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    : 
0.00/0.01	#!/bin/sh
0.00/0.01	
0.00/0.01	./zipperposition.native ${1:+"$1"} \
0.00/0.01	  -i tptp \
0.00/0.01	  -o tptp \
0.00/0.01	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.01	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.01	  --no-ho \
0.00/0.01	  --no-avatar \
0.00/0.01	  --no-induction \
0.00/0.01	  --no-unif-pattern \
0.00/0.01	  --ord $2 \
0.00/0.01	  --simultaneous-sup false \
0.00/0.01	  --no-max-vars \
0.00/0.01	  --no-fool
0.00/0.20	% Computer   : n127.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 07:07:09 CST 2018
37.49/37.69	% done 4147 iterations in 37.486s
37.49/37.69	% SZS status Theorem for 'stdin'
37.49/37.69	% SZS output start Refutation
37.49/37.70	tff(zf_stmt_69, axiom,
37.49/37.70	  (app_encode_app(bool,$o,pp,
37.49/37.70	                  app_encode_app(type,bool,
37.49/37.70	                                 app_encode_app(fun(type,bool),
37.49/37.70	                                                app_encode_fun(type,bool),
37.49/37.70	                                                aa(type,bool),
37.49/37.70	                                                app_encode_app(dB,
37.49/37.70	                                                               fun(type,bool),
37.49/37.70	                                                               app_encode_app(
37.49/37.70	                                                               fun(dB,
37.49/37.70	                                                                   fun(
37.49/37.70	                                                                   type,bool)),
37.49/37.70	                                                               app_encode_fun(
37.49/37.70	                                                               dB,
37.49/37.70	                                                               fun(type,bool)),
37.49/37.70	                                                               aa(dB,
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  type,bool)),
37.49/37.70	                                                               app_encode_app(
37.49/37.70	                                                               fun(nat,type),
37.49/37.70	                                                               fun(dB,
37.49/37.70	                                                                   fun(
37.49/37.70	                                                                   type,bool)),
37.49/37.70	                                                               app_encode_app(
37.49/37.70	                                                               fun(fun(
37.49/37.70	                                                                   nat,type),
37.49/37.70	                                                                   fun(
37.49/37.70	                                                                   dB,
37.49/37.70	                                                                   fun(
37.49/37.70	                                                                   type,bool))),
37.49/37.70	                                                               app_encode_fun(
37.49/37.70	                                                               fun(nat,type),
37.49/37.70	                                                               fun(dB,
37.49/37.70	                                                                   fun(
37.49/37.70	                                                                   type,bool))),
37.49/37.70	                                                               aa(fun(
37.49/37.70	                                                                  nat,type),
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  dB,
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  type,bool))),
37.49/37.70	                                                               typing),
37.49/37.70	                                                               app_encode_app(
37.49/37.70	                                                               type,
37.49/37.70	                                                               fun(nat,type),
37.49/37.70	                                                               app_encode_app(
37.49/37.70	                                                               fun(type,
37.49/37.70	                                                                   fun(
37.49/37.70	                                                                   nat,type)),
37.49/37.70	                                                               app_encode_fun(
37.49/37.70	                                                               type,
37.49/37.70	                                                               fun(nat,type)),
37.49/37.70	                                                               aa(type,
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  nat,type)),
37.49/37.70	                                                               app_encode_app(
37.49/37.70	                                                               nat,
37.49/37.70	                                                               fun(type,
37.49/37.70	                                                                   fun(
37.49/37.70	                                                                   nat,type)),
37.49/37.70	                                                               app_encode_app(
37.49/37.70	                                                               fun(nat,
37.49/37.70	                                                                   fun(
37.49/37.70	                                                                   type,
37.49/37.70	                                                                   fun(
37.49/37.70	                                                                   nat,type))),
37.49/37.70	                                                               app_encode_fun(
37.49/37.70	                                                               nat,
37.49/37.70	                                                               fun(type,
37.49/37.70	                                                                   fun(
37.49/37.70	                                                                   nat,type))),
37.49/37.70	                                                               aa(nat,
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  type,
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  nat,type))),
37.49/37.70	                                                               app_encode_app(
37.49/37.70	                                                               fun(nat,type),
37.49/37.70	                                                               fun(nat,
37.49/37.70	                                                                   fun(
37.49/37.70	                                                                   type,
37.49/37.70	                                                                   fun(
37.49/37.70	                                                                   nat,type))),
37.49/37.70	                                                               app_encode_app(
37.49/37.70	                                                               fun(fun(
37.49/37.70	                                                                   nat,type),
37.49/37.70	                                                                   fun(
37.49/37.70	                                                                   nat,
37.49/37.70	                                                                   fun(
37.49/37.70	                                                                   type,
37.49/37.70	                                                                   fun(
37.49/37.70	                                                                   nat,type)))),
37.49/37.70	                                                               app_encode_fun(
37.49/37.70	                                                               fun(nat,type),
37.49/37.70	                                                               fun(nat,
37.49/37.70	                                                                   fun(
37.49/37.70	                                                                   type,
37.49/37.70	                                                                   fun(
37.49/37.70	                                                                   nat,type)))),
37.49/37.70	                                                               aa(fun(
37.49/37.70	                                                                  nat,type),
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  nat,
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  type,
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  nat,type)))),
37.49/37.70	                                                               shift(type)),e)),
37.49/37.70	                                                               i)),t))),b)),
37.49/37.70	                                 ua1)))).
