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    : 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 $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n030.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 18:32:54 CST 2018
0.71/0.88	% done 273 iterations in 0.680s
0.71/0.88	% SZS status Theorem for 'stdin'
0.71/0.88	% SZS output start Refutation
0.71/0.88	tff(zf_stmt_6, axiom,
0.71/0.88	  (![A:$tType,A0:app_encode_fun(A,$o),A1:app_encode_fun(A,$o)]:
0.71/0.88	     ((A0 = A1) <=>
0.71/0.88	      (![A2:A]:
0.71/0.88	         (app_encode_app(app_encode_fun(A,$o),$o,
0.71/0.88	                         app_encode_app(A,
0.71/0.88	                                        app_encode_fun(app_encode_fun(A,$o),
0.71/0.88	                                                       $o),
0.71/0.88	                                        'const/sets/IN'(A),A2),
0.71/0.88	                         A0) <=>
0.71/0.88	          app_encode_app(app_encode_fun(A,$o),$o,
0.71/0.88	                         app_encode_app(A,
0.71/0.88	                                        app_encode_fun(app_encode_fun(A,$o),
0.71/0.88	                                                       $o),
0.71/0.88	                                        'const/sets/IN'(A),A2),
0.71/0.88	                         A1)))))).
0.71/0.88	tff('0', plain,
0.71/0.88	    ![X11 : $tType, X14 : app_encode_fun(X11, $o), 
0.71/0.88	      X16 : app_encode_fun(X11, $o)]:
0.71/0.88	      (X14 = X16
0.71/0.88	       | app_encode_app(app_encode_fun(X11, $o), $o, 
0.71/0.88	           app_encode_app(X11, app_encode_fun(app_encode_fun(X11, $o), $o), 
0.71/0.88	             'const/sets/IN'(X11), sk_A2(X11, X16, X14)), X16)
0.71/0.88	       | app_encode_app(app_encode_fun(X11, $o), $o, 
0.71/0.88	           app_encode_app(X11, app_encode_fun(app_encode_fun(X11, $o), $o), 
0.71/0.88	             'const/sets/IN'(X11), sk_A2(X11, X16, X14)), X14)),
0.71/0.88	    inference('cnf', [status(esa)], [zf_stmt_6])).
0.71/0.88	tff(zf_stmt_4, axiom,
0.71/0.88	  (![A:$tType,P:app_encode_fun(A,$o),A0:A]:
0.71/0.88	     (app_encode_app(app_encode_fun(A,$o),$o,
0.71/0.88	                     app_encode_app(A,
0.71/0.88	                                    app_encode_fun(app_encode_fun(A,$o),$o),
0.71/0.88	                                    'const/sets/IN'(A),A0),
0.71/0.88	                     P) <=>
0.71/0.88	      app_encode_app(A,$o,P,A0)))).
0.71/0.88	tff('1', plain,
0.71/0.88	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : X0]:
0.71/0.88	      (app_encode_app(X0, $o, X1, X2)
0.71/0.88	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
0.71/0.88	             app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
0.71/0.88	               'const/sets/IN'(X0), X2), X1)),
0.71/0.88	    inference('cnf', [status(esa)], [zf_stmt_4])).
0.71/0.88	tff('2', plain,
0.71/0.88	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : app_encode_fun(X0, $o)]:
0.71/0.88	      (~ $true
0.71/0.88	       | app_encode_app(app_encode_fun(X0, $o), $o, 
0.71/0.88	           app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
0.71/0.88	             'const/sets/IN'(X0), sk_A2(X0, X2, X1)), X2)
0.71/0.88	       | X1 = X2
0.71/0.88	       | app_encode_app(X0, $o, X1, sk_A2(X0, X2, X1))),
0.71/0.88	    inference('sup-', [status(thm)], ['0', '1'])).
0.71/0.88	tff('3', plain,
0.71/0.88	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : app_encode_fun(X0, $o)]:
0.71/0.88	      (app_encode_app(X0, $o, X1, sk_A2(X0, X2, X1))
0.71/0.88	       | X1 = X2
0.71/0.88	       | app_encode_app(app_encode_fun(X0, $o), $o, 
0.71/0.88	           app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
0.71/0.88	             'const/sets/IN'(X0), sk_A2(X0, X2, X1)), X2)),
0.71/0.88	    inference('simplify', [status(thm)], ['2'])).
0.71/0.88	tff(zf_stmt_7, conjecture,
0.71/0.88	  (![A:$tType,A0:$tType,A1:app_encode_fun(A,A0),A2:app_encode_fun(A,$o),
0.71/0.88	     A3:app_encode_fun(A0,$o)]:
0.71/0.88	     (((![A4:A0]:
0.71/0.88	          (app_encode_app(app_encode_fun(A0,$o),$o,
0.71/0.88	                          app_encode_app(A0,
0.71/0.88	                                         app_encode_fun(app_encode_fun(A0,$o),
0.71/0.88	                                                        $o),
0.71/0.88	                                         'const/sets/IN'(A0),A4),
0.71/0.88	                          A3) =>
0.71/0.88	           (?[A5:A]: (app_encode_app(A,A0,A1,A5) = A4)))) & 
0.71/0.88	       (![A4:A]:
0.71/0.88	          (app_encode_app(app_encode_fun(A0,$o),$o,
0.71/0.88	                          app_encode_app(A0,
0.71/0.88	                                         app_encode_fun(app_encode_fun(A0,$o),
0.71/0.88	                                                        $o),
0.71/0.88	                                         'const/sets/IN'(A0),
0.71/0.88	                                         app_encode_app(A,A0,A1,A4)),
0.71/0.88	                          A3) <=>
0.71/0.88	           app_encode_app(app_encode_fun(A,$o),$o,
0.71/0.88	                          app_encode_app(A,
0.71/0.88	                                         app_encode_fun(app_encode_fun(A,$o),
0.71/0.88	                                                        $o),
0.71/0.88	                                         'const/sets/IN'(A),A4),
0.71/0.88	                          A2)))) =>
0.71/0.88	      (app_encode_app(app_encode_fun(A,$o),app_encode_fun(A0,$o),
0.71/0.88	                      app_encode_app(app_encode_fun(A,A0),
0.71/0.88	                                     app_encode_fun(app_encode_fun(A,$o),
0.71/0.88	                                                    app_encode_fun(A0,$o)),
0.71/0.88	                                     'const/sets/IMAGE'(A,A0),A1),
0.71/0.88	                      A2) =
0.71/0.88	       A3)))).
0.71/0.88	tff(zf_stmt_0, negated_conjecture,
0.71/0.88	  (~
0.71/0.88	    (![A:$tType,A0:$tType,A1:app_encode_fun(A,A0),A2:app_encode_fun(A,$o),
0.71/0.88	       A3:app_encode_fun(A0,$o)]:
0.71/0.88	       (((![A4:A0]:
0.71/0.88	            (app_encode_app(app_encode_fun(A0,$o),$o,
0.71/0.88	                            app_encode_app(A0,
0.71/0.88	                                           app_encode_fun(app_encode_fun(
0.71/0.88	                                                          A0,$o),$o),
0.71/0.88	                                           'const/sets/IN'(A0),A4),
0.71/0.88	                            A3) =>
0.71/0.88	             (?[A5:A]: (app_encode_app(A,A0,A1,A5) = A4)))) & 
0.71/0.88	         (![A4:A]:
0.71/0.88	            (app_encode_app(app_encode_fun(A0,$o),$o,
0.71/0.88	                            app_encode_app(A0,
0.71/0.88	                                           app_encode_fun(app_encode_fun(
0.71/0.88	                                                          A0,$o),$o),
0.71/0.88	                                           'const/sets/IN'(A0),
0.71/0.88	                                           app_encode_app(A,A0,A1,A4)),
0.71/0.88	                            A3) <=>
0.71/0.88	             app_encode_app(app_encode_fun(A,$o),$o,
0.71/0.88	                            app_encode_app(A,
0.71/0.88	                                           app_encode_fun(app_encode_fun(
0.71/0.88	                                                          A,$o),$o),
0.71/0.88	                                           'const/sets/IN'(A),A4),
0.71/0.88	                            A2)))) =>
0.71/0.88	        (app_encode_app(app_encode_fun(A,$o),app_encode_fun(A0,$o),
0.71/0.88	                        app_encode_app(app_encode_fun(A,A0),
0.71/0.88	                                       app_encode_fun(app_encode_fun(A,$o),
0.71/0.88	                                                      app_encode_fun(A0,$o)),
0.71/0.88	                                       'const/sets/IMAGE'(A,A0),A1),
0.71/0.88	                        A2) =
0.71/0.88	         A3))))).
