0.00/0.00	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : app
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : kbo
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n151.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 07:22:39 CST 2018
10.45/10.69	% done 2185 iterations in 10.486s
10.45/10.69	% SZS status Theorem for 'stdin'
10.45/10.69	% SZS output start Refutation
10.45/10.69	tff(zf_stmt_63, axiom,
10.45/10.69	  (app_encode_app(bool,$o,pp,
10.45/10.69	                  app_encode_app(type,bool,
10.45/10.69	                                 app_encode_app(fun(type,bool),
10.45/10.69	                                                app_encode_fun(type,bool),
10.45/10.69	                                                aa(type,bool),
10.45/10.69	                                                app_encode_app(dB,
10.45/10.69	                                                               fun(type,bool),
10.45/10.69	                                                               app_encode_app(
10.45/10.69	                                                               fun(dB,
10.45/10.69	                                                                   fun(
10.45/10.69	                                                                   type,bool)),
10.45/10.69	                                                               app_encode_fun(
10.45/10.69	                                                               dB,
10.45/10.69	                                                               fun(type,bool)),
10.45/10.69	                                                               aa(dB,
10.45/10.69	                                                                  fun(
10.45/10.69	                                                                  type,bool)),
10.45/10.69	                                                               app_encode_app(
10.45/10.69	                                                               fun(nat,type),
10.45/10.69	                                                               fun(dB,
10.45/10.69	                                                                   fun(
10.45/10.69	                                                                   type,bool)),
10.45/10.69	                                                               typing,
10.45/10.69	                                                               app_encode_app(
10.45/10.69	                                                               type,
10.45/10.69	                                                               fun(nat,type),
10.45/10.69	                                                               app_encode_app(
10.45/10.69	                                                               nat,
10.45/10.69	                                                               app_encode_fun(
10.45/10.69	                                                               type,
10.45/10.69	                                                               fun(nat,type)),
10.45/10.69	                                                               app_encode_app(
10.45/10.69	                                                               fun(nat,type),
10.45/10.69	                                                               app_encode_fun(
10.45/10.69	                                                               nat,
10.45/10.69	                                                               app_encode_fun(
10.45/10.69	                                                               type,
10.45/10.69	                                                               fun(nat,type))),
10.45/10.69	                                                               shift(type),e),
10.45/10.69	                                                               i),t1))),a)),
10.45/10.69	                                 t)))).
10.45/10.69	tff('0', plain,
10.45/10.69	    app_encode_app(bool, $o, pp, 
10.45/10.69	      app_encode_app(type, bool, 
10.45/10.69	        app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
10.45/10.69	          aa(type, bool), 
10.45/10.69	          app_encode_app(dB, fun(type, bool), 
10.45/10.69	            app_encode_app(fun(dB, fun(type, bool)), 
10.45/10.69	              app_encode_fun(dB, fun(type, bool)), aa(dB, fun(type, bool)), 
10.45/10.69	              app_encode_app(fun(nat, type), fun(dB, fun(type, bool)), 
10.45/10.69	                typing, 
10.45/10.69	                app_encode_app(type, fun(nat, type), 
10.45/10.69	                  app_encode_app(nat, app_encode_fun(type, fun(nat, type)), 
10.45/10.69	                    app_encode_app(fun(nat, type), 
10.45/10.69	                      app_encode_fun(nat, 
10.45/10.69	                        app_encode_fun(type, fun(nat, type))), shift(type), 
10.45/10.69	                      e), i), t1))), a)), t)),
10.45/10.69	    inference('cnf', [status(esa)], [zf_stmt_63])).
10.45/10.69	tff(zf_stmt_66, axiom,
10.45/10.69	  (![Ib:nat,Ua:type,Ub:dB,E:fun(nat,type),Ta1:type,Ta:dB,Eb:fun(nat,type)]:
10.45/10.69	     (app_encode_app(bool,$o,pp,
10.45/10.69	                     app_encode_app(type,bool,
10.45/10.69	                                    app_encode_app(fun(type,bool),
10.45/10.69	                                                   app_encode_fun(type,bool),
10.45/10.69	                                                   aa(type,bool),
10.45/10.69	                                                   app_encode_app(dB,
10.45/10.69	                                                                  fun(
10.45/10.69	                                                                  type,bool),
10.45/10.69	                                                                  app_encode_app(
10.45/10.69	                                                                  fun(
10.45/10.69	                                                                  dB,
10.45/10.69	                                                                  fun(
10.45/10.69	                                                                  type,bool)),
10.45/10.69	                                                                  app_encode_fun(
10.45/10.69	                                                                  dB,
10.45/10.69	                                                                  fun(
10.45/10.69	                                                                  type,bool)),
10.45/10.69	                                                                  aa(
10.45/10.69	                                                                  dB,
10.45/10.69	                                                                  fun(
10.45/10.69	                                                                  type,bool)),
10.45/10.69	                                                                  app_encode_app(
10.45/10.69	                                                                  fun(
10.45/10.69	                                                                  nat,type),
10.45/10.69	                                                                  fun(
10.45/10.69	                                                                  dB,
10.45/10.69	                                                                  fun(
10.45/10.69	                                                                  type,bool)),
10.45/10.69	                                                                  typing,Eb)),
10.45/10.69	                                                                  Ta)),
10.45/10.69	                                    Ta1)) =>
10.45/10.69	      (app_encode_app(bool,$o,pp,
10.45/10.69	                      app_encode_app(type,bool,
10.45/10.69	                                     app_encode_app(fun(type,bool),
10.45/10.69	                                                    app_encode_fun(type,bool),
10.45/10.69	                                                    aa(type,bool),
10.45/10.69	                                                    app_encode_app(dB,
10.45/10.69	                                                                   fun(
10.45/10.69	                                                                   type,bool),
10.45/10.69	                                                                   app_encode_app(
10.45/10.69	                                                                   fun(
10.45/10.69	                                                                   dB,
10.45/10.69	                                                                   fun(
10.45/10.69	                                                                   type,bool)),
10.45/10.69	                                                                   app_encode_fun(
10.45/10.69	                                                                   dB,
10.45/10.69	                                                                   fun(
10.45/10.69	                                                                   type,bool)),
10.45/10.69	                                                                   aa(
