0.00/0.00	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : appext
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 $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n150.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 07:22:24 CST 2018
17.24/17.39	% done 2942 iterations in 17.193s
17.24/17.39	% SZS status Theorem for 'stdin'
17.24/17.39	% SZS output start Refutation
17.25/17.39	tff(zf_stmt_62, axiom,
17.25/17.39	  (app_encode_app(bool,$o,pp,
17.25/17.39	                  app_encode_app(type,bool,
17.25/17.39	                                 app_encode_app(fun(type,bool),
17.25/17.39	                                                app_encode_fun(type,bool),
17.25/17.39	                                                aa(type,bool),
17.25/17.39	                                                app_encode_app(dB,
17.25/17.39	                                                               fun(type,bool),
17.25/17.39	                                                               app_encode_app(
17.25/17.39	                                                               fun(nat,type),
17.25/17.39	                                                               app_encode_fun(
17.25/17.39	                                                               dB,
17.25/17.39	                                                               fun(type,bool)),
17.25/17.39	                                                               typing,
17.25/17.39	                                                               app_encode_app(
17.25/17.39	                                                               type,
17.25/17.39	                                                               fun(nat,type),
17.25/17.39	                                                               app_encode_app(
17.25/17.39	                                                               nat,
17.25/17.39	                                                               app_encode_fun(
17.25/17.39	                                                               type,
17.25/17.39	                                                               fun(nat,type)),
17.25/17.39	                                                               app_encode_app(
17.25/17.39	                                                               fun(nat,type),
17.25/17.39	                                                               app_encode_fun(
17.25/17.39	                                                               nat,
17.25/17.39	                                                               app_encode_fun(
17.25/17.39	                                                               type,
17.25/17.39	                                                               fun(nat,type))),
17.25/17.39	                                                               shift(type),e),
17.25/17.39	                                                               i),t)),
17.25/17.39	                                                               app_encode_app(
17.25/17.39	                                                               list(dB),dB,
17.25/17.39	                                                               app_encode_app(
17.25/17.39	                                                               dB,
17.25/17.39	                                                               app_encode_fun(
17.25/17.39	                                                               list(dB),dB),
17.25/17.39	                                                               app_encode_app(
17.25/17.39	                                                               fun(dB,
17.25/17.39	                                                                   fun(dB,dB)),
17.25/17.39	                                                               app_encode_fun(
17.25/17.39	                                                               dB,
17.25/17.39	                                                               app_encode_fun(
17.25/17.39	                                                               list(dB),dB)),
17.25/17.39	                                                               foldl(dB,dB),
17.25/17.39	                                                               app),
17.25/17.39	                                                               app_encode_app(
17.25/17.39	                                                               nat,dB,
17.25/17.39	                                                               app_encode_app(
17.25/17.39	                                                               fun(nat,dB),
17.25/17.39	                                                               app_encode_fun(
17.25/17.39	                                                               nat,dB),
17.25/17.39	                                                               aa(nat,dB),
17.25/17.39	                                                               app_encode_app(
17.25/17.39	                                                               dB,
17.25/17.39	                                                               fun(nat,dB),
17.25/17.39	                                                               app_encode_app(
17.25/17.39	                                                               fun(dB,
17.25/17.39	                                                                   fun(
17.25/17.39	                                                                   nat,dB)),
17.25/17.39	                                                               app_encode_fun(
17.25/17.39	                                                               dB,fun(nat,dB)),
17.25/17.39	                                                               aa(dB,
17.25/17.39	                                                                  fun(nat,dB)),
17.25/17.39	                                                               app_encode_app(
17.25/17.39	                                                               dB,
17.25/17.39	                                                               fun(dB,
17.25/17.39	                                                                   fun(
17.25/17.39	                                                                   nat,dB)),
17.25/17.39	                                                               app_encode_app(
17.25/17.39	                                                               fun(dB,
17.25/17.39	                                                                   fun(
17.25/17.39	                                                                   dB,
17.25/17.39	                                                                   fun(
17.25/17.39	                                                                   nat,dB))),
17.25/17.39	                                                               app_encode_fun(
17.25/17.39	                                                               dB,
17.25/17.39	                                                               fun(dB,
17.25/17.39	                                                                   fun(
17.25/17.39	                                                                   nat,dB))),
17.25/17.39	                                                               aa(dB,
17.25/17.39	                                                                  fun(
17.25/17.39	                                                                  dB,
17.25/17.39	                                                                  fun(nat,dB))),
17.25/17.39	                                                               subst),r)),a)),
17.25/17.39	                                                               zero_zero(nat))),
17.25/17.39	                                                               as))),
17.25/17.39	                                 t1)))).
17.25/17.39	tff('0', plain,
17.25/17.39	    app_encode_app(bool, $o, pp, 
17.25/17.39	      app_encode_app(type, bool, 
17.25/17.39	        app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
17.25/17.39	          aa(type, bool), 
17.25/17.39	          app_encode_app(dB, fun(type, bool), 
17.25/17.39	            app_encode_app(fun(nat, type), 
17.25/17.39	              app_encode_fun(dB, fun(type, bool)), typing, 
17.25/17.39	              app_encode_app(type, fun(nat, type), 
17.25/17.39	                app_encode_app(nat, app_encode_fun(type, fun(nat, type)), 
17.25/17.39	                  app_encode_app(fun(nat, type), 
17.25/17.39	                    app_encode_fun(nat, app_encode_fun(type, fun(nat, type))), 
17.25/17.39	                    shift(type), e), i), t)), 
17.25/17.39	            app_encode_app(list(dB), dB, 
17.25/17.39	              app_encode_app(dB, app_encode_fun(list(dB), dB), 
17.25/17.39	                app_encode_app(fun(dB, fun(dB, dB)), 
17.25/17.39	                  app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
17.25/17.39	                  foldl(dB, dB), app), 
17.25/17.39	                app_encode_app(nat, dB, 
17.25/17.39	                  app_encode_app(fun(nat, dB), app_encode_fun(nat, dB), 
17.25/17.39	                    aa(nat, dB), 
17.25/17.39	                    app_encode_app(dB, fun(nat, dB), 
17.25/17.39	                      app_encode_app(fun(dB, fun(nat, dB)), 
17.25/17.39	                        app_encode_fun(dB, fun(nat, dB)), 
17.25/17.39	                        aa(dB, fun(nat, dB)), 
17.25/17.39	                        app_encode_app(dB, fun(dB, fun(nat, dB)), 
17.25/17.39	                          app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
17.25/17.39	                            app_encode_fun(dB, fun(dB, fun(nat, dB))), 
17.25/17.39	                            aa(dB, fun(dB, fun(nat, dB))), subst), r)), a)), 
17.25/17.39	                  zero_zero(nat))), as))), t1)),
17.25/17.39	    inference('cnf', [status(esa)], [zf_stmt_62])).