0.71/0.88	tff('4', plain,
0.71/0.88	    ![X17 : sk_A0]:
0.71/0.88	      (app_encode_app(sk_A, sk_A0, sk_A1, sk_A5(X17)) = X17
0.71/0.88	       | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
0.71/0.88	             app_encode_app(sk_A0, 
0.71/0.88	               app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
0.71/0.88	               'const/sets/IN'(sk_A0), X17), sk_A31)),
0.71/0.88	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.71/0.88	tff('5', plain,
0.71/0.88	    ![X19 : sk_A]:
0.71/0.88	      (app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.71/0.88	         app_encode_app(sk_A, app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.71/0.88	           'const/sets/IN'(sk_A), X19), sk_A21)
0.71/0.88	       | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
0.71/0.88	             app_encode_app(sk_A0, 
0.71/0.88	               app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
0.71/0.88	               'const/sets/IN'(sk_A0), 
0.71/0.88	               app_encode_app(sk_A, sk_A0, sk_A1, X19)), sk_A31)),
0.71/0.88	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.71/0.88	tff('6', plain,
0.71/0.88	    ![X0 : sk_A]:
0.71/0.88	      (~ $true
0.71/0.88	       | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
0.71/0.88	             app_encode_app(sk_A0, 
0.71/0.88	               app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
0.71/0.88	               'const/sets/IN'(sk_A0), 
0.71/0.88	               app_encode_app(sk_A, sk_A0, sk_A1, X0)), sk_A31)
0.71/0.88	       | app_encode_app(sk_A, $o, sk_A21, X0)),
0.71/0.88	    inference('sup-', [status(thm)], ['5', '1'])).
0.71/0.88	tff('7', plain,
0.71/0.88	    ![X0 : sk_A]:
0.71/0.88	      (app_encode_app(sk_A, $o, sk_A21, X0)
0.71/0.88	       | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
0.71/0.88	             app_encode_app(sk_A0, 
0.71/0.88	               app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
0.71/0.88	               'const/sets/IN'(sk_A0), 
0.71/0.88	               app_encode_app(sk_A, sk_A0, sk_A1, X0)), sk_A31)),
0.71/0.88	    inference('simplify', [status(thm)], ['6'])).
0.71/0.88	tff('8', plain,
0.71/0.88	    ![X0 : sk_A0]:
0.71/0.88	      (~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
0.71/0.88	           app_encode_app(sk_A0, 
0.71/0.88	             app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
0.71/0.88	             'const/sets/IN'(sk_A0), X0), sk_A31)
0.71/0.88	       | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
0.71/0.88	             app_encode_app(sk_A0, 
0.71/0.88	               app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
0.71/0.88	               'const/sets/IN'(sk_A0), X0), sk_A31)
0.71/0.88	       | app_encode_app(sk_A, $o, sk_A21, sk_A5(X0))),
0.71/0.88	    inference('sup-', [status(thm)], ['4', '7'])).
0.71/0.88	tff('9', plain,
0.71/0.88	    ![X0 : sk_A0]:
0.71/0.88	      (app_encode_app(sk_A, $o, sk_A21, sk_A5(X0))
0.71/0.88	       | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
0.71/0.88	             app_encode_app(sk_A0, 
0.71/0.88	               app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
0.71/0.88	               'const/sets/IN'(sk_A0), X0), sk_A31)),
0.71/0.88	    inference('simplify', [status(thm)], ['8'])).
0.71/0.88	tff('10', plain,
0.71/0.88	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X3 : X0]:
0.71/0.88	      (app_encode_app(app_encode_fun(X0, $o), $o, 
0.71/0.88	         app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
0.71/0.88	           'const/sets/IN'(X0), X3), X1)
0.71/0.88	       | ~ app_encode_app(X0, $o, X1, X3)),
0.71/0.88	    inference('cnf', [status(esa)], [zf_stmt_4])).
0.71/0.88	tff(zf_stmt_5, axiom,
0.71/0.88	  (![B:$tType,A:$tType,A0:B,A1:app_encode_fun(A,$o),A2:app_encode_fun(A,B)]:
0.71/0.88	     (app_encode_app(app_encode_fun(B,$o),$o,
0.71/0.88	                     app_encode_app(B,
0.71/0.88	                                    app_encode_fun(app_encode_fun(B,$o),$o),
0.71/0.88	                                    'const/sets/IN'(B),A0),
0.71/0.88	                     app_encode_app(app_encode_fun(A,$o),
0.71/0.88	                                    app_encode_fun(B,$o),
0.71/0.88	                                    app_encode_app(app_encode_fun(A,B),
0.71/0.88	                                                   app_encode_fun(app_encode_fun(
0.71/0.88	                                                                  A,$o),
0.71/0.88	                                                                  app_encode_fun(
0.71/0.88	                                                                  B,$o)),
0.71/0.88	                                                   'const/sets/IMAGE'(A,B),A2),
0.71/0.88	                                    A1)) <=>
0.71/0.88	      (?[A3:A]:
0.71/0.88	         ((A0 = app_encode_app(A,B,A2,A3)) & 
0.71/0.88	          app_encode_app(app_encode_fun(A,$o),$o,
0.71/0.88	                         app_encode_app(A,
0.71/0.88	                                        app_encode_fun(app_encode_fun(A,$o),
0.71/0.88	                                                       $o),
0.71/0.88	                                        'const/sets/IN'(A),A3),
0.71/0.88	                         A1)))))).
0.71/0.88	tff('11', plain,
0.71/0.88	    ![X4 : $tType, X5 : $tType, X7 : app_encode_fun(X4, $o), X8 : X5, 
0.71/0.88	      X9 : app_encode_fun(X4, X5), X10 : X4]:
0.71/0.88	      (app_encode_app(app_encode_fun(X5, $o), $o, 
0.71/0.88	         app_encode_app(X5, app_encode_fun(app_encode_fun(X5, $o), $o), 
0.71/0.88	           'const/sets/IN'(X5), X8), 
0.71/0.88	         app_encode_app(app_encode_fun(X4, $o), app_encode_fun(X5, $o), 
0.71/0.88	           app_encode_app(app_encode_fun(X4, X5), 
0.71/0.88	             app_encode_fun(app_encode_fun(X4, $o), app_encode_fun(X5, $o)), 
0.71/0.88	             'const/sets/IMAGE'(X4, X5), X9), X7))
0.71/0.88	       | ~ app_encode_app(app_encode_fun(X4, $o), $o, 
0.71/0.88	             app_encode_app(X4, app_encode_fun(app_encode_fun(X4, $o), $o), 
0.71/0.88	               'const/sets/IN'(X4), X10), X7)
0.71/0.88	       | X8 != app_encode_app(X4, X5, X9, X10)),
0.71/0.88	    inference('cnf', [status(esa)], [zf_stmt_5])).
