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 $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n119.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 07:10:38 CST 2018
99.05/99.21	% done 8648 iterations in 99.018s
99.05/99.21	% SZS status Theorem for 'stdin'
99.05/99.21	% SZS output start Refutation
99.05/99.22	tff(zf_stmt_63, axiom,
99.05/99.22	  (app_encode_app(bool,$o,pp,
99.05/99.22	                  app_encode_app(list(type),bool,
99.05/99.22	                                 app_encode_app(fun(list(type),bool),
99.05/99.22	                                                app_encode_fun(list(type),
99.05/99.22	                                                               bool),
99.05/99.22	                                                aa(list(type),bool),
99.05/99.22	                                                app_encode_app(list(dB),
99.05/99.22	                                                               fun(list(type),
99.05/99.22	                                                                   bool),
99.05/99.22	                                                               app_encode_app(
99.05/99.22	                                                               fun(nat,type),
99.05/99.22	                                                               app_encode_fun(
99.05/99.22	                                                               list(dB),
99.05/99.22	                                                               fun(list(type),
99.05/99.22	                                                                   bool)),
99.05/99.22	                                                               typings,
99.05/99.22	                                                               app_encode_app(
99.05/99.22	                                                               type,
99.05/99.22	                                                               fun(nat,type),
99.05/99.22	                                                               app_encode_app(
99.05/99.22	                                                               nat,
99.05/99.22	                                                               app_encode_fun(
99.05/99.22	                                                               type,
99.05/99.22	                                                               fun(nat,type)),
99.05/99.22	                                                               app_encode_app(
99.05/99.22	                                                               fun(nat,type),
99.05/99.22	                                                               app_encode_fun(
99.05/99.22	                                                               nat,
99.05/99.22	                                                               app_encode_fun(
99.05/99.22	                                                               type,
99.05/99.22	                                                               fun(nat,type))),
99.05/99.22	                                                               shift(type),e),
99.05/99.22	                                                               zero_zero(nat)),
99.05/99.22	                                                               app_encode_app(
99.05/99.22	                                                               type,type,
99.05/99.22	                                                               app_encode_app(
99.05/99.22	                                                               list(type),
99.05/99.22	                                                               app_encode_fun(
99.05/99.22	                                                               type,type),
99.05/99.22	                                                               app_encode_app(
99.05/99.22	                                                               fun(type,
99.05/99.22	                                                                   fun(
99.05/99.22	                                                                   type,type)),
99.05/99.22	                                                               app_encode_fun(
99.05/99.22	                                                               list(type),
99.05/99.22	                                                               app_encode_fun(
99.05/99.22	                                                               type,type)),
99.05/99.22	                                                               foldr(
99.05/99.22	                                                               type,type),
99.05/99.22	                                                               fun1),ts),t))),
99.05/99.22	                                                               app_encode_app(
99.05/99.22	                                                               list(dB),
99.05/99.22	                                                               list(dB),
99.05/99.22	                                                               app_encode_app(
99.05/99.22	                                                               fun(dB,dB),
99.05/99.22	                                                               app_encode_fun(
99.05/99.22	                                                               list(dB),
99.05/99.22	                                                               list(dB)),
99.05/99.22	                                                               map(dB,dB),
99.05/99.22	                                                               app_encode_app(
99.05/99.22	                                                               nat,
99.05/99.22	                                                               fun(dB,dB),
99.05/99.22	                                                               app_encode_app(
99.05/99.22	                                                               fun(dB,
99.05/99.22	                                                                   fun(
99.05/99.22	                                                                   nat,dB)),
99.05/99.22	                                                               app_encode_fun(
99.05/99.22	                                                               nat,fun(dB,dB)),
99.05/99.22	                                                               combc(
99.05/99.22	                                                               dB,nat,dB),
99.05/99.22	                                                               lift),
99.05/99.22	                                                               zero_zero(nat))),
99.05/99.22	                                                               app_encode_app(
99.05/99.22	                                                               list(dB),
99.05/99.22	                                                               list(dB),
99.05/99.22	                                                               app_encode_app(
99.05/99.22	                                                               fun(dB,dB),
99.05/99.22	                                                               app_encode_fun(
99.05/99.22	                                                               list(dB),
99.05/99.22	                                                               list(dB)),
99.05/99.22	                                                               map(dB,dB),
99.05/99.22	                                                               app_encode_app(
99.05/99.22	                                                               nat,
99.05/99.22	                                                               fun(dB,dB),
99.05/99.22	                                                               app_encode_app(
99.05/99.22	                                                               fun(dB,
99.05/99.22	                                                                   fun(
99.05/99.22	                                                                   nat,dB)),
99.05/99.22	                                                               app_encode_fun(
99.05/99.22	                                                               nat,fun(dB,dB)),
99.05/99.22	                                                               combc(
99.05/99.22	                                                               dB,nat,dB),
99.05/99.22	                                                               app_encode_app(
99.05/99.22	                                                               dB,
99.05/99.22	                                                               fun(dB,
99.05/99.22	                                                                   fun(
99.05/99.22	                                                                   nat,dB)),
99.05/99.22	                                                               app_encode_app(
99.05/99.22	                                                               fun(dB,
99.05/99.22	                                                                   fun(
99.05/99.22	                                                                   dB,
99.05/99.22	                                                                   fun(
99.05/99.22	                                                                   nat,dB))),
99.05/99.22	                                                               app_encode_fun(
99.05/99.22	                                                               dB,
99.05/99.22	                                                               fun(dB,
99.05/99.22	                                                                   fun(
99.05/99.22	                                                                   nat,dB))),
99.05/99.22	                                                               combc(
99.05/99.22	                                                               dB,dB,
99.05/99.22	                                                               fun(nat,dB)),
99.05/99.22	                                                               subst),u)),i)),
99.05/99.22	                                                               as)))),
99.05/99.22	                                 ts)))).
