0.00/0.01	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.01	% app-encoded or not : app
0.00/0.01	% Variant    : fo
0.00/0.01	% Ordering    : rpo6
0.00/0.01	% Command    : 
0.00/0.01	#!/bin/sh
0.00/0.01	
0.00/0.01	./zipperposition.native ${1:+"$1"} \
0.00/0.01	  -i tptp \
0.00/0.01	  -o tptp \
0.00/0.01	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.01	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.01	  --no-ho \
0.00/0.01	  --no-avatar \
0.00/0.01	  --no-induction \
0.00/0.01	  --no-unif-pattern \
0.00/0.01	  --ord $2 \
0.00/0.01	  --simultaneous-sup false \
0.00/0.01	  --no-max-vars \
0.00/0.01	  --no-fool
0.00/0.20	% Computer   : n096.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 18:29:09 CST 2018
0.00/0.33	% done 175 iterations in 0.130s
0.00/0.33	% SZS status Theorem for 'stdin'
0.00/0.33	% SZS output start Refutation
0.00/0.33	tff(zf_stmt_10, axiom,
0.00/0.33	  (![A:$tType,A0:app_encode_fun(A,$o),A1:app_encode_fun(A,$o)]:
0.00/0.33	     ((A0 = A1) <=>
0.00/0.33	      (![A2:A]:
0.00/0.33	         (app_encode_app(app_encode_fun(A,$o),$o,
0.00/0.33	                         app_encode_app(A,
0.00/0.33	                                        app_encode_fun(app_encode_fun(A,$o),
0.00/0.33	                                                       $o),
0.00/0.33	                                        'const/sets/IN'(A),A2),
0.00/0.33	                         A0) <=>
0.00/0.33	          app_encode_app(app_encode_fun(A,$o),$o,
0.00/0.33	                         app_encode_app(A,
0.00/0.33	                                        app_encode_fun(app_encode_fun(A,$o),
0.00/0.33	                                                       $o),
0.00/0.33	                                        'const/sets/IN'(A),A2),
0.00/0.33	                         A1)))))).
0.00/0.33	tff('0', plain,
0.00/0.33	    ![X13 : $tType, X16 : app_encode_fun(X13, $o), 
0.00/0.33	      X18 : app_encode_fun(X13, $o)]:
0.00/0.33	      (X16 = X18
0.00/0.33	       | app_encode_app(app_encode_fun(X13, $o), $o, 
0.00/0.33	           app_encode_app(X13, app_encode_fun(app_encode_fun(X13, $o), $o), 
0.00/0.33	             'const/sets/IN'(X13), sk_A21(X13, X18, X16)), X18)
0.00/0.33	       | app_encode_app(app_encode_fun(X13, $o), $o, 
0.00/0.33	           app_encode_app(X13, app_encode_fun(app_encode_fun(X13, $o), $o), 
0.00/0.33	             'const/sets/IN'(X13), sk_A21(X13, X18, X16)), X16)),
0.00/0.33	    inference('cnf', [status(esa)], [zf_stmt_10])).
0.00/0.33	tff(zf_stmt_7, axiom,
0.00/0.33	  (![A:$tType,A0:A]:
0.00/0.33	     (~
0.00/0.33	       app_encode_app(app_encode_fun(A,$o),$o,
0.00/0.33	                      app_encode_app(A,
0.00/0.33	                                     app_encode_fun(app_encode_fun(A,$o),$o),
0.00/0.33	                                     'const/sets/IN'(A),A0),
0.00/0.33	                      'const/sets/EMPTY'(A))))).
0.00/0.33	tff('1', plain,
0.00/0.33	    ![X2 : $tType, X3 : X2]:
0.00/0.33	      ~ app_encode_app(app_encode_fun(X2, $o), $o, 
0.00/0.33	          app_encode_app(X2, app_encode_fun(app_encode_fun(X2, $o), $o), 
0.00/0.33	            'const/sets/IN'(X2), X3), 'const/sets/EMPTY'(X2)),
0.00/0.33	    inference('cnf', [status(esa)], [zf_stmt_7])).