0.71/0.88	tff('12', plain,
0.71/0.88	    ![X4 : $tType, X5 : $tType, X7 : app_encode_fun(X4, $o), 
0.71/0.88	      X9 : app_encode_fun(X4, X5), X10 : X4]:
0.71/0.88	      (~ app_encode_app(app_encode_fun(X4, $o), $o, 
0.71/0.88	           app_encode_app(X4, app_encode_fun(app_encode_fun(X4, $o), $o), 
0.71/0.88	             'const/sets/IN'(X4), X10), X7)
0.71/0.88	       | app_encode_app(app_encode_fun(X5, $o), $o, 
0.71/0.88	           app_encode_app(X5, app_encode_fun(app_encode_fun(X5, $o), $o), 
0.71/0.88	             'const/sets/IN'(X5), app_encode_app(X4, X5, X9, X10)), 
0.71/0.88	           app_encode_app(app_encode_fun(X4, $o), app_encode_fun(X5, $o), 
0.71/0.88	             app_encode_app(app_encode_fun(X4, X5), 
0.71/0.88	               app_encode_fun(app_encode_fun(X4, $o), app_encode_fun(X5, $o)), 
0.71/0.88	               'const/sets/IMAGE'(X4, X5), X9), X7))),
0.71/0.88	    inference('simplify', [status(thm)], ['11'])).
0.71/0.88	tff('13', plain,
0.71/0.88	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : X0, X3 : $tType, 
0.71/0.88	      X4 : app_encode_fun(X0, X3)]:
0.71/0.88	      (~ $true
0.71/0.88	       | ~ app_encode_app(X0, $o, X1, X2)
0.71/0.88	       | app_encode_app(app_encode_fun(X3, $o), $o, 
0.71/0.88	           app_encode_app(X3, app_encode_fun(app_encode_fun(X3, $o), $o), 
0.71/0.88	             'const/sets/IN'(X3), app_encode_app(X0, X3, X4, X2)), 
0.71/0.88	           app_encode_app(app_encode_fun(X0, $o), app_encode_fun(X3, $o), 
0.71/0.88	             app_encode_app(app_encode_fun(X0, X3), 
0.71/0.88	               app_encode_fun(app_encode_fun(X0, $o), app_encode_fun(X3, $o)), 
0.71/0.88	               'const/sets/IMAGE'(X0, X3), X4), X1))),
0.71/0.88	    inference('sup-', [status(thm)], ['10', '12'])).
0.71/0.88	tff('14', plain,
0.71/0.88	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : X0, X3 : $tType, 
0.71/0.88	      X4 : app_encode_fun(X0, X3)]:
0.71/0.88	      (app_encode_app(app_encode_fun(X3, $o), $o, 
0.71/0.88	         app_encode_app(X3, app_encode_fun(app_encode_fun(X3, $o), $o), 
0.71/0.88	           'const/sets/IN'(X3), app_encode_app(X0, X3, X4, X2)), 
0.71/0.88	         app_encode_app(app_encode_fun(X0, $o), app_encode_fun(X3, $o), 
0.71/0.88	           app_encode_app(app_encode_fun(X0, X3), 
0.71/0.88	             app_encode_fun(app_encode_fun(X0, $o), app_encode_fun(X3, $o)), 
0.71/0.88	             'const/sets/IMAGE'(X0, X3), X4), X1))
0.71/0.88	       | ~ app_encode_app(X0, $o, X1, X2)),
0.71/0.88	    inference('simplify', [status(thm)], ['13'])).
0.71/0.88	tff('15', plain,
0.71/0.88	    ![X0 : sk_A0, X1 : $tType, X2 : app_encode_fun(sk_A, X1)]:
0.71/0.88	      (~ $true
0.71/0.88	       | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
0.71/0.88	             app_encode_app(sk_A0, 
0.71/0.88	               app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
0.71/0.88	               'const/sets/IN'(sk_A0), X0), sk_A31)
0.71/0.88	       | app_encode_app(app_encode_fun(X1, $o), $o, 
0.71/0.88	           app_encode_app(X1, app_encode_fun(app_encode_fun(X1, $o), $o), 
0.71/0.88	             'const/sets/IN'(X1), app_encode_app(sk_A, X1, X2, sk_A5(X0))), 
0.71/0.88	           app_encode_app(app_encode_fun(sk_A, $o), app_encode_fun(X1, $o), 
0.71/0.88	             app_encode_app(app_encode_fun(sk_A, X1), 
0.71/0.88	               app_encode_fun(app_encode_fun(sk_A, $o), 
0.71/0.88	                 app_encode_fun(X1, $o)), 'const/sets/IMAGE'(sk_A, X1), X2), 
0.71/0.88	             sk_A21))),
0.71/0.88	    inference('sup-', [status(thm)], ['9', '14'])).
0.71/0.88	tff('16', plain,
0.71/0.88	    ![X0 : sk_A0, X1 : $tType, X2 : app_encode_fun(sk_A, X1)]:
0.71/0.88	      (app_encode_app(app_encode_fun(X1, $o), $o, 
0.71/0.88	         app_encode_app(X1, app_encode_fun(app_encode_fun(X1, $o), $o), 
0.71/0.88	           'const/sets/IN'(X1), app_encode_app(sk_A, X1, X2, sk_A5(X0))), 
0.71/0.88	         app_encode_app(app_encode_fun(sk_A, $o), app_encode_fun(X1, $o), 
0.71/0.88	           app_encode_app(app_encode_fun(sk_A, X1), 
0.71/0.88	             app_encode_fun(app_encode_fun(sk_A, $o), app_encode_fun(X1, $o)), 
0.71/0.88	             'const/sets/IMAGE'(sk_A, X1), X2), sk_A21))
0.71/0.88	       | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
0.71/0.88	             app_encode_app(sk_A0, 
0.71/0.88	               app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
0.71/0.88	               'const/sets/IN'(sk_A0), X0), sk_A31)),
0.71/0.88	    inference('simplify', [status(thm)], ['15'])).
0.71/0.88	tff('17', plain,
0.71/0.88	    ![X0 : $tType, X1 : app_encode_fun(sk_A, X0), X2 : sk_A0]:
0.71/0.88	      (~ $true
0.71/0.88	       | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
0.71/0.88	             app_encode_app(sk_A0, 
0.71/0.88	               app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
0.71/0.88	               'const/sets/IN'(sk_A0), X2), sk_A31)
0.71/0.88	       | app_encode_app(X0, $o, 
0.71/0.88	           app_encode_app(app_encode_fun(sk_A, $o), app_encode_fun(X0, $o), 
0.71/0.88	             app_encode_app(app_encode_fun(sk_A, X0), 
0.71/0.88	               app_encode_fun(app_encode_fun(sk_A, $o), 
0.71/0.88	                 app_encode_fun(X0, $o)), 'const/sets/IMAGE'(sk_A, X0), X1), 
0.71/0.88	             sk_A21), app_encode_app(sk_A, X0, X1, sk_A5(X2)))),
0.71/0.88	    inference('sup-', [status(thm)], ['16', '1'])).
0.71/0.88	tff('18', plain,
0.71/0.88	    ![X0 : $tType, X1 : app_encode_fun(sk_A, X0), X2 : sk_A0]:
0.71/0.88	      (app_encode_app(X0, $o, 
0.71/0.88	         app_encode_app(app_encode_fun(sk_A, $o), app_encode_fun(X0, $o), 
0.71/0.88	           app_encode_app(app_encode_fun(sk_A, X0), 
0.71/0.88	             app_encode_fun(app_encode_fun(sk_A, $o), app_encode_fun(X0, $o)), 
0.71/0.88	             'const/sets/IMAGE'(sk_A, X0), X1), sk_A21), 
0.71/0.88	         app_encode_app(sk_A, X0, X1, sk_A5(X2)))
0.71/0.88	       | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
0.71/0.88	             app_encode_app(sk_A0, 
0.71/0.88	               app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
0.71/0.88	               'const/sets/IN'(sk_A0), X2), sk_A31)),
0.71/0.88	    inference('simplify', [status(thm)], ['17'])).