99.05/99.22	tff('0', plain,
99.05/99.22	    app_encode_app(bool, $o, pp, 
99.05/99.22	      app_encode_app(list(type), bool, 
99.05/99.22	        app_encode_app(fun(list(type), bool), 
99.05/99.22	          app_encode_fun(list(type), bool), aa(list(type), bool), 
99.05/99.22	          app_encode_app(list(dB), fun(list(type), bool), 
99.05/99.22	            app_encode_app(fun(nat, type), 
99.05/99.22	              app_encode_fun(list(dB), fun(list(type), bool)), typings, 
99.05/99.22	              app_encode_app(type, fun(nat, type), 
99.05/99.22	                app_encode_app(nat, app_encode_fun(type, fun(nat, type)), 
99.05/99.22	                  app_encode_app(fun(nat, type), 
99.05/99.22	                    app_encode_fun(nat, app_encode_fun(type, fun(nat, type))), 
99.05/99.22	                    shift(type), e), zero_zero(nat)), 
99.05/99.22	                app_encode_app(type, type, 
99.05/99.22	                  app_encode_app(list(type), app_encode_fun(type, type), 
99.05/99.22	                    app_encode_app(fun(type, fun(type, type)), 
99.05/99.22	                      app_encode_fun(list(type), app_encode_fun(type, type)), 
99.05/99.22	                      foldr(type, type), fun1), ts), t))), 
99.05/99.22	            app_encode_app(list(dB), list(dB), 
99.05/99.22	              app_encode_app(fun(dB, dB), 
99.05/99.22	                app_encode_fun(list(dB), list(dB)), map(dB, dB), 
99.05/99.22	                app_encode_app(nat, fun(dB, dB), 
99.05/99.22	                  app_encode_app(fun(dB, fun(nat, dB)), 
99.05/99.22	                    app_encode_fun(nat, fun(dB, dB)), combc(dB, nat, dB), 
99.05/99.22	                    lift), zero_zero(nat))), 
99.05/99.22	              app_encode_app(list(dB), list(dB), 
99.05/99.22	                app_encode_app(fun(dB, dB), 
99.05/99.22	                  app_encode_fun(list(dB), list(dB)), map(dB, dB), 
99.05/99.22	                  app_encode_app(nat, fun(dB, dB), 
99.05/99.22	                    app_encode_app(fun(dB, fun(nat, dB)), 
99.05/99.22	                      app_encode_fun(nat, fun(dB, dB)), combc(dB, nat, dB), 
99.05/99.22	                      app_encode_app(dB, fun(dB, fun(nat, dB)), 
99.05/99.22	                        app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
99.05/99.22	                          app_encode_fun(dB, fun(dB, fun(nat, dB))), 
99.05/99.22	                          combc(dB, dB, fun(nat, dB)), subst), u)), i)), as)))), 
99.05/99.22	        ts)),
99.05/99.22	    inference('cnf', [status(esa)], [zf_stmt_63])).