17.25/17.39	tff(zf_stmt_68, axiom,
17.25/17.39	  (![Ub:dB,T_b:type,Ib:nat,Eb:fun(nat,type)]:
17.25/17.39	     (app_encode_app(bool,$o,pp,
17.25/17.39	                     app_encode_app(type,bool,
17.25/17.39	                                    app_encode_app(fun(type,bool),
17.25/17.39	                                                   app_encode_fun(type,bool),
17.25/17.39	                                                   aa(type,bool),
17.25/17.39	                                                   app_encode_app(dB,
17.25/17.39	                                                                  fun(
17.25/17.39	                                                                  type,bool),
17.25/17.39	                                                                  app_encode_app(
17.25/17.39	                                                                  fun(
17.25/17.39	                                                                  nat,type),
17.25/17.39	                                                                  app_encode_fun(
17.25/17.39	                                                                  dB,
17.25/17.39	                                                                  fun(
17.25/17.39	                                                                  type,bool)),
17.25/17.39	                                                                  typing,
17.25/17.39	                                                                  app_encode_app(
17.25/17.39	                                                                  type,
17.25/17.39	                                                                  fun(
17.25/17.39	                                                                  nat,type),
17.25/17.39	                                                                  app_encode_app(
17.25/17.39	                                                                  nat,
17.25/17.39	                                                                  app_encode_fun(
17.25/17.39	                                                                  type,
17.25/17.39	                                                                  fun(
17.25/17.39	                                                                  nat,type)),
17.25/17.39	                                                                  app_encode_app(
17.25/17.39	                                                                  fun(
17.25/17.39	                                                                  nat,type),
17.25/17.39	                                                                  app_encode_fun(
17.25/17.39	                                                                  nat,
17.25/17.39	                                                                  app_encode_fun(
17.25/17.39	                                                                  type,
17.25/17.39	                                                                  fun(
17.25/17.39	                                                                  nat,type))),
17.25/17.39	                                                                  shift(type),
17.25/17.39	                                                                  Eb),Ib),t)),
17.25/17.39	                                                                  app_encode_app(
17.25/17.39	                                                                  list(dB),
17.25/17.39	                                                                  dB,
17.25/17.39	                                                                  app_encode_app(
17.25/17.39	                                                                  dB,
17.25/17.39	                                                                  app_encode_fun(
17.25/17.39	                                                                  list(dB),dB),
17.25/17.39	                                                                  app_encode_app(
17.25/17.39	                                                                  fun(
17.25/17.39	                                                                  dB,
17.25/17.39	                                                                  fun(dB,dB)),
17.25/17.39	                                                                  app_encode_fun(
17.25/17.39	                                                                  dB,
17.25/17.39	                                                                  app_encode_fun(
17.25/17.39	                                                                  list(dB),dB)),
17.25/17.39	                                                                  foldl(
17.25/17.39	                                                                  dB,dB),app),
17.25/17.39	                                                                  app_encode_app(
17.25/17.39	                                                                  nat,dB,
17.25/17.39	                                                                  app_encode_app(
17.25/17.39	                                                                  fun(nat,dB),
17.25/17.39	                                                                  app_encode_fun(
17.25/17.39	                                                                  nat,dB),
17.25/17.39	                                                                  aa(nat,dB),
17.25/17.39	                                                                  app_encode_app(
17.25/17.39	                                                                  dB,
17.25/17.39	                                                                  fun(nat,dB),
17.25/17.39	                                                                  app_encode_app(
17.25/17.39	                                                                  fun(
17.25/17.39	                                                                  dB,
17.25/17.39	                                                                  fun(nat,dB)),
17.25/17.39	                                                                  app_encode_fun(
17.25/17.39	                                                                  dB,
17.25/17.39	                                                                  fun(nat,dB)),
17.25/17.39	                                                                  aa(
17.25/17.39	                                                                  dB,
17.25/17.39	                                                                  fun(nat,dB)),
17.25/17.39	                                                                  app_encode_app(
17.25/17.39	                                                                  dB,
17.25/17.39	                                                                  fun(
17.25/17.39	                                                                  dB,
17.25/17.39	                                                                  fun(nat,dB)),
17.25/17.39	                                                                  app_encode_app(
17.25/17.39	                                                                  fun(
17.25/17.39	                                                                  dB,
17.25/17.39	                                                                  fun(
17.25/17.39	                                                                  dB,
17.25/17.39	                                                                  fun(nat,dB))),
17.25/17.39	                                                                  app_encode_fun(
17.25/17.39	                                                                  dB,
17.25/17.39	                                                                  fun(
17.25/17.39	                                                                  dB,
17.25/17.39	                                                                  fun(nat,dB))),
17.25/17.39	                                                                  aa(
17.25/17.39	                                                                  dB,
17.25/17.39	                                                                  fun(
17.25/17.39	                                                                  dB,
17.25/17.39	                                                                  fun(nat,dB))),
17.25/17.39	                                                                  subst),r)),
17.25/17.39	                                                                  a)),
17.25/17.39	                                                                  zero_zero(
17.25/17.39	                                                                  nat))),as))),
17.25/17.39	                                    T_b)) =>
17.25/17.39	      (app_encode_app(bool,$o,pp,
17.25/17.39	                      app_encode_app(dB,bool,
17.25/17.39	                                     app_encode_app(fun(dB,bool),
17.25/17.39	                                                    app_encode_fun(dB,bool),
17.25/17.39	                                                    aa(dB,bool),it),
17.25/17.39	                                     Ub)) =>
17.25/17.39	       (app_encode_app(bool,$o,pp,
17.25/17.39	                       app_encode_app(type,bool,
17.25/17.39	                                      app_encode_app(fun(type,bool),
17.25/17.39	                                                     app_encode_fun(type,bool),
17.25/17.39	                                                     aa(type,bool),
17.25/17.39	                                                     app_encode_app(dB,
17.25/17.39	                                                                    fun(
17.25/17.39	                                                                    type,bool),
17.25/17.39	                                                                    app_encode_app(
17.25/17.39	                                                                    fun(
17.25/17.39	                                                                    nat,type),
17.25/17.39	                                                                    app_encode_fun(
17.25/17.39	                                                                    dB,
17.25/17.39	                                                                    fun(
17.25/17.39	                                                                    type,bool)),