0.71/0.88	tff('19', plain,
0.71/0.88	    ![X0 : sk_A0]:
0.71/0.88	      (app_encode_app(sk_A0, $o, 
0.71/0.88	         app_encode_app(app_encode_fun(sk_A, $o), app_encode_fun(sk_A0, $o), 
0.71/0.88	           app_encode_app(app_encode_fun(sk_A, sk_A0), 
0.71/0.88	             app_encode_fun(app_encode_fun(sk_A, $o), 
0.71/0.88	               app_encode_fun(sk_A0, $o)), 'const/sets/IMAGE'(sk_A, sk_A0), 
0.71/0.88	             sk_A1), sk_A21), X0)
0.71/0.88	       | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
0.71/0.88	             app_encode_app(sk_A0, 
0.71/0.88	               app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
0.71/0.88	               'const/sets/IN'(sk_A0), X0), sk_A31)
0.71/0.88	       | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
0.71/0.88	             app_encode_app(sk_A0, 
0.71/0.88	               app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
0.71/0.88	               'const/sets/IN'(sk_A0), X0), sk_A31)),
0.71/0.88	    inference('sup+', [status(thm)], ['4', '18'])).
0.71/0.88	tff('20', plain,
0.71/0.88	    ![X0 : sk_A0]:
0.71/0.88	      (~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
0.71/0.88	           app_encode_app(sk_A0, 
0.71/0.88	             app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
0.71/0.88	             'const/sets/IN'(sk_A0), X0), sk_A31)
0.71/0.88	       | app_encode_app(sk_A0, $o, 
0.71/0.88	           app_encode_app(app_encode_fun(sk_A, $o), 
0.71/0.88	             app_encode_fun(sk_A0, $o), 
0.71/0.88	             app_encode_app(app_encode_fun(sk_A, sk_A0), 
0.71/0.88	               app_encode_fun(app_encode_fun(sk_A, $o), 
0.71/0.88	                 app_encode_fun(sk_A0, $o)), 
0.71/0.88	               'const/sets/IMAGE'(sk_A, sk_A0), sk_A1), sk_A21), X0)),
0.71/0.88	    inference('simplify', [status(thm)], ['19'])).
0.71/0.88	tff('21', plain,
0.71/0.88	    ![X0 : app_encode_fun(sk_A0, $o)]:
0.71/0.88	      (~ $true
0.71/0.88	       | X0 = sk_A31
0.71/0.88	       | app_encode_app(sk_A0, $o, X0, sk_A2(sk_A0, sk_A31, X0))
0.71/0.88	       | app_encode_app(sk_A0, $o, 
0.71/0.88	           app_encode_app(app_encode_fun(sk_A, $o), 
0.71/0.88	             app_encode_fun(sk_A0, $o), 
0.71/0.88	             app_encode_app(app_encode_fun(sk_A, sk_A0), 
0.71/0.88	               app_encode_fun(app_encode_fun(sk_A, $o), 
0.71/0.88	                 app_encode_fun(sk_A0, $o)), 
0.71/0.88	               'const/sets/IMAGE'(sk_A, sk_A0), sk_A1), sk_A21), 
0.71/0.88	           sk_A2(sk_A0, sk_A31, X0))),
0.71/0.88	    inference('sup-', [status(thm)], ['3', '20'])).
0.71/0.88	tff('22', plain,
0.71/0.88	    ![X0 : app_encode_fun(sk_A0, $o)]:
0.71/0.88	      (app_encode_app(sk_A0, $o, 
0.71/0.88	         app_encode_app(app_encode_fun(sk_A, $o), app_encode_fun(sk_A0, $o), 
0.71/0.88	           app_encode_app(app_encode_fun(sk_A, sk_A0), 
0.71/0.88	             app_encode_fun(app_encode_fun(sk_A, $o), 
0.71/0.88	               app_encode_fun(sk_A0, $o)), 'const/sets/IMAGE'(sk_A, sk_A0), 
0.71/0.88	             sk_A1), sk_A21), sk_A2(sk_A0, sk_A31, X0))
0.71/0.88	       | app_encode_app(sk_A0, $o, X0, sk_A2(sk_A0, sk_A31, X0))
0.71/0.88	       | X0 = sk_A31),
0.71/0.88	    inference('simplify', [status(thm)], ['21'])).
0.71/0.88	tff('23', plain,
0.71/0.88	    (~ $true
0.71/0.88	     | app_encode_app(app_encode_fun(sk_A, $o), app_encode_fun(sk_A0, $o), 
0.71/0.88	         app_encode_app(app_encode_fun(sk_A, sk_A0), 
0.71/0.88	           app_encode_fun(app_encode_fun(sk_A, $o), 
0.71/0.88	             app_encode_fun(sk_A0, $o)), 'const/sets/IMAGE'(sk_A, sk_A0), 
0.71/0.88	           sk_A1), sk_A21)
0.71/0.88	        = sk_A31
0.71/0.88	     | app_encode_app(sk_A0, $o, 
0.71/0.88	         app_encode_app(app_encode_fun(sk_A, $o), app_encode_fun(sk_A0, $o), 
0.71/0.88	           app_encode_app(app_encode_fun(sk_A, sk_A0), 
0.71/0.88	             app_encode_fun(app_encode_fun(sk_A, $o), 
0.71/0.88	               app_encode_fun(sk_A0, $o)), 'const/sets/IMAGE'(sk_A, sk_A0), 
0.71/0.88	             sk_A1), sk_A21), 
0.71/0.88	         sk_A2(sk_A0, sk_A31, 
0.71/0.88	           app_encode_app(app_encode_fun(sk_A, $o), 
0.71/0.88	             app_encode_fun(sk_A0, $o), 
0.71/0.88	             app_encode_app(app_encode_fun(sk_A, sk_A0), 
0.71/0.88	               app_encode_fun(app_encode_fun(sk_A, $o), 
0.71/0.88	                 app_encode_fun(sk_A0, $o)), 
0.71/0.88	               'const/sets/IMAGE'(sk_A, sk_A0), sk_A1), sk_A21)))),
0.71/0.88	    inference('eq_fact', [status(thm)], ['22'])).
0.71/0.88	tff('24', plain,
0.71/0.88	    (app_encode_app(sk_A0, $o, 
0.71/0.88	       app_encode_app(app_encode_fun(sk_A, $o), app_encode_fun(sk_A0, $o), 
0.71/0.88	         app_encode_app(app_encode_fun(sk_A, sk_A0), 
0.71/0.88	           app_encode_fun(app_encode_fun(sk_A, $o), 
0.71/0.88	             app_encode_fun(sk_A0, $o)), 'const/sets/IMAGE'(sk_A, sk_A0), 
0.71/0.88	           sk_A1), sk_A21), 
0.71/0.88	       sk_A2(sk_A0, sk_A31, 
0.71/0.88	         app_encode_app(app_encode_fun(sk_A, $o), app_encode_fun(sk_A0, $o), 
0.71/0.88	           app_encode_app(app_encode_fun(sk_A, sk_A0), 
0.71/0.88	             app_encode_fun(app_encode_fun(sk_A, $o), 
0.71/0.88	               app_encode_fun(sk_A0, $o)), 'const/sets/IMAGE'(sk_A, sk_A0), 
0.71/0.88	             sk_A1), sk_A21)))
0.71/0.88	     | app_encode_app(app_encode_fun(sk_A, $o), app_encode_fun(sk_A0, $o), 
0.71/0.88	         app_encode_app(app_encode_fun(sk_A, sk_A0), 
0.71/0.88	           app_encode_fun(app_encode_fun(sk_A, $o), 
0.71/0.88	             app_encode_fun(sk_A0, $o)), 'const/sets/IMAGE'(sk_A, sk_A0), 
0.71/0.88	           sk_A1), sk_A21)
0.71/0.88	        = sk_A31),
0.71/0.88	    inference('simplify', [status(thm)], ['23'])).