10.45/10.69	                                                                   dB,
10.45/10.69	                                                                   fun(
10.45/10.69	                                                                   type,bool)),
10.45/10.69	                                                                   app_encode_app(
10.45/10.69	                                                                   fun(
10.45/10.69	                                                                   nat,type),
10.45/10.69	                                                                   fun(
10.45/10.69	                                                                   dB,
10.45/10.69	                                                                   fun(
10.45/10.69	                                                                   type,bool)),
10.45/10.69	                                                                   typing,E)),
10.45/10.69	                                                                   Ub)),
10.45/10.69	                                     Ua)) =>
10.45/10.69	       ((Eb =
10.45/10.69	         app_encode_app(type,fun(nat,type),
10.45/10.69	                        app_encode_app(nat,
10.45/10.69	                                       app_encode_fun(type,fun(nat,type)),
10.45/10.69	                                       app_encode_app(fun(nat,type),
10.45/10.69	                                                      app_encode_fun(
10.45/10.69	                                                      nat,
10.45/10.69	                                                      app_encode_fun(
10.45/10.69	                                                      type,fun(nat,type))),
10.45/10.69	                                                      shift(type),E),
10.45/10.69	                                       Ib),
10.45/10.69	                        Ua)) =>
10.45/10.69	        app_encode_app(bool,$o,pp,
10.45/10.69	                       app_encode_app(type,bool,
10.45/10.69	                                      app_encode_app(fun(type,bool),
10.45/10.69	                                                     app_encode_fun(type,bool),
10.45/10.69	                                                     aa(type,bool),
10.45/10.69	                                                     app_encode_app(dB,
10.45/10.69	                                                                    fun(
10.45/10.69	                                                                    type,bool),
10.45/10.69	                                                                    app_encode_app(
10.45/10.69	                                                                    fun(
10.45/10.69	                                                                    dB,
10.45/10.69	                                                                    fun(
10.45/10.69	                                                                    type,bool)),
10.45/10.69	                                                                    app_encode_fun(
10.45/10.69	                                                                    dB,
10.45/10.69	                                                                    fun(
10.45/10.69	                                                                    type,bool)),
10.45/10.69	                                                                    aa(
10.45/10.69	                                                                    dB,
10.45/10.69	                                                                    fun(
10.45/10.69	                                                                    type,bool)),
10.45/10.69	                                                                    app_encode_app(
10.45/10.69	                                                                    fun(
10.45/10.69	                                                                    nat,type),
10.45/10.69	                                                                    fun(
10.45/10.69	                                                                    dB,
10.45/10.69	                                                                    fun(
10.45/10.69	                                                                    type,bool)),
10.45/10.69	                                                                    typing,E)),
10.45/10.69	                                                                    app_encode_app(
10.45/10.69	                                                                    nat,dB,
10.45/10.69	                                                                    app_encode_app(
10.45/10.69	                                                                    fun(
10.45/10.69	                                                                    nat,dB),
10.45/10.69	                                                                    app_encode_fun(
10.45/10.69	                                                                    nat,dB),
10.45/10.69	                                                                    aa(
10.45/10.69	                                                                    nat,dB),
10.45/10.69	                                                                    app_encode_app(
10.45/10.69	                                                                    dB,
10.45/10.69	                                                                    fun(
10.45/10.69	                                                                    nat,dB),
10.45/10.69	                                                                    app_encode_app(
10.45/10.69	                                                                    fun(
10.45/10.69	                                                                    dB,
10.45/10.69	                                                                    fun(
10.45/10.69	                                                                    nat,dB)),
10.45/10.69	                                                                    app_encode_fun(
10.45/10.69	                                                                    dB,
10.45/10.69	                                                                    fun(
10.45/10.69	                                                                    nat,dB)),
10.45/10.69	                                                                    aa(
10.45/10.69	                                                                    dB,
10.45/10.69	                                                                    fun(
10.45/10.69	                                                                    nat,dB)),
10.45/10.69	                                                                    app_encode_app(
10.45/10.69	                                                                    dB,
10.45/10.69	                                                                    fun(
10.45/10.69	                                                                    dB,
10.45/10.69	                                                                    fun(
10.45/10.69	                                                                    nat,dB)),
10.45/10.69	                                                                    app_encode_app(
10.45/10.69	                                                                    fun(
10.45/10.69	                                                                    dB,
10.45/10.69	                                                                    fun(
10.45/10.69	                                                                    dB,
10.45/10.69	                                                                    fun(
10.45/10.69	                                                                    nat,dB))),
10.45/10.69	                                                                    app_encode_fun(
10.45/10.69	                                                                    dB,
10.45/10.69	                                                                    fun(
10.45/10.69	                                                                    dB,
10.45/10.69	                                                                    fun(
10.45/10.69	                                                                    nat,dB))),
10.45/10.69	                                                                    aa(
10.45/10.69	                                                                    dB,
10.45/10.69	                                                                    fun(
10.45/10.69	                                                                    dB,
10.45/10.69	                                                                    fun(
10.45/10.69	                                                                    nat,dB))),
10.45/10.69	                                                                    subst),Ta)),
10.45/10.69	                                                                    Ub)),Ib))),
10.45/10.69	                                      Ta1))))))).
