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    : 
0.00/0.01	#!/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 $2 \
0.00/0.01	  --simultaneous-sup false \
0.00/0.01	  --no-max-vars \
0.00/0.01	  --no-fool
0.00/0.19	% Computer   : n084.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 07:05:08 CST 2018
34.19/34.39	% done 1353 iterations in 34.195s
34.19/34.39	% SZS status Theorem for 'stdin'
34.19/34.39	% SZS output start Refutation
34.19/34.40	tff(zf_stmt_62, axiom,
34.19/34.40	  (app_encode_app(bool,$o,pp,
34.19/34.40	                  app_encode_app(type,bool,
34.19/34.40	                                 app_encode_app(fun(type,bool),
34.19/34.40	                                                app_encode_fun(type,bool),
34.19/34.40	                                                aa(type,bool),
34.19/34.40	                                                app_encode_app(dB,
34.19/34.40	                                                               fun(type,bool),
34.19/34.40	                                                               app_encode_app(
34.19/34.40	                                                               fun(nat,type),
34.19/34.40	                                                               app_encode_fun(
34.19/34.40	                                                               dB,
34.19/34.40	                                                               fun(type,bool)),
34.19/34.40	                                                               typing,
34.19/34.40	                                                               app_encode_app(
34.19/34.40	                                                               type,
34.19/34.40	                                                               fun(nat,type),
34.19/34.40	                                                               app_encode_app(
34.19/34.40	                                                               nat,
34.19/34.40	                                                               app_encode_fun(
34.19/34.40	                                                               type,
34.19/34.40	                                                               fun(nat,type)),
34.19/34.40	                                                               app_encode_app(
34.19/34.40	                                                               fun(nat,type),
34.19/34.40	                                                               app_encode_fun(
34.19/34.40	                                                               nat,
34.19/34.40	                                                               app_encode_fun(
34.19/34.40	                                                               type,
34.19/34.40	                                                               fun(nat,type))),
34.19/34.40	                                                               shift(type),e),
34.19/34.40	                                                               i),t)),a)),
34.19/34.40	                                 t2)))).
34.19/34.40	tff('0', plain,
34.19/34.40	    app_encode_app(bool, $o, pp, 
34.19/34.40	      app_encode_app(type, bool, 
34.19/34.40	        app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
34.19/34.40	          aa(type, bool), 
34.19/34.40	          app_encode_app(dB, fun(type, bool), 
34.19/34.40	            app_encode_app(fun(nat, type), 
34.19/34.40	              app_encode_fun(dB, fun(type, bool)), typing, 
34.19/34.40	              app_encode_app(type, fun(nat, type), 
34.19/34.40	                app_encode_app(nat, app_encode_fun(type, fun(nat, type)), 
34.19/34.40	                  app_encode_app(fun(nat, type), 
34.19/34.40	                    app_encode_fun(nat, app_encode_fun(type, fun(nat, type))), 
34.19/34.40	                    shift(type), e), i), t)), a)), t2)),
34.19/34.40	    inference('cnf', [status(esa)], [zf_stmt_62])).
34.19/34.40	tff(zf_stmt_69, axiom,
34.19/34.40	  (![N1:nat]:
34.19/34.40	     app_encode_app(bool,$o,pp,
34.19/34.40	                    app_encode_app(dB,bool,
34.19/34.40	                                   app_encode_app(fun(dB,bool),
34.19/34.40	                                                  app_encode_fun(dB,bool),
34.19/34.40	                                                  aa(dB,bool),it),
34.19/34.40	                                   app_encode_app(nat,dB,var,N1))))).
34.19/34.40	tff('1', plain,
34.19/34.40	    ![X23 : nat]:
34.19/34.40	      app_encode_app(bool, $o, pp, 
34.19/34.40	        app_encode_app(dB, bool, 
34.19/34.40	          app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
34.19/34.40	            aa(dB, bool), it), app_encode_app(nat, dB, var, X23))),
34.19/34.40	    inference('cnf', [status(esa)], [zf_stmt_69])).
34.19/34.40	tff(zf_stmt_166, axiom, (![P:bool]: ((P = fTrue) | (P = fFalse)))).
34.19/34.40	tff('2', plain, ![X346 : bool]: (X346 = fTrue | X346 = fFalse),
34.19/34.40	    inference('cnf', [status(esa)], [zf_stmt_166])).
34.19/34.40	tff(zf_stmt_156, axiom, (~app_encode_app(bool,$o,pp,fFalse))).
