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 $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n119.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 07:22:38 CST 2018
13.47/13.62	% done 2630 iterations in 13.428s
13.47/13.62	% SZS status Theorem for 'stdin'
13.47/13.62	% SZS output start Refutation
13.47/13.63	tff(zf_stmt_61, axiom,
13.47/13.63	  (app_encode_app(bool,$o,pp,
13.47/13.63	                  app_encode_app(type,bool,
13.47/13.63	                                 app_encode_app(fun(type,bool),
13.47/13.63	                                                app_encode_fun(type,bool),
13.47/13.63	                                                aa(type,bool),
13.47/13.63	                                                app_encode_app(dB,
13.47/13.63	                                                               fun(type,bool),
13.47/13.63	                                                               app_encode_app(
13.47/13.63	                                                               fun(nat,type),
13.47/13.63	                                                               app_encode_fun(
13.47/13.63	                                                               dB,
13.47/13.63	                                                               fun(type,bool)),
13.47/13.63	                                                               typing,
13.47/13.63	                                                               app_encode_app(
13.47/13.63	                                                               type,
13.47/13.63	                                                               fun(nat,type),
13.47/13.63	                                                               app_encode_app(
13.47/13.63	                                                               nat,
13.47/13.63	                                                               app_encode_fun(
13.47/13.63	                                                               type,
13.47/13.63	                                                               fun(nat,type)),
13.47/13.63	                                                               app_encode_app(
13.47/13.63	                                                               fun(nat,type),
13.47/13.63	                                                               app_encode_fun(
13.47/13.63	                                                               nat,
13.47/13.63	                                                               app_encode_fun(
13.47/13.63	                                                               type,
13.47/13.63	                                                               fun(nat,type))),
13.47/13.63	                                                               shift(type),e),
13.47/13.63	                                                               i),t)),
13.47/13.63	                                                               app_encode_app(
13.47/13.63	                                                               list(dB),dB,
13.47/13.63	                                                               app_encode_app(
13.47/13.63	                                                               dB,
13.47/13.63	                                                               app_encode_fun(
13.47/13.63	                                                               list(dB),dB),
13.47/13.63	                                                               app_encode_app(
13.47/13.63	                                                               fun(dB,
13.47/13.63	                                                                   fun(dB,dB)),
13.47/13.63	                                                               app_encode_fun(
13.47/13.63	                                                               dB,
13.47/13.63	                                                               app_encode_fun(
13.47/13.63	                                                               list(dB),dB)),
13.47/13.63	                                                               foldl(dB,dB),
13.47/13.63	                                                               app),
13.47/13.63	                                                               app_encode_app(
13.47/13.63	                                                               nat,dB,
13.47/13.63	                                                               app_encode_app(
13.47/13.63	                                                               fun(nat,dB),
13.47/13.63	                                                               app_encode_fun(
13.47/13.63	                                                               nat,dB),
13.47/13.63	                                                               aa(nat,dB),
13.47/13.63	                                                               app_encode_app(
13.47/13.63	                                                               dB,
13.47/13.63	                                                               fun(nat,dB),
13.47/13.63	                                                               app_encode_app(
13.47/13.63	                                                               fun(dB,
13.47/13.63	                                                                   fun(
13.47/13.63	                                                                   nat,dB)),
13.47/13.63	                                                               app_encode_fun(
13.47/13.63	                                                               dB,fun(nat,dB)),
13.47/13.63	                                                               aa(dB,
13.47/13.63	                                                                  fun(nat,dB)),
13.47/13.63	                                                               app_encode_app(
13.47/13.63	                                                               dB,
13.47/13.63	                                                               fun(dB,
13.47/13.63	                                                                   fun(
13.47/13.63	                                                                   nat,dB)),
13.47/13.63	                                                               app_encode_app(
13.47/13.63	                                                               fun(dB,
13.47/13.63	                                                                   fun(
13.47/13.63	                                                                   dB,
13.47/13.63	                                                                   fun(
13.47/13.63	                                                                   nat,dB))),
13.47/13.63	                                                               app_encode_fun(
13.47/13.63	                                                               dB,
13.47/13.63	                                                               fun(dB,
13.47/13.63	                                                                   fun(
13.47/13.63	                                                                   nat,dB))),
13.47/13.63	                                                               aa(dB,
13.47/13.63	                                                                  fun(
13.47/13.63	                                                                  dB,
13.47/13.63	                                                                  fun(nat,dB))),
13.47/13.63	                                                               subst),r)),a)),
13.47/13.63	                                                               zero_zero(nat))),
13.47/13.63	                                                               as))),
13.47/13.63	                                 t1)))).
13.47/13.63	tff('0', plain,
13.47/13.63	    app_encode_app(bool, $o, pp, 
13.47/13.63	      app_encode_app(type, bool, 
13.47/13.63	        app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
13.47/13.63	          aa(type, bool), 
13.47/13.63	          app_encode_app(dB, fun(type, bool), 
13.47/13.63	            app_encode_app(fun(nat, type), 
13.47/13.63	              app_encode_fun(dB, fun(type, bool)), typing, 
13.47/13.63	              app_encode_app(type, fun(nat, type), 
13.47/13.63	                app_encode_app(nat, app_encode_fun(type, fun(nat, type)), 
13.47/13.63	                  app_encode_app(fun(nat, type), 
13.47/13.63	                    app_encode_fun(nat, app_encode_fun(type, fun(nat, type))), 
13.47/13.63	                    shift(type), e), i), t)), 
13.47/13.63	            app_encode_app(list(dB), dB, 
13.47/13.63	              app_encode_app(dB, app_encode_fun(list(dB), dB), 
13.47/13.63	                app_encode_app(fun(dB, fun(dB, dB)), 
13.47/13.63	                  app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
13.47/13.63	                  foldl(dB, dB), app), 
13.47/13.63	                app_encode_app(nat, dB, 
13.47/13.63	                  app_encode_app(fun(nat, dB), app_encode_fun(nat, dB), 
13.47/13.63	                    aa(nat, dB), 
13.47/13.63	                    app_encode_app(dB, fun(nat, dB), 
13.47/13.63	                      app_encode_app(fun(dB, fun(nat, dB)), 
13.47/13.63	                        app_encode_fun(dB, fun(nat, dB)), 
13.47/13.63	                        aa(dB, fun(nat, dB)), 
13.47/13.63	                        app_encode_app(dB, fun(dB, fun(nat, dB)), 
13.47/13.63	                          app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
13.47/13.63	                            app_encode_fun(dB, fun(dB, fun(nat, dB))), 
13.47/13.63	                            aa(dB, fun(dB, fun(nat, dB))), subst), r)), a)), 
13.47/13.63	                  zero_zero(nat))), as))), t1)),
13.47/13.63	    inference('cnf', [status(esa)], [zf_stmt_61])).