10.45/10.69	tff('1', plain,
10.45/10.69	    ![X0 : fun(nat, type), X1 : dB, X2 : type, X3 : dB, X4 : nat, X5 : type, 
10.45/10.69	      X6 : fun(nat, type)]:
10.45/10.69	      (~ app_encode_app(bool, $o, pp, 
10.45/10.69	           app_encode_app(type, bool, 
10.45/10.69	             app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
10.45/10.69	               aa(type, bool), 
10.45/10.69	               app_encode_app(dB, fun(type, bool), 
10.45/10.69	                 app_encode_app(fun(dB, fun(type, bool)), 
10.45/10.69	                   app_encode_fun(dB, fun(type, bool)), 
10.45/10.69	                   aa(dB, fun(type, bool)), 
10.45/10.69	                   app_encode_app(fun(nat, type), fun(dB, fun(type, bool)), 
10.45/10.69	                     typing, X0)), X1)), X2))
10.45/10.69	       | app_encode_app(bool, $o, pp, 
10.45/10.69	           app_encode_app(type, bool, 
10.45/10.69	             app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
10.45/10.69	               aa(type, bool), 
10.45/10.69	               app_encode_app(dB, fun(type, bool), 
10.45/10.69	                 app_encode_app(fun(dB, fun(type, bool)), 
10.45/10.69	                   app_encode_fun(dB, fun(type, bool)), 
10.45/10.69	                   aa(dB, fun(type, bool)), 
10.45/10.69	                   app_encode_app(fun(nat, type), fun(dB, fun(type, bool)), 
10.45/10.69	                     typing, X0)), 
10.45/10.69	                 app_encode_app(nat, dB, 
10.45/10.69	                   app_encode_app(fun(nat, dB), app_encode_fun(nat, dB), 
10.45/10.69	                     aa(nat, dB), 
10.45/10.69	                     app_encode_app(dB, fun(nat, dB), 
10.45/10.69	                       app_encode_app(fun(dB, fun(nat, dB)), 
10.45/10.69	                         app_encode_fun(dB, fun(nat, dB)), 
10.45/10.69	                         aa(dB, fun(nat, dB)), 
10.45/10.69	                         app_encode_app(dB, fun(dB, fun(nat, dB)), 
10.45/10.69	                           app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
10.45/10.69	                             app_encode_fun(dB, fun(dB, fun(nat, dB))), 
10.45/10.69	                             aa(dB, fun(dB, fun(nat, dB))), subst), X3)), X1)), 
10.45/10.69	                   X4))), X5))
10.45/10.69	       | ~ app_encode_app(bool, $o, pp, 
10.45/10.69	             app_encode_app(type, bool, 
10.45/10.69	               app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
10.45/10.69	                 aa(type, bool), 
10.45/10.69	                 app_encode_app(dB, fun(type, bool), 
10.45/10.69	                   app_encode_app(fun(dB, fun(type, bool)), 
10.45/10.69	                     app_encode_fun(dB, fun(type, bool)), 
10.45/10.69	                     aa(dB, fun(type, bool)), 
10.45/10.69	                     app_encode_app(fun(nat, type), 
10.45/10.69	                       fun(dB, fun(type, bool)), typing, X6)), X3)), X5))
10.45/10.69	       | X6
10.45/10.69	          != app_encode_app(type, fun(nat, type), 
10.45/10.69	               app_encode_app(nat, app_encode_fun(type, fun(nat, type)), 
10.45/10.69	                 app_encode_app(fun(nat, type), 
10.45/10.69	                   app_encode_fun(nat, app_encode_fun(type, fun(nat, type))), 
10.45/10.69	                   shift(type), X0), X4), X2)),
10.45/10.69	    inference('cnf', [status(esa)], [zf_stmt_66])).
10.45/10.69	tff('2', plain,
10.45/10.69	    ![X0 : fun(nat, type), X1 : dB, X2 : type, X3 : dB, X4 : nat, X5 : type]:
10.45/10.69	      (~ app_encode_app(bool, $o, pp, 
10.45/10.69	           app_encode_app(type, bool, 
10.45/10.69	             app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
10.45/10.69	               aa(type, bool), 
10.45/10.69	               app_encode_app(dB, fun(type, bool), 
10.45/10.69	                 app_encode_app(fun(dB, fun(type, bool)), 
10.45/10.69	                   app_encode_fun(dB, fun(type, bool)), 
10.45/10.69	                   aa(dB, fun(type, bool)), 
10.45/10.69	                   app_encode_app(fun(nat, type), fun(dB, fun(type, bool)), 
10.45/10.69	                     typing, 
10.45/10.69	                     app_encode_app(type, fun(nat, type), 
10.45/10.69	                       app_encode_app(nat, 
10.45/10.69	                         app_encode_fun(type, fun(nat, type)), 
10.45/10.69	                         app_encode_app(fun(nat, type), 
10.45/10.69	                           app_encode_fun(nat, 
10.45/10.69	                             app_encode_fun(type, fun(nat, type))), 
10.45/10.69	                           shift(type), X0), X4), X2))), X3)), X5))
10.45/10.69	       | app_encode_app(bool, $o, pp, 
10.45/10.69	           app_encode_app(type, bool, 
10.45/10.69	             app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
10.45/10.69	               aa(type, bool), 
10.45/10.69	               app_encode_app(dB, fun(type, bool), 
10.45/10.69	                 app_encode_app(fun(dB, fun(type, bool)), 
10.45/10.69	                   app_encode_fun(dB, fun(type, bool)), 
10.45/10.69	                   aa(dB, fun(type, bool)), 
10.45/10.69	                   app_encode_app(fun(nat, type), fun(dB, fun(type, bool)), 
10.45/10.69	                     typing, X0)), 
10.45/10.69	                 app_encode_app(nat, dB, 
10.45/10.69	                   app_encode_app(fun(nat, dB), app_encode_fun(nat, dB), 
10.45/10.69	                     aa(nat, dB), 
10.45/10.69	                     app_encode_app(dB, fun(nat, dB), 
10.45/10.69	                       app_encode_app(fun(dB, fun(nat, dB)), 
10.45/10.69	                         app_encode_fun(dB, fun(nat, dB)), 