0.71/0.88	tff('25', plain,
0.71/0.88	    app_encode_app(app_encode_fun(sk_A, $o), app_encode_fun(sk_A0, $o), 
0.71/0.88	      app_encode_app(app_encode_fun(sk_A, sk_A0), 
0.71/0.88	        app_encode_fun(app_encode_fun(sk_A, $o), app_encode_fun(sk_A0, $o)), 
0.71/0.88	        'const/sets/IMAGE'(sk_A, sk_A0), sk_A1), sk_A21)
0.71/0.88	     != sk_A31,
0.71/0.88	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.71/0.88	tff('26', plain,
0.71/0.88	    app_encode_app(sk_A0, $o, 
0.71/0.88	      app_encode_app(app_encode_fun(sk_A, $o), app_encode_fun(sk_A0, $o), 
0.71/0.88	        app_encode_app(app_encode_fun(sk_A, sk_A0), 
0.71/0.88	          app_encode_fun(app_encode_fun(sk_A, $o), app_encode_fun(sk_A0, $o)), 
0.71/0.88	          'const/sets/IMAGE'(sk_A, sk_A0), sk_A1), sk_A21), 
0.71/0.88	      sk_A2(sk_A0, sk_A31, 
0.71/0.88	        app_encode_app(app_encode_fun(sk_A, $o), app_encode_fun(sk_A0, $o), 
0.71/0.88	          app_encode_app(app_encode_fun(sk_A, sk_A0), 
0.71/0.88	            app_encode_fun(app_encode_fun(sk_A, $o), 
0.71/0.88	              app_encode_fun(sk_A0, $o)), 'const/sets/IMAGE'(sk_A, sk_A0), 
0.71/0.88	            sk_A1), sk_A21))),
0.71/0.88	    inference('simplify_reflect-', [status(thm)], ['24', '25'])).
0.71/0.88	tff('27', plain,
0.71/0.88	    ![X0 : $tType, X1 : app_encode_fun(sk_A0, X0)]:
0.71/0.88	      (~ $true
0.71/0.88	       | app_encode_app(app_encode_fun(X0, $o), $o, 
0.71/0.88	           app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
0.71/0.88	             'const/sets/IN'(X0), 
0.71/0.88	             app_encode_app(sk_A0, X0, X1, 
0.71/0.88	               sk_A2(sk_A0, sk_A31, 
0.71/0.88	                 app_encode_app(app_encode_fun(sk_A, $o), 
0.71/0.88	                   app_encode_fun(sk_A0, $o), 
0.71/0.88	                   app_encode_app(app_encode_fun(sk_A, sk_A0), 
0.71/0.88	                     app_encode_fun(app_encode_fun(sk_A, $o), 
0.71/0.88	                       app_encode_fun(sk_A0, $o)), 
0.71/0.88	                     'const/sets/IMAGE'(sk_A, sk_A0), sk_A1), sk_A21)))), 
0.71/0.88	           app_encode_app(app_encode_fun(sk_A0, $o), app_encode_fun(X0, $o), 
0.71/0.88	             app_encode_app(app_encode_fun(sk_A0, X0), 
0.71/0.88	               app_encode_fun(app_encode_fun(sk_A0, $o), 
0.71/0.88	                 app_encode_fun(X0, $o)), 'const/sets/IMAGE'(sk_A0, X0), X1), 
0.71/0.88	             app_encode_app(app_encode_fun(sk_A, $o), 
0.71/0.88	               app_encode_fun(sk_A0, $o), 
0.71/0.88	               app_encode_app(app_encode_fun(sk_A, sk_A0), 
0.71/0.88	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.71/0.88	                   app_encode_fun(sk_A0, $o)), 
0.71/0.88	                 'const/sets/IMAGE'(sk_A, sk_A0), sk_A1), sk_A21)))),
0.71/0.88	    inference('sup-', [status(thm)], ['26', '14'])).
0.71/0.88	tff('28', plain,
0.71/0.88	    ![X0 : $tType, X1 : app_encode_fun(sk_A0, X0)]:
0.71/0.88	      app_encode_app(app_encode_fun(X0, $o), $o, 
0.71/0.88	        app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
0.71/0.88	          'const/sets/IN'(X0), 
0.71/0.88	          app_encode_app(sk_A0, X0, X1, 
0.71/0.88	            sk_A2(sk_A0, sk_A31, 
0.71/0.88	              app_encode_app(app_encode_fun(sk_A, $o), 
0.71/0.88	                app_encode_fun(sk_A0, $o), 
0.71/0.88	                app_encode_app(app_encode_fun(sk_A, sk_A0), 
0.71/0.88	                  app_encode_fun(app_encode_fun(sk_A, $o), 
0.71/0.88	                    app_encode_fun(sk_A0, $o)), 
0.71/0.88	                  'const/sets/IMAGE'(sk_A, sk_A0), sk_A1), sk_A21)))), 
0.71/0.88	        app_encode_app(app_encode_fun(sk_A0, $o), app_encode_fun(X0, $o), 
0.71/0.88	          app_encode_app(app_encode_fun(sk_A0, X0), 
0.71/0.88	            app_encode_fun(app_encode_fun(sk_A0, $o), app_encode_fun(X0, $o)), 
0.71/0.88	            'const/sets/IMAGE'(sk_A0, X0), X1), 
0.71/0.88	          app_encode_app(app_encode_fun(sk_A, $o), 
0.71/0.88	            app_encode_fun(sk_A0, $o), 
0.71/0.88	            app_encode_app(app_encode_fun(sk_A, sk_A0), 
0.71/0.88	              app_encode_fun(app_encode_fun(sk_A, $o), 
0.71/0.88	                app_encode_fun(sk_A0, $o)), 'const/sets/IMAGE'(sk_A, sk_A0), 
0.71/0.88	              sk_A1), sk_A21))),
0.71/0.88	    inference('simplify', [status(thm)], ['27'])).
0.71/0.88	tff('29', plain,
0.71/0.88	    ![X4 : $tType, X5 : $tType, X6 : app_encode_fun(X4, X5), 
0.71/0.88	      X7 : app_encode_fun(X4, $o), X8 : X5]:
0.71/0.88	      (X8 = app_encode_app(X4, X5, X6, sk_A3(X4, X5, X6, X7, X8))
0.71/0.88	       | ~ app_encode_app(app_encode_fun(X5, $o), $o, 
0.71/0.88	             app_encode_app(X5, app_encode_fun(app_encode_fun(X5, $o), $o), 
0.71/0.88	               'const/sets/IN'(X5), X8), 
0.71/0.88	             app_encode_app(app_encode_fun(X4, $o), app_encode_fun(X5, $o), 
0.71/0.88	               app_encode_app(app_encode_fun(X4, X5), 
0.71/0.88	                 app_encode_fun(app_encode_fun(X4, $o), 
0.71/0.88	                   app_encode_fun(X5, $o)), 'const/sets/IMAGE'(X4, X5), X6), 
0.71/0.88	               X7))),
0.71/0.88	    inference('cnf', [status(esa)], [zf_stmt_5])).
0.71/0.88	tff('30', plain,
0.71/0.88	    ![X4 : $tType, X5 : $tType, X6 : app_encode_fun(X4, X5), 
0.71/0.88	      X7 : app_encode_fun(X4, $o), X8 : X5]:
0.71/0.88	      (app_encode_app(app_encode_fun(X4, $o), $o, 
0.71/0.88	         app_encode_app(X4, app_encode_fun(app_encode_fun(X4, $o), $o), 
0.71/0.88	           'const/sets/IN'(X4), sk_A3(X4, X5, X6, X7, X8)), X7)
0.71/0.88	       | ~ app_encode_app(app_encode_fun(X5, $o), $o, 
0.71/0.88	             app_encode_app(X5, app_encode_fun(app_encode_fun(X5, $o), $o), 
0.71/0.88	               'const/sets/IN'(X5), X8), 
0.71/0.88	             app_encode_app(app_encode_fun(X4, $o), app_encode_fun(X5, $o), 
0.71/0.88	               app_encode_app(app_encode_fun(X4, X5), 
0.71/0.88	                 app_encode_fun(app_encode_fun(X4, $o), 
0.71/0.88	                   app_encode_fun(X5, $o)), 'const/sets/IMAGE'(X4, X5), X6), 
0.71/0.88	               X7))),
0.71/0.88	    inference('cnf', [status(esa)], [zf_stmt_5])).