13.47/13.63	tff(zf_stmt_67, axiom,
13.47/13.63	  (![Ub:dB,T_b:type,Ib:nat,Eb:fun(nat,type)]:
13.47/13.63	     (app_encode_app(bool,$o,pp,
13.47/13.63	                     app_encode_app(type,bool,
13.47/13.63	                                    app_encode_app(fun(type,bool),
13.47/13.63	                                                   app_encode_fun(type,bool),
13.47/13.63	                                                   aa(type,bool),
13.47/13.63	                                                   app_encode_app(dB,
13.47/13.63	                                                                  fun(
13.47/13.63	                                                                  type,bool),
13.47/13.63	                                                                  app_encode_app(
13.47/13.63	                                                                  fun(
13.47/13.63	                                                                  nat,type),
13.47/13.63	                                                                  app_encode_fun(
13.47/13.63	                                                                  dB,
13.47/13.63	                                                                  fun(
13.47/13.63	                                                                  type,bool)),
13.47/13.63	                                                                  typing,
13.47/13.63	                                                                  app_encode_app(
13.47/13.63	                                                                  type,
13.47/13.63	                                                                  fun(
13.47/13.63	                                                                  nat,type),
13.47/13.63	                                                                  app_encode_app(
13.47/13.63	                                                                  nat,
13.47/13.63	                                                                  app_encode_fun(
13.47/13.63	                                                                  type,
13.47/13.63	                                                                  fun(
13.47/13.63	                                                                  nat,type)),
13.47/13.63	                                                                  app_encode_app(
13.47/13.63	                                                                  fun(
13.47/13.63	                                                                  nat,type),
13.47/13.63	                                                                  app_encode_fun(
13.47/13.63	                                                                  nat,
13.47/13.63	                                                                  app_encode_fun(
13.47/13.63	                                                                  type,
13.47/13.63	                                                                  fun(
13.47/13.63	                                                                  nat,type))),
13.47/13.63	                                                                  shift(type),
13.47/13.63	                                                                  Eb),Ib),t)),
13.47/13.63	                                                                  app_encode_app(
13.47/13.63	                                                                  list(dB),
13.47/13.63	                                                                  dB,
13.47/13.63	                                                                  app_encode_app(
13.47/13.63	                                                                  dB,
13.47/13.63	                                                                  app_encode_fun(
13.47/13.63	                                                                  list(dB),dB),
13.47/13.63	                                                                  app_encode_app(
13.47/13.63	                                                                  fun(
13.47/13.63	                                                                  dB,
13.47/13.63	                                                                  fun(dB,dB)),
13.47/13.63	                                                                  app_encode_fun(
13.47/13.63	                                                                  dB,
13.47/13.63	                                                                  app_encode_fun(
13.47/13.63	                                                                  list(dB),dB)),
13.47/13.63	                                                                  foldl(
13.47/13.63	                                                                  dB,dB),app),
13.47/13.63	                                                                  app_encode_app(
13.47/13.63	                                                                  nat,dB,
13.47/13.63	                                                                  app_encode_app(
13.47/13.63	                                                                  fun(nat,dB),
13.47/13.63	                                                                  app_encode_fun(
13.47/13.63	                                                                  nat,dB),
13.47/13.63	                                                                  aa(nat,dB),
13.47/13.63	                                                                  app_encode_app(
13.47/13.63	                                                                  dB,
13.47/13.63	                                                                  fun(nat,dB),
13.47/13.63	                                                                  app_encode_app(
13.47/13.63	                                                                  fun(
13.47/13.63	                                                                  dB,
13.47/13.63	                                                                  fun(nat,dB)),
13.47/13.63	                                                                  app_encode_fun(
13.47/13.63	                                                                  dB,
13.47/13.63	                                                                  fun(nat,dB)),
13.47/13.63	                                                                  aa(
13.47/13.63	                                                                  dB,
13.47/13.63	                                                                  fun(nat,dB)),
13.47/13.63	                                                                  app_encode_app(
13.47/13.63	                                                                  dB,
13.47/13.63	                                                                  fun(
13.47/13.63	                                                                  dB,
13.47/13.63	                                                                  fun(nat,dB)),
13.47/13.63	                                                                  app_encode_app(
13.47/13.63	                                                                  fun(
13.47/13.63	                                                                  dB,
13.47/13.63	                                                                  fun(
13.47/13.63	                                                                  dB,
13.47/13.63	                                                                  fun(nat,dB))),
13.47/13.63	                                                                  app_encode_fun(
13.47/13.63	                                                                  dB,
13.47/13.63	                                                                  fun(
13.47/13.63	                                                                  dB,
13.47/13.63	                                                                  fun(nat,dB))),
13.47/13.63	                                                                  aa(
13.47/13.63	                                                                  dB,
13.47/13.63	                                                                  fun(
13.47/13.63	                                                                  dB,
13.47/13.63	                                                                  fun(nat,dB))),
13.47/13.63	                                                                  subst),r)),
13.47/13.63	                                                                  a)),
13.47/13.63	                                                                  zero_zero(
13.47/13.63	                                                                  nat))),as))),
13.47/13.63	                                    T_b)) =>
13.47/13.63	      (app_encode_app(bool,$o,pp,
13.47/13.63	                      app_encode_app(dB,bool,
13.47/13.63	                                     app_encode_app(fun(dB,bool),
13.47/13.63	                                                    app_encode_fun(dB,bool),
13.47/13.63	                                                    aa(dB,bool),it),
13.47/13.63	                                     Ub)) =>
13.47/13.63	       (app_encode_app(bool,$o,pp,
13.47/13.63	                       app_encode_app(type,bool,
13.47/13.63	                                      app_encode_app(fun(type,bool),
13.47/13.63	                                                     app_encode_fun(type,bool),
13.47/13.63	                                                     aa(type,bool),
13.47/13.63	                                                     app_encode_app(dB,
13.47/13.63	                                                                    fun(
13.47/13.63	                                                                    type,bool),
13.47/13.63	                                                                    app_encode_app(
13.47/13.63	                                                                    fun(
13.47/13.63	                                                                    nat,type),
13.47/13.63	                                                                    app_encode_fun(
13.47/13.63	                                                                    dB,
13.47/13.63	                                                                    fun(
13.47/13.63	                                                                    type,bool)),
