app(sk_A, $o, 
130.02/130.29	             app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	               app_encode_fun(sk_A, $o), 'const/sets/INTERS'(sk_A), 
130.02/130.29	               app_encode_app(app_encode_fun(sk_A, $o), 
130.02/130.29	                 app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	                 'const/sets/SUBSET'(sk_A), sk_A0)), 
130.02/130.29	             sk_A21(sk_A, sk_A22, X0))
130.02/130.29	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	             app_encode_app(app_encode_fun(sk_A, $o), 
130.02/130.29	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	               'const/sets/SUBSET'(sk_A), sk_A0), 
130.02/130.29	             app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	               app_encode_fun(sk_A, $o), 'const/sets/INTERS'(sk_A), sk_A1))
130.02/130.29	       | app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	           app_encode_app(app_encode_fun(sk_A, $o), 
130.02/130.29	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	             'const/sets/SUBSET'(sk_A), X0), sk_A22)),
130.02/130.29	    inference('sup-', [status(thm)], ['45', '50'])).
130.02/130.29	tff('52', plain,
130.02/130.29	    ![X0 : app_encode_fun(sk_A, $o)]:
130.02/130.29	      (~ $true
130.02/130.29	       | ~ app_encode_app(sk_A, $o, 
130.02/130.29	             app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	               app_encode_fun(sk_A, $o), 'const/sets/INTERS'(sk_A), 
130.02/130.29	               app_encode_app(app_encode_fun(sk_A, $o), 
130.02/130.29	                 app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	                 'const/sets/SUBSET'(sk_A), sk_A0)), 
130.02/130.29	             sk_A21(sk_A, sk_A22, X0))
130.02/130.29	       | ~ $true
130.02/130.29	       | app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	           app_encode_app(app_encode_fun(sk_A, $o), 
130.02/130.29	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	             'const/sets/SUBSET'(sk_A), X0), sk_A22)),
130.02/130.29	    inference('demod', [status(thm)], ['51', '38'])).
130.02/130.29	tff('53', plain,
130.02/130.29	    ![X0 : app_encode_fun(sk_A, $o)]:
130.02/130.29	      (app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	         app_encode_app(app_encode_fun(sk_A, $o), 
130.02/130.29	           app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	           'const/sets/SUBSET'(sk_A), X0), sk_A22)
130.02/130.29	       | ~ app_encode_app(sk_A, $o, 
130.02/130.29	             app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	               app_encode_fun(sk_A, $o), 'const/sets/INTERS'(sk_A), 
130.02/130.29	               app_encode_app(app_encode_fun(sk_A, $o), 
130.02/130.29	                 app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	                 'const/sets/SUBSET'(sk_A), sk_A0)), 
130.02/130.29	             sk_A21(sk_A, sk_A22, X0))),
130.02/130.29	    inference('simplify', [status(thm)], ['52'])).
130.02/130.29	tff('54', plain,
130.02/130.29	    (~ $true
130.02/130.29	     | app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	         app_encode_app(app_encode_fun(sk_A, $o), 
130.02/130.29	           app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	           'const/sets/SUBSET'(sk_A), sk_A0), sk_A22)
130.02/130.29	     | app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	         app_encode_app(app_encode_fun(sk_A, $o), 
130.02/130.29	           app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	           'const/sets/SUBSET'(sk_A), sk_A0), sk_A22)),
130.02/130.29	    inference('sup-', [status(thm)], ['26', '53'])).
130.02/130.29	tff('55', plain,
130.02/130.29	    app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	      app_encode_app(app_encode_fun(sk_A, $o), 
130.02/130.29	        app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	        'const/sets/SUBSET'(sk_A), sk_A0), sk_A22),
130.02/130.29	    inference('simplify', [status(thm)], ['54'])).
130.02/130.29	tff('56', plain,
130.02/130.29	    (~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	         app_encode_app(app_encode_fun(sk_A, $o), 
130.02/130.29	           app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	           'const/sets/SUBSET'(sk_A), sk_A0), sk_A22)
130.02/130.29	     | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	           app_encode_app(app_encode_fun(sk_A, $o), 
130.02/130.29	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	             'const/sets/SUBSET'(sk_A), sk_A0), 
130.02/130.29	           app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	             app_encode_fun(sk_A, $o), 'const/sets/INTERS'(sk_A), sk_A1))),
130.02/130.29	    inference('cnf', [status(esa)], [zf_stmt_0])).
130.02/130.29	tff('57', plain,
130.02/130.29	    (~ $true
130.02/130.29	     | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
130.02/130.29	           app_encode_app(app_encode_fun(sk_A, $o), 
130.02/130.29	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	             'const/sets/SUBSET'(sk_A), sk_A0), 
130.02/130.29	           app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
130.02/130.29	             app_encode_fun(sk_A, $o), 'const/sets/INTERS'(sk_A), sk_A1))),
130.02/130.29	    inference('sup-', [status(thm)], ['55', '56'])).
130.02/130.29	tff('58', plain, (~ $true | ~ $true),
130.02/130.29	    inference('demod', [status(thm)], ['57', '38'])).
130.02/130.29	tff('59', plain, $false, inference('simplify', [status(thm)], ['58'])).
130.02/130.29	
130.02/130.29	% SZS output end Refutation
130.02/130.29	EOF