17.25/17.39	                                                                    typing,Eb),
17.25/17.39	                                                                    Ub)),
17.25/17.39	                                      t)) =>
17.25/17.39	        app_encode_app(bool,$o,pp,
17.25/17.39	                       app_encode_app(dB,bool,
17.25/17.39	                                      app_encode_app(fun(dB,bool),
17.25/17.39	                                                     app_encode_fun(dB,bool),
17.25/17.40	                                                     aa(dB,bool),it),
17.25/17.40	                                      app_encode_app(nat,dB,
17.25/17.40	                                                     app_encode_app(fun(
17.25/17.40	                                                                    nat,dB),
17.25/17.40	                                                                    app_encode_fun(
17.25/17.40	                                                                    nat,dB),
17.25/17.40	                                                                    aa(
17.25/17.40	                                                                    nat,dB),
17.25/17.40	                                                                    app_encode_app(
17.25/17.40	                                                                    dB,
17.25/17.40	                                                                    fun(
17.25/17.40	                                                                    nat,dB),
17.25/17.40	                                                                    app_encode_app(
17.25/17.40	                                                                    fun(
17.25/17.40	                                                                    dB,
17.25/17.40	                                                                    fun(
17.25/17.40	                                                                    nat,dB)),
17.25/17.40	                                                                    app_encode_fun(
17.25/17.40	                                                                    dB,
17.25/17.40	                                                                    fun(
17.25/17.40	                                                                    nat,dB)),
17.25/17.40	                                                                    aa(
17.25/17.40	                                                                    dB,
17.25/17.40	                                                                    fun(
17.25/17.40	                                                                    nat,dB)),
17.25/17.40	                                                                    app_encode_app(
17.25/17.40	                                                                    dB,
17.25/17.40	                                                                    fun(
17.25/17.40	                                                                    dB,
17.25/17.40	                                                                    fun(
17.25/17.40	                                                                    nat,dB)),
17.25/17.40	                                                                    app_encode_app(
17.25/17.40	                                                                    fun(
17.25/17.40	                                                                    dB,
17.25/17.40	                                                                    fun(
17.25/17.40	                                                                    dB,
17.25/17.40	                                                                    fun(
17.25/17.40	                                                                    nat,dB))),
17.25/17.40	                                                                    app_encode_fun(
17.25/17.40	                                                                    dB,
17.25/17.40	                                                                    fun(
17.25/17.40	                                                                    dB,
17.25/17.40	                                                                    fun(
17.25/17.40	                                                                    nat,dB))),
17.25/17.40	                                                                    aa(
17.25/17.40	                                                                    dB,
17.25/17.40	                                                                    fun(
17.25/17.40	                                                                    dB,
17.25/17.40	                                                                    fun(
17.25/17.40	                                                                    nat,dB))),
17.25/17.40	                                                                    subst),
17.25/17.40	                                                                    app_encode_app(
17.25/17.40	                                                                    list(dB),
17.25/17.40	                                                                    dB,
17.25/17.40	                                                                    app_encode_app(
17.25/17.40	                                                                    dB,
17.25/17.40	                                                                    app_encode_fun(
17.25/17.40	                                                                    list(dB),
17.25/17.40	                                                                    dB),
17.25/17.40	                                                                    app_encode_app(
17.25/17.40	                                                                    fun(
17.25/17.40	                                                                    dB,
17.25/17.40	                                                                    fun(
17.25/17.40	                                                                    dB,dB)),
17.25/17.40	                                                                    app_encode_fun(
17.25/17.40	                                                                    dB,
17.25/17.40	                                                                    app_encode_fun(
17.25/17.40	                                                                    list(dB),
17.25/17.40	                                                                    dB)),
17.25/17.40	                                                                    foldl(
17.25/17.40	                                                                    dB,dB),
17.25/17.40	                                                                    app),
17.25/17.40	                                                                    app_encode_app(
17.25/17.40	                                                                    nat,dB,
17.25/17.40	                                                                    app_encode_app(
17.25/17.40	                                                                    fun(
17.25/17.40	                                                                    nat,dB),
17.25/17.40	                                                                    app_encode_fun(
17.25/17.40	                                                                    nat,dB),
17.25/17.40	                                                                    aa(
17.25/17.40	                                                                    nat,dB),
17.25/17.40	                                                                    app_encode_app(
17.25/17.40	                                                                    dB,
17.25/17.40	                                                                    fun(
17.25/17.40	                                                                    nat,dB),
17.25/17.40	                                                                    app_encode_app(
17.25/17.40	                                                                    fun(
17.25/17.40	                                                                    dB,
17.25/17.40	                                                                    fun(
17.25/17.40	                                                                    nat,dB)),
17.25/17.40	                                                                    app_encode_fun(
17.25/17.40	                                                                    dB,
17.25/17.40	                                                                    fun(
17.25/17.40	                                                                    nat,dB)),
17.25/17.40	                                                                    aa(
17.25/17.40	                                                                    dB,
17.25/17.40	                                                                    fun(
17.25/17.40	                                                                    nat,dB)),
17.25/17.40	                                                                    app_encode_app(
17.25/17.40	                                                                    dB,
17.25/17.40	                                                                    fun(
17.25/17.40	                                                                    dB,
17.25/17.40	                                                                    fun(
17.25/17.40	                                                                    nat,dB)),
17.25/17.40	                                                                    app_encode_app(
17.25/17.40	                                                                    fun(
17.25/17.40	                                                                    dB,
17.25/17.40	                                                                    fun(
17.25/17.40	                                                                    dB,
17.25/17.40	                                                                    fun(
17.25/17.40	                                                                    nat,dB))),
17.25/17.40	                                                                    app_encode_fun(