99.05/99.22	tff(zf_stmt_102, axiom,
99.05/99.22	  (![Ts:list(dB),Ta1:type,Tsa:list(type),Ta:dB,Eb:fun(nat,type)]:
99.05/99.22	     (app_encode_app(bool,$o,pp,
99.05/99.22	                     app_encode_app(type,bool,
99.05/99.22	                                    app_encode_app(fun(type,bool),
99.05/99.22	                                                   app_encode_fun(type,bool),
99.05/99.22	                                                   aa(type,bool),
99.05/99.22	                                                   app_encode_app(dB,
99.05/99.22	                                                                  fun(
99.05/99.22	                                                                  type,bool),
99.05/99.22	                                                                  app_encode_app(
99.05/99.22	                                                                  fun(
99.05/99.22	                                                                  dB,
99.05/99.22	                                                                  fun(
99.05/99.22	                                                                  type,bool)),
99.05/99.22	                                                                  app_encode_fun(
99.05/99.22	                                                                  dB,
99.05/99.22	                                                                  fun(
99.05/99.22	                                                                  type,bool)),
99.05/99.22	                                                                  aa(
99.05/99.22	                                                                  dB,
99.05/99.22	                                                                  fun(
99.05/99.22	                                                                  type,bool)),
99.05/99.22	                                                                  app_encode_app(
99.05/99.22	                                                                  fun(
99.05/99.22	                                                                  nat,type),
99.05/99.22	                                                                  fun(
99.05/99.22	                                                                  dB,
99.05/99.22	                                                                  fun(
99.05/99.22	                                                                  type,bool)),
99.05/99.22	                                                                  typing,Eb)),
99.05/99.22	                                                                  Ta)),
99.05/99.22	                                    app_encode_app(type,type,
99.05/99.22	                                                   app_encode_app(list(type),
99.05/99.22	                                                                  app_encode_fun(
99.05/99.22	                                                                  type,type),
99.05/99.22	                                                                  app_encode_app(
99.05/99.22	                                                                  fun(
99.05/99.22	                                                                  type,
99.05/99.22	                                                                  fun(
99.05/99.22	                                                                  type,type)),
99.05/99.22	                                                                  app_encode_fun(
99.05/99.22	                                                                  list(type),
99.05/99.22	                                                                  app_encode_fun(
99.05/99.22	                                                                  type,type)),
99.05/99.22	                                                                  foldr(
99.05/99.22	                                                                  type,type),
99.05/99.22	                                                                  fun1),Tsa),
99.05/99.22	                                                   Ta1))) =>
99.05/99.22	      (app_encode_app(bool,$o,pp,
99.05/99.22	                      app_encode_app(list(type),bool,
99.05/99.22	                                     app_encode_app(fun(list(type),bool),
99.05/99.22	                                                    app_encode_fun(list(type),
99.05/99.22	                                                                   bool),
99.05/99.22	                                                    aa(list(type),bool),
99.05/99.22	                                                    app_encode_app(list(dB),
99.05/99.22	                                                                   fun(
99.05/99.22	                                                                   list(type),
99.05/99.22	                                                                   bool),
99.05/99.22	                                                                   app_encode_app(
99.05/99.22	                                                                   fun(
99.05/99.22	                                                                   nat,type),
99.05/99.22	                                                                   app_encode_fun(
99.05/99.22	                                                                   list(dB),
99.05/99.22	                                                                   fun(
99.05/99.22	                                                                   list(type),
99.05/99.22	                                                                   bool)),
99.05/99.22	                                                                   typings,Eb),
99.05/99.22	                                                                   Ts)),
99.05/99.22	                                     Tsa)) =>
99.05/99.22	       app_encode_app(bool,$o,pp,
99.05/99.22	                      app_encode_app(type,bool,
99.05/99.22	                                     app_encode_app(fun(type,bool),
99.05/99.22	                                                    app_encode_fun(type,bool),
99.05/99.22	                                                    aa(type,bool),
99.05/99.22	                                                    app_encode_app(dB,
99.05/99.22	                                                                   fun(
99.05/99.22	                                                                   type,bool),
99.05/99.22	                                                                   app_encode_app(
99.05/99.22	                                                                   fun(
99.05/99.22	                                                                   dB,
99.05/99.22	                                                                   fun(
99.05/99.22	                                                                   type,bool)),
99.05/99.22	                                                                   app_encode_fun(
99.05/99.22	                                                                   dB,
99.05/99.22	                                                                   fun(
99.05/99.22	                                                                   type,bool)),
99.05/99.22	                                                                   aa(
99.05/99.22	                                                                   dB,
99.05/99.22	                                                                   fun(
99.05/99.22	                                                                   type,bool)),
99.05/99.22	                                                                   app_encode_app(
99.05/99.22	                                                                   fun(
99.05/99.22	                                                                   nat,type),
99.05/99.22	                                                                   fun(
99.05/99.22	                                                                   dB,
99.05/99.22	                                                                   fun(
99.05/99.22	                                                                   type,bool)),
99.05/99.22	                                                                   typing,Eb)),
99.05/99.22	                                                                   app_encode_app(
99.05/99.22	                                                                   list(dB),
99.05/99.22	                                                                   dB,
99.05/99.22	                                                                   app_encode_app(
99.05/99.22	                                                                   dB,
99.05/99.22	                                                                   app_encode_fun(
99.05/99.22	                                                                   list(dB),
99.05/99.22	                                                                   dB),
99.05/99.22	                                                                   app_encode_app(
99.05/99.22	                                                                   fun(
99.05/99.22	                                                                   dB,
99.05/99.22	                                                                   fun(dB,dB)),
99.05/99.22	                                                                   app_encode_fun(
99.05/99.22	                                                                   dB,
99.05/99.22	                                                                   app_encode_fun(
99.05/99.22	                                                                   list(dB),
99.05/99.22	                                                                   dB)),
99.05/99.22	                                                                   foldl(
99.05/99.22	                                                                   dB,dB),app),
99.05/99.22	                                                                   Ta),Ts))),
99.05/99.22	                                     Ta1)))))).