0.00/0.33	tff('2', plain,
0.00/0.33	    ![X0 : $tType, X1 : app_encode_fun(X0, $o)]:
0.00/0.33	      (~ $true
0.00/0.33	       | app_encode_app(app_encode_fun(X0, $o), $o, 
0.00/0.33	           app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
0.00/0.33	             'const/sets/IN'(X0), sk_A21(X0, X1, 'const/sets/EMPTY'(X0))), 
0.00/0.33	           X1)
0.00/0.33	       | 'const/sets/EMPTY'(X0) = X1),
0.00/0.33	    inference('sup-', [status(thm)], ['0', '1'])).
0.00/0.33	tff('3', plain,
0.00/0.33	    ![X0 : $tType, X1 : app_encode_fun(X0, $o)]:
0.00/0.33	      ('const/sets/EMPTY'(X0) = X1
0.00/0.33	       | app_encode_app(app_encode_fun(X0, $o), $o, 
0.00/0.33	           app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
0.00/0.33	             'const/sets/IN'(X0), sk_A21(X0, X1, 'const/sets/EMPTY'(X0))), 
0.00/0.33	           X1)),
0.00/0.33	    inference('simplify', [status(thm)], ['2'])).
0.00/0.33	tff(zf_stmt_8, axiom,
0.00/0.33	  (![A:$tType,P:app_encode_fun(A,$o),A0:A]:
0.00/0.33	     (app_encode_app(app_encode_fun(A,$o),$o,
0.00/0.33	                     app_encode_app(A,
0.00/0.33	                                    app_encode_fun(app_encode_fun(A,$o),$o),
0.00/0.33	                                    'const/sets/IN'(A),A0),
0.00/0.33	                     P) <=>
0.00/0.33	      app_encode_app(A,$o,P,A0)))).
0.00/0.33	tff('4', plain,
0.00/0.33	    ![X4 : $tType, X5 : app_encode_fun(X4, $o), X6 : X4]:
0.00/0.33	      (app_encode_app(X4, $o, X5, X6)
0.00/0.33	       | ~ app_encode_app(app_encode_fun(X4, $o), $o, 
0.00/0.33	             app_encode_app(X4, app_encode_fun(app_encode_fun(X4, $o), $o), 
0.00/0.33	               'const/sets/IN'(X4), X6), X5)),
0.00/0.33	    inference('cnf', [status(esa)], [zf_stmt_8])).
0.00/0.33	tff('5', plain,
0.00/0.33	    ![X0 : $tType, X1 : app_encode_fun(X0, $o)]:
0.00/0.33	      (~ $true
0.00/0.33	       | 'const/sets/EMPTY'(X0) = X1
0.00/0.33	       | app_encode_app(X0, $o, X1, sk_A21(X0, X1, 'const/sets/EMPTY'(X0)))),
0.00/0.33	    inference('sup-', [status(thm)], ['3', '4'])).
0.00/0.33	tff('6', plain,
0.00/0.33	    ![X0 : $tType, X1 : app_encode_fun(X0, $o)]:
0.00/0.33	      (app_encode_app(X0, $o, X1, sk_A21(X0, X1, 'const/sets/EMPTY'(X0)))
0.00/0.33	       | 'const/sets/EMPTY'(X0) = X1),
0.00/0.33	    inference('simplify', [status(thm)], ['5'])).