17.25/17.40	                                                                    dB,
17.25/17.40	                                                                    fun(
17.25/17.40	                                                                    dB,
17.25/17.40	                                                                    fun(
17.25/17.40	                                                                    nat,dB))),
17.25/17.40	                                                                    aa(
17.25/17.40	                                                                    dB,
17.25/17.40	                                                                    fun(
17.25/17.40	                                                                    dB,
17.25/17.40	                                                                    fun(
17.25/17.40	                                                                    nat,dB))),
17.25/17.40	                                                                    subst),r)),
17.25/17.40	                                                                    a)),
17.25/17.40	                                                                    zero_zero(
17.25/17.40	                                                                    nat))),as))),
17.25/17.40	                                                                    Ub)),
17.25/17.40	                                                     Ib)))))))).
17.25/17.40	tff('1', plain,
17.25/17.40	    ![X17 : dB, X18 : nat, X19 : fun(nat, type), X20 : type]:
17.25/17.40	      (~ app_encode_app(bool, $o, pp, 
17.25/17.40	           app_encode_app(dB, bool, 
17.25/17.40	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
17.25/17.40	               aa(dB, bool), it), X17))
17.25/17.40	       | app_encode_app(bool, $o, pp, 
17.25/17.40	           app_encode_app(dB, bool, 
17.25/17.40	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
17.25/17.40	               aa(dB, bool), it), 
17.25/17.40	             app_encode_app(nat, dB, 
17.25/17.40	               app_encode_app(fun(nat, dB), app_encode_fun(nat, dB), 
17.25/17.40	                 aa(nat, dB), 
17.25/17.40	                 app_encode_app(dB, fun(nat, dB), 
17.25/17.40	                   app_encode_app(fun(dB, fun(nat, dB)), 
17.25/17.40	                     app_encode_fun(dB, fun(nat, dB)), aa(dB, fun(nat, dB)), 
17.25/17.40	                     app_encode_app(dB, fun(dB, fun(nat, dB)), 
17.25/17.40	                       app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
17.25/17.40	                         app_encode_fun(dB, fun(dB, fun(nat, dB))), 
17.25/17.40	                         aa(dB, fun(dB, fun(nat, dB))), subst), 
17.25/17.40	                       app_encode_app(list(dB), dB, 
17.25/17.40	                         app_encode_app(dB, app_encode_fun(list(dB), dB), 
17.25/17.40	                           app_encode_app(fun(dB, fun(dB, dB)), 
17.25/17.40	                             app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
17.25/17.40	                             foldl(dB, dB), app), 
17.25/17.40	                           app_encode_app(nat, dB, 
17.25/17.40	                             app_encode_app(fun(nat, dB), 
17.25/17.40	                               app_encode_fun(nat, dB), aa(nat, dB), 
17.25/17.40	                               app_encode_app(dB, fun(nat, dB), 
17.25/17.40	                                 app_encode_app(fun(dB, fun(nat, dB)), 
17.25/17.40	                                   app_encode_fun(dB, fun(nat, dB)), 
17.25/17.40	                                   aa(dB, fun(nat, dB)), 
17.25/17.40	                                   app_encode_app(dB, fun(dB, fun(nat, dB)), 
17.25/17.40	                                     app_encode_app(
17.25/17.40	                                       fun(dB, fun(dB, fun(nat, dB))), 
17.25/17.40	                                       app_encode_fun(dB, 
17.25/17.40	                                         fun(dB, fun(nat, dB))), 
17.25/17.40	                                       aa(dB, fun(dB, fun(nat, dB))), subst), 
17.25/17.40	                                     r)), a)), zero_zero(nat))), as))), X17)), 
17.25/17.40	               X18)))
17.25/17.40	       | ~ app_encode_app(bool, $o, pp, 
17.25/17.40	             app_encode_app(type, bool, 
17.25/17.40	               app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
17.25/17.40	                 aa(type, bool), 
17.25/17.40	                 app_encode_app(dB, fun(type, bool), 
17.25/17.40	                   app_encode_app(fun(nat, type), 
17.25/17.40	                     app_encode_fun(dB, fun(type, bool)), typing, 
17.25/17.40	                     app_encode_app(type, fun(nat, type), 
17.25/17.40	                       app_encode_app(nat, 
17.25/17.40	                         app_encode_fun(type, fun(nat, type)), 
17.25/17.40	                         app_encode_app(fun(nat, type), 
17.25/17.40	                           app_encode_fun(nat, 
17.25/17.40	                             app_encode_fun(type, fun(nat, type))), 
17.25/17.40	                           shift(type), X19), X18), t)), 
17.25/17.40	                   app_encode_app(list(dB), dB, 
17.25/17.40	                     app_encode_app(dB, app_encode_fun(list(dB), dB), 
17.25/17.40	                       app_encode_app(fun(dB, fun(dB, dB)), 
17.25/17.40	                         app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
17.25/17.40	                         foldl(dB, dB), app), 
17.25/17.40	                       app_encode_app(nat, dB, 
17.25/17.40	                         app_encode_app(fun(nat, dB), 
17.25/17.40	                           app_encode_fun(nat, dB), aa(nat, dB), 
17.25/17.40	                           app_encode_app(dB, fun(nat, dB), 
17.25/17.40	                             app_encode_app(fun(dB, fun(nat, dB)), 
17.25/17.40	                               app_encode_fun(dB, fun(nat, dB)), 
17.25/17.40	                               aa(dB, fun(nat, dB)), 
17.25/17.40	                               app_encode_app(dB, fun(dB, fun(nat, dB)), 
17.25/17.40	                                 app_encode_app(
17.25/17.40	                                   fun(dB, fun(dB, fun(nat, dB))), 
17.25/17.40	                                   app_encode_fun(dB, fun(dB, fun(nat, dB))), 
17.25/17.40	                                   aa(dB, fun(dB, fun(nat, dB))), subst), r)), 
17.25/17.40	                             a)), zero_zero(nat))), as))), X20))
17.25/17.40	       | ~ app_encode_app(bool, $o, pp, 
17.25/17.40	             app_encode_app(type, bool, 
17.25/17.40	               app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
17.25/17.40	                 aa(type, bool), 
17.25/17.40	                 app_encode_app(dB, fun(type, bool), 
17.25/17.40	                   app_encode_app(fun(nat, type), 
17.25/17.40	                     app_encode_fun(dB, fun(type, bool)), typing, X19), X17)), 
17.25/17.40	               t))),
17.25/17.40	    inference('cnf', [status(esa)], [zf_stmt_68])).
17.25/17.40	tff('2', plain,
17.25/17.40	    ![X0 : dB]:
17.25/17.40	      (~ $true
17.25/17.40	       | ~ app_encode_app(bool, $o, pp, 
17.25/17.40	             app_encode_app(type, bool, 
17.25/17.40	               app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
17.25/17.40	                 aa(type, bool), 
17.25/17.40	                 app_encode_app(dB, fun(type, bool), 
17.25/17.40	                   app_encode_app(fun(nat, type), 
17.25/17.40	                     app_encode_fun(dB, fun(type, bool)), typing, e), X0)), 
17.25/17.40	               t))
17.25/17.40	       | app_encode_app(bool, $o, pp, 
17.25/17.40	           app_encode_app(dB, bool, 
17.25/17.40	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
17.25/17.40	               aa(dB, bool), it), 
17.25/17.40	             app_encode_app(nat, dB, 
17.25/17.40	               app_encode_app(fun(nat, dB), app_encode_fun(nat, dB), 
17.25/17.40	                 aa(nat, dB), 
17.25/17.40	                 app_encode_app(dB, fun(nat, dB), 
17.25/17.40	                   app_encode_app(fun(dB, fun(nat, dB)), 
17.25/17.40	                     app_encode_fun(dB, fun(nat, dB)), aa(dB, fun(nat, dB)), 
17.25/17.40	                     app_encode_app(dB, fun(dB, fun(nat, dB)), 
17.25/17.40	                       app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
17.25/17.40	                         app_encode_fun(dB, fun(dB, fun(nat, dB))), 
17.25/17.40	                         aa(dB, fun(dB, fun(nat, dB))), subst), 
17.25/17.40	                       app_encode_app(list(dB), dB, 
17.25/17.40	                         app_encode_app(dB, app_encode_fun(list(dB), dB), 
17.25/17.40	                           app_encode_app(fun(dB, fun(dB, dB)), 
17.25/17.40	                             app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
17.25/17.40	                             foldl(dB, dB), app), 
17.25/17.40	                           app_encode_app(nat, dB, 
17.25/17.40	                             app_encode_app(fun(nat, dB), 
17.25/17.40	                               app_encode_fun(nat, dB), aa(nat, dB), 
17.25/17.40	                               app_encode_app(dB, fun(nat, dB), 
17.25/17.40	                                 app_encode_app(fun(dB, fun(nat, dB)), 
17.25/17.40	                                   app_encode_fun(dB, fun(nat, dB)), 
17.25/17.40	                                   aa(dB, fun(nat, dB)), 
17.25/17.40	                                   app_encode_app(dB, fun(dB, fun(nat, dB)), 
17.25/17.40	                                     app_encode_app(
17.25/17.40	                                       fun(dB, fun(dB, fun(nat, dB))), 
17.25/17.40	                                       app_encode_fun(dB, 
17.25/17.40	                                         fun(dB, fun(nat, dB))), 
17.25/17.40	                                       aa(dB, fun(dB, fun(nat, dB))), subst), 
17.25/17.40	                                     r)), a)), zero_zero(nat))), as))), X0)), 
17.25/17.40	               i)))
17.25/17.40	       | ~ app_encode_app(bool, $o, pp, 
17.25/17.40	             app_encode_app(dB, bool, 
17.25/17.40	               app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
17.25/17.40	                 aa(dB, bool), it), X0))),
17.25/17.40	    inference('sup-', [status(thm)], ['0', '1'])).