34.19/34.40	tff('3', plain, ~ app_encode_app(bool, $o, pp, fFalse),
34.19/34.40	    inference('cnf', [status(esa)], [zf_stmt_156])).
34.19/34.40	tff('4', plain,
34.19/34.40	    ![X0 : bool]: (~ app_encode_app(bool, $o, pp, X0) | X0 = fTrue),
34.19/34.40	    inference('sup-', [status(thm)], ['2', '3'])).
34.19/34.40	tff(zf_stmt_58, axiom,
34.19/34.40	  (app_encode_app(bool,$o,pp,
34.19/34.40	                  app_encode_app(dB,bool,
34.19/34.40	                                 app_encode_app(fun(dB,bool),
34.19/34.40	                                                app_encode_fun(dB,bool),
34.19/34.40	                                                aa(dB,bool),it),
34.19/34.40	                                 u)))).
34.19/34.40	tff('5', plain,
34.19/34.40	    app_encode_app(bool, $o, pp, 
34.19/34.40	      app_encode_app(dB, bool, 
34.19/34.40	        app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
34.19/34.40	          aa(dB, bool), it), u)),
34.19/34.40	    inference('cnf', [status(esa)], [zf_stmt_58])).
34.19/34.40	tff('6', plain,
34.19/34.40	    (~ $true
34.19/34.40	     | app_encode_app(dB, bool, 
34.19/34.40	         app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
34.19/34.40	           aa(dB, bool), it), u)
34.19/34.40	        = fTrue),
34.19/34.40	    inference('sup-', [status(thm)], ['5', '4'])).
34.19/34.40	tff('7', plain,
34.19/34.40	    app_encode_app(dB, bool, 
34.19/34.40	      app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), aa(dB, bool), 
34.19/34.40	        it), u)
34.19/34.40	     = fTrue,
34.19/34.40	    inference('simplify', [status(thm)], ['6'])).
34.19/34.40	tff('8', plain,
34.19/34.40	    ![X0 : bool]:
34.19/34.40	      (~ app_encode_app(bool, $o, pp, X0)
34.19/34.40	       | X0
34.19/34.40	          = app_encode_app(dB, bool, 
34.19/34.40	              app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
34.19/34.40	                aa(dB, bool), it), u)),
34.19/34.40	    inference('demod', [status(thm)], ['4', '7'])).
34.19/34.40	tff('9', plain,
34.19/34.40	    ![X0 : nat]:
34.19/34.40	      (~ $true
34.19/34.40	       | app_encode_app(dB, bool, 
34.19/34.40	           app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
34.19/34.40	             aa(dB, bool), it), app_encode_app(nat, dB, var, X0))
34.19/34.40	          = app_encode_app(dB, bool, 
34.19/34.40	              app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
34.19/34.40	                aa(dB, bool), it), u)),
34.19/34.40	    inference('sup-', [status(thm)], ['1', '8'])).
34.19/34.40	tff('10', plain,
34.19/34.40	    ![X0 : nat]:
34.19/34.40	      app_encode_app(dB, bool, 
34.19/34.40	        app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
34.19/34.40	          aa(dB, bool), it), app_encode_app(nat, dB, var, X0))
34.19/34.40	       = app_encode_app(dB, bool, 
34.19/34.40	           app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
34.19/34.40	             aa(dB, bool), it), u),
34.19/34.40	    inference('simplify', [status(thm)], ['9'])).
34.19/34.40	tff('11', plain,
34.19/34.40	    ![X346 : bool]:
34.19/34.40	      (X346
34.19/34.40	        = app_encode_app(dB, bool, 
34.19/34.40	            app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
34.19/34.40	              aa(dB, bool), it), u)
34.19/34.40	       | X346 = fFalse),
34.19/34.40	    inference('demod', [status(thm)], ['2', '7'])).
34.19/34.40	tff('12', plain,
34.19/34.40	    ![X0 : nat, X1 : bool]:
34.19/34.40	      (X1
34.19/34.40	        = app_encode_app(dB, bool, 
34.19/34.40	            app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
34.19/34.40	              aa(dB, bool), it), app_encode_app(nat, dB, var, X0))
34.19/34.40	       | X1 = fFalse),
34.19/34.40	    inference('sup+', [status(thm)], ['10', '11'])).
34.19/34.40	tff('13', plain,
34.19/34.40	    ![X0 : bool, X1 : bool]: (X1 = X0 | X0 = fFalse | X1 = fFalse),
34.19/34.40	    inference('sup+', [status(thm)], ['2', '2'])).