0.00/0.33	tff(zf_stmt_11, conjecture,
0.00/0.33	  (![A:$tType,A0:app_encode_fun(app_encode_fun(A,$o),$o)]:
0.00/0.33	     ((app_encode_app(app_encode_fun(app_encode_fun(A,$o),$o),
0.00/0.33	                      app_encode_fun(A,$o),'const/sets/UNIONS'(A),A0) =
0.00/0.33	       'const/sets/EMPTY'(A)) <=>
0.00/0.33	      (![A1:app_encode_fun(A,$o)]:
0.00/0.33	         (app_encode_app(app_encode_fun(app_encode_fun(A,$o),$o),$o,
0.00/0.33	                         app_encode_app(app_encode_fun(A,$o),
0.00/0.33	                                        app_encode_fun(app_encode_fun(
0.00/0.33	                                                       app_encode_fun(A,$o),
0.00/0.33	                                                       $o),$o),
0.00/0.33	                                        'const/sets/IN'(app_encode_fun(A,$o)),
0.00/0.33	                                        A1),
0.00/0.33	                         A0) =>
0.00/0.33	          (A1 = 'const/sets/EMPTY'(A))))))).
0.00/0.33	tff(zf_stmt_0, negated_conjecture,
0.00/0.33	  (~
0.00/0.33	    (![A:$tType,A0:app_encode_fun(app_encode_fun(A,$o),$o)]:
0.00/0.33	       ((app_encode_app(app_encode_fun(app_encode_fun(A,$o),$o),
0.00/0.33	                        app_encode_fun(A,$o),'const/sets/UNIONS'(A),A0) =
0.00/0.33	         'const/sets/EMPTY'(A)) <=>
0.00/0.33	        (![A1:app_encode_fun(A,$o)]:
0.00/0.33	           (app_encode_app(app_encode_fun(app_encode_fun(A,$o),$o),$o,
0.00/0.33	                           app_encode_app(app_encode_fun(A,$o),
0.00/0.33	                                          app_encode_fun(app_encode_fun(
0.00/0.33	                                                         app_encode_fun(A,$o),
0.00/0.33	                                                         $o),$o),
0.00/0.33	                                          'const/sets/IN'(app_encode_fun(
0.00/0.33	                                                          A,$o)),
0.00/0.33	                                          A1),
0.00/0.33	                           A0) =>
0.00/0.33	            (A1 = 'const/sets/EMPTY'(A)))))))).
0.00/0.33	tff('7', plain,
0.00/0.33	    (app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), $o, 
0.00/0.33	       app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.33	         app_encode_fun(app_encode_fun(app_encode_fun(sk_A, $o), $o), $o), 
0.00/0.33	         'const/sets/IN'(app_encode_fun(sk_A, $o)), sk_A1), sk_A0)
0.00/0.33	     | app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.33	         app_encode_fun(sk_A, $o), 'const/sets/UNIONS'(sk_A), sk_A0)
0.00/0.33	        != 'const/sets/EMPTY'(sk_A)),
0.00/0.33	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.33	tff(zf_stmt_9, axiom,
0.00/0.33	  (![A:$tType,A0:app_encode_fun(app_encode_fun(A,$o),$o),A1:A]:
0.00/0.33	     (app_encode_app(app_encode_fun(A,$o),$o,
0.00/0.33	                     app_encode_app(A,
0.00/0.33	                                    app_encode_fun(app_encode_fun(A,$o),$o),
0.00/0.33	                                    'const/sets/IN'(A),A1),
0.00/0.33	                     app_encode_app(app_encode_fun(app_encode_fun(A,$o),$o),
0.00/0.33	                                    app_encode_fun(A,$o),
0.00/0.33	                                    'const/sets/UNIONS'(A),A0)) <=>
0.00/0.33	      (?[A2:app_encode_fun(A,$o)]:
0.00/0.33	         (app_encode_app(app_encode_fun(app_encode_fun(A,$o),$o),$o,
0.00/0.33	                         app_encode_app(app_encode_fun(A,$o),
0.00/0.33	                                        app_encode_fun(app_encode_fun(
0.00/0.33	                                                       app_encode_fun(A,$o),
0.00/0.33	                                                       $o),$o),
0.00/0.33	                                        'const/sets/IN'(app_encode_fun(A,$o)),
0.00/0.33	                                        A2),
0.00/0.33	                         A0) & 
0.00/0.33	          app_encode_app(app_encode_fun(A,$o),$o,
0.00/0.33	                         app_encode_app(A,
0.00/0.33	                                        app_encode_fun(app_encode_fun(A,$o),
0.00/0.33	                                                       $o),
0.00/0.33	                                        'const/sets/IN'(A),A1),
0.00/0.33	                         A2)))))).