17.25/17.40	tff('3', plain,
17.25/17.40	    ![X0 : dB]:
17.25/17.40	      (~ app_encode_app(bool, $o, pp, 
17.25/17.40	           app_encode_app(dB, bool, 
17.25/17.40	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
17.25/17.40	               aa(dB, bool), it), X0))
17.25/17.40	       | app_encode_app(bool, $o, pp, 
17.25/17.40	           app_encode_app(dB, bool, 
17.25/17.40	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
17.25/17.40	               aa(dB, bool), it), 
17.25/17.40	             app_encode_app(nat, dB, 
17.25/17.40	               app_encode_app(fun(nat, dB), app_encode_fun(nat, dB), 
17.25/17.40	                 aa(nat, dB), 
17.25/17.40	                 app_encode_app(dB, fun(nat, dB), 
17.25/17.40	                   app_encode_app(fun(dB, fun(nat, dB)), 
17.25/17.40	                     app_encode_fun(dB, fun(nat, dB)), aa(dB, fun(nat, dB)), 
17.25/17.40	                     app_encode_app(dB, fun(dB, fun(nat, dB)), 
17.25/17.40	                       app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
17.25/17.40	                         app_encode_fun(dB, fun(dB, fun(nat, dB))), 
17.25/17.40	                         aa(dB, fun(dB, fun(nat, dB))), subst), 
17.25/17.40	                       app_encode_app(list(dB), dB, 
17.25/17.40	                         app_encode_app(dB, app_encode_fun(list(dB), dB), 
17.25/17.40	                           app_encode_app(fun(dB, fun(dB, dB)), 
17.25/17.40	                             app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
17.25/17.40	                             foldl(dB, dB), app), 
17.25/17.40	                           app_encode_app(nat, dB, 
17.25/17.40	                             app_encode_app(fun(nat, dB), 
17.25/17.40	                               app_encode_fun(nat, dB), aa(nat, dB), 
17.25/17.40	                               app_encode_app(dB, fun(nat, dB), 
17.25/17.40	                                 app_encode_app(fun(dB, fun(nat, dB)), 
17.25/17.40	                                   app_encode_fun(dB, fun(nat, dB)), 
17.25/17.40	                                   aa(dB, fun(nat, dB)), 
17.25/17.40	                                   app_encode_app(dB, fun(dB, fun(nat, dB)), 
17.25/17.40	                                     app_encode_app(
17.25/17.40	                                       fun(dB, fun(dB, fun(nat, dB))), 
17.25/17.40	                                       app_encode_fun(dB, 
17.25/17.40	                                         fun(dB, fun(nat, dB))), 
17.25/17.40	                                       aa(dB, fun(dB, fun(nat, dB))), subst), 
17.25/17.40	                                     r)), a)), zero_zero(nat))), as))), X0)), 
17.25/17.40	               i)))
17.25/17.40	       | ~ app_encode_app(bool, $o, pp, 
17.25/17.40	             app_encode_app(type, bool, 
17.25/17.40	               app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
17.25/17.40	                 aa(type, bool), 
17.25/17.40	                 app_encode_app(dB, fun(type, bool), 
17.25/17.40	                   app_encode_app(fun(nat, type), 
17.25/17.40	                     app_encode_fun(dB, fun(type, bool)), typing, e), X0)), 
17.25/17.40	               t))),
17.25/17.40	    inference('simplify', [status(thm)], ['2'])).
17.25/17.40	tff(zf_stmt_159, axiom,
17.25/17.40	  (![A:$tType,C:$tType,B:$tType,R:A,Q:B,P:fun(A,fun(B,C))]:
17.25/17.40	     (app_encode_app(A,C,
17.25/17.40	                     app_encode_app(fun(A,C),app_encode_fun(A,C),aa(A,C),
17.25/17.40	                                    app_encode_app(B,fun(A,C),
17.25/17.40	                                                   app_encode_app(fun(
17.25/17.40	                                                                  A,fun(B,C)),
17.25/17.40	                                                                  app_encode_fun(
17.25/17.40	                                                                  B,fun(A,C)),
17.25/17.40	                                                                  combc(
17.25/17.40	                                                                  A,B,C),P),
17.25/17.40	                                                   Q)),
17.25/17.40	                     R) =
17.25/17.40	      app_encode_app(B,C,
17.25/17.40	                     app_encode_app(fun(B,C),app_encode_fun(B,C),aa(B,C),
17.25/17.40	                                    app_encode_app(A,fun(B,C),
17.25/17.40	                                                   app_encode_app(fun(
17.25/17.40	                                                                  A,fun(B,C)),
17.25/17.40	                                                                  app_encode_fun(
17.25/17.40	                                                                  A,fun(B,C)),
17.25/17.40	                                                                  aa(
17.25/17.40	                                                                  A,fun(B,C)),
17.25/17.40	                                                                  P),
17.25/17.40	                                                   R)),
17.25/17.40	                     Q)))).
17.25/17.40	tff('4', plain,
17.25/17.40	    ![X381 : $tType, X382 : $tType, X383 : $tType, 
17.25/17.40	      X384 : fun(X383, fun(X381, X382)), X385 : X383, X386 : X381]:
17.25/17.40	      app_encode_app(X383, X382, 
17.25/17.40	        app_encode_app(fun(X383, X382), app_encode_fun(X383, X382), 
17.25/17.40	          aa(X383, X382), 
17.25/17.40	          app_encode_app(X381, fun(X383, X382), 
17.25/17.40	            app_encode_app(fun(X383, fun(X381, X382)), 
17.25/17.40	              app_encode_fun(X381, fun(X383, X382)), 
17.25/17.40	              combc(X383, X381, X382), X384), X386)), X385)
17.25/17.40	       = app_encode_app(X381, X382, 
17.25/17.40	           app_encode_app(fun(X381, X382), app_encode_fun(X381, X382), 
17.25/17.40	             aa(X381, X382), 
17.25/17.40	             app_encode_app(X383, fun(X381, X382), 
17.25/17.40	               app_encode_app(fun(X383, fun(X381, X382)), 
17.25/17.40	                 app_encode_fun(X383, fun(X381, X382)), 
17.25/17.40	                 aa(X383, fun(X381, X382)), X384), X385)), X386),
17.25/17.40	    inference('cnf', [status(esa)], [zf_stmt_159])).
17.25/17.40	tff('5', plain,
17.25/17.40	    ![X0 : dB]:
17.25/17.40	      (~ app_encode_app(bool, $o, pp, 
17.25/17.40	           app_encode_app(dB, bool, 
17.25/17.40	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
17.25/17.40	               aa(dB, bool), it), X0))
17.25/17.40	       | app_encode_app(bool, $o, pp, 
17.25/17.40	           app_encode_app(dB, bool, 
17.25/17.40	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
17.25/17.40	               aa(dB, bool), it), 
17.25/17.40	             app_encode_app(dB, dB, 
17.25/17.40	               app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), 
17.25/17.40	                 aa(dB, dB), 
17.25/17.40	                 app_encode_app(nat, fun(dB, dB), 
17.25/17.40	                   app_encode_app(fun(dB, fun(nat, dB)), 
17.25/17.40	                     app_encode_fun(nat, fun(dB, dB)), combc(dB, nat, dB), 
17.25/17.40	                     app_encode_app(dB, fun(dB, fun(nat, dB)), 
17.25/17.40	                       app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
17.25/17.40	                         app_encode_fun(dB, fun(dB, fun(nat, dB))), 
17.25/17.40	                         combc(dB, dB, fun(nat, dB)), subst), X0)), i)), 
17.25/17.40	               app_encode_app(list(dB), dB, 
17.25/17.40	                 app_encode_app(dB, app_encode_fun(list(dB), dB), 
17.25/17.40	                   app_encode_app(fun(dB, fun(dB, dB)), 
17.25/17.40	                     app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
17.25/17.40	                     foldl(dB, dB), app), 
17.25/17.40	                   app_encode_app(dB, dB, 
17.25/17.40	                     app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), 
17.25/17.40	                       aa(dB, dB), 
17.25/17.40	                       app_encode_app(nat, fun(dB, dB), 
17.25/17.40	                         app_encode_app(fun(dB, fun(nat, dB)), 
17.25/17.40	                           app_encode_fun(nat, fun(dB, dB)), 
17.25/17.40	                           combc(dB, nat, dB), 
17.25/17.40	                           app_encode_app(dB, fun(dB, fun(nat, dB)), 
17.25/17.40	                             app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
17.25/17.40	                               app_encode_fun(dB, fun(dB, fun(nat, dB))), 
17.25/17.40	                               combc(dB, dB, fun(nat, dB)), subst), a)), 
17.25/17.40	                         zero_zero(nat))), r)), as))))
17.25/17.40	       | ~ app_encode_app(bool, $o, pp, 
17.25/17.40	             app_encode_app(type, bool, 
17.25/17.40	               app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
17.25/17.40	                 aa(type, bool), 
17.25/17.40	                 app_encode_app(dB, fun(type, bool), 
17.25/17.40	                   app_encode_app(fun(nat, type), 
17.25/17.40	                     app_encode_fun(dB, fun(type, bool)), typing, e), X0)), 
17.25/17.40	               t))),
17.25/17.40	    inference('demod', [status(thm)], ['3', '4', '4', '4', '4'])).