99.05/99.22	tff('1', plain,
99.05/99.22	    ![X101 : fun(nat, type), X102 : list(dB), X103 : list(type), X104 : dB, 
99.05/99.22	      X105 : type]:
99.05/99.22	      (~ app_encode_app(bool, $o, pp, 
99.05/99.22	           app_encode_app(list(type), bool, 
99.05/99.22	             app_encode_app(fun(list(type), bool), 
99.05/99.22	               app_encode_fun(list(type), bool), aa(list(type), bool), 
99.05/99.22	               app_encode_app(list(dB), fun(list(type), bool), 
99.05/99.22	                 app_encode_app(fun(nat, type), 
99.05/99.22	                   app_encode_fun(list(dB), fun(list(type), bool)), typings, 
99.05/99.22	                   X101), X102)), X103))
99.05/99.22	       | app_encode_app(bool, $o, pp, 
99.05/99.22	           app_encode_app(type, bool, 
99.05/99.22	             app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
99.05/99.22	               aa(type, bool), 
99.05/99.22	               app_encode_app(dB, fun(type, bool), 
99.05/99.22	                 app_encode_app(fun(dB, fun(type, bool)), 
99.05/99.22	                   app_encode_fun(dB, fun(type, bool)), 
99.05/99.22	                   aa(dB, fun(type, bool)), 
99.05/99.22	                   app_encode_app(fun(nat, type), fun(dB, fun(type, bool)), 
99.05/99.22	                     typing, X101)), 
99.05/99.22	                 app_encode_app(list(dB), dB, 
99.05/99.22	                   app_encode_app(dB, app_encode_fun(list(dB), dB), 
99.05/99.22	                     app_encode_app(fun(dB, fun(dB, dB)), 
99.05/99.22	                       app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
99.05/99.22	                       foldl(dB, dB), app), X104), X102))), X105))
99.05/99.22	       | ~ app_encode_app(bool, $o, pp, 
99.05/99.22	             app_encode_app(type, bool, 
99.05/99.22	               app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
99.05/99.22	                 aa(type, bool), 
99.05/99.22	                 app_encode_app(dB, fun(type, bool), 
99.05/99.22	                   app_encode_app(fun(dB, fun(type, bool)), 
99.05/99.22	                     app_encode_fun(dB, fun(type, bool)), 
99.05/99.22	                     aa(dB, fun(type, bool)), 
99.05/99.22	                     app_encode_app(fun(nat, type), 
99.05/99.22	                       fun(dB, fun(type, bool)), typing, X101)), X104)), 
99.05/99.22	               app_encode_app(type, type, 
99.05/99.22	                 app_encode_app(list(type), app_encode_fun(type, type), 
99.05/99.22	                   app_encode_app(fun(type, fun(type, type)), 
99.05/99.22	                     app_encode_fun(list(type), app_encode_fun(type, type)), 
99.05/99.22	                     foldr(type, type), fun1), X103), X105)))),
99.05/99.22	    inference('cnf', [status(esa)], [zf_stmt_102])).
99.05/99.22	tff('2', plain,
99.05/99.22	    ![X0 : type, X1 : dB]:
99.05/99.22	      (~ $true
99.05/99.22	       | ~ app_encode_app(bool, $o, pp, 
99.05/99.22	             app_encode_app(type, bool, 
99.05/99.22	               app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
99.05/99.22	                 aa(type, bool), 
99.05/99.22	                 app_encode_app(dB, fun(type, bool), 
99.05/99.22	                   app_encode_app(fun(dB, fun(type, bool)), 
99.05/99.22	                     app_encode_fun(dB, fun(type, bool)), 
99.05/99.22	                     aa(dB, fun(type, bool)), 
99.05/99.22	                     app_encode_app(fun(nat, type), 
99.05/99.22	                       fun(dB, fun(type, bool)), typing, 
99.05/99.22	                       app_encode_app(type, fun(nat, type), 
99.05/99.22	                         app_encode_app(nat, 
99.05/99.22	                           app_encode_fun(type, fun(nat, type)), 
99.05/99.22	                           app_encode_app(fun(nat, type), 
99.05/99.22	                             app_encode_fun(nat, 
99.05/99.22	                               app_encode_fun(type, fun(nat, type))), 
99.05/99.22	                             shift(type), e), zero_zero(nat)), 
99.05/99.22	                         app_encode_app(type, type, 
99.05/99.22	                           app_encode_app(list(type), 
99.05/99.22	                             app_encode_fun(type, type), 