37.49/37.70	tff('0', plain,
37.49/37.70	    app_encode_app(bool, $o, pp, 
37.49/37.70	      app_encode_app(type, bool, 
37.49/37.70	        app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
37.49/37.70	          aa(type, bool), 
37.49/37.70	          app_encode_app(dB, fun(type, bool), 
37.49/37.70	            app_encode_app(fun(dB, fun(type, bool)), 
37.49/37.70	              app_encode_fun(dB, fun(type, bool)), aa(dB, fun(type, bool)), 
37.49/37.70	              app_encode_app(fun(nat, type), fun(dB, fun(type, bool)), 
37.49/37.70	                app_encode_app(
37.49/37.70	                  fun(fun(nat, type), fun(dB, fun(type, bool))), 
37.49/37.70	                  app_encode_fun(fun(nat, type), fun(dB, fun(type, bool))), 
37.49/37.70	                  aa(fun(nat, type), fun(dB, fun(type, bool))), typing), 
37.49/37.70	                app_encode_app(type, fun(nat, type), 
37.49/37.70	                  app_encode_app(fun(type, fun(nat, type)), 
37.49/37.70	                    app_encode_fun(type, fun(nat, type)), 
37.49/37.70	                    aa(type, fun(nat, type)), 
37.49/37.70	                    app_encode_app(nat, fun(type, fun(nat, type)), 
37.49/37.70	                      app_encode_app(fun(nat, fun(type, fun(nat, type))), 
37.49/37.70	                        app_encode_fun(nat, fun(type, fun(nat, type))), 
37.49/37.70	                        aa(nat, fun(type, fun(nat, type))), 
37.49/37.70	                        app_encode_app(fun(nat, type), 
37.49/37.70	                          fun(nat, fun(type, fun(nat, type))), 
37.49/37.70	                          app_encode_app(
37.49/37.70	                            fun(fun(nat, type), 
37.49/37.70	                              fun(nat, fun(type, fun(nat, type)))), 
37.49/37.70	                            app_encode_fun(fun(nat, type), 
37.49/37.70	                              fun(nat, fun(type, fun(nat, type)))), 
37.49/37.70	                            aa(fun(nat, type), 
37.49/37.70	                              fun(nat, fun(type, fun(nat, type)))), 
37.49/37.70	                            shift(type)), e)), i)), t))), b)), ua1)),
37.49/37.70	    inference('cnf', [status(esa)], [zf_stmt_69])).
37.49/37.70	tff(zf_stmt_66, axiom,
37.49/37.70	  (app_encode_app(bool,$o,pp,
37.49/37.70	                  app_encode_app(type,bool,
37.49/37.70	                                 app_encode_app(fun(type,bool),
37.49/37.70	                                                app_encode_fun(type,bool),
37.49/37.70	                                                aa(type,bool),
37.49/37.70	                                                app_encode_app(dB,
37.49/37.70	                                                               fun(type,bool),
37.49/37.70	                                                               app_encode_app(
37.49/37.70	                                                               fun(dB,
37.49/37.70	                                                                   fun(
37.49/37.70	                                                                   type,bool)),
37.49/37.70	                                                               app_encode_fun(
37.49/37.70	                                                               dB,
37.49/37.70	                                                               fun(type,bool)),
37.49/37.70	                                                               aa(dB,
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  type,bool)),
37.49/37.70	                                                               app_encode_app(
37.49/37.70	                                                               fun(nat,type),
37.49/37.70	                                                               fun(dB,
37.49/37.70	                                                                   fun(
37.49/37.70	                                                                   type,bool)),
37.49/37.70	                                                               app_encode_app(
37.49/37.70	                                                               fun(fun(
37.49/37.70	                                                                   nat,type),
37.49/37.70	                                                                   fun(
37.49/37.70	                                                                   dB,
37.49/37.70	                                                                   fun(
37.49/37.70	                                                                   type,bool))),
37.49/37.70	                                                               app_encode_fun(
37.49/37.70	                                                               fun(nat,type),
37.49/37.70	                                                               fun(dB,
37.49/37.70	                                                                   fun(
37.49/37.70	                                                                   type,bool))),
37.49/37.70	                                                               aa(fun(
37.49/37.70	                                                                  nat,type),
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  dB,
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  type,bool))),
37.49/37.70	                                                               typing),e)),u)),
37.49/37.70	                                 t)))).
37.49/37.70	tff('1', plain,
37.49/37.70	    app_encode_app(bool, $o, pp, 
37.49/37.70	      app_encode_app(type, bool, 
37.49/37.70	        app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
37.49/37.70	          aa(type, bool), 
37.49/37.70	          app_encode_app(dB, fun(type, bool), 
37.49/37.70	            app_encode_app(fun(dB, fun(type, bool)), 
37.49/37.70	              app_encode_fun(dB, fun(type, bool)), aa(dB, fun(type, bool)), 
37.49/37.70	              app_encode_app(fun(nat, type), fun(dB, fun(type, bool)), 
37.49/37.70	                app_encode_app(
37.49/37.70	                  fun(fun(nat, type), fun(dB, fun(type, bool))), 
37.49/37.70	                  app_encode_fun(fun(nat, type), fun(dB, fun(type, bool))), 
37.49/37.70	                  aa(fun(nat, type), fun(dB, fun(type, bool))), typing), e)), 
37.49/37.70	            u)), t)),
37.49/37.70	    inference('cnf', [status(esa)], [zf_stmt_66])).