17.25/17.40	tff(zf_stmt_167, conjecture,
17.25/17.40	  (app_encode_app(bool,$o,pp,
17.25/17.40	                  app_encode_app(dB,bool,
17.25/17.40	                                 app_encode_app(fun(dB,bool),
17.25/17.40	                                                app_encode_fun(dB,bool),
17.25/17.40	                                                aa(dB,bool),it),
17.25/17.40	                                 app_encode_app(nat,dB,
17.25/17.40	                                                app_encode_app(fun(nat,dB),
17.25/17.40	                                                               app_encode_fun(
17.25/17.40	                                                               nat,dB),
17.25/17.40	                                                               aa(nat,dB),
17.25/17.40	                                                               app_encode_app(
17.25/17.40	                                                               dB,
17.25/17.40	                                                               fun(nat,dB),
17.25/17.40	                                                               app_encode_app(
17.25/17.40	                                                               fun(dB,
17.25/17.40	                                                                   fun(
17.25/17.40	                                                                   nat,dB)),
17.25/17.40	                                                               app_encode_fun(
17.25/17.40	                                                               dB,fun(nat,dB)),
17.25/17.40	                                                               aa(dB,
17.25/17.40	                                                                  fun(nat,dB)),
17.25/17.40	                                                               app_encode_app(
17.25/17.40	                                                               dB,
17.25/17.40	                                                               fun(dB,
17.25/17.40	                                                                   fun(
17.25/17.40	                                                                   nat,dB)),
17.25/17.40	                                                               app_encode_app(
17.25/17.40	                                                               fun(dB,
17.25/17.40	                                                                   fun(
17.25/17.40	                                                                   dB,
17.25/17.40	                                                                   fun(
17.25/17.40	                                                                   nat,dB))),
17.25/17.40	                                                               app_encode_fun(
17.25/17.40	                                                               dB,
17.25/17.40	                                                               fun(dB,
17.25/17.40	                                                                   fun(
17.25/17.40	                                                                   nat,dB))),
17.25/17.40	                                                               aa(dB,
17.25/17.40	                                                                  fun(
17.25/17.40	                                                                  dB,
17.25/17.40	                                                                  fun(nat,dB))),
17.25/17.40	                                                               subst),
17.25/17.40	                                                               app_encode_app(
17.25/17.40	                                                               list(dB),dB,
17.25/17.40	                                                               app_encode_app(
17.25/17.40	                                                               dB,
17.25/17.40	                                                               app_encode_fun(
17.25/17.40	                                                               list(dB),dB),
17.25/17.40	                                                               app_encode_app(
17.25/17.40	                                                               fun(dB,
17.25/17.40	                                                                   fun(dB,dB)),
17.25/17.40	                                                               app_encode_fun(
17.25/17.40	                                                               dB,
17.25/17.40	                                                               app_encode_fun(
17.25/17.40	                                                               list(dB),dB)),
17.25/17.40	                                                               foldl(dB,dB),
17.25/17.40	                                                               app),
17.25/17.40	                                                               app_encode_app(
17.25/17.40	                                                               nat,dB,
17.25/17.40	                                                               app_encode_app(
17.25/17.40	                                                               fun(nat,dB),
17.25/17.40	                                                               app_encode_fun(
17.25/17.40	                                                               nat,dB),
17.25/17.40	                                                               aa(nat,dB),
17.25/17.40	                                                               app_encode_app(
17.25/17.40	                                                               dB,
17.25/17.40	                                                               fun(nat,dB),
17.25/17.40	                                                               app_encode_app(
17.25/17.40	                                                               fun(dB,
17.25/17.40	                                                                   fun(
17.25/17.40	                                                                   nat,dB)),
17.25/17.40	                                                               app_encode_fun(
17.25/17.40	                                                               dB,fun(nat,dB)),
17.25/17.40	                                                               aa(dB,
17.25/17.40	                                                                  fun(nat,dB)),
17.25/17.40	                                                               app_encode_app(
17.25/17.40	                                                               dB,
17.25/17.40	                                                               fun(dB,
17.25/17.40	                                                                   fun(
17.25/17.40	                                                                   nat,dB)),
17.25/17.40	                                                               app_encode_app(
17.25/17.40	                                                               fun(dB,
17.25/17.40	                                                                   fun(
17.25/17.40	                                                                   dB,
17.25/17.40	                                                                   fun(
17.25/17.40	                                                                   nat,dB))),
17.25/17.40	                                                               app_encode_fun(
17.25/17.40	                                                               dB,
17.25/17.40	                                                               fun(dB,
17.25/17.40	                                                                   fun(
17.25/17.40	                                                                   nat,dB))),
17.25/17.40	                                                               aa(dB,
17.25/17.40	                                                                  fun(
17.25/17.40	                                                                  dB,
17.25/17.40	                                                                  fun(nat,dB))),
17.25/17.40	                                                               subst),r)),a)),
17.25/17.40	                                                               zero_zero(nat))),
17.25/17.40	                                                               as))),u)),
17.25/17.40	                                                i))))).