34.19/34.40	tff('14', plain,
34.19/34.40	    ![X0 : bool, X1 : bool]:
34.19/34.40	      (~ app_encode_app(bool, $o, pp, X0) | X1 = fFalse | X1 = X0),
34.19/34.40	    inference('sup-', [status(thm)], ['13', '3'])).
34.19/34.40	tff('15', plain,
34.19/34.40	    ![X0 : nat, X1 : bool]:
34.19/34.40	      (~ $true
34.19/34.40	       | X1
34.19/34.40	          = app_encode_app(dB, bool, 
34.19/34.40	              app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
34.19/34.40	                aa(dB, bool), it), app_encode_app(nat, dB, var, X0))
34.19/34.40	       | X1 = fFalse),
34.19/34.40	    inference('sup-', [status(thm)], ['1', '14'])).
34.19/34.40	tff('16', plain,
34.19/34.40	    ![X0 : nat, X1 : bool]:
34.19/34.40	      (X1 = fFalse
34.19/34.40	       | X1
34.19/34.40	          = app_encode_app(dB, bool, 
34.19/34.40	              app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
34.19/34.40	                aa(dB, bool), it), app_encode_app(nat, dB, var, X0))),
34.19/34.40	    inference('simplify', [status(thm)], ['15'])).
34.19/34.40	tff(zf_stmt_167, conjecture,
34.19/34.40	  (app_encode_app(bool,$o,pp,
34.19/34.40	                  app_encode_app(dB,bool,
34.19/34.40	                                 app_encode_app(fun(dB,bool),
34.19/34.40	                                                app_encode_fun(dB,bool),
34.19/34.40	                                                aa(dB,bool),it),
34.19/34.40	                                 app_encode_app(nat,dB,
34.19/34.40	                                                app_encode_app(dB,
34.19/34.40	                                                               app_encode_fun(
34.19/34.40	                                                               nat,dB),
34.19/34.40	                                                               app_encode_app(
34.19/34.40	                                                               dB,
34.19/34.40	                                                               app_encode_fun(
34.19/34.40	                                                               dB,
34.19/34.40	                                                               app_encode_fun(
34.19/34.40	                                                               nat,dB)),
34.19/34.40	                                                               subst,a),u),
34.19/34.40	                                                i))))).
34.19/34.40	tff(zf_stmt_0, negated_conjecture,
34.19/34.40	  (~
34.19/34.40	    app_encode_app(bool,$o,pp,
34.19/34.40	                   app_encode_app(dB,bool,
34.19/34.40	                                  app_encode_app(fun(dB,bool),
34.19/34.40	                                                 app_encode_fun(dB,bool),
34.19/34.40	                                                 aa(dB,bool),it),
34.19/34.40	                                  app_encode_app(nat,dB,
34.19/34.40	                                                 app_encode_app(dB,
34.19/34.40	                                                                app_encode_fun(
34.19/34.40	                                                                nat,dB),
34.19/34.40	                                                                app_encode_app(
34.19/34.40	                                                                dB,
34.19/34.40	                                                                app_encode_fun(
34.19/34.40	                                                                dB,
34.19/34.40	                                                                app_encode_fun(
34.19/34.40	                                                                nat,dB)),
34.19/34.40	                                                                subst,a),u),
34.19/34.40	                                                 i))))).
34.19/34.40	tff('17', plain,
34.19/34.40	    ~ app_encode_app(bool, $o, pp, 
34.19/34.40	        app_encode_app(dB, bool, 
34.19/34.40	          app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
34.19/34.40	            aa(dB, bool), it), 
34.19/34.40	          app_encode_app(nat, dB, 
34.19/34.40	            app_encode_app(dB, app_encode_fun(nat, dB), 
34.19/34.40	              app_encode_app(dB, 
34.19/34.40	                app_encode_fun(dB, app_encode_fun(nat, dB)), subst, a), u), 
34.19/34.40	            i))),
34.19/34.40	    inference('cnf', [status(esa)], [zf_stmt_0])).
34.19/34.40	tff('18', plain,
34.19/34.40	    ![X0 : nat]:
34.19/34.40	      (~ app_encode_app(bool, $o, pp, 
34.19/34.40	           app_encode_app(dB, bool, 
34.19/34.40	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
34.19/34.40	               aa(dB, bool), it), app_encode_app(nat, dB, var, X0)))
34.19/34.40	       | app_encode_app(dB, bool, 
34.19/34.40	           app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
34.19/34.40	             aa(dB, bool), it), 
34.19/34.40	           app_encode_app(nat, dB, 
34.19/34.40	             app_encode_app(dB, app_encode_fun(nat, dB), 
34.19/34.40	               app_encode_app(dB, 
34.19/34.40	                 app_encode_fun(dB, app_encode_fun(nat, dB)), subst, a), u), 
34.19/34.40	             i))
34.19/34.40	          = fFalse),
34.19/34.40	    inference('sup-', [status(thm)], ['16', '17'])).