37.49/37.70	tff(zf_stmt_68, axiom,
37.49/37.70	  (![E1:fun(nat,type),T3:type,U2:dB,I1:nat]:
37.49/37.70	     (app_encode_app(bool,$o,pp,
37.49/37.70	                     app_encode_app(type,bool,
37.49/37.70	                                    app_encode_app(fun(type,bool),
37.49/37.70	                                                   app_encode_fun(type,bool),
37.49/37.70	                                                   aa(type,bool),
37.49/37.70	                                                   app_encode_app(dB,
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  type,bool),
37.49/37.70	                                                                  app_encode_app(
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  dB,
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  type,bool)),
37.49/37.70	                                                                  app_encode_fun(
37.49/37.70	                                                                  dB,
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  type,bool)),
37.49/37.70	                                                                  aa(
37.49/37.70	                                                                  dB,
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  type,bool)),
37.49/37.70	                                                                  app_encode_app(
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  nat,type),
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  dB,
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  type,bool)),
37.49/37.70	                                                                  app_encode_app(
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  nat,type),
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  dB,
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  type,bool))),
37.49/37.70	                                                                  app_encode_fun(
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  nat,type),
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  dB,
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  type,bool))),
37.49/37.70	                                                                  aa(
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  nat,type),
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  dB,
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  type,bool))),
37.49/37.70	                                                                  typing),
37.49/37.70	                                                                  app_encode_app(
37.49/37.70	                                                                  type,
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  nat,type),
37.49/37.70	                                                                  app_encode_app(
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  type,
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  nat,type)),
37.49/37.70	                                                                  app_encode_fun(
37.49/37.70	                                                                  type,
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  nat,type)),
37.49/37.70	                                                                  aa(
37.49/37.70	                                                                  type,
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  nat,type)),
37.49/37.70	                                                                  app_encode_app(
37.49/37.70	                                                                  nat,
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  type,
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  nat,type)),
37.49/37.70	                                                                  app_encode_app(
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  nat,
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  type,
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  nat,type))),
37.49/37.70	                                                                  app_encode_fun(
37.49/37.70	                                                                  nat,
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  type,
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  nat,type))),
37.49/37.70	                                                                  aa(
37.49/37.70	                                                                  nat,
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  type,
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  nat,type))),
37.49/37.70	                                                                  app_encode_app(
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  nat,type),
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  nat,
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  type,
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  nat,type))),
37.49/37.70	                                                                  app_encode_app(
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  nat,type),
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  nat,
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  type,
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  nat,type)))),
37.49/37.70	                                                                  app_encode_fun(
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  nat,type),
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  nat,
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  type,
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  nat,type)))),
37.49/37.70	                                                                  aa(
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  nat,type),
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  nat,
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  type,
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  nat,type)))),
37.49/37.70	                                                                  shift(type)),
37.49/37.70	                                                                  E1)),I1)),t))),
37.49/37.70	                                                                  b)),
37.49/37.70	                                    T3)) =>
37.49/37.70	      (app_encode_app(bool,$o,pp,
37.49/37.70	                      app_encode_app(dB,bool,
37.49/37.70	                                     app_encode_app(fun(dB,bool),
37.49/37.70	                                                    app_encode_fun(dB,bool),
37.49/37.70	                                                    aa(dB,bool),it),
37.49/37.70	                                     U2)) =>
37.49/37.70	       (app_encode_app(bool,$o,pp,
37.49/37.70	                       app_encode_app(type,bool,
37.49/37.70	                                      app_encode_app(fun(type,bool),
37.49/37.70	                                                     app_encode_fun(type,bool),
37.49/37.70	                                                     aa(type,bool),
37.49/37.70	                                                     app_encode_app(dB,
37.49/37.70	                                                                    fun(
37.49/37.70	                                                                    type,bool),
37.49/37.70	                                                                    app_encode_app(
37.49/37.70	                                                                    fun(
37.49/37.70	                                                                    dB,
37.49/37.70	                                                                    fun(
37.49/37.70	                                                                    type,bool)),
37.49/37.70	                                                                    app_encode_fun(
37.49/37.70	                                                                    dB,
37.49/37.70	                                                                    fun(
37.49/37.70	                                                                    type,bool)),
37.49/37.70	                                                                    aa(
37.49/37.70	                                                                    dB,
37.49/37.70	                                                                    fun(
37.49/37.70	                                                                    type,bool)),
37.49/37.70	                                                                    app_encode_app(
37.49/37.70	                                                                    fun(
37.49/37.70	                                                                    nat,type),
37.49/37.70	                                                                    fun(
37.49/37.70	                                                                    dB,
37.49/37.70	                                                                    fun(
37.49/37.70	                                                                    type,bool)),
37.49/37.70	                                                                    app_encode_app(
37.49/37.70	                                                                    fun(
37.49/37.70	                                                                    fun(
37.49/37.70	                                                                    nat,type),
37.49/37.70	                                                                    fun(
37.49/37.70	                                                                    dB,
37.49/37.70	                                                                    fun(
37.49/37.70	                                                                    type,bool))),
37.49/37.70	                                                                    app_encode_fun(
37.49/37.70	                                                                    fun(
37.49/37.70	                                                                    nat,type),
37.49/37.70	                                                                    fun(
37.49/37.70	                                                                    dB,
37.49/37.70	                                                                    fun(
37.49/37.70	                                                                    type,bool))),
37.49/37.70	                                                                    aa(
37.49/37.70	                                                                    fun(
37.49/37.70	                                                                    nat,type),
37.49/37.70	                                                                    fun(
37.49/37.70	                                                                    dB,
37.49/37.70	                                                                    fun(
37.49/37.70	                                                                    type,bool))),
37.49/37.70	                                                                    typing),
37.49/37.70	                                                                    E1)),U2)),
37.49/37.70	                                      t)) =>
37.49/37.70	        app_encode_app(bool,$o,pp,
37.49/37.70	                       app_encode_app(dB,bool,
37.49/37.70	                                      app_encode_app(fun(dB,bool),
37.49/37.70	                                                     app_encode_fun(dB,bool),
37.49/37.70	                                                     aa(dB,bool),it),
37.49/37.70	                                      app_encode_app(nat,dB,
37.49/37.70	                                                     app_encode_app(fun(
37.49/37.70	                                                                    nat,dB),
37.49/37.70	                                                                    app_encode_fun(
37.49/37.70	                                                                    nat,dB),
37.49/37.70	                                                                    aa(
37.49/37.70	                                                                    nat,dB),
37.49/37.70	                                                                    app_encode_app(
37.49/37.70	                                                                    dB,
37.49/37.70	                                                                    fun(
37.49/37.70	                                                                    nat,dB),
37.49/37.70	                                                                    app_encode_app(
37.49/37.70	                                                                    fun(
37.49/37.70	                                                                    dB,
37.49/37.70	                                                                    fun(
37.49/37.70	                                                                    nat,dB)),
37.49/37.70	                                                                    app_encode_fun(
37.49/37.70	                                                                    dB,
37.49/37.70	                                                                    fun(
37.49/37.70	                                                                    nat,dB)),
37.49/37.70	                                                                    aa(
37.49/37.70	                                                                    dB,
37.49/37.70	                                                                    fun(
37.49/37.70	                                                                    nat,dB)),
37.49/37.70	                                                                    app_encode_app(
37.49/37.70	                                                                    dB,
37.49/37.70	                                                                    fun(
37.49/37.70	                                                                    dB,
37.49/37.70	                                                                    fun(
37.49/37.70	                                                                    nat,dB)),
37.49/37.70	                                                                    app_encode_app(
37.49/37.70	                                                                    fun(
37.49/37.70	                                                                    dB,
37.49/37.70	                                                                    fun(
37.49/37.70	                                                                    dB,
37.49/37.70	                                                                    fun(
37.49/37.70	                                                                    nat,dB))),
37.49/37.70	                                                                    app_encode_fun(
37.49/37.70	                                                                    dB,
37.49/37.70	                                                                    fun(
37.49/37.70	                                                                    dB,
37.49/37.70	                                                                    fun(
37.49/37.70	                                                                    nat,dB))),
37.49/37.70	                                                                    aa(
37.49/37.70	                                                                    dB,
37.49/37.70	                                                                    fun(
37.49/37.70	                                                                    dB,
37.49/37.70	                                                                    fun(
37.49/37.70	                                                                    nat,dB))),
37.49/37.70	                                                                    subst),b)),
37.49/37.70	                                                                    U2)),
37.49/37.70	                                                     I1)))))))).