10.45/10.69	                         aa(dB, fun(nat, dB)), 
10.45/10.69	                         app_encode_app(dB, fun(dB, fun(nat, dB)), 
10.45/10.69	                           app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
10.45/10.69	                             app_encode_fun(dB, fun(dB, fun(nat, dB))), 
10.45/10.69	                             aa(dB, fun(dB, fun(nat, dB))), subst), X3)), X1)), 
10.45/10.69	                   X4))), X5))
10.45/10.69	       | ~ app_encode_app(bool, $o, pp, 
10.45/10.69	             app_encode_app(type, bool, 
10.45/10.69	               app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
10.45/10.69	                 aa(type, bool), 
10.45/10.69	                 app_encode_app(dB, fun(type, bool), 
10.45/10.69	                   app_encode_app(fun(dB, fun(type, bool)), 
10.45/10.69	                     app_encode_fun(dB, fun(type, bool)), 
10.45/10.69	                     aa(dB, fun(type, bool)), 
10.45/10.69	                     app_encode_app(fun(nat, type), 
10.45/10.69	                       fun(dB, fun(type, bool)), typing, X0)), X1)), X2))),
10.45/10.69	    inference('simplify', [status(thm)], ['1'])).
10.45/10.69	tff('3', plain,
10.45/10.69	    ![X0 : dB]:
10.45/10.69	      (~ $true
10.45/10.69	       | ~ app_encode_app(bool, $o, pp, 
10.45/10.69	             app_encode_app(type, bool, 
10.45/10.69	               app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
10.45/10.69	                 aa(type, bool), 
10.45/10.69	                 app_encode_app(dB, fun(type, bool), 
10.45/10.69	                   app_encode_app(fun(dB, fun(type, bool)), 
10.45/10.69	                     app_encode_fun(dB, fun(type, bool)), 
10.45/10.69	                     aa(dB, fun(type, bool)), 
10.45/10.69	                     app_encode_app(fun(nat, type), 
10.45/10.69	                       fun(dB, fun(type, bool)), typing, e)), X0)), t1))
10.45/10.69	       | app_encode_app(bool, $o, pp, 
10.45/10.69	           app_encode_app(type, bool, 
10.45/10.69	             app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
10.45/10.69	               aa(type, bool), 
10.45/10.69	               app_encode_app(dB, fun(type, bool), 
10.45/10.69	                 app_encode_app(fun(dB, fun(type, bool)), 
10.45/10.69	                   app_encode_fun(dB, fun(type, bool)), 
10.45/10.69	                   aa(dB, fun(type, bool)), 
10.45/10.69	                   app_encode_app(fun(nat, type), fun(dB, fun(type, bool)), 
10.45/10.69	                     typing, e)), 
10.45/10.69	                 app_encode_app(nat, dB, 
10.45/10.69	                   app_encode_app(fun(nat, dB), app_encode_fun(nat, dB), 
10.45/10.69	                     aa(nat, dB), 
10.45/10.69	                     app_encode_app(dB, fun(nat, dB), 
10.45/10.69	                       app_encode_app(fun(dB, fun(nat, dB)), 
10.45/10.69	                         app_encode_fun(dB, fun(nat, dB)), 
10.45/10.69	                         aa(dB, fun(nat, dB)), 
10.45/10.69	                         app_encode_app(dB, fun(dB, fun(nat, dB)), 
10.45/10.69	                           app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
10.45/10.69	                             app_encode_fun(dB, fun(dB, fun(nat, dB))), 
10.45/10.69	                             aa(dB, fun(dB, fun(nat, dB))), subst), a)), X0)), 
10.45/10.69	                   i))), t))),
10.45/10.69	    inference('sup-', [status(thm)], ['0', '2'])).
10.45/10.69	tff('4', plain,
10.45/10.69	    ![X0 : dB]:
10.45/10.69	      (app_encode_app(bool, $o, pp, 
10.45/10.69	         app_encode_app(type, bool, 
10.45/10.69	           app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
10.45/10.69	             aa(type, bool), 
10.45/10.69	             app_encode_app(dB, fun(type, bool), 
10.45/10.69	               app_encode_app(fun(dB, fun(type, bool)), 
10.45/10.69	                 app_encode_fun(dB, fun(type, bool)), 
10.45/10.69	                 aa(dB, fun(type, bool)), 
10.45/10.69	                 app_encode_app(fun(nat, type), fun(dB, fun(type, bool)), 
10.45/10.69	                   typing, e)), 
10.45/10.69	               app_encode_app(nat, dB, 
10.45/10.69	                 app_encode_app(fun(nat, dB), app_encode_fun(nat, dB), 
10.45/10.69	                   aa(nat, dB), 
10.45/10.69	                   app_encode_app(dB, fun(nat, dB), 
10.45/10.69	                     app_encode_app(fun(dB, fun(nat, dB)), 
10.45/10.69	                       app_encode_fun(dB, fun(nat, dB)), 
10.45/10.69	                       aa(dB, fun(nat, dB)), 
10.45/10.69	                       app_encode_app(dB, fun(dB, fun(nat, dB)), 
10.45/10.69	                         app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
10.45/10.69	                           app_encode_fun(dB, fun(dB, fun(nat, dB))), 
10.45/10.69	                           aa(dB, fun(dB, fun(nat, dB))), subst), a)), X0)), 
10.45/10.69	                 i))), t))
10.45/10.69	       | ~ app_encode_app(bool, $o, pp, 
10.45/10.69	             app_encode_app(type, bool, 
10.45/10.69	               app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
10.45/10.69	                 aa(type, bool), 
10.45/10.69	                 app_encode_app(dB, fun(type, bool), 
10.45/10.69	                   app_encode_app(fun(dB, fun(type, bool)), 
10.45/10.69	                     app_encode_fun(dB, fun(type, bool)), 
10.45/10.69	                     aa(dB, fun(type, bool)), 
10.45/10.69	                     app_encode_app(fun(nat, type), 
10.45/10.69	                       fun(dB, fun(type, bool)), typing, e)), X0)), t1))),
10.45/10.69	    inference('simplify', [status(thm)], ['3'])).