13.47/13.63	                                                                    typing,Eb),
13.47/13.63	                                                                    Ub)),
13.47/13.63	                                      t)) =>
13.47/13.63	        app_encode_app(bool,$o,pp,
13.47/13.63	                       app_encode_app(dB,bool,
13.47/13.63	                                      app_encode_app(fun(dB,bool),
13.47/13.63	                                                     app_encode_fun(dB,bool),
13.47/13.63	                                                     aa(dB,bool),it),
13.47/13.63	                                      app_encode_app(nat,dB,
13.47/13.63	                                                     app_encode_app(fun(
13.47/13.63	                                                                    nat,dB),
13.47/13.63	                                                                    app_encode_fun(
13.47/13.63	                                                                    nat,dB),
13.47/13.63	                                                                    aa(
13.47/13.63	                                                                    nat,dB),
13.47/13.63	                                                                    app_encode_app(
13.47/13.63	                                                                    dB,
13.47/13.63	                                                                    fun(
13.47/13.63	                                                                    nat,dB),
13.47/13.63	                                                                    app_encode_app(
13.47/13.63	                                                                    fun(
13.47/13.63	                                                                    dB,
13.47/13.63	                                                                    fun(
13.47/13.63	                                                                    nat,dB)),
13.47/13.63	                                                                    app_encode_fun(
13.47/13.63	                                                                    dB,
13.47/13.63	                                                                    fun(
13.47/13.63	                                                                    nat,dB)),
13.47/13.63	                                                                    aa(
13.47/13.63	                                                                    dB,
13.47/13.63	                                                                    fun(
13.47/13.63	                                                                    nat,dB)),
13.47/13.63	                                                                    app_encode_app(
13.47/13.63	                                                                    dB,
13.47/13.63	                                                                    fun(
13.47/13.63	                                                                    dB,
13.47/13.63	                                                                    fun(
13.47/13.63	                                                                    nat,dB)),
13.47/13.63	                                                                    app_encode_app(
13.47/13.63	                                                                    fun(
13.47/13.63	                                                                    dB,
13.47/13.63	                                                                    fun(
13.47/13.63	                                                                    dB,
13.47/13.63	                                                                    fun(
13.47/13.63	                                                                    nat,dB))),
13.47/13.63	                                                                    app_encode_fun(
13.47/13.63	                                                                    dB,
13.47/13.63	                                                                    fun(
13.47/13.63	                                                                    dB,
13.47/13.63	                                                                    fun(
13.47/13.63	                                                                    nat,dB))),
13.47/13.63	                                                                    aa(
13.47/13.63	                                                                    dB,
13.47/13.63	                                                                    fun(
13.47/13.63	                                                                    dB,
13.47/13.63	                                                                    fun(
13.47/13.63	                                                                    nat,dB))),
13.47/13.63	                                                                    subst),
13.47/13.63	                                                                    app_encode_app(
13.47/13.63	                                                                    list(dB),
13.47/13.63	                                                                    dB,
13.47/13.63	                                                                    app_encode_app(
13.47/13.63	                                                                    dB,
13.47/13.63	                                                                    app_encode_fun(
13.47/13.63	                                                                    list(dB),
13.47/13.63	                                                                    dB),
13.47/13.63	                                                                    app_encode_app(
13.47/13.63	                                                                    fun(
13.47/13.63	                                                                    dB,
13.47/13.63	                                                                    fun(
13.47/13.63	                                                                    dB,dB)),
13.47/13.63	                                                                    app_encode_fun(
13.47/13.63	                                                                    dB,
13.47/13.63	                                                                    app_encode_fun(
13.47/13.63	                                                                    list(dB),
13.47/13.63	                                                                    dB)),
13.47/13.63	                                                                    foldl(
13.47/13.63	                                                                    dB,dB),
13.47/13.63	                                                                    app),
13.47/13.63	                                                                    app_encode_app(
13.47/13.63	                                                                    nat,dB,
13.47/13.63	                                                                    app_encode_app(
13.47/13.63	                                                                    fun(
13.47/13.63	                                                                    nat,dB),
13.47/13.63	                                                                    app_encode_fun(
13.47/13.63	                                                                    nat,dB),
13.47/13.63	                                                                    aa(
13.47/13.63	                                                                    nat,dB),
13.47/13.63	                                                                    app_encode_app(
13.47/13.63	                                                                    dB,
13.47/13.63	                                                                    fun(
13.47/13.63	                                                                    nat,dB),
13.47/13.63	                                                                    app_encode_app(
13.47/13.63	                                                                    fun(
13.47/13.63	                                                                    dB,
13.47/13.63	                                                                    fun(
13.47/13.63	                                                                    nat,dB)),
13.47/13.63	                                                                    app_encode_fun(
13.47/13.63	                                                                    dB,
13.47/13.63	                                                                    fun(
13.47/13.63	                                                                    nat,dB)),
13.47/13.63	                                                                    aa(
13.47/13.63	                                                                    dB,
13.47/13.63	                                                                    fun(
13.47/13.63	                                                                    nat,dB)),
13.47/13.63	                                                                    app_encode_app(
13.47/13.63	                                                                    dB,
13.47/13.63	                                                                    fun(
13.47/13.63	                                                                    dB,
13.47/13.63	                                                                    fun(
13.47/13.63	                                                                    nat,dB)),
13.47/13.63	                                                                    app_encode_app(
13.47/13.63	                                                                    fun(
13.47/13.63	                                                                    dB,
13.47/13.63	                                                                    fun(
13.47/13.63	                                                                    dB,
13.47/13.63	                                                                    fun(
13.47/13.63	                                                                    nat,dB))),
13.47/13.63	                                                                    app_encode_fun(