37.49/37.70	tff('2', plain,
37.49/37.70	    ![X0 : dB, X1 : fun(nat, type), X2 : nat, X3 : type]:
37.49/37.70	      (~ app_encode_app(bool, $o, pp, 
37.49/37.70	           app_encode_app(dB, bool, 
37.49/37.70	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
37.49/37.70	               aa(dB, bool), it), X0))
37.49/37.70	       | ~ app_encode_app(bool, $o, pp, 
37.49/37.70	             app_encode_app(type, bool, 
37.49/37.70	               app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
37.49/37.70	                 aa(type, bool), 
37.49/37.70	                 app_encode_app(dB, fun(type, bool), 
37.49/37.70	                   app_encode_app(fun(dB, fun(type, bool)), 
37.49/37.70	                     app_encode_fun(dB, fun(type, bool)), 
37.49/37.70	                     aa(dB, fun(type, bool)), 
37.49/37.70	                     app_encode_app(fun(nat, type), 
37.49/37.70	                       fun(dB, fun(type, bool)), 
37.49/37.70	                       app_encode_app(
37.49/37.70	                         fun(fun(nat, type), fun(dB, fun(type, bool))), 
37.49/37.70	                         app_encode_fun(fun(nat, type), 
37.49/37.70	                           fun(dB, fun(type, bool))), 
37.49/37.70	                         aa(fun(nat, type), fun(dB, fun(type, bool))), 
37.49/37.70	                         typing), X1)), X0)), t))
37.49/37.70	       | ~ app_encode_app(bool, $o, pp, 
37.49/37.70	             app_encode_app(type, bool, 
37.49/37.70	               app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
37.49/37.70	                 aa(type, bool), 
37.49/37.70	                 app_encode_app(dB, fun(type, bool), 
37.49/37.70	                   app_encode_app(fun(dB, fun(type, bool)), 
37.49/37.70	                     app_encode_fun(dB, fun(type, bool)), 
37.49/37.70	                     aa(dB, fun(type, bool)), 
37.49/37.70	                     app_encode_app(fun(nat, type), 
37.49/37.70	                       fun(dB, fun(type, bool)), 
37.49/37.70	                       app_encode_app(
37.49/37.70	                         fun(fun(nat, type), fun(dB, fun(type, bool))), 
37.49/37.70	                         app_encode_fun(fun(nat, type), 
37.49/37.70	                           fun(dB, fun(type, bool))), 
37.49/37.70	                         aa(fun(nat, type), fun(dB, fun(type, bool))), 
37.49/37.70	                         typing), 
37.49/37.70	                       app_encode_app(type, fun(nat, type), 
37.49/37.70	                         app_encode_app(fun(type, fun(nat, type)), 
37.49/37.70	                           app_encode_fun(type, fun(nat, type)), 
37.49/37.70	                           aa(type, fun(nat, type)), 
37.49/37.70	                           app_encode_app(nat, fun(type, fun(nat, type)), 
37.49/37.70	                             app_encode_app(
37.49/37.70	                               fun(nat, fun(type, fun(nat, type))), 
37.49/37.70	                               app_encode_fun(nat, fun(type, fun(nat, type))), 
37.49/37.70	                               aa(nat, fun(type, fun(nat, type))), 
37.49/37.70	                               app_encode_app(fun(nat, type), 
37.49/37.70	                                 fun(nat, fun(type, fun(nat, type))), 
37.49/37.70	                                 app_encode_app(
37.49/37.70	                                   fun(fun(nat, type), 
37.49/37.70	                                     fun(nat, fun(type, fun(nat, type)))), 
37.49/37.70	                                   app_encode_fun(fun(nat, type), 
37.49/37.70	                                     fun(nat, fun(type, fun(nat, type)))), 
37.49/37.70	                                   aa(fun(nat, type), 
37.49/37.70	                                     fun(nat, fun(type, fun(nat, type)))), 
37.49/37.70	                                   shift(type)), X1)), X2)), t))), b)), X3))
37.49/37.70	       | app_encode_app(bool, $o, pp, 
37.49/37.70	           app_encode_app(dB, bool, 
37.49/37.70	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
37.49/37.70	               aa(dB, bool), it), 
37.49/37.70	             app_encode_app(nat, dB, 
37.49/37.70	               app_encode_app(fun(nat, dB), app_encode_fun(nat, dB), 
37.49/37.70	                 aa(nat, dB), 
37.49/37.70	                 app_encode_app(dB, fun(nat, dB), 
37.49/37.70	                   app_encode_app(fun(dB, fun(nat, dB)), 
37.49/37.70	                     app_encode_fun(dB, fun(nat, dB)), aa(dB, fun(nat, dB)), 
37.49/37.70	                     app_encode_app(dB, fun(dB, fun(nat, dB)), 
37.49/37.70	                       app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
37.49/37.70	                         app_encode_fun(dB, fun(dB, fun(nat, dB))), 
37.49/37.70	                         aa(dB, fun(dB, fun(nat, dB))), subst), b)), X0)), 
37.49/37.70	               X2)))),
37.49/37.70	    inference('cnf', [status(esa)], [zf_stmt_68])).