0.00/0.33	tff('8', plain,
0.00/0.33	    ![X8 : $tType, X9 : X8, X10 : app_encode_fun(app_encode_fun(X8, $o), $o)]:
0.00/0.33	      (app_encode_app(app_encode_fun(app_encode_fun(X8, $o), $o), $o, 
0.00/0.33	         app_encode_app(app_encode_fun(X8, $o), 
0.00/0.33	           app_encode_fun(app_encode_fun(app_encode_fun(X8, $o), $o), $o), 
0.00/0.33	           'const/sets/IN'(app_encode_fun(X8, $o)), sk_A2(X8, X9, X10)), X10)
0.00/0.33	       | ~ app_encode_app(app_encode_fun(X8, $o), $o, 
0.00/0.33	             app_encode_app(X8, app_encode_fun(app_encode_fun(X8, $o), $o), 
0.00/0.33	               'const/sets/IN'(X8), X9), 
0.00/0.33	             app_encode_app(app_encode_fun(app_encode_fun(X8, $o), $o), 
0.00/0.33	               app_encode_fun(X8, $o), 'const/sets/UNIONS'(X8), X10))),
0.00/0.33	    inference('cnf', [status(esa)], [zf_stmt_9])).
0.00/0.33	tff('9', plain,
0.00/0.33	    ![X19 : app_encode_fun(sk_A, $o)]:
0.00/0.33	      (~ app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), $o, 
0.00/0.33	           app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.33	             app_encode_fun(app_encode_fun(app_encode_fun(sk_A, $o), $o), $o), 
0.00/0.33	             'const/sets/IN'(app_encode_fun(sk_A, $o)), X19), sk_A0)
0.00/0.33	       | X19 = 'const/sets/EMPTY'(sk_A)
0.00/0.33	       | app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.33	           app_encode_fun(sk_A, $o), 'const/sets/UNIONS'(sk_A), sk_A0)
0.00/0.33	          = 'const/sets/EMPTY'(sk_A)),
0.00/0.33	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.33	tff('10', plain,
0.00/0.33	    ![X0 : sk_A]:
0.00/0.33	      (~ $true
0.00/0.33	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.33	             app_encode_app(sk_A, 
0.00/0.33	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.33	               'const/sets/IN'(sk_A), X0), 
0.00/0.33	             app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.33	               app_encode_fun(sk_A, $o), 'const/sets/UNIONS'(sk_A), sk_A0))
0.00/0.33	       | app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.33	           app_encode_fun(sk_A, $o), 'const/sets/UNIONS'(sk_A), sk_A0)
0.00/0.33	          = 'const/sets/EMPTY'(sk_A)
0.00/0.33	       | sk_A2(sk_A, X0, sk_A0) = 'const/sets/EMPTY'(sk_A)),
0.00/0.33	    inference('sup-', [status(thm)], ['8', '9'])).
0.00/0.33	tff('11', plain,
0.00/0.33	    ![X0 : sk_A]:
0.00/0.33	      (sk_A2(sk_A, X0, sk_A0) = 'const/sets/EMPTY'(sk_A)
0.00/0.33	       | app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.33	           app_encode_fun(sk_A, $o), 'const/sets/UNIONS'(sk_A), sk_A0)
0.00/0.33	          = 'const/sets/EMPTY'(sk_A)
0.00/0.33	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.33	             app_encode_app(sk_A, 
0.00/0.33	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.33	               'const/sets/IN'(sk_A), X0), 
0.00/0.33	             app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.33	               app_encode_fun(sk_A, $o), 'const/sets/UNIONS'(sk_A), sk_A0))),
0.00/0.33	    inference('simplify', [status(thm)], ['10'])).