13.47/13.63	                                                                    dB,
13.47/13.63	                                                                    fun(
13.47/13.63	                                                                    dB,
13.47/13.63	                                                                    fun(
13.47/13.63	                                                                    nat,dB))),
13.47/13.63	                                                                    aa(
13.47/13.63	                                                                    dB,
13.47/13.63	                                                                    fun(
13.47/13.63	                                                                    dB,
13.47/13.63	                                                                    fun(
13.47/13.63	                                                                    nat,dB))),
13.47/13.63	                                                                    subst),r)),
13.47/13.63	                                                                    a)),
13.47/13.63	                                                                    zero_zero(
13.47/13.63	                                                                    nat))),as))),
13.47/13.63	                                                                    Ub)),
13.47/13.63	                                                     Ib)))))))).
13.47/13.63	tff('1', plain,
13.47/13.63	    ![X13 : dB, X14 : nat, X15 : fun(nat, type), X16 : type]:
13.47/13.63	      (~ app_encode_app(bool, $o, pp, 
13.47/13.63	           app_encode_app(dB, bool, 
13.47/13.63	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
13.47/13.63	               aa(dB, bool), it), X13))
13.47/13.63	       | app_encode_app(bool, $o, pp, 
13.47/13.63	           app_encode_app(dB, bool, 
13.47/13.63	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
13.47/13.63	               aa(dB, bool), it), 
13.47/13.63	             app_encode_app(nat, dB, 
13.47/13.63	               app_encode_app(fun(nat, dB), app_encode_fun(nat, dB), 
13.47/13.63	                 aa(nat, dB), 
13.47/13.63	                 app_encode_app(dB, fun(nat, dB), 
13.47/13.63	                   app_encode_app(fun(dB, fun(nat, dB)), 
13.47/13.63	                     app_encode_fun(dB, fun(nat, dB)), aa(dB, fun(nat, dB)), 
13.47/13.63	                     app_encode_app(dB, fun(dB, fun(nat, dB)), 
13.47/13.63	                       app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
13.47/13.63	                         app_encode_fun(dB, fun(dB, fun(nat, dB))), 
13.47/13.63	                         aa(dB, fun(dB, fun(nat, dB))), subst), 
13.47/13.63	                       app_encode_app(list(dB), dB, 
13.47/13.63	                         app_encode_app(dB, app_encode_fun(list(dB), dB), 
13.47/13.63	                           app_encode_app(fun(dB, fun(dB, dB)), 
13.47/13.63	                             app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
13.47/13.63	                             foldl(dB, dB), app), 
13.47/13.63	                           app_encode_app(nat, dB, 
13.47/13.63	                             app_encode_app(fun(nat, dB), 
13.47/13.63	                               app_encode_fun(nat, dB), aa(nat, dB), 
13.47/13.63	                               app_encode_app(dB, fun(nat, dB), 
13.47/13.63	                                 app_encode_app(fun(dB, fun(nat, dB)), 
13.47/13.63	                                   app_encode_fun(dB, fun(nat, dB)), 
13.47/13.63	                                   aa(dB, fun(nat, dB)), 
13.47/13.63	                                   app_encode_app(dB, fun(dB, fun(nat, dB)), 
13.47/13.63	                                     app_encode_app(
13.47/13.63	                                       fun(dB, fun(dB, fun(nat, dB))), 
13.47/13.63	                                       app_encode_fun(dB, 
13.47/13.63	                                         fun(dB, fun(nat, dB))), 
13.47/13.63	                                       aa(dB, fun(dB, fun(nat, dB))), subst), 
13.47/13.63	                                     r)), a)), zero_zero(nat))), as))), X13)), 
13.47/13.63	               X14)))
13.47/13.63	       | ~ app_encode_app(bool, $o, pp, 
13.47/13.63	             app_encode_app(type, bool, 
13.47/13.63	               app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
13.47/13.63	                 aa(type, bool), 
13.47/13.63	                 app_encode_app(dB, fun(type, bool), 
13.47/13.63	                   app_encode_app(fun(nat, type), 
13.47/13.63	                     app_encode_fun(dB, fun(type, bool)), typing, 
13.47/13.63	                     app_encode_app(type, fun(nat, type), 
13.47/13.63	                       app_encode_app(nat, 
13.47/13.63	                         app_encode_fun(type, fun(nat, type)), 
13.47/13.63	                         app_encode_app(fun(nat, type), 
13.47/13.63	                           app_encode_fun(nat, 
13.47/13.63	                             app_encode_fun(type, fun(nat, type))), 
13.47/13.63	                           shift(type), X15), X14), t)), 
13.47/13.63	                   app_encode_app(list(dB), dB, 
13.47/13.63	                     app_encode_app(dB, app_encode_fun(list(dB), dB), 
13.47/13.63	                       app_encode_app(fun(dB, fun(dB, dB)), 
13.47/13.63	                         app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
13.47/13.63	                         foldl(dB, dB), app), 
13.47/13.63	                       app_encode_app(nat, dB, 
13.47/13.63	                         app_encode_app(fun(nat, dB), 
13.47/13.63	                           app_encode_fun(nat, dB), aa(nat, dB), 
13.47/13.63	                           app_encode_app(dB, fun(nat, dB), 
13.47/13.63	                             app_encode_app(fun(dB, fun(nat, dB)), 
13.47/13.63	                               app_encode_fun(dB, fun(nat, dB)), 
13.47/13.63	                               aa(dB, fun(nat, dB)), 
13.47/13.63	                               app_encode_app(dB, fun(dB, fun(nat, dB)), 
13.47/13.63	                                 app_encode_app(
13.47/13.63	                                   fun(dB, fun(dB, fun(nat, dB))), 
13.47/13.63	                                   app_encode_fun(dB, fun(dB, fun(nat, dB))), 
13.47/13.63	                                   aa(dB, fun(dB, fun(nat, dB))), subst), r)), 
13.47/13.63	                             a)), zero_zero(nat))), as))), X16))
13.47/13.63	       | ~ app_encode_app(bool, $o, pp, 
13.47/13.63	             app_encode_app(type, bool, 
13.47/13.63	               app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
13.47/13.63	                 aa(type, bool), 
13.47/13.63	                 app_encode_app(dB, fun(type, bool), 
13.47/13.63	                   app_encode_app(fun(nat, type), 
13.47/13.63	                     app_encode_fun(dB, fun(type, bool)), typing, X15), X13)), 
13.47/13.63	               t))),
13.47/13.63	    inference('cnf', [status(esa)], [zf_stmt_67])).
13.47/13.63	tff('2', plain,
13.47/13.63	    ![X0 : dB]:
13.47/13.63	      (~ $true
13.47/13.63	       | ~ app_encode_app(bool, $o, pp, 
13.47/13.63	             app_encode_app(type, bool, 
13.47/13.63	               app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
13.47/13.63	                 aa(type, bool), 
13.47/13.63	                 app_encode_app(dB, fun(type, bool), 
13.47/13.63	                   app_encode_app(fun(nat, type), 
13.47/13.63	                     app_encode_fun(dB, fun(type, bool)), typing, e), X0)), 
13.47/13.63	               t))
13.47/13.63	       | app_encode_app(bool, $o, pp, 
13.47/13.63	           app_encode_app(dB, bool, 
13.47/13.63	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
13.47/13.63	               aa(dB, bool), it), 
13.47/13.63	             app_encode_app(nat, dB, 
13.47/13.63	               app_encode_app(fun(nat, dB), app_encode_fun(nat, dB), 
13.47/13.63	                 aa(nat, dB), 
13.47/13.63	                 app_encode_app(dB, fun(nat, dB), 
13.47/13.63	                   app_encode_app(fun(dB, fun(nat, dB)), 
13.47/13.63	                     app_encode_fun(dB, fun(nat, dB)), aa(dB, fun(nat, dB)), 
13.47/13.63	                     app_encode_app(dB, fun(dB, fun(nat, dB)), 
13.47/13.63	                       app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
13.47/13.63	                         app_encode_fun(dB, fun(dB, fun(nat, dB))), 
13.47/13.63	                         aa(dB, fun(dB, fun(nat, dB))), subst), 
13.47/13.63	                       app_encode_app(list(dB), dB, 
13.47/13.63	                         app_encode_app(dB, app_encode_fun(list(dB), dB), 
13.47/13.63	                           app_encode_app(fun(dB, fun(dB, dB)), 
13.47/13.63	                             app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
13.47/13.63	                             foldl(dB, dB), app), 
13.47/13.63	                           app_encode_app(nat, dB, 
13.47/13.63	                             app_encode_app(fun(nat, dB), 
13.47/13.63	                               app_encode_fun(nat, dB), aa(nat, dB), 
13.47/13.63	                               app_encode_app(dB, fun(nat, dB), 
13.47/13.63	                                 app_encode_app(fun(dB, fun(nat, dB)), 
13.47/13.63	                                   app_encode_fun(dB, fun(nat, dB)), 
13.47/13.63	                                   aa(dB, fun(nat, dB)), 
13.47/13.63	                                   app_encode_app(dB, fun(dB, fun(nat, dB)), 
13.47/13.63	                                     app_encode_app(
13.47/13.63	                                       fun(dB, fun(dB, fun(nat, dB))), 
13.47/13.63	                                       app_encode_fun(dB, 
13.47/13.63	                                         fun(dB, fun(nat, dB))), 
13.47/13.63	                                       aa(dB, fun(dB, fun(nat, dB))), subst), 
13.47/13.63	                                     r)), a)), zero_zero(nat))), as))), X0)), 
13.47/13.63	               i)))
13.47/13.63	       | ~ app_encode_app(bool, $o, pp, 
13.47/13.63	             app_encode_app(dB, bool, 
13.47/13.63	               app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
13.47/13.63	                 aa(dB, bool), it), X0))),
13.47/13.63	    inference('sup-', [status(thm)], ['0', '1'])).