10.45/10.69	tff(zf_stmt_163, axiom,
10.45/10.69	  (![A:$tType,C:$tType,B:$tType,R:A,Q:B,P:fun(A,fun(B,C))]:
10.45/10.69	     (app_encode_app(A,C,
10.45/10.69	                     app_encode_app(fun(A,C),app_encode_fun(A,C),aa(A,C),
10.45/10.69	                                    app_encode_app(B,fun(A,C),
10.45/10.69	                                                   app_encode_app(fun(
10.45/10.69	                                                                  A,fun(B,C)),
10.45/10.69	                                                                  app_encode_fun(
10.45/10.69	                                                                  B,fun(A,C)),
10.45/10.69	                                                                  combc(
10.45/10.69	                                                                  A,B,C),P),
10.45/10.69	                                                   Q)),
10.45/10.69	                     R) =
10.45/10.69	      app_encode_app(B,C,
10.45/10.69	                     app_encode_app(fun(B,C),app_encode_fun(B,C),aa(B,C),
10.45/10.69	                                    app_encode_app(A,fun(B,C),
10.45/10.69	                                                   app_encode_app(fun(
10.45/10.69	                                                                  A,fun(B,C)),
10.45/10.69	                                                                  app_encode_fun(
10.45/10.69	                                                                  A,fun(B,C)),
10.45/10.69	                                                                  aa(
10.45/10.69	                                                                  A,fun(B,C)),
10.45/10.69	                                                                  P),
10.45/10.69	                                                   R)),
10.45/10.69	                     Q)))).
10.45/10.69	tff('5', plain,
10.45/10.69	    ![X305 : $tType, X306 : $tType, X307 : $tType, 
10.45/10.69	      X308 : fun(X307, fun(X305, X306)), X309 : X307, X310 : X305]:
10.45/10.69	      app_encode_app(X307, X306, 
10.45/10.69	        app_encode_app(fun(X307, X306), app_encode_fun(X307, X306), 
10.45/10.69	          aa(X307, X306), 
10.45/10.69	          app_encode_app(X305, fun(X307, X306), 
10.45/10.69	            app_encode_app(fun(X307, fun(X305, X306)), 
10.45/10.69	              app_encode_fun(X305, fun(X307, X306)), 
10.45/10.69	              combc(X307, X305, X306), X308), X310)), X309)
10.45/10.69	       = app_encode_app(X305, X306, 
10.45/10.69	           app_encode_app(fun(X305, X306), app_encode_fun(X305, X306), 
10.45/10.69	             aa(X305, X306), 
10.45/10.69	             app_encode_app(X307, fun(X305, X306), 
10.45/10.69	               app_encode_app(fun(X307, fun(X305, X306)), 
10.45/10.69	                 app_encode_fun(X307, fun(X305, X306)), 
10.45/10.69	                 aa(X307, fun(X305, X306)), X308), X309)), X310),
10.45/10.69	    inference('cnf', [status(esa)], [zf_stmt_163])).
10.45/10.69	tff('6', plain,
10.45/10.69	    ![X0 : dB]:
10.45/10.69	      (app_encode_app(bool, $o, pp, 
10.45/10.69	         app_encode_app(dB, bool, 
10.45/10.69	           app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
10.45/10.69	             aa(dB, bool), 
10.45/10.69	             app_encode_app(type, fun(dB, bool), 
10.45/10.69	               app_encode_app(fun(dB, fun(type, bool)), 
10.45/10.69	                 app_encode_fun(type, fun(dB, bool)), combc(dB, type, bool), 
10.45/10.69	                 app_encode_app(fun(nat, type), fun(dB, fun(type, bool)), 
10.45/10.69	                   typing, e)), t)), 
10.45/10.69	           app_encode_app(dB, dB, 
10.45/10.69	             app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), aa(dB, dB), 
10.45/10.69	               app_encode_app(nat, fun(dB, dB), 
10.45/10.69	                 app_encode_app(fun(dB, fun(nat, dB)), 
10.45/10.69	                   app_encode_fun(nat, fun(dB, dB)), combc(dB, nat, dB), 
10.45/10.69	                   app_encode_app(dB, fun(dB, fun(nat, dB)), 
10.45/10.69	                     app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
10.45/10.69	                       app_encode_fun(dB, fun(dB, fun(nat, dB))), 
10.45/10.69	                       combc(dB, dB, fun(nat, dB)), subst), X0)), i)), a)))
10.45/10.69	       | ~ app_encode_app(bool, $o, pp, 
10.45/10.69	             app_encode_app(dB, bool, 
10.45/10.69	               app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
10.45/10.69	                 aa(dB, bool), 
10.45/10.69	                 app_encode_app(type, fun(dB, bool), 
10.45/10.69	                   app_encode_app(fun(dB, fun(type, bool)), 
10.45/10.69	                     app_encode_fun(type, fun(dB, bool)), 
10.45/10.69	                     combc(dB, type, bool), 
10.45/10.69	                     app_encode_app(fun(nat, type), 
10.45/10.69	                       fun(dB, fun(type, bool)), typing, e)), t1)), X0))),
10.45/10.69	    inference('demod', [status(thm)], ['4', '5', '5', '5', '5'])).