37.49/37.70	tff('3', plain,
37.49/37.70	    ![X0 : nat, X1 : type]:
37.49/37.70	      (~ $true
37.49/37.70	       | app_encode_app(bool, $o, pp, 
37.49/37.70	           app_encode_app(dB, bool, 
37.49/37.70	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
37.49/37.70	               aa(dB, bool), it), 
37.49/37.70	             app_encode_app(nat, dB, 
37.49/37.70	               app_encode_app(fun(nat, dB), app_encode_fun(nat, dB), 
37.49/37.70	                 aa(nat, dB), 
37.49/37.70	                 app_encode_app(dB, fun(nat, dB), 
37.49/37.70	                   app_encode_app(fun(dB, fun(nat, dB)), 
37.49/37.70	                     app_encode_fun(dB, fun(nat, dB)), aa(dB, fun(nat, dB)), 
37.49/37.70	                     app_encode_app(dB, fun(dB, fun(nat, dB)), 
37.49/37.70	                       app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
37.49/37.70	                         app_encode_fun(dB, fun(dB, fun(nat, dB))), 
37.49/37.70	                         aa(dB, fun(dB, fun(nat, dB))), subst), b)), u)), X0)))
37.49/37.70	       | ~ app_encode_app(bool, $o, pp, 
37.49/37.70	             app_encode_app(type, bool, 
37.49/37.70	               app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
37.49/37.70	                 aa(type, bool), 
37.49/37.70	                 app_encode_app(dB, fun(type, bool), 
37.49/37.70	                   app_encode_app(fun(dB, fun(type, bool)), 
37.49/37.70	                     app_encode_fun(dB, fun(type, bool)), 
37.49/37.70	                     aa(dB, fun(type, bool)), 
37.49/37.70	                     app_encode_app(fun(nat, type), 
37.49/37.70	                       fun(dB, fun(type, bool)), 
37.49/37.70	                       app_encode_app(
37.49/37.70	                         fun(fun(nat, type), fun(dB, fun(type, bool))), 
37.49/37.70	                         app_encode_fun(fun(nat, type), 
37.49/37.70	                           fun(dB, fun(type, bool))), 
37.49/37.70	                         aa(fun(nat, type), fun(dB, fun(type, bool))), 
37.49/37.70	                         typing), 
37.49/37.70	                       app_encode_app(type, fun(nat, type), 
37.49/37.70	                         app_encode_app(fun(type, fun(nat, type)), 
37.49/37.70	                           app_encode_fun(type, fun(nat, type)), 
37.49/37.70	                           aa(type, fun(nat, type)), 
37.49/37.70	                           app_encode_app(nat, fun(type, fun(nat, type)), 
37.49/37.70	                             app_encode_app(
37.49/37.70	                               fun(nat, fun(type, fun(nat, type))), 
37.49/37.70	                               app_encode_fun(nat, fun(type, fun(nat, type))), 
37.49/37.70	                               aa(nat, fun(type, fun(nat, type))), 
37.49/37.70	                               app_encode_app(fun(nat, type), 
37.49/37.70	                                 fun(nat, fun(type, fun(nat, type))), 
37.49/37.70	                                 app_encode_app(
37.49/37.70	                                   fun(fun(nat, type), 
37.49/37.70	                                     fun(nat, fun(type, fun(nat, type)))), 
37.49/37.70	                                   app_encode_fun(fun(nat, type), 
37.49/37.70	                                     fun(nat, fun(type, fun(nat, type)))), 
37.49/37.70	                                   aa(fun(nat, type), 
37.49/37.70	                                     fun(nat, fun(type, fun(nat, type)))), 
37.49/37.70	                                   shift(type)), e)), X0)), t))), b)), X1))
37.49/37.70	       | ~ app_encode_app(bool, $o, pp, 
37.49/37.70	             app_encode_app(dB, bool, 
37.49/37.70	               app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
37.49/37.70	                 aa(dB, bool), it), u))),
37.49/37.70	    inference('sup-', [status(thm)], ['1', '2'])).
37.49/37.70	tff(zf_stmt_65, axiom,
37.49/37.70	  (app_encode_app(bool,$o,pp,
37.49/37.70	                  app_encode_app(dB,bool,
37.49/37.70	                                 app_encode_app(fun(dB,bool),
37.49/37.70	                                                app_encode_fun(dB,bool),
37.49/37.70	                                                aa(dB,bool),it),
37.49/37.70	                                 u)))).
37.49/37.70	tff('4', plain,
37.49/37.70	    app_encode_app(bool, $o, pp, 
37.49/37.70	      app_encode_app(dB, bool, 
37.49/37.70	        app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
37.49/37.70	          aa(dB, bool), it), u)),
37.49/37.70	    inference('cnf', [status(esa)], [zf_stmt_65])).
37.49/37.70	tff(zf_stmt_175, axiom, (![P:bool]: ((P = fTrue) | (P = fFalse)))).
37.49/37.70	tff('5', plain, ![X334 : bool]: (X334 = fTrue | X334 = fFalse),
37.49/37.70	    inference('cnf', [status(esa)], [zf_stmt_175])).
37.49/37.70	tff(zf_stmt_163, axiom, (~app_encode_app(bool,$o,pp,fFalse))).
37.49/37.70	tff('6', plain, ~ app_encode_app(bool, $o, pp, fFalse),
37.49/37.70	    inference('cnf', [status(esa)], [zf_stmt_163])).
37.49/37.70	tff('7', plain,
37.49/37.70	    ![X0 : bool]: (~ app_encode_app(bool, $o, pp, X0) | X0 = fTrue),
37.49/37.70	    inference('sup-', [status(thm)], ['5', '6'])).
37.49/37.70	tff('8', plain,
37.49/37.70	    (~ $true
37.49/37.70	     | app_encode_app(dB, bool, 
37.49/37.70	         app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
37.49/37.70	           aa(dB, bool), it), u)
37.49/37.70	        = fTrue),
37.49/37.70	    inference('sup-', [status(thm)], ['4', '7'])).
37.49/37.70	tff('9', plain,
37.49/37.70	    app_encode_app(dB, bool, 
37.49/37.70	      app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), aa(dB, bool), 
37.49/37.70	        it), u)
37.49/37.70	     = fTrue,
37.49/37.70	    inference('simplify', [status(thm)], ['8'])).
37.49/37.70	tff(zf_stmt_164, axiom, (app_encode_app(bool,$o,pp,fTrue))).
37.49/37.70	tff('10', plain, app_encode_app(bool, $o, pp, fTrue),
37.49/37.70	    inference('cnf', [status(esa)], [zf_stmt_164])).