0.71/0.88	tff('31', plain,
0.71/0.88	    ![X0 : $tType, X1 : app_encode_fun(app_encode_fun(X0, $o), $o), 
0.71/0.88	      X2 : app_encode_fun(X0, $o)]:
0.71/0.88	      (app_encode_app(app_encode_fun(X0, $o), $o, X1, X2)
0.71/0.88	       | ~ app_encode_app(
0.71/0.88	             app_encode_fun(app_encode_fun(app_encode_fun(X0, $o), $o), $o), 
0.71/0.88	             $o, 
0.71/0.88	             app_encode_app(app_encode_fun(app_encode_fun(X0, $o), $o), 
0.71/0.88	               app_encode_fun(
0.71/0.88	                 app_encode_fun(app_encode_fun(app_encode_fun(X0, $o), $o), 
0.71/0.88	                   $o), $o), 
0.71/0.88	               'const/sets/IN'(app_encode_fun(app_encode_fun(X0, $o), $o)), 
0.71/0.88	               X1), 
0.71/0.88	             app_encode_app(app_encode_fun(X0, $o), 
0.71/0.88	               app_encode_fun(app_encode_fun(app_encode_fun(X0, $o), $o), $o), 
0.71/0.88	               app_encode_app(
0.71/0.88	                 app_encode_fun(X0, 
0.71/0.88	                   app_encode_fun(app_encode_fun(X0, $o), $o)), 
0.71/0.88	                 app_encode_fun(app_encode_fun(X0, $o), 
0.71/0.88	                   app_encode_fun(
0.71/0.88	                     app_encode_fun(app_encode_fun(X0, $o), $o), $o)), 
0.71/0.88	                 'const/sets/IMAGE'(X0, 
0.71/0.88	                   app_encode_fun(app_encode_fun(X0, $o), $o)), 
0.71/0.88	                 'const/sets/IN'(X0)), X2))
0.71/0.88	       | ~ app_encode_app(
0.71/0.88	             app_encode_fun(app_encode_fun(app_encode_fun(X0, $o), $o), $o), 
0.71/0.88	             $o, 
0.71/0.88	             app_encode_app(app_encode_fun(app_encode_fun(X0, $o), $o), 
0.71/0.88	               app_encode_fun(
0.71/0.88	                 app_encode_fun(app_encode_fun(app_encode_fun(X0, $o), $o), 
0.71/0.88	                   $o), $o), 
0.71/0.88	               'const/sets/IN'(app_encode_fun(app_encode_fun(X0, $o), $o)), 
0.71/0.88	               X1), 
0.71/0.88	             app_encode_app(app_encode_fun(X0, $o), 
0.71/0.88	               app_encode_fun(app_encode_fun(app_encode_fun(X0, $o), $o), $o), 
0.71/0.88	               app_encode_app(
0.71/0.88	                 app_encode_fun(X0, 
0.71/0.88	                   app_encode_fun(app_encode_fun(X0, $o), $o)), 
0.71/0.88	                 app_encode_fun(app_encode_fun(X0, $o), 
0.71/0.88	                   app_encode_fun(
0.71/0.88	                     app_encode_fun(app_encode_fun(X0, $o), $o), $o)), 
0.71/0.88	                 'const/sets/IMAGE'(X0, 
0.71/0.88	                   app_encode_fun(app_encode_fun(X0, $o), $o)), 
0.71/0.88	                 'const/sets/IN'(X0)), X2))),
0.71/0.88	    inference('sup+', [status(thm)], ['29', '30'])).
0.71/0.88	tff('32', plain,
0.71/0.88	    ![X0 : $tType, X1 : app_encode_fun(app_encode_fun(X0, $o), $o), 
0.71/0.88	      X2 : app_encode_fun(X0, $o)]:
0.71/0.88	      (~ app_encode_app(
0.71/0.88	           app_encode_fun(app_encode_fun(app_encode_fun(X0, $o), $o), $o), 
0.71/0.88	           $o, 
0.71/0.88	           app_encode_app(app_encode_fun(app_encode_fun(X0, $o), $o), 
0.71/0.88	             app_encode_fun(
0.71/0.88	               app_encode_fun(app_encode_fun(app_encode_fun(X0, $o), $o), $o), 
0.71/0.88	               $o), 
0.71/0.88	             'const/sets/IN'(app_encode_fun(app_encode_fun(X0, $o), $o)), X1), 
0.71/0.88	           app_encode_app(app_encode_fun(X0, $o), 
0.71/0.88	             app_encode_fun(app_encode_fun(app_encode_fun(X0, $o), $o), $o), 
0.71/0.88	             app_encode_app(
0.71/0.88	               app_encode_fun(X0, app_encode_fun(app_encode_fun(X0, $o), $o)), 
0.71/0.88	               app_encode_fun(app_encode_fun(X0, $o), 
0.71/0.88	                 app_encode_fun(app_encode_fun(app_encode_fun(X0, $o), $o), 
0.71/0.88	                   $o)), 
0.71/0.88	               'const/sets/IMAGE'(X0, 
0.71/0.88	                 app_encode_fun(app_encode_fun(X0, $o), $o)), 
0.71/0.88	               'const/sets/IN'(X0)), X2))
0.71/0.88	       | app_encode_app(app_encode_fun(X0, $o), $o, X1, X2)),
0.71/0.88	    inference('simplify', [status(thm)], ['31'])).
0.71/0.88	tff('33', plain,
0.71/0.88	    (~ $true
0.71/0.88	     | app_encode_app(app_encode_fun(sk_A0, $o), $o, 
0.71/0.88	         app_encode_app(sk_A0, 
0.71/0.88	           app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
0.71/0.88	           'const/sets/IN'(sk_A0), 
0.71/0.88	           sk_A2(sk_A0, sk_A31, 
0.71/0.88	             app_encode_app(app_encode_fun(sk_A, $o), 
0.71/0.88	               app_encode_fun(sk_A0, $o), 
0.71/0.88	               app_encode_app(app_encode_fun(sk_A, sk_A0), 
0.71/0.88	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.71/0.88	                   app_encode_fun(sk_A0, $o)), 
0.71/0.88	                 'const/sets/IMAGE'(sk_A, sk_A0), sk_A1), sk_A21))), 
0.71/0.88	         app_encode_app(app_encode_fun(sk_A, $o), app_encode_fun(sk_A0, $o), 
0.71/0.88	           app_encode_app(app_encode_fun(sk_A, sk_A0), 
0.71/0.88	             app_encode_fun(app_encode_fun(sk_A, $o), 
0.71/0.88	               app_encode_fun(sk_A0, $o)), 'const/sets/IMAGE'(sk_A, sk_A0), 
0.71/0.88	             sk_A1), sk_A21))),
0.71/0.88	    inference('sup-', [status(thm)], ['28', '32'])).
0.71/0.88	tff('34', plain,
0.71/0.88	    app_encode_app(app_encode_fun(sk_A0, $o), $o, 
0.71/0.88	      app_encode_app(sk_A0, app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
0.71/0.88	        'const/sets/IN'(sk_A0), 
0.71/0.88	        sk_A2(sk_A0, sk_A31, 
0.71/0.88	          app_encode_app(app_encode_fun(sk_A, $o), 
0.71/0.88	            app_encode_fun(sk_A0, $o), 
0.71/0.88	            app_encode_app(app_encode_fun(sk_A, sk_A0), 
0.71/0.88	              app_encode_fun(app_encode_fun(sk_A, $o), 
0.71/0.88	                app_encode_fun(sk_A0, $o)), 'const/sets/IMAGE'(sk_A, sk_A0), 
0.71/0.88	              sk_A1), sk_A21))), 
0.71/0.88	      app_encode_app(app_encode_fun(sk_A, $o), app_encode_fun(sk_A0, $o), 
0.71/0.88	        app_encode_app(app_encode_fun(sk_A, sk_A0), 
0.71/0.88	          app_encode_fun(app_encode_fun(sk_A, $o), app_encode_fun(sk_A0, $o)), 
0.71/0.88	          'const/sets/IMAGE'(sk_A, sk_A0), sk_A1), sk_A21)),
0.71/0.88	    inference('simplify', [status(thm)], ['33'])).