10.45/10.69	tff(zf_stmt_173, conjecture,
10.45/10.69	  (app_encode_app(bool,$o,pp,
10.45/10.69	                  app_encode_app(type,bool,
10.45/10.69	                                 app_encode_app(fun(type,bool),
10.45/10.69	                                                app_encode_fun(type,bool),
10.45/10.69	                                                aa(type,bool),
10.45/10.69	                                                app_encode_app(dB,
10.45/10.69	                                                               fun(type,bool),
10.45/10.69	                                                               app_encode_app(
10.45/10.69	                                                               fun(dB,
10.45/10.69	                                                                   fun(
10.45/10.69	                                                                   type,bool)),
10.45/10.69	                                                               app_encode_fun(
10.45/10.69	                                                               dB,
10.45/10.69	                                                               fun(type,bool)),
10.45/10.69	                                                               aa(dB,
10.45/10.69	                                                                  fun(
10.45/10.69	                                                                  type,bool)),
10.45/10.69	                                                               app_encode_app(
10.45/10.69	                                                               fun(nat,type),
10.45/10.69	                                                               fun(dB,
10.45/10.69	                                                                   fun(
10.45/10.69	                                                                   type,bool)),
10.45/10.69	                                                               typing,e)),
10.45/10.69	                                                               app_encode_app(
10.45/10.69	                                                               nat,dB,
10.45/10.69	                                                               app_encode_app(
10.45/10.69	                                                               fun(nat,dB),
10.45/10.69	                                                               app_encode_fun(
10.45/10.69	                                                               nat,dB),
10.45/10.69	                                                               aa(nat,dB),
10.45/10.69	                                                               app_encode_app(
10.45/10.69	                                                               dB,
10.45/10.69	                                                               fun(nat,dB),
10.45/10.69	                                                               app_encode_app(
10.45/10.69	                                                               fun(dB,
10.45/10.69	                                                                   fun(
10.45/10.69	                                                                   nat,dB)),
10.45/10.69	                                                               app_encode_fun(
10.45/10.69	                                                               dB,fun(nat,dB)),
10.45/10.69	                                                               aa(dB,
10.45/10.69	                                                                  fun(nat,dB)),
10.45/10.69	                                                               app_encode_app(
10.45/10.69	                                                               dB,
10.45/10.69	                                                               fun(dB,
10.45/10.69	                                                                   fun(
10.45/10.69	                                                                   nat,dB)),
10.45/10.69	                                                               app_encode_app(
10.45/10.69	                                                               fun(dB,
10.45/10.69	                                                                   fun(
10.45/10.69	                                                                   dB,
10.45/10.69	                                                                   fun(
10.45/10.69	                                                                   nat,dB))),
10.45/10.69	                                                               app_encode_fun(
10.45/10.69	                                                               dB,
10.45/10.69	                                                               fun(dB,
10.45/10.69	                                                                   fun(
10.45/10.69	                                                                   nat,dB))),
10.45/10.69	                                                               aa(dB,
10.45/10.69	                                                                  fun(
10.45/10.69	                                                                  dB,
10.45/10.69	                                                                  fun(nat,dB))),
10.45/10.69	                                                               subst),a)),u)),
10.45/10.69	                                                               i))),
10.45/10.69	                                 t)))).
10.45/10.69	tff(zf_stmt_0, negated_conjecture,
10.45/10.69	  (~
10.45/10.69	    app_encode_app(bool,$o,pp,
10.45/10.69	                   app_encode_app(type,bool,
10.45/10.69	                                  app_encode_app(fun(type,bool),
10.45/10.69	                                                 app_encode_fun(type,bool),
10.45/10.69	                                                 aa(type,bool),
10.45/10.69	                                                 app_encode_app(dB,
10.45/10.69	                                                                fun(type,bool),
10.45/10.69	                                                                app_encode_app(
10.45/10.69	                                                                fun(dB,
10.45/10.69	                                                                    fun(
10.45/10.69	                                                                    type,bool)),
10.45/10.69	                                                                app_encode_fun(
10.45/10.69	                                                                dB,
10.45/10.69	                                                                fun(type,bool)),
10.45/10.69	                                                                aa(dB,
10.45/10.69	                                                                   fun(
10.45/10.69	                                                                   type,bool)),
10.45/10.69	                                                                app_encode_app(
10.45/10.69	                                                                fun(nat,type),
10.45/10.69	                                                                fun(dB,
10.45/10.69	                                                                    fun(
10.45/10.69	                                                                    type,bool)),
10.45/10.69	                                                                typing,e)),
10.45/10.69	                                                                app_encode_app(
10.45/10.69	                                                                nat,dB,
10.45/10.69	                                                                app_encode_app(
10.45/10.69	                                                                fun(nat,dB),
10.45/10.69	                                                                app_encode_fun(
10.45/10.69	                                                                nat,dB),
10.45/10.69	                                                                aa(nat,dB),
10.45/10.69	                                                                app_encode_app(
10.45/10.69	                                                                dB,
10.45/10.69	                                                                fun(nat,dB),
10.45/10.69	                                                                app_encode_app(
10.45/10.69	                                                                fun(dB,
10.45/10.69	                                                                    fun(
10.45/10.69	                                                                    nat,dB)),
10.45/10.69	                                                                app_encode_fun(
10.45/10.69	                                                                dB,
10.45/10.69	                                                                fun(nat,dB)),
10.45/10.69	                                                                aa(dB,
10.45/10.69	                                                                   fun(
10.45/10.69	                                                                   nat,dB)),
10.45/10.69	                                                                app_encode_app(
10.45/10.69	                                                                dB,
10.45/10.69	                                                                fun(dB,
10.45/10.69	                                                                    fun(
10.45/10.69	                                                                    nat,dB)),
10.45/10.69	                                                                app_encode_app(
10.45/10.69	                                                                fun(dB,
10.45/10.69	                                                                    fun(
10.45/10.69	                                                                    dB,
10.45/10.69	                                                                    fun(
10.45/10.69	                                                                    nat,dB))),
10.45/10.69	                                                                app_encode_fun(
10.45/10.69	                                                                dB,
10.45/10.69	                                                                fun(dB,
10.45/10.69	                                                                    fun(
10.45/10.69	                                                                    nat,dB))),
10.45/10.69	                                                                aa(dB,
10.45/10.69	                                                                   fun(
10.45/10.69	                                                                   dB,
10.45/10.69	                                                                   fun(
10.45/10.69	                                                                   nat,dB))),
10.45/10.69	                                                                subst),a)),u)),
10.45/10.69	                                                                i))),
10.45/10.69	                                  t)))).