17.25/17.40	tff(zf_stmt_0, negated_conjecture,
17.25/17.40	  (~
17.25/17.40	    app_encode_app(bool,$o,pp,
17.25/17.40	                   app_encode_app(dB,bool,
17.25/17.40	                                  app_encode_app(fun(dB,bool),
17.25/17.40	                                                 app_encode_fun(dB,bool),
17.25/17.40	                                                 aa(dB,bool),it),
17.25/17.40	                                  app_encode_app(nat,dB,
17.25/17.40	                                                 app_encode_app(fun(nat,dB),
17.25/17.40	                                                                app_encode_fun(
17.25/17.40	                                                                nat,dB),
17.25/17.40	                                                                aa(nat,dB),
17.25/17.40	                                                                app_encode_app(
17.25/17.40	                                                                dB,
17.25/17.40	                                                                fun(nat,dB),
17.25/17.40	                                                                app_encode_app(
17.25/17.40	                                                                fun(dB,
17.25/17.40	                                                                    fun(
17.25/17.40	                                                                    nat,dB)),
17.25/17.40	                                                                app_encode_fun(
17.25/17.40	                                                                dB,
17.25/17.40	                                                                fun(nat,dB)),
17.25/17.40	                                                                aa(dB,
17.25/17.40	                                                                   fun(
17.25/17.40	                                                                   nat,dB)),
17.25/17.40	                                                                app_encode_app(
17.25/17.40	                                                                dB,
17.25/17.40	                                                                fun(dB,
17.25/17.40	                                                                    fun(
17.25/17.40	                                                                    nat,dB)),
17.25/17.40	                                                                app_encode_app(
17.25/17.40	                                                                fun(dB,
17.25/17.40	                                                                    fun(
17.25/17.40	                                                                    dB,
17.25/17.40	                                                                    fun(
17.25/17.40	                                                                    nat,dB))),
17.25/17.40	                                                                app_encode_fun(
17.25/17.40	                                                                dB,
17.25/17.40	                                                                fun(dB,
17.25/17.40	                                                                    fun(
17.25/17.40	                                                                    nat,dB))),
17.25/17.40	                                                                aa(dB,
17.25/17.40	                                                                   fun(
17.25/17.40	                                                                   dB,
17.25/17.40	                                                                   fun(
17.25/17.40	                                                                   nat,dB))),
17.25/17.40	                                                                subst),
17.25/17.40	                                                                app_encode_app(
17.25/17.40	                                                                list(dB),dB,
17.25/17.40	                                                                app_encode_app(
17.25/17.40	                                                                dB,
17.25/17.40	                                                                app_encode_fun(
17.25/17.40	                                                                list(dB),dB),
17.25/17.40	                                                                app_encode_app(
17.25/17.40	                                                                fun(dB,
17.25/17.40	                                                                    fun(
17.25/17.40	                                                                    dB,dB)),
17.25/17.40	                                                                app_encode_fun(
17.25/17.40	                                                                dB,
17.25/17.40	                                                                app_encode_fun(
17.25/17.40	                                                                list(dB),dB)),
17.25/17.40	                                                                foldl(dB,dB),
17.25/17.40	                                                                app),
17.25/17.40	                                                                app_encode_app(
17.25/17.40	                                                                nat,dB,
17.25/17.40	                                                                app_encode_app(
17.25/17.40	                                                                fun(nat,dB),
17.25/17.40	                                                                app_encode_fun(
17.25/17.40	                                                                nat,dB),
17.25/17.40	                                                                aa(nat,dB),
17.25/17.40	                                                                app_encode_app(
17.25/17.40	                                                                dB,
17.25/17.40	                                                                fun(nat,dB),
17.25/17.40	                                                                app_encode_app(
17.25/17.40	                                                                fun(dB,
17.25/17.40	                                                                    fun(
17.25/17.40	                                                                    nat,dB)),
17.25/17.40	                                                                app_encode_fun(
17.25/17.40	                                                                dB,
17.25/17.40	                                                                fun(nat,dB)),
17.25/17.40	                                                                aa(dB,
17.25/17.40	                                                                   fun(
17.25/17.40	                                                                   nat,dB)),
17.25/17.40	                                                                app_encode_app(
17.25/17.40	                                                                dB,
17.25/17.40	                                                                fun(dB,
17.25/17.40	                                                                    fun(
17.25/17.40	                                                                    nat,dB)),
17.25/17.40	                                                                app_encode_app(
17.25/17.40	                                                                fun(dB,
17.25/17.40	                                                                    fun(
17.25/17.40	                                                                    dB,
17.25/17.40	                                                                    fun(
17.25/17.40	                                                                    nat,dB))),
17.25/17.40	                                                                app_encode_fun(
17.25/17.40	                                                                dB,
17.25/17.40	                                                                fun(dB,
17.25/17.40	                                                                    fun(
17.25/17.40	                                                                    nat,dB))),
17.25/17.40	                                                                aa(dB,
17.25/17.40	                                                                   fun(
17.25/17.40	                                                                   dB,
17.25/17.40	                                                                   fun(
17.25/17.40	                                                                   nat,dB))),
17.25/17.40	                                                                subst),r)),a)),
17.25/17.40	                                                                zero_zero(
17.25/17.40	                                                                nat))),as))),
17.25/17.40	                                                                u)),
17.25/17.40	                                                 i))))).
17.25/17.40	tff('6', plain,
17.25/17.40	    ~ app_encode_app(bool, $o, pp, 
17.25/17.40	        app_encode_app(dB, bool, 
17.25/17.40	          app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
17.25/17.40	            aa(dB, bool), it), 
17.25/17.40	          app_encode_app(nat, dB, 
17.25/17.40	            app_encode_app(fun(nat, dB), app_encode_fun(nat, dB), 
17.25/17.40	              aa(nat, dB), 
17.25/17.40	              app_encode_app(dB, fun(nat, dB), 
17.25/17.40	                app_encode_app(fun(dB, fun(nat, dB)), 
17.25/17.40	                  app_encode_fun(dB, fun(nat, dB)), aa(dB, fun(nat, dB)), 
17.25/17.40	                  app_encode_app(dB, fun(dB, fun(nat, dB)), 
17.25/17.40	                    app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
17.25/17.40	                      app_encode_fun(dB, fun(dB, fun(nat, dB))), 
17.25/17.40	                      aa(dB, fun(dB, fun(nat, dB))), subst), 
17.25/17.40	                    app_encode_app(list(dB), dB, 
17.25/17.40	                      app_encode_app(dB, app_encode_fun(list(dB), dB), 
17.25/17.40	                        app_encode_app(fun(dB, fun(dB, dB)), 
17.25/17.40	                          app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
17.25/17.40	                          foldl(dB, dB), app), 
17.25/17.40	                        app_encode_app(nat, dB, 
17.25/17.40	                          app_encode_app(fun(nat, dB), 
17.25/17.40	                            app_encode_fun(nat, dB), aa(nat, dB), 
17.25/17.40	                            app_encode_app(dB, fun(nat, dB), 
17.25/17.40	                              app_encode_app(fun(dB, fun(nat, dB)), 
17.25/17.40	                                app_encode_fun(dB, fun(nat, dB)), 
17.25/17.40	                                aa(dB, fun(nat, dB)), 
17.25/17.40	                                app_encode_app(dB, fun(dB, fun(nat, dB)), 
17.25/17.40	                                  app_encode_app(
17.25/17.40	                                    fun(dB, fun(dB, fun(nat, dB))), 
17.25/17.40	                                    app_encode_fun(dB, fun(dB, fun(nat, dB))), 
17.25/17.40	                                    aa(dB, fun(dB, fun(nat, dB))), subst), r)), 
17.25/17.40	                              a)), zero_zero(nat))), as))), u)), i))),
17.25/17.40	    inference('cnf', [status(esa)], [zf_stmt_0])).
17.25/17.40	tff('7', plain,
17.25/17.40	    ~ app_encode_app(bool, $o, pp, 
17.25/17.40	        app_encode_app(dB, bool, 
17.25/17.40	          app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
17.25/17.40	            aa(dB, bool), it), 
17.25/17.40	          app_encode_app(dB, dB, 
17.25/17.40	            app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), aa(dB, dB), 
17.25/17.40	              app_encode_app(nat, fun(dB, dB), 
17.25/17.40	                app_encode_app(fun(dB, fun(nat, dB)), 
17.25/17.40	                  app_encode_fun(nat, fun(dB, dB)), combc(dB, nat, dB), 
17.25/17.40	                  app_encode_app(dB, fun(dB, fun(nat, dB)), 
17.25/17.40	                    app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
17.25/17.40	                      app_encode_fun(dB, fun(dB, fun(nat, dB))), 
17.25/17.40	                      combc(dB, dB, fun(nat, dB)), subst), u)), i)), 
17.25/17.40	            app_encode_app(list(dB), dB, 
17.25/17.40	              app_encode_app(dB, app_encode_fun(list(dB), dB), 
17.25/17.40	                app_encode_app(fun(dB, fun(dB, dB)), 
17.25/17.40	                  app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
17.25/17.40	                  foldl(dB, dB), app), 
17.25/17.40	                app_encode_app(dB, dB, 
17.25/17.40	                  app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), 
17.25/17.40	                    aa(dB, dB), 
17.25/17.40	                    app_encode_app(nat, fun(dB, dB), 
17.25/17.40	                      app_encode_app(fun(dB, fun(nat, dB)), 
17.25/17.40	                        app_encode_fun(nat, fun(dB, dB)), 
17.25/17.40	                        combc(dB, nat, dB), 
17.25/17.40	                        app_encode_app(dB, fun(dB, fun(nat, dB)), 
17.25/17.40	                          app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
17.25/17.40	                            app_encode_fun(dB, fun(dB, fun(nat, dB))), 
17.25/17.40	                            combc(dB, dB, fun(nat, dB)), subst), a)), 
17.25/17.40	                      zero_zero(nat))), r)), as)))),
17.25/17.40	    inference('demod', [status(thm)], ['6', '4', '4', '4', '4'])).