99.05/99.22	                             app_encode_app(fun(type, fun(type, type)), 
99.05/99.22	                               app_encode_fun(list(type), 
99.05/99.22	                                 app_encode_fun(type, type)), 
99.05/99.22	                               foldr(type, type), fun1), ts), t)))), X1)), 
99.05/99.22	               app_encode_app(type, type, 
99.05/99.22	                 app_encode_app(list(type), app_encode_fun(type, type), 
99.05/99.22	                   app_encode_app(fun(type, fun(type, type)), 
99.05/99.22	                     app_encode_fun(list(type), app_encode_fun(type, type)), 
99.05/99.22	                     foldr(type, type), fun1), ts), X0)))
99.05/99.22	       | app_encode_app(bool, $o, pp, 
99.05/99.22	           app_encode_app(type, bool, 
99.05/99.22	             app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
99.05/99.22	               aa(type, bool), 
99.05/99.22	               app_encode_app(dB, fun(type, bool), 
99.05/99.22	                 app_encode_app(fun(dB, fun(type, bool)), 
99.05/99.22	                   app_encode_fun(dB, fun(type, bool)), 
99.05/99.22	                   aa(dB, fun(type, bool)), 
99.05/99.22	                   app_encode_app(fun(nat, type), fun(dB, fun(type, bool)), 
99.05/99.22	                     typing, 
99.05/99.22	                     app_encode_app(type, fun(nat, type), 
99.05/99.22	                       app_encode_app(nat, 
99.05/99.22	                         app_encode_fun(type, fun(nat, type)), 
99.05/99.22	                         app_encode_app(fun(nat, type), 
99.05/99.22	                           app_encode_fun(nat, 
99.05/99.22	                             app_encode_fun(type, fun(nat, type))), 
99.05/99.22	                           shift(type), e), zero_zero(nat)), 
99.05/99.22	                       app_encode_app(type, type, 
99.05/99.22	                         app_encode_app(list(type), 
99.05/99.22	                           app_encode_fun(type, type), 
99.05/99.22	                           app_encode_app(fun(type, fun(type, type)), 
99.05/99.22	                             app_encode_fun(list(type), 
99.05/99.22	                               app_encode_fun(type, type)), 
99.05/99.22	                             foldr(type, type), fun1), ts), t)))), 
99.05/99.22	                 app_encode_app(list(dB), dB, 
99.05/99.22	                   app_encode_app(dB, app_encode_fun(list(dB), dB), 
99.05/99.22	                     app_encode_app(fun(dB, fun(dB, dB)), 
99.05/99.22	                       app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
99.05/99.22	                       foldl(dB, dB), app), X1), 
99.05/99.22	                   app_encode_app(list(dB), list(dB), 
99.05/99.22	                     app_encode_app(fun(dB, dB), 
99.05/99.22	                       app_encode_fun(list(dB), list(dB)), map(dB, dB), 
99.05/99.22	                       app_encode_app(nat, fun(dB, dB), 
99.05/99.22	                         app_encode_app(fun(dB, fun(nat, dB)), 
99.05/99.22	                           app_encode_fun(nat, fun(dB, dB)), 
99.05/99.22	                           combc(dB, nat, dB), lift), zero_zero(nat))), 
99.05/99.22	                     app_encode_app(list(dB), list(dB), 
99.05/99.22	                       app_encode_app(fun(dB, dB), 
99.05/99.22	                         app_encode_fun(list(dB), list(dB)), map(dB, dB), 
99.05/99.22	                         app_encode_app(nat, fun(dB, dB), 
99.05/99.22	                           app_encode_app(fun(dB, fun(nat, dB)), 
99.05/99.22	                             app_encode_fun(nat, fun(dB, dB)), 
99.05/99.22	                             combc(dB, nat, dB), 
99.05/99.22	                             app_encode_app(dB, fun(dB, fun(nat, dB)), 
99.05/99.22	                               app_encode_app(
99.05/99.22	                                 fun(dB, fun(dB, fun(nat, dB))), 
99.05/99.22	                                 app_encode_fun(dB, fun(dB, fun(nat, dB))), 
99.05/99.22	                                 combc(dB, dB, fun(nat, dB)), subst), u)), i)), 
99.05/99.22	                       as))))), X0))),
99.05/99.22	    inference('sup-', [status(thm)], ['0', '1'])).