37.49/37.70	tff('11', plain,
37.49/37.70	    ![X0 : nat, X1 : type]:
37.49/37.70	      (~ $true
37.49/37.70	       | app_encode_app(bool, $o, pp, 
37.49/37.70	           app_encode_app(dB, bool, 
37.49/37.70	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
37.49/37.70	               aa(dB, bool), it), 
37.49/37.70	             app_encode_app(nat, dB, 
37.49/37.70	               app_encode_app(fun(nat, dB), app_encode_fun(nat, dB), 
37.49/37.70	                 aa(nat, dB), 
37.49/37.70	                 app_encode_app(dB, fun(nat, dB), 
37.49/37.70	                   app_encode_app(fun(dB, fun(nat, dB)), 
37.49/37.70	                     app_encode_fun(dB, fun(nat, dB)), aa(dB, fun(nat, dB)), 
37.49/37.70	                     app_encode_app(dB, fun(dB, fun(nat, dB)), 
37.49/37.70	                       app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
37.49/37.70	                         app_encode_fun(dB, fun(dB, fun(nat, dB))), 
37.49/37.70	                         aa(dB, fun(dB, fun(nat, dB))), subst), b)), u)), X0)))
37.49/37.70	       | ~ app_encode_app(bool, $o, pp, 
37.49/37.70	             app_encode_app(type, bool, 
37.49/37.70	               app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
37.49/37.70	                 aa(type, bool), 
37.49/37.70	                 app_encode_app(dB, fun(type, bool), 
37.49/37.70	                   app_encode_app(fun(dB, fun(type, bool)), 
37.49/37.70	                     app_encode_fun(dB, fun(type, bool)), 
37.49/37.70	                     aa(dB, fun(type, bool)), 
37.49/37.70	                     app_encode_app(fun(nat, type), 
37.49/37.70	                       fun(dB, fun(type, bool)), 
37.49/37.70	                       app_encode_app(
37.49/37.70	                         fun(fun(nat, type), fun(dB, fun(type, bool))), 
37.49/37.70	                         app_encode_fun(fun(nat, type), 
37.49/37.70	                           fun(dB, fun(type, bool))), 
37.49/37.70	                         aa(fun(nat, type), fun(dB, fun(type, bool))), 
37.49/37.70	                         typing), 
37.49/37.70	                       app_encode_app(type, fun(nat, type), 
37.49/37.70	                         app_encode_app(fun(type, fun(nat, type)), 
37.49/37.70	                           app_encode_fun(type, fun(nat, type)), 
37.49/37.70	                           aa(type, fun(nat, type)), 
37.49/37.70	                           app_encode_app(nat, fun(type, fun(nat, type)), 
37.49/37.70	                             app_encode_app(
37.49/37.70	                               fun(nat, fun(type, fun(nat, type))), 
37.49/37.70	                               app_encode_fun(nat, fun(type, fun(nat, type))), 
37.49/37.70	                               aa(nat, fun(type, fun(nat, type))), 
37.49/37.70	                               app_encode_app(fun(nat, type), 
37.49/37.70	                                 fun(nat, fun(type, fun(nat, type))), 
37.49/37.70	                                 app_encode_app(
37.49/37.70	                                   fun(fun(nat, type), 
37.49/37.70	                                     fun(nat, fun(type, fun(nat, type)))), 
37.49/37.70	                                   app_encode_fun(fun(nat, type), 
37.49/37.70	                                     fun(nat, fun(type, fun(nat, type)))), 
37.49/37.70	                                   aa(fun(nat, type), 
37.49/37.70	                                     fun(nat, fun(type, fun(nat, type)))), 
37.49/37.70	                                   shift(type)), e)), X0)), t))), b)), X1))
37.49/37.70	       | ~ $true),
37.49/37.70	    inference('demod', [status(thm)], ['3', '9', '10'])).
37.49/37.70	tff('12', plain,
37.49/37.70	    ![X0 : nat, X1 : type]:
37.49/37.70	      (~ app_encode_app(bool, $o, pp, 
37.49/37.70	           app_encode_app(type, bool, 
37.49/37.70	             app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
37.49/37.70	               aa(type, bool), 
37.49/37.70	               app_encode_app(dB, fun(type, bool), 
37.49/37.70	                 app_encode_app(fun(dB, fun(type, bool)), 
37.49/37.70	                   app_encode_fun(dB, fun(type, bool)), 
37.49/37.70	                   aa(dB, fun(type, bool)), 
37.49/37.70	                   app_encode_app(fun(nat, type), fun(dB, fun(type, bool)), 
37.49/37.70	                     app_encode_app(
37.49/37.70	                       fun(fun(nat, type), fun(dB, fun(type, bool))), 
37.49/37.70	                       app_encode_fun(fun(nat, type), 
37.49/37.70	                         fun(dB, fun(type, bool))), 
37.49/37.70	                       aa(fun(nat, type), fun(dB, fun(type, bool))), typing), 
37.49/37.70	                     app_encode_app(type, fun(nat, type), 
37.49/37.70	                       app_encode_app(fun(type, fun(nat, type)), 
37.49/37.70	                         app_encode_fun(type, fun(nat, type)), 
37.49/37.70	                         aa(type, fun(nat, type)), 
37.49/37.70	                         app_encode_app(nat, fun(type, fun(nat, type)), 
37.49/37.70	                           app_encode_app(
37.49/37.70	                             fun(nat, fun(type, fun(nat, type))), 
37.49/37.70	                             app_encode_fun(nat, fun(type, fun(nat, type))), 
37.49/37.70	                             aa(nat, fun(type, fun(nat, type))), 
37.49/37.70	                             app_encode_app(fun(nat, type), 
37.49/37.70	                               fun(nat, fun(type, fun(nat, type))), 
37.49/37.70	                               app_encode_app(
37.49/37.70	                                 fun(fun(nat, type), 
37.49/37.70	                                   fun(nat, fun(type, fun(nat, type)))), 
37.49/37.70	                                 app_encode_fun(fun(nat, type), 
37.49/37.70	                                   fun(nat, fun(type, fun(nat, type)))), 
37.49/37.70	                                 aa(fun(nat, type), 
37.49/37.70	                                   fun(nat, fun(type, fun(nat, type)))), 
37.49/37.70	                                 shift(type)), e)), X0)), t))), b)), X1))
37.49/37.70	       | app_encode_app(bool, $o, pp, 
37.49/37.70	           app_encode_app(dB, bool, 
37.49/37.70	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
37.49/37.70	               aa(dB, bool), it), 
37.49/37.70	             app_encode_app(nat, dB, 
37.49/37.70	               app_encode_app(fun(nat, dB), app_encode_fun(nat, dB), 
37.49/37.70	                 aa(nat, dB), 
37.49/37.70	                 app_encode_app(dB, fun(nat, dB), 
37.49/37.70	                   app_encode_app(fun(dB, fun(nat, dB)), 
37.49/37.70	                     app_encode_fun(dB, fun(nat, dB)), aa(dB, fun(nat, dB)), 
37.49/37.70	                     app_encode_app(dB, fun(dB, fun(nat, dB)), 
37.49/37.70	                       app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
37.49/37.70	                         app_encode_fun(dB, fun(dB, fun(nat, dB))), 
37.49/37.70	                         aa(dB, fun(dB, fun(nat, dB))), subst), b)), u)), X0)))),
37.49/37.70	    inference('simplify', [status(thm)], ['11'])).