13.47/13.63	tff('3', plain,
13.47/13.63	    ![X0 : dB]:
13.47/13.63	      (~ app_encode_app(bool, $o, pp, 
13.47/13.63	           app_encode_app(dB, bool, 
13.47/13.63	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
13.47/13.63	               aa(dB, bool), it), X0))
13.47/13.63	       | app_encode_app(bool, $o, pp, 
13.47/13.63	           app_encode_app(dB, bool, 
13.47/13.63	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
13.47/13.63	               aa(dB, bool), it), 
13.47/13.63	             app_encode_app(nat, dB, 
13.47/13.63	               app_encode_app(fun(nat, dB), app_encode_fun(nat, dB), 
13.47/13.63	                 aa(nat, dB), 
13.47/13.63	                 app_encode_app(dB, fun(nat, dB), 
13.47/13.63	                   app_encode_app(fun(dB, fun(nat, dB)), 
13.47/13.63	                     app_encode_fun(dB, fun(nat, dB)), aa(dB, fun(nat, dB)), 
13.47/13.63	                     app_encode_app(dB, fun(dB, fun(nat, dB)), 
13.47/13.63	                       app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
13.47/13.63	                         app_encode_fun(dB, fun(dB, fun(nat, dB))), 
13.47/13.63	                         aa(dB, fun(dB, fun(nat, dB))), subst), 
13.47/13.63	                       app_encode_app(list(dB), dB, 
13.47/13.63	                         app_encode_app(dB, app_encode_fun(list(dB), dB), 
13.47/13.63	                           app_encode_app(fun(dB, fun(dB, dB)), 
13.47/13.63	                             app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
13.47/13.63	                             foldl(dB, dB), app), 
13.47/13.63	                           app_encode_app(nat, dB, 
13.47/13.63	                             app_encode_app(fun(nat, dB), 
13.47/13.63	                               app_encode_fun(nat, dB), aa(nat, dB), 
13.47/13.63	                               app_encode_app(dB, fun(nat, dB), 
13.47/13.63	                                 app_encode_app(fun(dB, fun(nat, dB)), 
13.47/13.63	                                   app_encode_fun(dB, fun(nat, dB)), 
13.47/13.63	                                   aa(dB, fun(nat, dB)), 
13.47/13.63	                                   app_encode_app(dB, fun(dB, fun(nat, dB)), 
13.47/13.63	                                     app_encode_app(
13.47/13.63	                                       fun(dB, fun(dB, fun(nat, dB))), 
13.47/13.63	                                       app_encode_fun(dB, 
13.47/13.63	                                         fun(dB, fun(nat, dB))), 
13.47/13.63	                                       aa(dB, fun(dB, fun(nat, dB))), subst), 
13.47/13.63	                                     r)), a)), zero_zero(nat))), as))), X0)), 
13.47/13.63	               i)))
13.47/13.63	       | ~ app_encode_app(bool, $o, pp, 
13.47/13.63	             app_encode_app(type, bool, 
13.47/13.63	               app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
13.47/13.63	                 aa(type, bool), 
13.47/13.63	                 app_encode_app(dB, fun(type, bool), 
13.47/13.63	                   app_encode_app(fun(nat, type), 
13.47/13.63	                     app_encode_fun(dB, fun(type, bool)), typing, e), X0)), 
13.47/13.63	               t))),
13.47/13.63	    inference('simplify', [status(thm)], ['2'])).
13.47/13.63	tff(zf_stmt_158, axiom,
13.47/13.63	  (![A:$tType,C:$tType,B:$tType,R:A,Q:B,P:fun(A,fun(B,C))]:
13.47/13.63	     (app_encode_app(A,C,
13.47/13.63	                     app_encode_app(fun(A,C),app_encode_fun(A,C),aa(A,C),
13.47/13.63	                                    app_encode_app(B,fun(A,C),
13.47/13.63	                                                   app_encode_app(fun(
13.47/13.63	                                                                  A,fun(B,C)),
13.47/13.63	                                                                  app_encode_fun(
13.47/13.63	                                                                  B,fun(A,C)),
13.47/13.63	                                                                  combc(
13.47/13.63	                                                                  A,B,C),P),
13.47/13.63	                                                   Q)),
13.47/13.63	                     R) =
13.47/13.63	      app_encode_app(B,C,
13.47/13.63	                     app_encode_app(fun(B,C),app_encode_fun(B,C),aa(B,C),
13.47/13.63	                                    app_encode_app(A,fun(B,C),
13.47/13.63	                                                   app_encode_app(fun(
13.47/13.63	                                                                  A,fun(B,C)),
13.47/13.63	                                                                  app_encode_fun(
13.47/13.63	                                                                  A,fun(B,C)),
13.47/13.63	                                                                  aa(
13.47/13.63	                                                                  A,fun(B,C)),
13.47/13.63	                                                                  P),
13.47/13.63	                                                   R)),
13.47/13.63	                     Q)))).
13.47/13.63	tff('4', plain,
13.47/13.63	    ![X377 : $tType, X378 : $tType, X379 : $tType, 
13.47/13.63	      X380 : fun(X379, fun(X377, X378)), X381 : X379, X382 : X377]:
13.47/13.63	      app_encode_app(X379, X378, 
13.47/13.63	        app_encode_app(fun(X379, X378), app_encode_fun(X379, X378), 
13.47/13.63	          aa(X379, X378), 
13.47/13.63	          app_encode_app(X377, fun(X379, X378), 
13.47/13.63	            app_encode_app(fun(X379, fun(X377, X378)), 
13.47/13.63	              app_encode_fun(X377, fun(X379, X378)), 
13.47/13.63	              combc(X379, X377, X378), X380), X382)), X381)
13.47/13.63	       = app_encode_app(X377, X378, 
13.47/13.63	           app_encode_app(fun(X377, X378), app_encode_fun(X377, X378), 
13.47/13.63	             aa(X377, X378), 
13.47/13.63	             app_encode_app(X379, fun(X377, X378), 
13.47/13.63	               app_encode_app(fun(X379, fun(X377, X378)), 
13.47/13.63	                 app_encode_fun(X379, fun(X377, X378)), 
13.47/13.63	                 aa(X379, fun(X377, X378)), X380), X381)), X382),
13.47/13.63	    inference('cnf', [status(esa)], [zf_stmt_158])).
13.47/13.63	tff('5', plain,
13.47/13.63	    ![X0 : dB]:
13.47/13.63	      (~ app_encode_app(bool, $o, pp, 
13.47/13.63	           app_encode_app(dB, bool, 
13.47/13.63	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
13.47/13.63	               aa(dB, bool), it), X0))
13.47/13.63	       | app_encode_app(bool, $o, pp, 
13.47/13.63	           app_encode_app(dB, bool, 
13.47/13.63	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
13.47/13.63	               aa(dB, bool), it), 
13.47/13.63	             app_encode_app(dB, dB, 
13.47/13.63	               app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), 
13.47/13.63	                 aa(dB, dB), 
13.47/13.63	                 app_encode_app(nat, fun(dB, dB), 
13.47/13.63	                   app_encode_app(fun(dB, fun(nat, dB)), 
13.47/13.63	                     app_encode_fun(nat, fun(dB, dB)), combc(dB, nat, dB), 
13.47/13.63	                     app_encode_app(dB, fun(dB, fun(nat, dB)), 
13.47/13.63	                       app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
13.47/13.63	                         app_encode_fun(dB, fun(dB, fun(nat, dB))), 
13.47/13.63	                         combc(dB, dB, fun(nat, dB)), subst), X0)), i)), 
13.47/13.63	               app_encode_app(list(dB), dB, 
13.47/13.63	                 app_encode_app(dB, app_encode_fun(list(dB), dB), 
13.47/13.63	                   app_encode_app(fun(dB, fun(dB, dB)), 
13.47/13.63	                     app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
13.47/13.63	                     foldl(dB, dB), app), 
13.47/13.63	                   app_encode_app(dB, dB, 
13.47/13.63	                     app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), 
13.47/13.63	                       aa(dB, dB), 
13.47/13.63	                       app_encode_app(nat, fun(dB, dB), 
13.47/13.63	                         app_encode_app(fun(dB, fun(nat, dB)), 
13.47/13.63	                           app_encode_fun(nat, fun(dB, dB)), 
13.47/13.63	                           combc(dB, nat, dB), 
13.47/13.63	                           app_encode_app(dB, fun(dB, fun(nat, dB)), 
13.47/13.63	                             app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
13.47/13.63	                               app_encode_fun(dB, fun(dB, fun(nat, dB))), 
13.47/13.63	                               combc(dB, dB, fun(nat, dB)), subst), a)), 
13.47/13.63	                         zero_zero(nat))), r)), as))))
13.47/13.63	       | ~ app_encode_app(bool, $o, pp, 
13.47/13.63	             app_encode_app(type, bool, 
13.47/13.63	               app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
13.47/13.63	                 aa(type, bool), 
13.47/13.63	                 app_encode_app(dB, fun(type, bool), 
13.47/13.63	                   app_encode_app(fun(nat, type), 
13.47/13.63	                     app_encode_fun(dB, fun(type, bool)), typing, e), X0)), 
13.47/13.63	               t))),
13.47/13.63	    inference('demod', [status(thm)], ['3', '4', '4', '4', '4'])).