99.05/99.22	tff('3', plain,
99.05/99.22	    ![X0 : type, X1 : dB]:
99.05/99.22	      (app_encode_app(bool, $o, pp, 
99.05/99.22	         app_encode_app(type, bool, 
99.05/99.22	           app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
99.05/99.22	             aa(type, bool), 
99.05/99.22	             app_encode_app(dB, fun(type, bool), 
99.05/99.22	               app_encode_app(fun(dB, fun(type, bool)), 
99.05/99.22	                 app_encode_fun(dB, fun(type, bool)), 
99.05/99.22	                 aa(dB, fun(type, bool)), 
99.05/99.22	                 app_encode_app(fun(nat, type), fun(dB, fun(type, bool)), 
99.05/99.22	                   typing, 
99.05/99.22	                   app_encode_app(type, fun(nat, type), 
99.05/99.22	                     app_encode_app(nat, 
99.05/99.22	                       app_encode_fun(type, fun(nat, type)), 
99.05/99.22	                       app_encode_app(fun(nat, type), 
99.05/99.22	                         app_encode_fun(nat, 
99.05/99.22	                           app_encode_fun(type, fun(nat, type))), 
99.05/99.22	                         shift(type), e), zero_zero(nat)), 
99.05/99.22	                     app_encode_app(type, type, 
99.05/99.22	                       app_encode_app(list(type), 
99.05/99.22	                         app_encode_fun(type, type), 
99.05/99.22	                         app_encode_app(fun(type, fun(type, type)), 
99.05/99.22	                           app_encode_fun(list(type), 
99.05/99.22	                             app_encode_fun(type, type)), foldr(type, type), 
99.05/99.22	                           fun1), ts), t)))), 
99.05/99.22	               app_encode_app(list(dB), dB, 
99.05/99.22	                 app_encode_app(dB, app_encode_fun(list(dB), dB), 
99.05/99.22	                   app_encode_app(fun(dB, fun(dB, dB)), 
99.05/99.22	                     app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
99.05/99.22	                     foldl(dB, dB), app), X1), 
99.05/99.22	                 app_encode_app(list(dB), list(dB), 
99.05/99.22	                   app_encode_app(fun(dB, dB), 
99.05/99.22	                     app_encode_fun(list(dB), list(dB)), map(dB, dB), 
99.05/99.22	                     app_encode_app(nat, fun(dB, dB), 
99.05/99.22	                       app_encode_app(fun(dB, fun(nat, dB)), 
99.05/99.22	                         app_encode_fun(nat, fun(dB, dB)), 
99.05/99.22	                         combc(dB, nat, dB), lift), zero_zero(nat))), 
99.05/99.22	                   app_encode_app(list(dB), list(dB), 
99.05/99.22	                     app_encode_app(fun(dB, dB), 
99.05/99.22	                       app_encode_fun(list(dB), list(dB)), map(dB, dB), 
99.05/99.22	                       app_encode_app(nat, fun(dB, dB), 
99.05/99.22	                         app_encode_app(fun(dB, fun(nat, dB)), 
99.05/99.22	                           app_encode_fun(nat, fun(dB, dB)), 
99.05/99.22	                           combc(dB, nat, dB), 
99.05/99.22	                           app_encode_app(dB, fun(dB, fun(nat, dB)), 
99.05/99.22	                             app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
99.05/99.22	                               app_encode_fun(dB, fun(dB, fun(nat, dB))), 
99.05/99.22	                               combc(dB, dB, fun(nat, dB)), subst), u)), i)), 
99.05/99.22	                     as))))), X0))
99.05/99.22	       | ~ app_encode_app(bool, $o, pp, 
99.05/99.22	             app_encode_app(type, bool, 
99.05/99.22	               app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
99.05/99.22	                 aa(type, bool), 
99.05/99.22	                 app_encode_app(dB, fun(type, bool), 
99.05/99.22	                   app_encode_app(fun(dB, fun(type, bool)), 
99.05/99.22	                     app_encode_fun(dB, fun(type, bool)), 
99.05/99.22	                     aa(dB, fun(type, bool)), 
99.05/99.22	                     app_encode_app(fun(nat, type), 
99.05/99.22	                       fun(dB, fun(type, bool)), typing, 
99.05/99.22	                       app_encode_app(type, fun(nat, type), 
99.05/99.22	                         app_encode_app(nat, 
99.05/99.22	                           app_encode_fun(type, fun(nat, type)), 
99.05/99.22	                           app_encode_app(fun(nat, type), 
99.05/99.22	                             app_encode_fun(nat, 
99.05/99.22	                               app_encode_fun(type, fun(nat, type))), 
99.05/99.22	                             shift(type), e), zero_zero(nat)), 
99.05/99.22	                         app_encode_app(type, type, 
99.05/99.22	                           app_encode_app(list(type), 
99.05/99.22	                             app_encode_fun(type, type), 
99.05/99.22	                             app_encode_app(fun(type, fun(type, type)), 
99.05/99.22	                               app_encode_fun(list(type), 
99.05/99.22	                                 app_encode_fun(type, type)), 
99.05/99.22	                               foldr(type, type), fun1), ts), t)))), X1)), 
99.05/99.22	               app_encode_app(type, type, 
99.05/99.22	                 app_encode_app(list(type), app_encode_fun(type, type), 
99.05/99.22	                   app_encode_app(fun(type, fun(type, type)), 
99.05/99.22	                     app_encode_fun(list(type), app_encode_fun(type, type)), 
99.05/99.22	                     foldr(type, type), fun1), ts), X0)))),
99.05/99.22	    inference('simplify', [status(thm)], ['2'])).