34.19/34.40	tff('19', plain,
34.19/34.40	    (~ $true
34.19/34.40	     | app_encode_app(dB, bool, 
34.19/34.40	         app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
34.19/34.40	           aa(dB, bool), it), 
34.19/34.40	         app_encode_app(nat, dB, 
34.19/34.40	           app_encode_app(dB, app_encode_fun(nat, dB), 
34.19/34.40	             app_encode_app(dB, app_encode_fun(dB, app_encode_fun(nat, dB)), 
34.19/34.40	               subst, a), u), i))
34.19/34.40	        = fFalse),
34.19/34.40	    inference('demod', [status(thm)], ['18', '1'])).
34.19/34.40	tff('20', plain,
34.19/34.40	    app_encode_app(dB, bool, 
34.19/34.40	      app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), aa(dB, bool), 
34.19/34.40	        it), 
34.19/34.40	      app_encode_app(nat, dB, 
34.19/34.40	        app_encode_app(dB, app_encode_fun(nat, dB), 
34.19/34.40	          app_encode_app(dB, app_encode_fun(dB, app_encode_fun(nat, dB)), 
34.19/34.40	            subst, a), u), i))
34.19/34.40	     = fFalse,
34.19/34.40	    inference('simplify', [status(thm)], ['19'])).
34.19/34.40	tff('21', plain,
34.19/34.40	    ![X0 : nat, X1 : bool]:
34.19/34.40	      (X1
34.19/34.40	        = app_encode_app(dB, bool, 
34.19/34.40	            app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
34.19/34.40	              aa(dB, bool), it), app_encode_app(nat, dB, var, X0))
34.19/34.40	       | X1
34.19/34.40	          = app_encode_app(dB, bool, 
34.19/34.40	              app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
34.19/34.40	                aa(dB, bool), it), 
34.19/34.40	              app_encode_app(nat, dB, 
34.19/34.40	                app_encode_app(dB, app_encode_fun(nat, dB), 
34.19/34.40	                  app_encode_app(dB, 
34.19/34.40	                    app_encode_fun(dB, app_encode_fun(nat, dB)), subst, a), 
34.19/34.40	                  u), i))),
34.19/34.40	    inference('demod', [status(thm)], ['12', '20'])).
34.19/34.40	tff('22', plain,
34.19/34.40	    ![X0 : bool, X1 : nat]:
34.19/34.40	      (~ app_encode_app(bool, $o, pp, X0)
34.19/34.40	       | X0
34.19/34.40	          = app_encode_app(dB, bool, 
34.19/34.40	              app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
34.19/34.40	                aa(dB, bool), it), app_encode_app(nat, dB, var, X1))),
34.19/34.40	    inference('sup-', [status(thm)], ['21', '17'])).
34.19/34.40	tff('23', plain,
34.19/34.40	    ![X0 : nat]:
34.19/34.40	      (~ $true
34.19/34.40	       | app_encode_app(type, bool, 
34.19/34.40	           app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
34.19/34.40	             aa(type, bool), 
34.19/34.40	             app_encode_app(dB, fun(type, bool), 
34.19/34.40	               app_encode_app(fun(nat, type), 
34.19/34.40	                 app_encode_fun(dB, fun(type, bool)), typing, 
34.19/34.40	                 app_encode_app(type, fun(nat, type), 
34.19/34.40	                   app_encode_app(nat, app_encode_fun(type, fun(nat, type)), 
34.19/34.40	                     app_encode_app(fun(nat, type), 
34.19/34.40	                       app_encode_fun(nat, 
34.19/34.40	                         app_encode_fun(type, fun(nat, type))), shift(type), 
34.19/34.40	                       e), i), t)), a)), t2)
34.19/34.40	          = app_encode_app(dB, bool, 
34.19/34.40	              app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
34.19/34.40	                aa(dB, bool), it), app_encode_app(nat, dB, var, X0))),
34.19/34.40	    inference('sup-', [status(thm)], ['0', '22'])).