37.49/37.70	tff('13', plain,
37.49/37.70	    (~ $true
37.49/37.70	     | app_encode_app(bool, $o, pp, 
37.49/37.70	         app_encode_app(dB, bool, 
37.49/37.70	           app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
37.49/37.70	             aa(dB, bool), it), 
37.49/37.70	           app_encode_app(nat, dB, 
37.49/37.70	             app_encode_app(fun(nat, dB), app_encode_fun(nat, dB), 
37.49/37.70	               aa(nat, dB), 
37.49/37.70	               app_encode_app(dB, fun(nat, dB), 
37.49/37.70	                 app_encode_app(fun(dB, fun(nat, dB)), 
37.49/37.70	                   app_encode_fun(dB, fun(nat, dB)), aa(dB, fun(nat, dB)), 
37.49/37.70	                   app_encode_app(dB, fun(dB, fun(nat, dB)), 
37.49/37.70	                     app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
37.49/37.70	                       app_encode_fun(dB, fun(dB, fun(nat, dB))), 
37.49/37.70	                       aa(dB, fun(dB, fun(nat, dB))), subst), b)), u)), i)))),
37.49/37.70	    inference('sup-', [status(thm)], ['0', '12'])).
37.49/37.70	tff('14', plain,
37.49/37.70	    app_encode_app(bool, $o, pp, 
37.49/37.70	      app_encode_app(dB, bool, 
37.49/37.70	        app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
37.49/37.70	          aa(dB, bool), it), 
37.49/37.70	        app_encode_app(nat, dB, 
37.49/37.70	          app_encode_app(fun(nat, dB), app_encode_fun(nat, dB), aa(nat, dB), 
37.49/37.70	            app_encode_app(dB, fun(nat, dB), 
37.49/37.70	              app_encode_app(fun(dB, fun(nat, dB)), 
37.49/37.70	                app_encode_fun(dB, fun(nat, dB)), aa(dB, fun(nat, dB)), 
37.49/37.70	                app_encode_app(dB, fun(dB, fun(nat, dB)), 
37.49/37.70	                  app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
37.49/37.70	                    app_encode_fun(dB, fun(dB, fun(nat, dB))), 
37.49/37.70	                    aa(dB, fun(dB, fun(nat, dB))), subst), b)), u)), i))),
37.49/37.70	    inference('simplify', [status(thm)], ['13'])).
37.49/37.70	tff('15', plain,
37.49/37.70	    ![X0 : bool]: (app_encode_app(bool, $o, pp, X0) | X0 = fFalse),
37.49/37.70	    inference('sup+', [status(thm)], ['5', '10'])).
37.49/37.70	tff(zf_stmt_181, conjecture,
37.49/37.70	  (app_encode_app(bool,$o,pp,
37.49/37.70	                  app_encode_app(dB,bool,
37.49/37.70	                                 app_encode_app(fun(dB,bool),
37.49/37.70	                                                app_encode_fun(dB,bool),
37.49/37.70	                                                aa(dB,bool),it),
37.49/37.70	                                 app_encode_app(nat,dB,
37.49/37.70	                                                app_encode_app(fun(nat,dB),
37.49/37.70	                                                               app_encode_fun(
37.49/37.70	                                                               nat,dB),
37.49/37.70	                                                               aa(nat,dB),
37.49/37.70	                                                               app_encode_app(
37.49/37.70	                                                               dB,
37.49/37.70	                                                               fun(nat,dB),
37.49/37.70	                                                               app_encode_app(
37.49/37.70	                                                               fun(dB,
37.49/37.70	                                                                   fun(
37.49/37.70	                                                                   nat,dB)),
37.49/37.70	                                                               app_encode_fun(
37.49/37.70	                                                               dB,fun(nat,dB)),
37.49/37.70	                                                               aa(dB,
37.49/37.70	                                                                  fun(nat,dB)),
37.49/37.70	                                                               app_encode_app(
37.49/37.70	                                                               dB,
37.49/37.70	                                                               fun(dB,
37.49/37.70	                                                                   fun(
37.49/37.70	                                                                   nat,dB)),
37.49/37.70	                                                               app_encode_app(
37.49/37.70	                                                               fun(dB,
37.49/37.70	                                                                   fun(
37.49/37.70	                                                                   dB,
37.49/37.70	                                                                   fun(
37.49/37.70	                                                                   nat,dB))),
37.49/37.70	                                                               app_encode_fun(
37.49/37.70	                                                               dB,
37.49/37.70	                                                               fun(dB,
37.49/37.70	                                                                   fun(
37.49/37.70	                                                                   nat,dB))),
37.49/37.70	                                                               aa(dB,
37.49/37.70	                                                                  fun(
37.49/37.70	                                                                  dB,
37.49/37.70	                                                                  fun(nat,dB))),
37.49/37.70	                                                               subst),b)),u)),
37.49/37.70	                                                i))))).