99.05/99.22	tff(zf_stmt_163, axiom,
99.05/99.22	  (![A:$tType,C:$tType,B:$tType,R:A,Q:B,P:fun(A,fun(B,C))]:
99.05/99.22	     (app_encode_app(A,C,
99.05/99.22	                     app_encode_app(fun(A,C),app_encode_fun(A,C),aa(A,C),
99.05/99.22	                                    app_encode_app(B,fun(A,C),
99.05/99.22	                                                   app_encode_app(fun(
99.05/99.22	                                                                  A,fun(B,C)),
99.05/99.22	                                                                  app_encode_fun(
99.05/99.22	                                                                  B,fun(A,C)),
99.05/99.22	                                                                  combc(
99.05/99.22	                                                                  A,B,C),P),
99.05/99.22	                                                   Q)),
99.05/99.22	                     R) =
99.05/99.22	      app_encode_app(B,C,
99.05/99.22	                     app_encode_app(fun(B,C),app_encode_fun(B,C),aa(B,C),
99.05/99.22	                                    app_encode_app(A,fun(B,C),
99.05/99.22	                                                   app_encode_app(fun(
99.05/99.22	                                                                  A,fun(B,C)),
99.05/99.22	                                                                  app_encode_fun(
99.05/99.22	                                                                  A,fun(B,C)),
99.05/99.22	                                                                  aa(
99.05/99.22	                                                                  A,fun(B,C)),
99.05/99.22	                                                                  P),
99.05/99.22	                                                   R)),
99.05/99.22	                     Q)))).
99.05/99.22	tff('4', plain,
99.05/99.22	    ![X308 : $tType, X309 : $tType, X310 : $tType, 
99.05/99.22	      X311 : fun(X310, fun(X308, X309)), X312 : X310, X313 : X308]:
99.05/99.22	      app_encode_app(X310, X309, 
99.05/99.22	        app_encode_app(fun(X310, X309), app_encode_fun(X310, X309), 
99.05/99.22	          aa(X310, X309), 
99.05/99.22	          app_encode_app(X308, fun(X310, X309), 
99.05/99.22	            app_encode_app(fun(X310, fun(X308, X309)), 
99.05/99.22	              app_encode_fun(X308, fun(X310, X309)), 
99.05/99.22	              combc(X310, X308, X309), X311), X313)), X312)
99.05/99.22	       = app_encode_app(X308, X309, 
99.05/99.22	           app_encode_app(fun(X308, X309), app_encode_fun(X308, X309), 
99.05/99.22	             aa(X308, X309), 
99.05/99.22	             app_encode_app(X310, fun(X308, X309), 
99.05/99.22	               app_encode_app(fun(X310, fun(X308, X309)), 
99.05/99.22	                 app_encode_fun(X310, fun(X308, X309)), 
99.05/99.22	                 aa(X310, fun(X308, X309)), X311), X312)), X313),
99.05/99.22	    inference('cnf', [status(esa)], [zf_stmt_163])).
99.05/99.22	tff('5', plain,
99.05/99.22	    ![X0 : type, X1 : dB]:
99.05/99.22	      (app_encode_app(bool, $o, pp, 
99.05/99.22	         app_encode_app(dB, bool, 
99.05/99.22	           app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
99.05/99.22	             aa(dB, bool), 
99.05/99.22	             app_encode_app(type, fun(dB, bool), 
99.05/99.22	               app_encode_app(fun(dB, fun(type, bool)), 
99.05/99.22	                 app_encode_fun(type, fun(dB, bool)), combc(dB, type, bool), 
99.05/99.22	                 app_encode_app(fun(nat, type), fun(dB, fun(type, bool)), 
99.05/99.22	                   typing, 
99.05/99.22	                   app_encode_app(type, fun(nat, type), 
99.05/99.22	                     app_encode_app(nat, 
99.05/99.22	                       app_encode_fun(type, fun(nat, type)), 
99.05/99.22	                       app_encode_app(fun(nat, type), 
99.05/99.22	                         app_encode_fun(nat, 
99.05/99.22	                           app_encode_fun(type, fun(nat, type))), 
99.05/99.22	                         shift(type), e), zero_zero(nat)), 
99.05/99.22	                     app_encode_app(type, type, 
99.05/99.22	                       app_encode_app(list(type), 
99.05/99.22	                         app_encode_fun(type, type), 
99.05/99.22	                         app_encode_app(fun(type, fun(type, type)), 
99.05/99.22	                           app_encode_fun(list(type), 
99.05/99.22	                             app_encode_fun(type, type)), foldr(type, type), 
99.05/99.22	                           fun1), ts), t)))), X0)), 
99.05/99.22	           app_encode_app(list(dB), dB, 
99.05/99.22	             app_encode_app(dB, app_encode_fun(list(dB), dB), 
99.05/99.22	               app_encode_app(fun(dB, fun(dB, dB)), 
99.05/99.22	                 app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
99.05/99.22	                 foldl(dB, dB), app), X1), 
99.05/99.22	             app_encode_app(list(dB), list(dB), 
99.05/99.22	               app_encode_app(fun(dB, dB), 