34.19/34.40	tff('24', plain,
34.19/34.40	    ![X0 : nat]:
34.19/34.40	      app_encode_app(type, bool, 
34.19/34.40	        app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
34.19/34.40	          aa(type, bool), 
34.19/34.40	          app_encode_app(dB, fun(type, bool), 
34.19/34.40	            app_encode_app(fun(nat, type), 
34.19/34.40	              app_encode_fun(dB, fun(type, bool)), typing, 
34.19/34.40	              app_encode_app(type, fun(nat, type), 
34.19/34.40	                app_encode_app(nat, app_encode_fun(type, fun(nat, type)), 
34.19/34.40	                  app_encode_app(fun(nat, type), 
34.19/34.40	                    app_encode_fun(nat, app_encode_fun(type, fun(nat, type))), 
34.19/34.40	                    shift(type), e), i), t)), a)), t2)
34.19/34.40	       = app_encode_app(dB, bool, 
34.19/34.40	           app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
34.19/34.40	             aa(dB, bool), it), app_encode_app(nat, dB, var, X0)),
34.19/34.40	    inference('simplify', [status(thm)], ['23'])).
34.19/34.40	tff('25', plain,
34.19/34.40	    app_encode_app(type, bool, 
34.19/34.40	      app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
34.19/34.40	        aa(type, bool), 
34.19/34.40	        app_encode_app(dB, fun(type, bool), 
34.19/34.40	          app_encode_app(fun(nat, type), 
34.19/34.40	            app_encode_fun(dB, fun(type, bool)), typing, 
34.19/34.40	            app_encode_app(type, fun(nat, type), 
34.19/34.40	              app_encode_app(nat, app_encode_fun(type, fun(nat, type)), 
34.19/34.40	                app_encode_app(fun(nat, type), 
34.19/34.40	                  app_encode_fun(nat, app_encode_fun(type, fun(nat, type))), 
34.19/34.40	                  shift(type), e), i), t)), a)), t2)
34.19/34.40	     = app_encode_app(dB, bool, 
34.19/34.40	         app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
34.19/34.40	           aa(dB, bool), it), u),
34.19/34.40	    inference('sup+', [status(thm)], ['24', '10'])).
34.19/34.40	tff(zf_stmt_59, axiom,
34.19/34.40	  (app_encode_app(bool,$o,pp,
34.19/34.40	                  app_encode_app(type,bool,
34.19/34.40	                                 app_encode_app(fun(type,bool),
34.19/34.40	                                                app_encode_fun(type,bool),
34.19/34.40	                                                aa(type,bool),
34.19/34.40	                                                app_encode_app(dB,
34.19/34.40	                                                               fun(type,bool),
34.19/34.40	                                                               app_encode_app(
34.19/34.40	                                                               fun(nat,type),
34.19/34.40	                                                               app_encode_fun(
34.19/34.40	                                                               dB,
34.19/34.40	                                                               fun(type,bool)),
34.19/34.40	                                                               typing,e),u)),
34.19/34.40	                                 t)))).
34.19/34.40	tff('26', plain,
34.19/34.40	    app_encode_app(bool, $o, pp, 
34.19/34.40	      app_encode_app(type, bool, 
34.19/34.40	        app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
34.19/34.40	          aa(type, bool), 
34.19/34.40	          app_encode_app(dB, fun(type, bool), 
34.19/34.40	            app_encode_app(fun(nat, type), 
34.19/34.40	              app_encode_fun(dB, fun(type, bool)), typing, e), u)), t)),
34.19/34.40	    inference('cnf', [status(esa)], [zf_stmt_59])).