0.00/0.33	tff('12', plain,
0.00/0.33	    ![X8 : $tType, X9 : X8, X10 : app_encode_fun(app_encode_fun(X8, $o), $o)]:
0.00/0.33	      (app_encode_app(app_encode_fun(X8, $o), $o, 
0.00/0.33	         app_encode_app(X8, app_encode_fun(app_encode_fun(X8, $o), $o), 
0.00/0.33	           'const/sets/IN'(X8), X9), sk_A2(X8, X9, X10))
0.00/0.33	       | ~ app_encode_app(app_encode_fun(X8, $o), $o, 
0.00/0.33	             app_encode_app(X8, app_encode_fun(app_encode_fun(X8, $o), $o), 
0.00/0.33	               'const/sets/IN'(X8), X9), 
0.00/0.33	             app_encode_app(app_encode_fun(app_encode_fun(X8, $o), $o), 
0.00/0.33	               app_encode_fun(X8, $o), 'const/sets/UNIONS'(X8), X10))),
0.00/0.33	    inference('cnf', [status(esa)], [zf_stmt_9])).
0.00/0.33	tff('13', plain,
0.00/0.33	    ![X0 : $tType, X1 : app_encode_fun(app_encode_fun(X0, $o), $o), X2 : X0]:
0.00/0.33	      (~ $true
0.00/0.33	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
0.00/0.33	             app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
0.00/0.33	               'const/sets/IN'(X0), X2), 
0.00/0.33	             app_encode_app(app_encode_fun(app_encode_fun(X0, $o), $o), 
0.00/0.33	               app_encode_fun(X0, $o), 'const/sets/UNIONS'(X0), X1))
0.00/0.33	       | app_encode_app(X0, $o, sk_A2(X0, X2, X1), X2)),
0.00/0.33	    inference('sup-', [status(thm)], ['12', '4'])).
0.00/0.33	tff('14', plain,
0.00/0.33	    ![X0 : $tType, X1 : app_encode_fun(app_encode_fun(X0, $o), $o), X2 : X0]:
0.00/0.33	      (app_encode_app(X0, $o, sk_A2(X0, X2, X1), X2)
0.00/0.33	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
0.00/0.33	             app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
0.00/0.33	               'const/sets/IN'(X0), X2), 
0.00/0.33	             app_encode_app(app_encode_fun(app_encode_fun(X0, $o), $o), 
0.00/0.33	               app_encode_fun(X0, $o), 'const/sets/UNIONS'(X0), X1))),
0.00/0.33	    inference('simplify', [status(thm)], ['13'])).
0.00/0.33	tff('15', plain,
0.00/0.33	    ![X0 : sk_A]:
0.00/0.33	      (app_encode_app(sk_A, $o, 'const/sets/EMPTY'(sk_A), X0)
0.00/0.33	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.33	             app_encode_app(sk_A, 
0.00/0.33	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.33	               'const/sets/IN'(sk_A), X0), 
0.00/0.33	             app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.33	               app_encode_fun(sk_A, $o), 'const/sets/UNIONS'(sk_A), sk_A0))
0.00/0.33	       | app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.33	           app_encode_fun(sk_A, $o), 'const/sets/UNIONS'(sk_A), sk_A0)
0.00/0.33	          = 'const/sets/EMPTY'(sk_A)
0.00/0.33	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.33	             app_encode_app(sk_A, 
0.00/0.33	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.33	               'const/sets/IN'(sk_A), X0), 
0.00/0.33	             app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.33	               app_encode_fun(sk_A, $o), 'const/sets/UNIONS'(sk_A), sk_A0))),
0.00/0.33	    inference('sup+', [status(thm)], ['11', '14'])).