13.47/13.63	tff(zf_stmt_166, conjecture,
13.47/13.63	  (app_encode_app(bool,$o,pp,
13.47/13.63	                  app_encode_app(dB,bool,
13.47/13.63	                                 app_encode_app(fun(dB,bool),
13.47/13.63	                                                app_encode_fun(dB,bool),
13.47/13.63	                                                aa(dB,bool),it),
13.47/13.63	                                 app_encode_app(nat,dB,
13.47/13.63	                                                app_encode_app(fun(nat,dB),
13.47/13.63	                                                               app_encode_fun(
13.47/13.63	                                                               nat,dB),
13.47/13.63	                                                               aa(nat,dB),
13.47/13.63	                                                               app_encode_app(
13.47/13.63	                                                               dB,
13.47/13.63	                                                               fun(nat,dB),
13.47/13.63	                                                               app_encode_app(
13.47/13.63	                                                               fun(dB,
13.47/13.63	                                                                   fun(
13.47/13.63	                                                                   nat,dB)),
13.47/13.63	                                                               app_encode_fun(
13.47/13.63	                                                               dB,fun(nat,dB)),
13.47/13.63	                                                               aa(dB,
13.47/13.63	                                                                  fun(nat,dB)),
13.47/13.63	                                                               app_encode_app(
13.47/13.63	                                                               dB,
13.47/13.63	                                                               fun(dB,
13.47/13.63	                                                                   fun(
13.47/13.63	                                                                   nat,dB)),
13.47/13.63	                                                               app_encode_app(
13.47/13.63	                                                               fun(dB,
13.47/13.63	                                                                   fun(
13.47/13.63	                                                                   dB,
13.47/13.63	                                                                   fun(
13.47/13.63	                                                                   nat,dB))),
13.47/13.63	                                                               app_encode_fun(
13.47/13.63	                                                               dB,
13.47/13.63	                                                               fun(dB,
13.47/13.63	                                                                   fun(
13.47/13.63	                                                                   nat,dB))),
13.47/13.63	                                                               aa(dB,
13.47/13.63	                                                                  fun(
13.47/13.63	                                                                  dB,
13.47/13.63	                                                                  fun(nat,dB))),
13.47/13.63	                                                               subst),
13.47/13.63	                                                               app_encode_app(
13.47/13.63	                                                               list(dB),dB,
13.47/13.63	                                                               app_encode_app(
13.47/13.63	                                                               dB,
13.47/13.63	                                                               app_encode_fun(
13.47/13.63	                                                               list(dB),dB),
13.47/13.63	                                                               app_encode_app(
13.47/13.63	                                                               fun(dB,
13.47/13.63	                                                                   fun(dB,dB)),
13.47/13.63	                                                               app_encode_fun(
13.47/13.63	                                                               dB,
13.47/13.63	                                                               app_encode_fun(
13.47/13.63	                                                               list(dB),dB)),
13.47/13.63	                                                               foldl(dB,dB),
13.47/13.63	                                                               app),
13.47/13.63	                                                               app_encode_app(
13.47/13.63	                                                               nat,dB,
13.47/13.63	                                                               app_encode_app(
13.47/13.63	                                                               fun(nat,dB),
13.47/13.63	                                                               app_encode_fun(
13.47/13.63	                                                               nat,dB),
13.47/13.63	                                                               aa(nat,dB),
13.47/13.63	                                                               app_encode_app(
13.47/13.63	                                                               dB,
13.47/13.63	                                                               fun(nat,dB),
13.47/13.63	                                                               app_encode_app(
13.47/13.63	                                                               fun(dB,
13.47/13.63	                                                                   fun(
13.47/13.63	                                                                   nat,dB)),
13.47/13.63	                                                               app_encode_fun(
13.47/13.63	                                                               dB,fun(nat,dB)),
13.47/13.63	                                                               aa(dB,
13.47/13.63	                                                                  fun(nat,dB)),
13.47/13.63	                                                               app_encode_app(
13.47/13.63	                                                               dB,
13.47/13.63	                                                               fun(dB,
13.47/13.63	                                                                   fun(
13.47/13.63	                                                                   nat,dB)),
13.47/13.63	                                                               app_encode_app(
13.47/13.63	                                                               fun(dB,
13.47/13.63	                                                                   fun(
13.47/13.63	                                                                   dB,
13.47/13.63	                                                                   fun(
13.47/13.63	                                                                   nat,dB))),
13.47/13.63	                                                               app_encode_fun(
13.47/13.63	                                                               dB,
13.47/13.63	                                                               fun(dB,
13.47/13.63	                                                                   fun(
13.47/13.63	                                                                   nat,dB))),
13.47/13.63	                                                               aa(dB,
13.47/13.63	                                                                  fun(
13.47/13.63	                                                                  dB,
13.47/13.63	                                                                  fun(nat,dB))),
13.47/13.63	                                                               subst),r)),a)),
13.47/13.63	                                                               zero_zero(nat))),
13.47/13.63	                                                               as))),u)),
13.47/13.63	                                                i))))).