34.19/34.40	tff(zf_stmt_60, axiom,
34.19/34.40	  (![E1:fun(nat,type),T5:type,U3:dB,I1:nat]:
34.19/34.40	     (app_encode_app(bool,$o,pp,
34.19/34.40	                     app_encode_app(type,bool,
34.19/34.40	                                    app_encode_app(fun(type,bool),
34.19/34.40	                                                   app_encode_fun(type,bool),
34.19/34.40	                                                   aa(type,bool),
34.19/34.40	                                                   app_encode_app(dB,
34.19/34.40	                                                                  fun(
34.19/34.40	                                                                  type,bool),
34.19/34.40	                                                                  app_encode_app(
34.19/34.40	                                                                  fun(
34.19/34.40	                                                                  nat,type),
34.19/34.40	                                                                  app_encode_fun(
34.19/34.40	                                                                  dB,
34.19/34.40	                                                                  fun(
34.19/34.40	                                                                  type,bool)),
34.19/34.40	                                                                  typing,
34.19/34.40	                                                                  app_encode_app(
34.19/34.40	                                                                  type,
34.19/34.40	                                                                  fun(
34.19/34.40	                                                                  nat,type),
34.19/34.40	                                                                  app_encode_app(
34.19/34.40	                                                                  nat,
34.19/34.40	                                                                  app_encode_fun(
34.19/34.40	                                                                  type,
34.19/34.40	                                                                  fun(
34.19/34.40	                                                                  nat,type)),
34.19/34.40	                                                                  app_encode_app(
34.19/34.40	                                                                  fun(
34.19/34.40	                                                                  nat,type),
34.19/34.40	                                                                  app_encode_fun(
34.19/34.40	                                                                  nat,
34.19/34.40	                                                                  app_encode_fun(
34.19/34.40	                                                                  type,
34.19/34.40	                                                                  fun(
34.19/34.40	                                                                  nat,type))),
34.19/34.40	                                                                  shift(type),
34.19/34.40	                                                                  E1),I1),t)),
34.19/34.40	                                                                  a)),
34.19/34.40	                                    T5)) =>
34.19/34.40	      (app_encode_app(bool,$o,pp,
34.19/34.40	                      app_encode_app(dB,bool,
34.19/34.40	                                     app_encode_app(fun(dB,bool),
34.19/34.40	                                                    app_encode_fun(dB,bool),
34.19/34.40	                                                    aa(dB,bool),it),
34.19/34.40	                                     U3)) =>
34.19/34.40	       (app_encode_app(bool,$o,pp,
34.19/34.40	                       app_encode_app(type,bool,
34.19/34.40	                                      app_encode_app(fun(type,bool),
34.19/34.40	                                                     app_encode_fun(type,bool),
34.19/34.40	                                                     aa(type,bool),
34.19/34.40	                                                     app_encode_app(dB,
34.19/34.40	                                                                    fun(
34.19/34.40	                                                                    type,bool),
34.19/34.40	                                                                    app_encode_app(
34.19/34.40	                                                                    fun(
34.19/34.40	                                                                    nat,type),
34.19/34.40	                                                                    app_encode_fun(
34.19/34.40	                                                                    dB,
34.19/34.40	                                                                    fun(
34.19/34.40	                                                                    type,bool)),
34.19/34.40	                                                                    typing,E1),
34.19/34.40	                                                                    U3)),
34.19/34.40	                                      t)) =>
34.19/34.40	        app_encode_app(bool,$o,pp,
34.19/34.40	                       app_encode_app(dB,bool,
34.19/34.40	                                      app_encode_app(fun(dB,bool),
34.19/34.40	                                                     app_encode_fun(dB,bool),
34.19/34.40	                                                     aa(dB,bool),it),
34.19/34.40	                                      app_encode_app(nat,dB,
34.19/34.40	                                                     app_encode_app(dB,
34.19/34.40	                                                                    app_encode_fun(
34.19/34.40	                                                                    nat,dB),
34.19/34.40	                                                                    app_encode_app(
34.19/34.40	                                                                    dB,
34.19/34.40	                                                                    app_encode_fun(
34.19/34.40	                                                                    dB,
34.19/34.40	                                                                    app_encode_fun(
34.19/34.40	                                                                    nat,dB)),
34.19/34.40	                                                                    subst,a),
34.19/34.40	                                                                    U3),
34.19/34.40	                                                     I1)))))))).
34.19/34.40	tff('27', plain,
34.19/34.40	    ![X0 : dB, X1 : fun(nat, type), X2 : nat, X3 : type]:
34.19/34.40	      (~ app_encode_app(bool, $o, pp, 
34.19/34.40	           app_encode_app(dB, bool, 
34.19/34.40	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
34.19/34.40	               aa(dB, bool), it), X0))
34.19/34.40	       | ~ app_encode_app(bool, $o, pp, 
34.19/34.40	             app_encode_app(type, bool, 
34.19/34.40	               app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
34.19/34.40	                 aa(type, bool), 
34.19/34.40	                 app_encode_app(dB, fun(type, bool), 
34.19/34.40	                   app_encode_app(fun(nat, type), 
34.19/34.40	                     app_encode_fun(dB, fun(type, bool)), typing, X1), X0)), 
34.19/34.40	               t))
34.19/34.40	       | ~ app_encode_app(bool, $o, pp, 
34.19/34.40	             app_encode_app(type, bool, 
34.19/34.40	               app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
34.19/34.40	                 aa(type, bool), 
34.19/34.40	                 app_encode_app(dB, fun(type, bool), 
34.19/34.40	                   app_encode_app(fun(nat, type), 
34.19/34.40	                     app_encode_fun(dB, fun(type, bool)), typing, 
34.19/34.40	                     app_encode_app(type, fun(nat, type), 
34.19/34.40	                       app_encode_app(nat, 
34.19/34.40	                         app_encode_fun(type, fun(nat, type)), 
34.19/34.40	                         app_encode_app(fun(nat, type), 
34.19/34.40	                           app_encode_fun(nat, 
34.19/34.40	                             app_encode_fun(type, fun(nat, type))), 
34.19/34.40	                           shift(type), X1), X2), t)), a)), X3))
34.19/34.40	       | app_encode_app(bool, $o, pp, 
34.19/34.40	           app_encode_app(dB, bool, 
34.19/34.40	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
34.19/34.40	               aa(dB, bool), it), 
34.19/34.40	             app_encode_app(nat, dB, 
34.19/34.40	               app_encode_app(dB, app_encode_fun(nat, dB), 
34.19/34.40	                 app_encode_app(dB, 
34.19/34.40	                   app_encode_fun(dB, app_encode_fun(nat, dB)), subst, a), 
34.19/34.40	                 X0), X2)))),
34.19/34.40	    inference('cnf', [status(esa)], [zf_stmt_60])).