0.71/0.88	tff('35', plain,
0.71/0.88	    ![X18 : sk_A]:
0.71/0.88	      (app_encode_app(app_encode_fun(sk_A0, $o), $o, 
0.71/0.88	         app_encode_app(sk_A0, 
0.71/0.88	           app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
0.71/0.88	           'const/sets/IN'(sk_A0), app_encode_app(sk_A, sk_A0, sk_A1, X18)), 
0.71/0.88	         sk_A31)
0.71/0.88	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.71/0.88	             app_encode_app(sk_A, 
0.71/0.88	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.71/0.88	               'const/sets/IN'(sk_A), X18), sk_A21)),
0.71/0.88	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.71/0.88	tff('36', plain,
0.71/0.88	    ![X0 : $tType, X1 : X0, X2 : app_encode_fun(sk_A, X0)]:
0.71/0.88	      (~ $true
0.71/0.88	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
0.71/0.88	             app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
0.71/0.88	               'const/sets/IN'(X0), X1), 
0.71/0.88	             app_encode_app(app_encode_fun(sk_A, $o), 
0.71/0.88	               app_encode_fun(X0, $o), 
0.71/0.88	               app_encode_app(app_encode_fun(sk_A, X0), 
0.71/0.88	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.71/0.88	                   app_encode_fun(X0, $o)), 'const/sets/IMAGE'(sk_A, X0), X2), 
0.71/0.88	               sk_A21))
0.71/0.88	       | app_encode_app(app_encode_fun(sk_A0, $o), $o, 
0.71/0.88	           app_encode_app(sk_A0, 
0.71/0.88	             app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
0.71/0.88	             'const/sets/IN'(sk_A0), 
0.71/0.88	             app_encode_app(sk_A, sk_A0, sk_A1, 
0.71/0.88	               sk_A3(sk_A, X0, X2, sk_A21, X1))), sk_A31)),
0.71/0.88	    inference('sup-', [status(thm)], ['30', '35'])).
0.71/0.88	tff('37', plain,
0.71/0.88	    ![X0 : $tType, X1 : X0, X2 : app_encode_fun(sk_A, X0)]:
0.71/0.88	      (app_encode_app(app_encode_fun(sk_A0, $o), $o, 
0.71/0.88	         app_encode_app(sk_A0, 
0.71/0.88	           app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
0.71/0.88	           'const/sets/IN'(sk_A0), 
0.71/0.88	           app_encode_app(sk_A, sk_A0, sk_A1, 
0.71/0.88	             sk_A3(sk_A, X0, X2, sk_A21, X1))), sk_A31)
0.71/0.88	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
0.71/0.88	             app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
0.71/0.88	               'const/sets/IN'(X0), X1), 
0.71/0.88	             app_encode_app(app_encode_fun(sk_A, $o), 
0.71/0.88	               app_encode_fun(X0, $o), 
0.71/0.88	               app_encode_app(app_encode_fun(sk_A, X0), 
0.71/0.88	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.71/0.88	                   app_encode_fun(X0, $o)), 'const/sets/IMAGE'(sk_A, X0), X2), 
0.71/0.88	               sk_A21))),
0.71/0.88	    inference('simplify', [status(thm)], ['36'])).
0.71/0.88	tff('38', plain,
0.71/0.88	    ![X0 : $tType, X1 : X0, X2 : app_encode_fun(sk_A, X0)]:
0.71/0.88	      (~ $true
0.71/0.88	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
0.71/0.88	             app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
0.71/0.88	               'const/sets/IN'(X0), X1), 
0.71/0.88	             app_encode_app(app_encode_fun(sk_A, $o), 
0.71/0.88	               app_encode_fun(X0, $o), 
0.71/0.88	               app_encode_app(app_encode_fun(sk_A, X0), 
0.71/0.88	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.71/0.88	                   app_encode_fun(X0, $o)), 'const/sets/IMAGE'(sk_A, X0), X2), 
0.71/0.88	               sk_A21))
0.71/0.88	       | app_encode_app(sk_A0, $o, sk_A31, 
0.71/0.88	           app_encode_app(sk_A, sk_A0, sk_A1, 
0.71/0.88	             sk_A3(sk_A, X0, X2, sk_A21, X1)))),
0.71/0.88	    inference('sup-', [status(thm)], ['37', '1'])).
0.71/0.88	tff('39', plain,
0.71/0.88	    ![X0 : $tType, X1 : X0, X2 : app_encode_fun(sk_A, X0)]:
0.71/0.88	      (app_encode_app(sk_A0, $o, sk_A31, 
0.71/0.88	         app_encode_app(sk_A, sk_A0, sk_A1, sk_A3(sk_A, X0, X2, sk_A21, X1)))
0.71/0.88	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
0.71/0.88	             app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
0.71/0.88	               'const/sets/IN'(X0), X1), 
0.71/0.88	             app_encode_app(app_encode_fun(sk_A, $o), 
0.71/0.88	               app_encode_fun(X0, $o), 
0.71/0.88	               app_encode_app(app_encode_fun(sk_A, X0), 
0.71/0.88	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.71/0.88	                   app_encode_fun(X0, $o)), 'const/sets/IMAGE'(sk_A, X0), X2), 
0.71/0.88	               sk_A21))),
0.71/0.88	    inference('simplify', [status(thm)], ['38'])).
0.71/0.88	tff('40', plain,
0.71/0.88	    ![X0 : sk_A0]:
0.71/0.88	      (app_encode_app(sk_A0, $o, sk_A31, X0)
0.71/0.88	       | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
0.71/0.88	             app_encode_app(sk_A0, 
0.71/0.88	               app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
0.71/0.88	               'const/sets/IN'(sk_A0), X0), 
0.71/0.88	             app_encode_app(app_encode_fun(sk_A, $o), 
0.71/0.88	               app_encode_fun(sk_A0, $o), 
0.71/0.88	               app_encode_app(app_encode_fun(sk_A, sk_A0), 
0.71/0.88	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.71/0.88	                   app_encode_fun(sk_A0, $o)), 
0.71/0.88	                 'const/sets/IMAGE'(sk_A, sk_A0), sk_A1), sk_A21))
0.71/0.88	       | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
0.71/0.88	             app_encode_app(sk_A0, 
0.71/0.88	               app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
0.71/0.88	               'const/sets/IN'(sk_A0), X0), 
0.71/0.88	             app_encode_app(app_encode_fun(sk_A, $o), 
0.71/0.88	               app_encode_fun(sk_A0, $o), 
0.71/0.88	               app_encode_app(app_encode_fun(sk_A, sk_A0), 
0.71/0.88	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.71/0.88	                   app_encode_fun(sk_A0, $o)), 
0.71/0.88	                 'const/sets/IMAGE'(sk_A, sk_A0), sk_A1), sk_A21))),
0.71/0.88	    inference('sup+', [status(thm)], ['29', '39'])).