10.45/10.69	tff('7', plain,
10.45/10.69	    ~ app_encode_app(bool, $o, pp, 
10.45/10.69	        app_encode_app(type, bool, 
10.45/10.69	          app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
10.45/10.69	            aa(type, bool), 
10.45/10.69	            app_encode_app(dB, fun(type, bool), 
10.45/10.69	              app_encode_app(fun(dB, fun(type, bool)), 
10.45/10.69	                app_encode_fun(dB, fun(type, bool)), 
10.45/10.69	                aa(dB, fun(type, bool)), 
10.45/10.69	                app_encode_app(fun(nat, type), fun(dB, fun(type, bool)), 
10.45/10.69	                  typing, e)), 
10.45/10.69	              app_encode_app(nat, dB, 
10.45/10.69	                app_encode_app(fun(nat, dB), app_encode_fun(nat, dB), 
10.45/10.69	                  aa(nat, dB), 
10.45/10.69	                  app_encode_app(dB, fun(nat, dB), 
10.45/10.69	                    app_encode_app(fun(dB, fun(nat, dB)), 
10.45/10.69	                      app_encode_fun(dB, fun(nat, dB)), 
10.45/10.69	                      aa(dB, fun(nat, dB)), 
10.45/10.69	                      app_encode_app(dB, fun(dB, fun(nat, dB)), 
10.45/10.69	                        app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
10.45/10.69	                          app_encode_fun(dB, fun(dB, fun(nat, dB))), 
10.45/10.69	                          aa(dB, fun(dB, fun(nat, dB))), subst), a)), u)), i))), 
10.45/10.69	          t)),
10.45/10.69	    inference('cnf', [status(esa)], [zf_stmt_0])).
10.45/10.69	tff('8', plain,
10.45/10.69	    ~ app_encode_app(bool, $o, pp, 
10.45/10.69	        app_encode_app(dB, bool, 
10.45/10.69	          app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
10.45/10.69	            aa(dB, bool), 
10.45/10.69	            app_encode_app(type, fun(dB, bool), 
10.45/10.69	              app_encode_app(fun(dB, fun(type, bool)), 
10.45/10.69	                app_encode_fun(type, fun(dB, bool)), combc(dB, type, bool), 
10.45/10.69	                app_encode_app(fun(nat, type), fun(dB, fun(type, bool)), 
10.45/10.69	                  typing, e)), t)), 
10.45/10.69	          app_encode_app(dB, dB, 
10.45/10.69	            app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), aa(dB, dB), 
10.45/10.69	              app_encode_app(nat, fun(dB, dB), 
10.45/10.69	                app_encode_app(fun(dB, fun(nat, dB)), 
10.45/10.69	                  app_encode_fun(nat, fun(dB, dB)), combc(dB, nat, dB), 
10.45/10.69	                  app_encode_app(dB, fun(dB, fun(nat, dB)), 
10.45/10.69	                    app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
10.45/10.69	                      app_encode_fun(dB, fun(dB, fun(nat, dB))), 
10.45/10.69	                      combc(dB, dB, fun(nat, dB)), subst), u)), i)), a))),
10.45/10.69	    inference('demod', [status(thm)], ['7', '5', '5', '5'])).
10.45/10.69	tff('9', plain,
10.45/10.69	    (~ $true
10.45/10.69	     | ~ app_encode_app(bool, $o, pp, 
10.45/10.69	           app_encode_app(dB, bool, 
10.45/10.69	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
10.45/10.69	               aa(dB, bool), 
10.45/10.69	               app_encode_app(type, fun(dB, bool), 
10.45/10.69	                 app_encode_app(fun(dB, fun(type, bool)), 
10.45/10.69	                   app_encode_fun(type, fun(dB, bool)), 
10.45/10.69	                   combc(dB, type, bool), 
10.45/10.69	                   app_encode_app(fun(nat, type), fun(dB, fun(type, bool)), 
10.45/10.69	                     typing, e)), t1)), u))),
10.45/10.69	    inference('sup-', [status(thm)], ['6', '8'])).