34.19/34.40	tff('28', plain,
34.19/34.40	    ![X0 : nat, X1 : type]:
34.19/34.40	      (~ $true
34.19/34.40	       | app_encode_app(bool, $o, pp, 
34.19/34.40	           app_encode_app(dB, bool, 
34.19/34.40	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
34.19/34.40	               aa(dB, bool), it), 
34.19/34.40	             app_encode_app(nat, dB, 
34.19/34.40	               app_encode_app(dB, app_encode_fun(nat, dB), 
34.19/34.40	                 app_encode_app(dB, 
34.19/34.40	                   app_encode_fun(dB, app_encode_fun(nat, dB)), subst, a), u), 
34.19/34.40	               X0)))
34.19/34.40	       | ~ app_encode_app(bool, $o, pp, 
34.19/34.40	             app_encode_app(type, bool, 
34.19/34.40	               app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
34.19/34.40	                 aa(type, bool), 
34.19/34.40	                 app_encode_app(dB, fun(type, bool), 
34.19/34.40	                   app_encode_app(fun(nat, type), 
34.19/34.40	                     app_encode_fun(dB, fun(type, bool)), typing, 
34.19/34.40	                     app_encode_app(type, fun(nat, type), 
34.19/34.40	                       app_encode_app(nat, 
34.19/34.40	                         app_encode_fun(type, fun(nat, type)), 
34.19/34.40	                         app_encode_app(fun(nat, type), 
34.19/34.40	                           app_encode_fun(nat, 
34.19/34.40	                             app_encode_fun(type, fun(nat, type))), 
34.19/34.40	                           shift(type), e), X0), t)), a)), X1))
34.19/34.40	       | ~ app_encode_app(bool, $o, pp, 
34.19/34.40	             app_encode_app(dB, bool, 
34.19/34.40	               app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
34.19/34.40	                 aa(dB, bool), it), u))),
34.19/34.40	    inference('sup-', [status(thm)], ['26', '27'])).
34.19/34.40	tff('29', plain,
34.19/34.40	    ![X0 : nat, X1 : type]:
34.19/34.40	      (~ $true
34.19/34.40	       | app_encode_app(bool, $o, pp, 
34.19/34.40	           app_encode_app(dB, bool, 
34.19/34.40	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
34.19/34.40	               aa(dB, bool), it), 
34.19/34.40	             app_encode_app(nat, dB, 
34.19/34.40	               app_encode_app(dB, app_encode_fun(nat, dB), 
34.19/34.40	                 app_encode_app(dB, 
34.19/34.40	                   app_encode_fun(dB, app_encode_fun(nat, dB)), subst, a), u), 
34.19/34.40	               X0)))
34.19/34.40	       | ~ app_encode_app(bool, $o, pp, 
34.19/34.40	             app_encode_app(type, bool, 
34.19/34.40	               app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
34.19/34.40	                 aa(type, bool), 
34.19/34.40	                 app_encode_app(dB, fun(type, bool), 
34.19/34.40	                   app_encode_app(fun(nat, type), 
34.19/34.40	                     app_encode_fun(dB, fun(type, bool)), typing, 
34.19/34.40	                     app_encode_app(type, fun(nat, type), 
34.19/34.40	                       app_encode_app(nat, 
34.19/34.40	                         app_encode_fun(type, fun(nat, type)), 
34.19/34.40	                         app_encode_app(fun(nat, type), 
34.19/34.40	                           app_encode_fun(nat, 
34.19/34.40	                             app_encode_fun(type, fun(nat, type))), 
34.19/34.40	                           shift(type), e), X0), t)), a)), X1))
34.19/34.40	       | ~ $true),
34.19/34.40	    inference('demod', [status(thm)], ['28', '5'])).