37.49/37.70	tff(zf_stmt_0, negated_conjecture,
37.49/37.70	  (~
37.49/37.70	    app_encode_app(bool,$o,pp,
37.49/37.70	                   app_encode_app(dB,bool,
37.49/37.70	                                  app_encode_app(fun(dB,bool),
37.49/37.70	                                                 app_encode_fun(dB,bool),
37.49/37.70	                                                 aa(dB,bool),it),
37.49/37.70	                                  app_encode_app(nat,dB,
37.49/37.70	                                                 app_encode_app(fun(nat,dB),
37.49/37.70	                                                                app_encode_fun(
37.49/37.70	                                                                nat,dB),
37.49/37.70	                                                                aa(nat,dB),
37.49/37.70	                                                                app_encode_app(
37.49/37.70	                                                                dB,
37.49/37.70	                                                                fun(nat,dB),
37.49/37.70	                                                                app_encode_app(
37.49/37.70	                                                                fun(dB,
37.49/37.70	                                                                    fun(
37.49/37.70	                                                                    nat,dB)),
37.49/37.70	                                                                app_encode_fun(
37.49/37.70	                                                                dB,
37.49/37.70	                                                                fun(nat,dB)),
37.49/37.70	                                                                aa(dB,
37.49/37.70	                                                                   fun(
37.49/37.70	                                                                   nat,dB)),
37.49/37.70	                                                                app_encode_app(
37.49/37.70	                                                                dB,
37.49/37.70	                                                                fun(dB,
37.49/37.70	                                                                    fun(
37.49/37.70	                                                                    nat,dB)),
37.49/37.70	                                                                app_encode_app(
37.49/37.70	                                                                fun(dB,
37.49/37.70	                                                                    fun(
37.49/37.70	                                                                    dB,
37.49/37.70	                                                                    fun(
37.49/37.70	                                                                    nat,dB))),
37.49/37.70	                                                                app_encode_fun(
37.49/37.70	                                                                dB,
37.49/37.70	                                                                fun(dB,
37.49/37.70	                                                                    fun(
37.49/37.70	                                                                    nat,dB))),
37.49/37.70	                                                                aa(dB,
37.49/37.70	                                                                   fun(
37.49/37.70	                                                                   dB,
37.49/37.70	                                                                   fun(
37.49/37.70	                                                                   nat,dB))),
37.49/37.70	                                                                subst),b)),u)),
37.49/37.70	                                                 i))))).
37.49/37.70	tff('16', plain,
37.49/37.70	    ~ app_encode_app(bool, $o, pp, 
37.49/37.70	        app_encode_app(dB, bool, 
37.49/37.70	          app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
37.49/37.70	            aa(dB, bool), it), 
37.49/37.70	          app_encode_app(nat, dB, 
37.49/37.70	            app_encode_app(fun(nat, dB), app_encode_fun(nat, dB), 
37.49/37.70	              aa(nat, dB), 
37.49/37.70	              app_encode_app(dB, fun(nat, dB), 
37.49/37.70	                app_encode_app(fun(dB, fun(nat, dB)), 
37.49/37.70	                  app_encode_fun(dB, fun(nat, dB)), aa(dB, fun(nat, dB)), 
37.49/37.70	                  app_encode_app(dB, fun(dB, fun(nat, dB)), 
37.49/37.70	                    app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
37.49/37.70	                      app_encode_fun(dB, fun(dB, fun(nat, dB))), 
37.49/37.70	                      aa(dB, fun(dB, fun(nat, dB))), subst), b)), u)), i))),
37.49/37.70	    inference('cnf', [status(esa)], [zf_stmt_0])).
37.49/37.70	tff('17', plain,
37.49/37.70	    (~ $true
37.49/37.70	     | app_encode_app(dB, bool, 
37.49/37.70	         app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
37.49/37.70	           aa(dB, bool), it), 
37.49/37.70	         app_encode_app(nat, dB, 
37.49/37.70	           app_encode_app(fun(nat, dB), app_encode_fun(nat, dB), 
37.49/37.70	             aa(nat, dB), 
37.49/37.70	             app_encode_app(dB, fun(nat, dB), 
37.49/37.70	               app_encode_app(fun(dB, fun(nat, dB)), 
37.49/37.70	                 app_encode_fun(dB, fun(nat, dB)), aa(dB, fun(nat, dB)), 
37.49/37.70	                 app_encode_app(dB, fun(dB, fun(nat, dB)), 
37.49/37.70	                   app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
37.49/37.70	                     app_encode_fun(dB, fun(dB, fun(nat, dB))), 
37.49/37.70	                     aa(dB, fun(dB, fun(nat, dB))), subst), b)), u)), i))
37.49/37.70	        = fFalse),
37.49/37.70	    inference('sup-', [status(thm)], ['15', '16'])).
37.49/37.70	tff('18', plain,
37.49/37.70	    app_encode_app(dB, bool, 
37.49/37.70	      app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), aa(dB, bool), 
37.49/37.70	        it), 
37.49/37.70	      app_encode_app(nat, dB, 
37.49/37.70	        app_encode_app(fun(nat, dB), app_encode_fun(nat, dB), aa(nat, dB), 
37.49/37.70	          app_encode_app(dB, fun(nat, dB), 
37.49/37.70	            app_encode_app(fun(dB, fun(nat, dB)), 
37.49/37.70	              app_encode_fun(dB, fun(nat, dB)), aa(dB, fun(nat, dB)), 
37.49/37.70	              app_encode_app(dB, fun(dB, fun(nat, dB)), 
37.49/37.70	                app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
37.49/37.70	                  app_encode_fun(dB, fun(dB, fun(nat, dB))), 
37.49/37.70	                  aa(dB, fun(dB, fun(nat, dB))), subst), b)), u)), i))
37.49/37.70	     = fFalse,
37.49/37.70	    inference('simplify', [status(thm)], ['17'])).
37.49/37.70	tff('19', plain, app_encode_app(bool, $o, pp, fFalse),
37.49/37.70	    inference('demod', [status(thm)], ['14', '18'])).
37.49/37.70	tff('20', plain, ~ $true, inference('sup-', [status(thm)], ['19', '6'])).
37.49/37.70	tff('21', plain, $false, inference('simplify', [status(thm)], ['20'])).
37.49/37.70	
37.49/37.70	% SZS output end Refutation
37.49/37.70	EOF