10.45/10.69	tff(zf_stmt_59, axiom,
10.45/10.69	  (app_encode_app(bool,$o,pp,
10.45/10.69	                  app_encode_app(type,bool,
10.45/10.69	                                 app_encode_app(fun(type,bool),
10.45/10.69	                                                app_encode_fun(type,bool),
10.45/10.69	                                                aa(type,bool),
10.45/10.69	                                                app_encode_app(dB,
10.45/10.69	                                                               fun(type,bool),
10.45/10.69	                                                               app_encode_app(
10.45/10.69	                                                               fun(dB,
10.45/10.69	                                                                   fun(
10.45/10.69	                                                                   type,bool)),
10.45/10.69	                                                               app_encode_fun(
10.45/10.69	                                                               dB,
10.45/10.69	                                                               fun(type,bool)),
10.45/10.69	                                                               aa(dB,
10.45/10.69	                                                                  fun(
10.45/10.69	                                                                  type,bool)),
10.45/10.69	                                                               app_encode_app(
10.45/10.69	                                                               fun(nat,type),
10.45/10.69	                                                               fun(dB,
10.45/10.69	                                                                   fun(
10.45/10.69	                                                                   type,bool)),
10.45/10.69	                                                               typing,e)),u)),
10.45/10.69	                                 t1)))).
10.45/10.69	tff('10', plain,
10.45/10.69	    app_encode_app(bool, $o, pp, 
10.45/10.69	      app_encode_app(type, bool, 
10.45/10.69	        app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
10.45/10.69	          aa(type, bool), 
10.45/10.69	          app_encode_app(dB, fun(type, bool), 
10.45/10.69	            app_encode_app(fun(dB, fun(type, bool)), 
10.45/10.69	              app_encode_fun(dB, fun(type, bool)), aa(dB, fun(type, bool)), 
10.45/10.69	              app_encode_app(fun(nat, type), fun(dB, fun(type, bool)), 
10.45/10.69	                typing, e)), u)), t1)),
10.45/10.69	    inference('cnf', [status(esa)], [zf_stmt_59])).
10.45/10.69	tff(zf_stmt_170, axiom, (![P:bool]: ((P = fTrue) | (P = fFalse)))).
10.45/10.69	tff('11', plain, ![X325 : bool]: (X325 = fTrue | X325 = fFalse),
10.45/10.69	    inference('cnf', [status(esa)], [zf_stmt_170])).
10.45/10.69	tff(zf_stmt_159, axiom, (~app_encode_app(bool,$o,pp,fFalse))).
10.45/10.69	tff('12', plain, ~ app_encode_app(bool, $o, pp, fFalse),
10.45/10.69	    inference('cnf', [status(esa)], [zf_stmt_159])).
10.45/10.69	tff('13', plain,
10.45/10.69	    ![X0 : bool]: (~ app_encode_app(bool, $o, pp, X0) | X0 = fTrue),
10.45/10.69	    inference('sup-', [status(thm)], ['11', '12'])).
10.45/10.69	tff('14', plain,
10.45/10.69	    (~ $true
10.45/10.69	     | app_encode_app(type, bool, 
10.45/10.69	         app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
10.45/10.69	           aa(type, bool), 
10.45/10.69	           app_encode_app(dB, fun(type, bool), 
10.45/10.69	             app_encode_app(fun(dB, fun(type, bool)), 
10.45/10.69	               app_encode_fun(dB, fun(type, bool)), aa(dB, fun(type, bool)), 
10.45/10.69	               app_encode_app(fun(nat, type), fun(dB, fun(type, bool)), 
10.45/10.69	                 typing, e)), u)), t1)
10.45/10.69	        = fTrue),
10.45/10.69	    inference('sup-', [status(thm)], ['10', '13'])).
10.45/10.69	tff('15', plain,
10.45/10.69	    app_encode_app(type, bool, 
10.45/10.69	      app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
10.45/10.69	        aa(type, bool), 
10.45/10.69	        app_encode_app(dB, fun(type, bool), 
10.45/10.69	          app_encode_app(fun(dB, fun(type, bool)), 
10.45/10.69	            app_encode_fun(dB, fun(type, bool)), aa(dB, fun(type, bool)), 
10.45/10.69	            app_encode_app(fun(nat, type), fun(dB, fun(type, bool)), typing, 
10.45/10.69	              e)), u)), t1)
10.45/10.69	     = fTrue,
10.45/10.69	    inference('simplify', [status(thm)], ['14'])).
10.45/10.69	tff('16', plain,
10.45/10.69	    app_encode_app(dB, bool, 
10.45/10.69	      app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), aa(dB, bool), 
10.45/10.69	        app_encode_app(type, fun(dB, bool), 
10.45/10.69	          app_encode_app(fun(dB, fun(type, bool)), 
10.45/10.69	            app_encode_fun(type, fun(dB, bool)), combc(dB, type, bool), 
10.45/10.69	            app_encode_app(fun(nat, type), fun(dB, fun(type, bool)), typing, 
10.45/10.69	              e)), t1)), u)
10.45/10.69	     = fTrue,
10.45/10.69	    inference('demod', [status(thm)], ['15', '5'])).
10.45/10.69	tff(zf_stmt_160, axiom, (app_encode_app(bool,$o,pp,fTrue))).
10.45/10.69	tff('17', plain, app_encode_app(bool, $o, pp, fTrue),
10.45/10.69	    inference('cnf', [status(esa)], [zf_stmt_160])).
10.45/10.69	tff('18', plain, (~ $true | ~ $true),
10.45/10.69	    inference('demod', [status(thm)], ['9', '16', '17'])).
10.45/10.69	tff('19', plain, $false, inference('simplify', [status(thm)], ['18'])).
10.45/10.69	
10.45/10.69	% SZS output end Refutation
10.56/10.69	EOF