0.71/0.88	tff('41', plain,
0.71/0.88	    ![X0 : sk_A0]:
0.71/0.88	      (~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
0.71/0.88	           app_encode_app(sk_A0, 
0.71/0.88	             app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
0.71/0.88	             'const/sets/IN'(sk_A0), X0), 
0.71/0.88	           app_encode_app(app_encode_fun(sk_A, $o), 
0.71/0.88	             app_encode_fun(sk_A0, $o), 
0.71/0.88	             app_encode_app(app_encode_fun(sk_A, sk_A0), 
0.71/0.88	               app_encode_fun(app_encode_fun(sk_A, $o), 
0.71/0.88	                 app_encode_fun(sk_A0, $o)), 
0.71/0.88	               'const/sets/IMAGE'(sk_A, sk_A0), sk_A1), sk_A21))
0.71/0.88	       | app_encode_app(sk_A0, $o, sk_A31, X0)),
0.71/0.88	    inference('simplify', [status(thm)], ['40'])).
0.71/0.88	tff('42', plain,
0.71/0.88	    (~ $true
0.71/0.88	     | app_encode_app(sk_A0, $o, sk_A31, 
0.71/0.88	         sk_A2(sk_A0, sk_A31, 
0.71/0.88	           app_encode_app(app_encode_fun(sk_A, $o), 
0.71/0.88	             app_encode_fun(sk_A0, $o), 
0.71/0.88	             app_encode_app(app_encode_fun(sk_A, sk_A0), 
0.71/0.88	               app_encode_fun(app_encode_fun(sk_A, $o), 
0.71/0.88	                 app_encode_fun(sk_A0, $o)), 
0.71/0.88	               'const/sets/IMAGE'(sk_A, sk_A0), sk_A1), sk_A21)))),
0.71/0.88	    inference('sup-', [status(thm)], ['34', '41'])).
0.71/0.88	tff('43', plain,
0.71/0.88	    app_encode_app(sk_A0, $o, sk_A31, 
0.71/0.88	      sk_A2(sk_A0, sk_A31, 
0.71/0.88	        app_encode_app(app_encode_fun(sk_A, $o), app_encode_fun(sk_A0, $o), 
0.71/0.88	          app_encode_app(app_encode_fun(sk_A, sk_A0), 
0.71/0.88	            app_encode_fun(app_encode_fun(sk_A, $o), 
0.71/0.88	              app_encode_fun(sk_A0, $o)), 'const/sets/IMAGE'(sk_A, sk_A0), 
0.71/0.88	            sk_A1), sk_A21))),
0.71/0.88	    inference('simplify', [status(thm)], ['42'])).
0.71/0.88	tff('44', plain,
0.71/0.88	    ![X11 : $tType, X14 : app_encode_fun(X11, $o), 
0.71/0.88	      X16 : app_encode_fun(X11, $o)]:
0.71/0.88	      (X14 = X16
0.71/0.88	       | ~ app_encode_app(app_encode_fun(X11, $o), $o, 
0.71/0.88	             app_encode_app(X11, 
0.71/0.88	               app_encode_fun(app_encode_fun(X11, $o), $o), 
0.71/0.88	               'const/sets/IN'(X11), sk_A2(X11, X16, X14)), X16)
0.71/0.88	       | ~ app_encode_app(app_encode_fun(X11, $o), $o, 
0.71/0.88	             app_encode_app(X11, 
0.71/0.88	               app_encode_fun(app_encode_fun(X11, $o), $o), 
0.71/0.88	               'const/sets/IN'(X11), sk_A2(X11, X16, X14)), X14)),
0.71/0.88	    inference('cnf', [status(esa)], [zf_stmt_6])).
0.71/0.88	tff('45', plain,
0.71/0.88	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : app_encode_fun(X0, $o)]:
0.71/0.88	      (~ $true
0.71/0.88	       | ~ app_encode_app(X0, $o, X1, sk_A2(X0, X1, X2))
0.71/0.88	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
0.71/0.88	             app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
0.71/0.88	               'const/sets/IN'(X0), sk_A2(X0, X1, X2)), X2)
0.71/0.88	       | X2 = X1),
0.71/0.88	    inference('sup-', [status(thm)], ['10', '44'])).
0.71/0.88	tff('46', plain,
0.71/0.88	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : app_encode_fun(X0, $o)]:
0.71/0.88	      (X2 = X1
0.71/0.88	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
0.71/0.88	             app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
0.71/0.88	               'const/sets/IN'(X0), sk_A2(X0, X1, X2)), X2)
0.71/0.88	       | ~ app_encode_app(X0, $o, X1, sk_A2(X0, X1, X2))),
0.71/0.88	    inference('simplify', [status(thm)], ['45'])).
0.71/0.88	tff('47', plain,
0.71/0.88	    (~ $true
0.71/0.88	     | ~ app_encode_app(sk_A0, $o, sk_A31, 
0.71/0.88	           sk_A2(sk_A0, sk_A31, 
0.71/0.88	             app_encode_app(app_encode_fun(sk_A, $o), 
0.71/0.88	               app_encode_fun(sk_A0, $o), 
0.71/0.88	               app_encode_app(app_encode_fun(sk_A, sk_A0), 
0.71/0.88	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.71/0.88	                   app_encode_fun(sk_A0, $o)), 
0.71/0.88	                 'const/sets/IMAGE'(sk_A, sk_A0), sk_A1), sk_A21)))
0.71/0.88	     | app_encode_app(app_encode_fun(sk_A, $o), app_encode_fun(sk_A0, $o), 
0.71/0.88	         app_encode_app(app_encode_fun(sk_A, sk_A0), 
0.71/0.88	           app_encode_fun(app_encode_fun(sk_A, $o), 
0.71/0.88	             app_encode_fun(sk_A0, $o)), 'const/sets/IMAGE'(sk_A, sk_A0), 
0.71/0.88	           sk_A1), sk_A21)
0.71/0.88	        = sk_A31),
0.71/0.88	    inference('sup-', [status(thm)], ['34', '46'])).
0.71/0.88	tff('48', plain,
0.71/0.88	    (app_encode_app(app_encode_fun(sk_A, $o), app_encode_fun(sk_A0, $o), 
0.71/0.88	       app_encode_app(app_encode_fun(sk_A, sk_A0), 
0.71/0.88	         app_encode_fun(app_encode_fun(sk_A, $o), app_encode_fun(sk_A0, $o)), 
0.71/0.88	         'const/sets/IMAGE'(sk_A, sk_A0), sk_A1), sk_A21)
0.71/0.88	      = sk_A31
0.71/0.88	     | ~ app_encode_app(sk_A0, $o, sk_A31, 
0.71/0.89	           sk_A2(sk_A0, sk_A31, 
0.71/0.89	             app_encode_app(app_encode_fun(sk_A, $o), 
0.71/0.89	               app_encode_fun(sk_A0, $o), 
0.71/0.89	               app_encode_app(app_encode_fun(sk_A, sk_A0), 
0.71/0.89	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.71/0.89	                   app_encode_fun(sk_A0, $o)), 
0.71/0.89	                 'const/sets/IMAGE'(sk_A, sk_A0), sk_A1), sk_A21)))),
0.71/0.89	    inference('simplify', [status(thm)], ['47'])).
0.71/0.89	tff('49', plain,
0.71/0.89	    ~ app_encode_app(sk_A0, $o, sk_A31, 
0.71/0.89	        sk_A2(sk_A0, sk_A31, 
0.71/0.89	          app_encode_app(app_encode_fun(sk_A, $o), 
0.71/0.89	            app_encode_fun(sk_A0, $o), 
0.71/0.89	            app_encode_app(app_encode_fun(sk_A, sk_A0), 
0.71/0.89	              app_encode_fun(app_encode_fun(sk_A, $o), 
0.71/0.89	                app_encode_fun(sk_A0, $o)), 'const/sets/IMAGE'(sk_A, sk_A0), 
0.71/0.89	              sk_A1), sk_A21))),
0.71/0.89	    inference('simplify_reflect-', [status(thm)], ['48', '25'])).
0.71/0.89	tff('50', plain, ~ $true, inference('sup-', [status(thm)], ['43', '49'])).
0.71/0.89	tff('51', plain, $false, inference('simplify', [status(thm)], ['50'])).
0.71/0.89	
0.71/0.89	% SZS output end Refutation
0.71/0.89	EOF