34.19/34.40	tff('30', plain,
34.19/34.40	    ![X0 : nat, X1 : type]:
34.19/34.40	      (~ app_encode_app(bool, $o, pp, 
34.19/34.40	           app_encode_app(type, bool, 
34.19/34.40	             app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
34.19/34.40	               aa(type, bool), 
34.19/34.40	               app_encode_app(dB, fun(type, bool), 
34.19/34.40	                 app_encode_app(fun(nat, type), 
34.19/34.40	                   app_encode_fun(dB, fun(type, bool)), typing, 
34.19/34.40	                   app_encode_app(type, fun(nat, type), 
34.19/34.40	                     app_encode_app(nat, 
34.19/34.40	                       app_encode_fun(type, fun(nat, type)), 
34.19/34.40	                       app_encode_app(fun(nat, type), 
34.19/34.40	                         app_encode_fun(nat, 
34.19/34.40	                           app_encode_fun(type, fun(nat, type))), 
34.19/34.40	                         shift(type), e), X0), t)), a)), X1))
34.19/34.40	       | app_encode_app(bool, $o, pp, 
34.19/34.40	           app_encode_app(dB, bool, 
34.19/34.40	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
34.19/34.40	               aa(dB, bool), it), 
34.19/34.40	             app_encode_app(nat, dB, 
34.19/34.40	               app_encode_app(dB, app_encode_fun(nat, dB), 
34.19/34.40	                 app_encode_app(dB, 
34.19/34.40	                   app_encode_fun(dB, app_encode_fun(nat, dB)), subst, a), u), 
34.19/34.40	               X0)))),
34.19/34.40	    inference('simplify', [status(thm)], ['29'])).
34.19/34.40	tff('31', plain,
34.19/34.40	    (~ app_encode_app(bool, $o, pp, 
34.19/34.40	         app_encode_app(dB, bool, 
34.19/34.40	           app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
34.19/34.40	             aa(dB, bool), it), u))
34.19/34.40	     | app_encode_app(bool, $o, pp, 
34.19/34.40	         app_encode_app(dB, bool, 
34.19/34.40	           app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
34.19/34.40	             aa(dB, bool), it), 
34.19/34.40	           app_encode_app(nat, dB, 
34.19/34.40	             app_encode_app(dB, app_encode_fun(nat, dB), 
34.19/34.40	               app_encode_app(dB, 
34.19/34.40	                 app_encode_fun(dB, app_encode_fun(nat, dB)), subst, a), u), 
34.19/34.40	             i)))),
34.19/34.40	    inference('sup-', [status(thm)], ['25', '30'])).
34.19/34.40	tff('32', plain,
34.19/34.40	    (~ $true
34.19/34.40	     | app_encode_app(bool, $o, pp, 
34.19/34.40	         app_encode_app(dB, bool, 
34.19/34.40	           app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
34.19/34.40	             aa(dB, bool), it), 
34.19/34.40	           app_encode_app(nat, dB, 
34.19/34.40	             app_encode_app(dB, app_encode_fun(nat, dB), 
34.19/34.40	               app_encode_app(dB, 
34.19/34.40	                 app_encode_fun(dB, app_encode_fun(nat, dB)), subst, a), u), 
34.19/34.40	             i)))),
34.19/34.40	    inference('demod', [status(thm)], ['31', '5'])).
34.19/34.40	tff('33', plain,
34.19/34.40	    app_encode_app(bool, $o, pp, 
34.19/34.40	      app_encode_app(dB, bool, 
34.19/34.40	        app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
34.19/34.40	          aa(dB, bool), it), 
34.19/34.40	        app_encode_app(nat, dB, 
34.19/34.40	          app_encode_app(dB, app_encode_fun(nat, dB), 
34.19/34.40	            app_encode_app(dB, app_encode_fun(dB, app_encode_fun(nat, dB)), 
34.19/34.40	              subst, a), u), i))),
34.19/34.40	    inference('simplify', [status(thm)], ['32'])).
34.19/34.40	tff('34', plain, ~ $true, inference('sup-', [status(thm)], ['33', '17'])).
34.19/34.40	tff('35', plain, $false, inference('simplify', [status(thm)], ['34'])).
34.19/34.40	
34.19/34.40	% SZS output end Refutation
34.19/34.40	EOF