13.47/13.63	tff(zf_stmt_0, negated_conjecture,
13.47/13.63	  (~
13.47/13.63	    app_encode_app(bool,$o,pp,
13.47/13.63	                   app_encode_app(dB,bool,
13.47/13.63	                                  app_encode_app(fun(dB,bool),
13.47/13.63	                                                 app_encode_fun(dB,bool),
13.47/13.63	                                                 aa(dB,bool),it),
13.47/13.63	                                  app_encode_app(nat,dB,
13.47/13.63	                                                 app_encode_app(fun(nat,dB),
13.47/13.63	                                                                app_encode_fun(
13.47/13.63	                                                                nat,dB),
13.47/13.63	                                                                aa(nat,dB),
13.47/13.63	                                                                app_encode_app(
13.47/13.63	                                                                dB,
13.47/13.63	                                                                fun(nat,dB),
13.47/13.63	                                                                app_encode_app(
13.47/13.63	                                                                fun(dB,
13.47/13.63	                                                                    fun(
13.47/13.63	                                                                    nat,dB)),
13.47/13.63	                                                                app_encode_fun(
13.47/13.63	                                                                dB,
13.47/13.63	                                                                fun(nat,dB)),
13.47/13.63	                                                                aa(dB,
13.47/13.63	                                                                   fun(
13.47/13.63	                                                                   nat,dB)),
13.47/13.63	                                                                app_encode_app(
13.47/13.63	                                                                dB,
13.47/13.63	                                                                fun(dB,
13.47/13.63	                                                                    fun(
13.47/13.63	                                                                    nat,dB)),
13.47/13.63	                                                                app_encode_app(
13.47/13.63	                                                                fun(dB,
13.47/13.63	                                                                    fun(
13.47/13.63	                                                                    dB,
13.47/13.63	                                                                    fun(
13.47/13.63	                                                                    nat,dB))),
13.47/13.63	                                                                app_encode_fun(
13.47/13.63	                                                                dB,
13.47/13.63	                                                                fun(dB,
13.47/13.63	                                                                    fun(
13.47/13.63	                                                                    nat,dB))),
13.47/13.63	                                                                aa(dB,
13.47/13.63	                                                                   fun(
13.47/13.63	                                                                   dB,
13.47/13.63	                                                                   fun(
13.47/13.63	                                                                   nat,dB))),
13.47/13.63	                                                                subst),
13.47/13.63	                                                                app_encode_app(
13.47/13.63	                                                                list(dB),dB,
13.47/13.63	                                                                app_encode_app(
13.47/13.63	                                                                dB,
13.47/13.63	                                                                app_encode_fun(
13.47/13.63	                                                                list(dB),dB),
13.47/13.63	                                                                app_encode_app(
13.47/13.63	                                                                fun(dB,
13.47/13.63	                                                                    fun(
13.47/13.63	                                                                    dB,dB)),
13.47/13.63	                                                                app_encode_fun(
13.47/13.63	                                                                dB,
13.47/13.63	                                                                app_encode_fun(
13.47/13.63	                                                                list(dB),dB)),
13.47/13.63	                                                                foldl(dB,dB),
13.47/13.63	                                                                app),
13.47/13.63	                                                                app_encode_app(
13.47/13.63	                                                                nat,dB,
13.47/13.63	                                                                app_encode_app(
13.47/13.63	                                                                fun(nat,dB),
13.47/13.63	                                                                app_encode_fun(
13.47/13.63	                                                                nat,dB),
13.47/13.63	                                                                aa(nat,dB),
13.47/13.63	                                                                app_encode_app(
13.47/13.63	                                                                dB,
13.47/13.63	                                                                fun(nat,dB),
13.47/13.63	                                                                app_encode_app(
13.47/13.63	                                                                fun(dB,
13.47/13.63	                                                                    fun(
13.47/13.63	                                                                    nat,dB)),
13.47/13.63	                                                                app_encode_fun(
13.47/13.63	                                                                dB,
13.47/13.63	                                                                fun(nat,dB)),
13.47/13.63	                                                                aa(dB,
13.47/13.63	                                                                   fun(
13.47/13.63	                                                                   nat,dB)),
13.47/13.63	                                                                app_encode_app(
13.47/13.63	                                                                dB,
13.47/13.63	                                                                fun(dB,
13.47/13.63	                                                                    fun(
13.47/13.63	                                                                    nat,dB)),
13.47/13.63	                                                                app_encode_app(
13.47/13.63	                                                                fun(dB,
13.47/13.63	                                                                    fun(
13.47/13.63	                                                                    dB,
13.47/13.63	                                                                    fun(
13.47/13.63	                                                                    nat,dB))),
13.47/13.63	                                                                app_encode_fun(
13.47/13.63	                                                                dB,
13.47/13.63	                                                                fun(dB,
13.47/13.63	                                                                    fun(
13.47/13.63	                                                                    nat,dB))),
13.47/13.63	                                                                aa(dB,
13.47/13.63	                                                                   fun(
13.47/13.63	                                                                   dB,
13.47/13.63	                                                                   fun(
13.47/13.63	                                                                   nat,dB))),
13.47/13.63	                                                                subst),r)),a)),
13.47/13.63	                                                                zero_zero(
13.47/13.63	                                                                nat))),as))),
13.47/13.63	                                                                u)),
13.47/13.63	                                                 i))))).
13.47/13.63	tff('6', plain,
13.47/13.63	    ~ app_encode_app(bool, $o, pp, 
13.47/13.63	        app_encode_app(dB, bool, 
13.47/13.63	          app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
13.47/13.63	            aa(dB, bool), it), 
13.47/13.63	          app_encode_app(nat, dB, 
13.47/13.63	            app_encode_app(fun(nat, dB), app_encode_fun(nat, dB), 
13.47/13.63	              aa(nat, dB), 
13.47/13.63	              app_encode_app(dB, fun(nat, dB), 
13.47/13.63	                app_encode_app(fun(dB, fun(nat, dB)), 
13.47/13.63	                  app_encode_fun(dB, fun(nat, dB)), aa(dB, fun(nat, dB)), 
13.47/13.63	                  app_encode_app(dB, fun(dB, fun(nat, dB)), 
13.47/13.63	                    app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
13.47/13.63	                      app_encode_fun(dB, fun(dB, fun(nat, dB))), 
13.47/13.63	                      aa(dB, fun(dB, fun(nat, dB))), subst), 
13.47/13.63	                    app_encode_app(list(dB), dB, 
13.47/13.63	                      app_encode_app(dB, app_encode_fun(list(dB), dB), 
13.47/13.63	                        app_encode_app(fun(dB, fun(dB, dB)), 
13.47/13.63	                          app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
13.47/13.63	                          foldl(dB, dB), app), 
13.47/13.63	                        app_encode_app(nat, dB, 
13.47/13.63	                          app_encode_app(fun(nat, dB), 
13.47/13.63	                            app_encode_fun(nat, dB), aa(nat, dB), 
13.47/13.63	                            app_encode_app(dB, fun(nat, dB), 
13.47/13.63	                              app_encode_app(fun(dB, fun(nat, dB)), 
13.47/13.63	                                app_encode_fun(dB, fun(nat, dB)), 
13.47/13.63	                                aa(dB, fun(nat, dB)), 
13.47/13.63	                                app_encode_app(dB, fun(dB, fun(nat, dB)), 
13.47/13.63	                                  app_encode_app(
13.47/13.63	                                    fun(dB, fun(dB, fun(nat, dB))), 
13.47/13.63	                                    app_encode_fun(dB, fun(dB, fun(nat, dB))), 
13.47/13.63	                                    aa(dB, fun(dB, fun(nat, dB))), subst), r)), 
13.47/13.63	                              a)), zero_zero(nat))), as))), u)), i))),
13.47/13.63	    inference('cnf', [status(esa)], [zf_stmt_0])).
13.47/13.63	tff('7', plain,
13.47/13.63	    ~ app_encode_app(bool, $o, pp, 
13.47/13.63	        app_encode_app(dB, bool, 
13.47/13.63	          app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
13.47/13.63	            aa(dB, bool), it), 
13.47/13.63	          app_encode_app(dB, dB, 
13.47/13.63	            app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), aa(dB, dB), 
13.47/13.63	              app_encode_app(nat, fun(dB, dB), 
13.47/13.63	                app_encode_app(fun(dB, fun(nat, dB)), 
13.47/13.63	                  app_encode_fun(nat, fun(dB, dB)), combc(dB, nat, dB), 
13.47/13.63	                  app_encode_app(dB, fun(dB, fun(nat, dB)), 
13.47/13.63	                    app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
13.47/13.63	                      app_encode_fun(dB, fun(dB, fun(nat, dB))), 
13.47/13.63	                      combc(dB, dB, fun(nat, dB)), subst), u)), i)), 
13.47/13.63	            app_encode_app(list(dB), dB, 
13.47/13.63	              app_encode_app(dB, app_encode_fun(list(dB), dB), 
13.47/13.63	                app_encode_app(fun(dB, fun(dB, dB)), 
13.47/13.63	                  app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
13.47/13.63	                  foldl(dB, dB), app), 
13.47/13.63	                app_encode_app(dB, dB, 
13.47/13.63	                  app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), 
13.47/13.63	                    aa(dB, dB), 
13.47/13.63	                    app_encode_app(nat, fun(dB, dB), 
13.47/13.63	                      app_encode_app(fun(dB, fun(nat, dB)), 
13.47/13.63	                        app_encode_fun(nat, fun(dB, dB)), 
13.47/13.63	                        combc(dB, nat, dB), 
13.47/13.63	                        app_encode_app(dB, fun(dB, fun(nat, dB)), 
13.47/13.63	                          app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
13.47/13.63	                            app_encode_fun(dB, fun(dB, fun(nat, dB))), 
13.47/13.63	                            combc(dB, dB, fun(nat, dB)), subst), a)), 
13.47/13.63	                      zero_zero(nat))), r)), as)))),
13.47/13.63	    inference('demod', [status(thm)], ['6', '4', '4', '4', '4'])).