17.25/17.40	tff('8', plain,
17.25/17.40	    (~ $true
17.25/17.40	     | ~ app_encode_app(bool, $o, pp, 
17.25/17.40	           app_encode_app(type, bool, 
17.25/17.40	             app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
17.25/17.40	               aa(type, bool), 
17.25/17.40	               app_encode_app(dB, fun(type, bool), 
17.25/17.40	                 app_encode_app(fun(nat, type), 
17.25/17.40	                   app_encode_fun(dB, fun(type, bool)), typing, e), u)), t))
17.25/17.40	     | ~ app_encode_app(bool, $o, pp, 
17.25/17.40	           app_encode_app(dB, bool, 
17.25/17.40	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
17.25/17.40	               aa(dB, bool), it), u))),
17.25/17.40	    inference('sup-', [status(thm)], ['5', '7'])).
17.25/17.40	tff(zf_stmt_60, axiom,
17.25/17.40	  (app_encode_app(bool,$o,pp,
17.25/17.40	                  app_encode_app(type,bool,
17.25/17.40	                                 app_encode_app(fun(type,bool),
17.25/17.40	                                                app_encode_fun(type,bool),
17.25/17.40	                                                aa(type,bool),
17.25/17.40	                                                app_encode_app(dB,
17.25/17.40	                                                               fun(type,bool),
17.25/17.40	                                                               app_encode_app(
17.25/17.40	                                                               fun(nat,type),
17.25/17.40	                                                               app_encode_fun(
17.25/17.40	                                                               dB,
17.25/17.40	                                                               fun(type,bool)),
17.25/17.40	                                                               typing,e),u)),
17.25/17.40	                                 t)))).
17.25/17.40	tff('9', plain,
17.25/17.40	    app_encode_app(bool, $o, pp, 
17.25/17.40	      app_encode_app(type, bool, 
17.25/17.40	        app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
17.25/17.40	          aa(type, bool), 
17.25/17.40	          app_encode_app(dB, fun(type, bool), 
17.25/17.40	            app_encode_app(fun(nat, type), 
17.25/17.40	              app_encode_fun(dB, fun(type, bool)), typing, e), u)), t)),
17.25/17.40	    inference('cnf', [status(esa)], [zf_stmt_60])).
17.25/17.40	tff(zf_stmt_166, axiom, (![P:bool]: ((P = fTrue) | (P = fFalse)))).
17.25/17.40	tff('10', plain, ![X401 : bool]: (X401 = fTrue | X401 = fFalse),
17.25/17.40	    inference('cnf', [status(esa)], [zf_stmt_166])).
17.25/17.40	tff(zf_stmt_156, axiom, (~app_encode_app(bool,$o,pp,fFalse))).
17.25/17.40	tff('11', plain, ~ app_encode_app(bool, $o, pp, fFalse),
17.25/17.40	    inference('cnf', [status(esa)], [zf_stmt_156])).
17.25/17.40	tff('12', plain,
17.25/17.40	    ![X0 : bool]: (~ app_encode_app(bool, $o, pp, X0) | X0 = fTrue),
17.25/17.40	    inference('sup-', [status(thm)], ['10', '11'])).
17.25/17.40	tff('13', plain,
17.25/17.40	    (~ $true
17.25/17.40	     | app_encode_app(type, bool, 
17.25/17.40	         app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
17.25/17.40	           aa(type, bool), 
17.25/17.40	           app_encode_app(dB, fun(type, bool), 
17.25/17.40	             app_encode_app(fun(nat, type), 
17.25/17.40	               app_encode_fun(dB, fun(type, bool)), typing, e), u)), t)
17.25/17.40	        = fTrue),
17.25/17.40	    inference('sup-', [status(thm)], ['9', '12'])).
17.25/17.40	tff('14', plain,
17.25/17.40	    app_encode_app(type, bool, 
17.25/17.40	      app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
17.25/17.40	        aa(type, bool), 
17.25/17.40	        app_encode_app(dB, fun(type, bool), 
17.25/17.40	          app_encode_app(fun(nat, type), 
17.25/17.40	            app_encode_fun(dB, fun(type, bool)), typing, e), u)), t)
17.25/17.40	     = fTrue,
17.25/17.40	    inference('simplify', [status(thm)], ['13'])).
17.25/17.40	tff(zf_stmt_157, axiom, (app_encode_app(bool,$o,pp,fTrue))).
17.25/17.40	tff('15', plain, app_encode_app(bool, $o, pp, fTrue),
17.25/17.40	    inference('cnf', [status(esa)], [zf_stmt_157])).
17.25/17.40	tff(zf_stmt_58, axiom,
17.25/17.40	  (app_encode_app(bool,$o,pp,
17.25/17.40	                  app_encode_app(dB,bool,
17.25/17.40	                                 app_encode_app(fun(dB,bool),
17.25/17.40	                                                app_encode_fun(dB,bool),
17.25/17.40	                                                aa(dB,bool),it),
17.25/17.40	                                 u)))).
17.25/17.40	tff('16', plain,
17.25/17.40	    app_encode_app(bool, $o, pp, 
17.25/17.40	      app_encode_app(dB, bool, 
17.25/17.40	        app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
17.25/17.40	          aa(dB, bool), it), u)),
17.25/17.40	    inference('cnf', [status(esa)], [zf_stmt_58])).
17.25/17.40	tff('17', plain,
17.25/17.40	    (~ $true
17.25/17.40	     | app_encode_app(dB, bool, 
17.25/17.40	         app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
17.25/17.40	           aa(dB, bool), it), u)
17.25/17.40	        = fTrue),
17.25/17.40	    inference('sup-', [status(thm)], ['16', '12'])).
17.25/17.40	tff('18', plain,
17.25/17.40	    app_encode_app(dB, bool, 
17.25/17.40	      app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), aa(dB, bool), 
17.25/17.40	        it), u)
17.25/17.40	     = fTrue,
17.25/17.40	    inference('simplify', [status(thm)], ['17'])).
17.25/17.40	tff('19', plain, (~ $true | ~ $true | ~ $true),
17.25/17.40	    inference('demod', [status(thm)], ['8', '14', '15', '18', '15'])).
17.25/17.40	tff('20', plain, $false, inference('simplify', [status(thm)], ['19'])).
17.25/17.40	
17.25/17.40	% SZS output end Refutation
17.25/17.40	EOF