0.00/0.33	tff('16', plain,
0.00/0.33	    ![X0 : sk_A]:
0.00/0.33	      (app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.33	         app_encode_fun(sk_A, $o), 'const/sets/UNIONS'(sk_A), sk_A0)
0.00/0.33	        = 'const/sets/EMPTY'(sk_A)
0.00/0.33	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.33	             app_encode_app(sk_A, 
0.00/0.33	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.33	               'const/sets/IN'(sk_A), X0), 
0.00/0.33	             app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.33	               app_encode_fun(sk_A, $o), 'const/sets/UNIONS'(sk_A), sk_A0))
0.00/0.33	       | app_encode_app(sk_A, $o, 'const/sets/EMPTY'(sk_A), X0)),
0.00/0.33	    inference('simplify', [status(thm)], ['15'])).
0.00/0.33	tff('17', plain,
0.00/0.33	    ![X4 : $tType, X5 : app_encode_fun(X4, $o), X7 : X4]:
0.00/0.33	      (app_encode_app(app_encode_fun(X4, $o), $o, 
0.00/0.33	         app_encode_app(X4, app_encode_fun(app_encode_fun(X4, $o), $o), 
0.00/0.33	           'const/sets/IN'(X4), X7), X5)
0.00/0.33	       | ~ app_encode_app(X4, $o, X5, X7)),
0.00/0.33	    inference('cnf', [status(esa)], [zf_stmt_8])).
0.00/0.33	tff('18', plain,
0.00/0.33	    ![X0 : $tType, X1 : X0]:
0.00/0.33	      (~ $true | ~ app_encode_app(X0, $o, 'const/sets/EMPTY'(X0), X1)),
0.00/0.33	    inference('sup-', [status(thm)], ['17', '1'])).
0.00/0.33	tff('19', plain,
0.00/0.33	    ![X0 : $tType, X1 : X0]:
0.00/0.33	      ~ app_encode_app(X0, $o, 'const/sets/EMPTY'(X0), X1),
0.00/0.33	    inference('simplify', [status(thm)], ['18'])).
0.00/0.33	tff('20', plain,
0.00/0.33	    ![X0 : sk_A]:
0.00/0.34	      (~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.34	           app_encode_app(sk_A, 
0.00/0.34	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.34	             'const/sets/IN'(sk_A), X0), 
0.00/0.34	           app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.34	             app_encode_fun(sk_A, $o), 'const/sets/UNIONS'(sk_A), sk_A0))
0.00/0.34	       | app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.34	           app_encode_fun(sk_A, $o), 'const/sets/UNIONS'(sk_A), sk_A0)
0.00/0.34	          = 'const/sets/EMPTY'(sk_A)),
0.00/0.34	    inference('clc', [status(thm)], ['16', '19'])).
0.00/0.34	tff('21', plain,
0.00/0.34	    (~ $true
0.00/0.34	     | 'const/sets/EMPTY'(sk_A)
0.00/0.34	        = app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.34	            app_encode_fun(sk_A, $o), 'const/sets/UNIONS'(sk_A), sk_A0)
0.00/0.34	     | app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.34	         app_encode_fun(sk_A, $o), 'const/sets/UNIONS'(sk_A), sk_A0)
0.00/0.34	        = 'const/sets/EMPTY'(sk_A)),
0.00/0.34	    inference('sup-', [status(thm)], ['3', '20'])).
0.00/0.34	tff('22', plain,
0.00/0.34	    'const/sets/EMPTY'(sk_A)
0.00/0.34	     = app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.34	         app_encode_fun(sk_A, $o), 'const/sets/UNIONS'(sk_A), sk_A0),
0.00/0.34	    inference('simplify', [status(thm)], ['21'])).
0.00/0.34	tff('23', plain,
0.00/0.34	    (app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), $o, 
0.00/0.34	       app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	         app_encode_fun(app_encode_fun(app_encode_fun(sk_A, $o), $o), $o), 
0.00/0.34	         'const/sets/IN'(app_encode_fun(sk_A, $o)), sk_A1), sk_A0)
0.00/0.34	     | 'const/sets/EMPTY'(sk_A) != 'const/sets/EMPTY'(sk_A)),
0.00/0.34	    inference('demod', [status(thm)], ['7', '22'])).