13.47/13.63	tff('8', plain,
13.47/13.63	    (~ $true
13.47/13.63	     | ~ app_encode_app(bool, $o, pp, 
13.47/13.63	           app_encode_app(type, bool, 
13.47/13.63	             app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
13.47/13.63	               aa(type, bool), 
13.47/13.63	               app_encode_app(dB, fun(type, bool), 
13.47/13.63	                 app_encode_app(fun(nat, type), 
13.47/13.63	                   app_encode_fun(dB, fun(type, bool)), typing, e), u)), t))
13.47/13.63	     | ~ app_encode_app(bool, $o, pp, 
13.47/13.63	           app_encode_app(dB, bool, 
13.47/13.63	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
13.47/13.63	               aa(dB, bool), it), u))),
13.47/13.63	    inference('sup-', [status(thm)], ['5', '7'])).
13.47/13.63	tff(zf_stmt_59, axiom,
13.47/13.63	  (app_encode_app(bool,$o,pp,
13.47/13.63	                  app_encode_app(type,bool,
13.47/13.63	                                 app_encode_app(fun(type,bool),
13.47/13.63	                                                app_encode_fun(type,bool),
13.47/13.63	                                                aa(type,bool),
13.47/13.63	                                                app_encode_app(dB,
13.47/13.63	                                                               fun(type,bool),
13.47/13.63	                                                               app_encode_app(
13.47/13.63	                                                               fun(nat,type),
13.47/13.63	                                                               app_encode_fun(
13.47/13.63	                                                               dB,
13.47/13.63	                                                               fun(type,bool)),
13.47/13.63	                                                               typing,e),u)),
13.47/13.63	                                 t)))).
13.47/13.63	tff('9', plain,
13.47/13.63	    app_encode_app(bool, $o, pp, 
13.47/13.63	      app_encode_app(type, bool, 
13.47/13.63	        app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
13.47/13.63	          aa(type, bool), 
13.47/13.63	          app_encode_app(dB, fun(type, bool), 
13.47/13.63	            app_encode_app(fun(nat, type), 
13.47/13.63	              app_encode_fun(dB, fun(type, bool)), typing, e), u)), t)),
13.47/13.63	    inference('cnf', [status(esa)], [zf_stmt_59])).
13.47/13.63	tff(zf_stmt_165, axiom, (![P:bool]: ((P = fTrue) | (P = fFalse)))).
13.47/13.63	tff('10', plain, ![X397 : bool]: (X397 = fTrue | X397 = fFalse),
13.47/13.63	    inference('cnf', [status(esa)], [zf_stmt_165])).
13.47/13.63	tff(zf_stmt_155, axiom, (~app_encode_app(bool,$o,pp,fFalse))).
13.47/13.63	tff('11', plain, ~ app_encode_app(bool, $o, pp, fFalse),
13.47/13.63	    inference('cnf', [status(esa)], [zf_stmt_155])).
13.47/13.63	tff('12', plain,
13.47/13.63	    ![X0 : bool]: (~ app_encode_app(bool, $o, pp, X0) | X0 = fTrue),
13.47/13.63	    inference('sup-', [status(thm)], ['10', '11'])).
13.47/13.63	tff('13', plain,
13.47/13.63	    (~ $true
13.47/13.63	     | app_encode_app(type, bool, 
13.47/13.63	         app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
13.47/13.63	           aa(type, bool), 
13.47/13.63	           app_encode_app(dB, fun(type, bool), 
13.47/13.63	             app_encode_app(fun(nat, type), 
13.47/13.63	               app_encode_fun(dB, fun(type, bool)), typing, e), u)), t)
13.47/13.63	        = fTrue),
13.47/13.63	    inference('sup-', [status(thm)], ['9', '12'])).
13.47/13.63	tff('14', plain,
13.47/13.63	    app_encode_app(type, bool, 
13.47/13.63	      app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
13.47/13.63	        aa(type, bool), 
13.47/13.63	        app_encode_app(dB, fun(type, bool), 
13.47/13.63	          app_encode_app(fun(nat, type), 
13.47/13.63	            app_encode_fun(dB, fun(type, bool)), typing, e), u)), t)
13.47/13.63	     = fTrue,
13.47/13.63	    inference('simplify', [status(thm)], ['13'])).
13.47/13.63	tff(zf_stmt_156, axiom, (app_encode_app(bool,$o,pp,fTrue))).
13.47/13.63	tff('15', plain, app_encode_app(bool, $o, pp, fTrue),
13.47/13.63	    inference('cnf', [status(esa)], [zf_stmt_156])).
13.47/13.63	tff(zf_stmt_57, axiom,
13.47/13.63	  (app_encode_app(bool,$o,pp,
13.47/13.63	                  app_encode_app(dB,bool,
13.47/13.63	                                 app_encode_app(fun(dB,bool),
13.47/13.63	                                                app_encode_fun(dB,bool),
13.47/13.63	                                                aa(dB,bool),it),
13.47/13.63	                                 u)))).
13.47/13.63	tff('16', plain,
13.47/13.63	    app_encode_app(bool, $o, pp, 
13.47/13.63	      app_encode_app(dB, bool, 
13.47/13.63	        app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
13.47/13.63	          aa(dB, bool), it), u)),
13.47/13.63	    inference('cnf', [status(esa)], [zf_stmt_57])).
13.47/13.63	tff('17', plain,
13.47/13.63	    (~ $true
13.47/13.63	     | app_encode_app(dB, bool, 
13.47/13.63	         app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
13.47/13.63	           aa(dB, bool), it), u)
13.47/13.63	        = fTrue),
13.47/13.63	    inference('sup-', [status(thm)], ['16', '12'])).
13.47/13.63	tff('18', plain,
13.47/13.63	    app_encode_app(dB, bool, 
13.47/13.63	      app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), aa(dB, bool), 
13.47/13.63	        it), u)
13.47/13.63	     = fTrue,
13.47/13.63	    inference('simplify', [status(thm)], ['17'])).
13.47/13.63	tff('19', plain, (~ $true | ~ $true | ~ $true),
13.47/13.63	    inference('demod', [status(thm)], ['8', '14', '15', '18', '15'])).
13.47/13.63	tff('20', plain, $false, inference('simplify', [status(thm)], ['19'])).
13.47/13.63	
13.47/13.63	% SZS output end Refutation
13.47/13.63	EOF