0.00/0.34	tff('24', plain,
0.00/0.34	    app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), $o, 
0.00/0.34	      app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	        app_encode_fun(app_encode_fun(app_encode_fun(sk_A, $o), $o), $o), 
0.00/0.34	        'const/sets/IN'(app_encode_fun(sk_A, $o)), sk_A1), sk_A0),
0.00/0.34	    inference('simplify', [status(thm)], ['23'])).
0.00/0.34	tff('25', plain,
0.00/0.34	    ![X8 : $tType, X10 : app_encode_fun(app_encode_fun(X8, $o), $o), 
0.00/0.34	      X11 : X8, X12 : app_encode_fun(X8, $o)]:
0.00/0.34	      (app_encode_app(app_encode_fun(X8, $o), $o, 
0.00/0.34	         app_encode_app(X8, app_encode_fun(app_encode_fun(X8, $o), $o), 
0.00/0.34	           'const/sets/IN'(X8), X11), 
0.00/0.34	         app_encode_app(app_encode_fun(app_encode_fun(X8, $o), $o), 
0.00/0.34	           app_encode_fun(X8, $o), 'const/sets/UNIONS'(X8), X10))
0.00/0.34	       | ~ app_encode_app(app_encode_fun(X8, $o), $o, 
0.00/0.34	             app_encode_app(X8, app_encode_fun(app_encode_fun(X8, $o), $o), 
0.00/0.34	               'const/sets/IN'(X8), X11), X12)
0.00/0.34	       | ~ app_encode_app(app_encode_fun(app_encode_fun(X8, $o), $o), $o, 
0.00/0.34	             app_encode_app(app_encode_fun(X8, $o), 
0.00/0.34	               app_encode_fun(app_encode_fun(app_encode_fun(X8, $o), $o), $o), 
0.00/0.34	               'const/sets/IN'(app_encode_fun(X8, $o)), X12), X10)),
0.00/0.34	    inference('cnf', [status(esa)], [zf_stmt_9])).
0.00/0.34	tff('26', plain,
0.00/0.34	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : X0, 
0.00/0.34	      X3 : app_encode_fun(app_encode_fun(X0, $o), $o)]:
0.00/0.34	      (~ $true
0.00/0.34	       | ~ app_encode_app(X0, $o, X1, X2)
0.00/0.34	       | ~ app_encode_app(app_encode_fun(app_encode_fun(X0, $o), $o), $o, 
0.00/0.34	             app_encode_app(app_encode_fun(X0, $o), 
0.00/0.34	               app_encode_fun(app_encode_fun(app_encode_fun(X0, $o), $o), $o), 
0.00/0.34	               'const/sets/IN'(app_encode_fun(X0, $o)), X1), X3)
0.00/0.34	       | app_encode_app(app_encode_fun(X0, $o), $o, 
0.00/0.34	           app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
0.00/0.34	             'const/sets/IN'(X0), X2), 
0.00/0.34	           app_encode_app(app_encode_fun(app_encode_fun(X0, $o), $o), 
0.00/0.34	             app_encode_fun(X0, $o), 'const/sets/UNIONS'(X0), X3))),
0.00/0.34	    inference('sup-', [status(thm)], ['17', '25'])).
0.00/0.34	tff('27', plain,
0.00/0.34	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : X0, 
0.00/0.34	      X3 : app_encode_fun(app_encode_fun(X0, $o), $o)]:
0.00/0.34	      (app_encode_app(app_encode_fun(X0, $o), $o, 
0.00/0.34	         app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
0.00/0.34	           'const/sets/IN'(X0), X2), 
0.00/0.34	         app_encode_app(app_encode_fun(app_encode_fun(X0, $o), $o), 
0.00/0.34	           app_encode_fun(X0, $o), 'const/sets/UNIONS'(X0), X3))
0.00/0.34	       | ~ app_encode_app(app_encode_fun(app_encode_fun(X0, $o), $o), $o, 
0.00/0.34	             app_encode_app(app_encode_fun(X0, $o), 
0.00/0.34	               app_encode_fun(app_encode_fun(app_encode_fun(X0, $o), $o), $o), 
0.00/0.34	               'const/sets/IN'(app_encode_fun(X0, $o)), X1), X3)
0.00/0.34	       | ~ app_encode_app(X0, $o, X1, X2)),
0.00/0.34	    inference('simplify', [status(thm)], ['26'])).
0.00/0.34	tff('28', plain,
0.00/0.34	    ![X0 : sk_A]:
0.00/0.34	      (~ $true
0.00/0.34	       | ~ app_encode_app(sk_A, $o, sk_A1, X0)
0.00/0.34	       | app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.34	           app_encode_app(sk_A, 
0.00/0.34	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.34	             'const/sets/IN'(sk_A), X0), 
0.00/0.34	           app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.34	             app_encode_fun(sk_A, $o), 'const/sets/UNIONS'(sk_A), sk_A0))),
0.00/0.34	    inference('sup-', [status(thm)], ['24', '27'])).
0.00/0.34	tff('29', plain,
0.00/0.34	    ![X0 : sk_A]:
0.00/0.34	      (~ $true
0.00/0.34	       | ~ app_encode_app(sk_A, $o, sk_A1, X0)
0.00/0.34	       | app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.34	           app_encode_app(sk_A, 
0.00/0.34	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.34	             'const/sets/IN'(sk_A), X0), 'const/sets/EMPTY'(sk_A))),
0.00/0.34	    inference('demod', [status(thm)], ['28', '22'])).
0.00/0.34	tff('30', plain,
0.00/0.34	    ![X0 : sk_A]:
0.00/0.34	      (app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.34	         app_encode_app(sk_A, app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.34	           'const/sets/IN'(sk_A), X0), 'const/sets/EMPTY'(sk_A))
0.00/0.34	       | ~ app_encode_app(sk_A, $o, sk_A1, X0)),
0.00/0.34	    inference('simplify', [status(thm)], ['29'])).
0.00/0.34	tff('31', plain, ![X0 : sk_A]: ~ app_encode_app(sk_A, $o, sk_A1, X0),
0.00/0.34	    inference('clc', [status(thm)], ['30', '1'])).
0.00/0.34	tff('32', plain, (~ $true | 'const/sets/EMPTY'(sk_A) = sk_A1),
0.00/0.34	    inference('sup-', [status(thm)], ['6', '31'])).
0.00/0.34	tff('33', plain, 'const/sets/EMPTY'(sk_A) = sk_A1,
0.00/0.34	    inference('simplify', [status(thm)], ['32'])).
0.00/0.34	tff('34', plain,
0.00/0.34	    (sk_A1 != 'const/sets/EMPTY'(sk_A)
0.00/0.34	     | app_encode_app(app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.34	         app_encode_fun(sk_A, $o), 'const/sets/UNIONS'(sk_A), sk_A0)
0.00/0.34	        != 'const/sets/EMPTY'(sk_A)),
0.00/0.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.34	tff('35', plain,
0.00/0.34	    (sk_A1 != 'const/sets/EMPTY'(sk_A)
0.00/0.34	     | 'const/sets/EMPTY'(sk_A) != 'const/sets/EMPTY'(sk_A)),
0.00/0.34	    inference('demod', [status(thm)], ['34', '22'])).
0.00/0.34	tff('36', plain, sk_A1 != 'const/sets/EMPTY'(sk_A),
0.00/0.34	    inference('simplify', [status(thm)], ['35'])).
0.00/0.34	tff('37', plain, $false,
0.00/0.34	    inference('simplify_reflect-', [status(thm)], ['33', '36'])).
0.00/0.34	
0.00/0.34	% SZS output end Refutation
0.00/0.34	EOF