99.05/99.22	                 app_encode_fun(list(dB), list(dB)), map(dB, dB), 
99.05/99.22	                 app_encode_app(nat, fun(dB, dB), 
99.05/99.22	                   app_encode_app(fun(dB, fun(nat, dB)), 
99.05/99.22	                     app_encode_fun(nat, fun(dB, dB)), combc(dB, nat, dB), 
99.05/99.22	                     lift), zero_zero(nat))), 
99.05/99.22	               app_encode_app(list(dB), list(dB), 
99.05/99.22	                 app_encode_app(fun(dB, dB), 
99.05/99.22	                   app_encode_fun(list(dB), list(dB)), map(dB, dB), 
99.05/99.22	                   app_encode_app(nat, fun(dB, dB), 
99.05/99.22	                     app_encode_app(fun(dB, fun(nat, dB)), 
99.05/99.22	                       app_encode_fun(nat, fun(dB, dB)), combc(dB, nat, dB), 
99.05/99.22	                       app_encode_app(dB, fun(dB, fun(nat, dB)), 
99.05/99.22	                         app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
99.05/99.22	                           app_encode_fun(dB, fun(dB, fun(nat, dB))), 
99.05/99.22	                           combc(dB, dB, fun(nat, dB)), subst), u)), i)), as)))))
99.05/99.22	       | ~ app_encode_app(bool, $o, pp, 
99.05/99.22	             app_encode_app(dB, bool, 
99.05/99.22	               app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
99.05/99.22	                 aa(dB, bool), 
99.05/99.22	                 app_encode_app(type, fun(dB, bool), 
99.05/99.22	                   app_encode_app(fun(dB, fun(type, bool)), 
99.05/99.22	                     app_encode_fun(type, fun(dB, bool)), 
99.05/99.22	                     combc(dB, type, bool), 
99.05/99.22	                     app_encode_app(fun(nat, type), 
99.05/99.22	                       fun(dB, fun(type, bool)), typing, 
99.05/99.22	                       app_encode_app(type, fun(nat, type), 
99.05/99.22	                         app_encode_app(nat, 
99.05/99.22	                           app_encode_fun(type, fun(nat, type)), 
99.05/99.22	                           app_encode_app(fun(nat, type), 
99.05/99.22	                             app_encode_fun(nat, 
99.05/99.22	                               app_encode_fun(type, fun(nat, type))), 
99.05/99.22	                             shift(type), e), zero_zero(nat)), 
99.05/99.22	                         app_encode_app(type, type, 
99.05/99.22	                           app_encode_app(list(type), 
99.05/99.22	                             app_encode_fun(type, type), 
99.05/99.22	                             app_encode_app(fun(type, fun(type, type)), 
99.05/99.22	                               app_encode_fun(list(type), 
99.05/99.22	                                 app_encode_fun(type, type)), 
99.05/99.22	                               foldr(type, type), fun1), ts), t)))), 
99.05/99.22	                   app_encode_app(type, type, 
99.05/99.22	                     app_encode_app(list(type), app_encode_fun(type, type), 
99.05/99.22	                       app_encode_app(fun(type, fun(type, type)), 
99.05/99.22	                         app_encode_fun(list(type), 
99.05/99.22	                           app_encode_fun(type, type)), foldr(type, type), 
99.05/99.22	                         fun1), ts), X0))), X1))),
99.05/99.22	    inference('demod', [status(thm)], ['3', '4', '4'])).
99.05/99.22	tff(zf_stmt_173, conjecture,
99.05/99.22	  (app_encode_app(bool,$o,pp,
99.05/99.22	                  app_encode_app(type,bool,
99.05/99.22	                                 app_encode_app(fun(type,bool),
99.05/99.22	                                                app_encode_fun(type,bool),
99.05/99.22	                                                aa(type,bool),
99.05/99.22	                                                app_encode_app(dB,
99.05/99.22	                                                               fun(type,bool),
99.05/99.22	                                                               app_encode_app(
99.05/99.22	                                                               fun(dB,
99.05/99.22	                                                                   fun(
99.05/99.22	                                                                   type,bool)),
99.05/99.22	                                                               app_encode_fun(
99.05/99.22	                                                               dB,
99.05/99.22	                                                               fun(type,bool)),
99.05/99.22	                                                               aa(dB,
99.05/99.22	                                                                  fun(
99.05/99.22	                                                                  type,bool)),
99.05/99.22	                                                               app_encode_app(
99.05/99.22	                                                               fun(nat,type),
99.05/99.22	                                                               fun(dB,
99.05/99.22	                                                                   fun(
99.05/99.22	                                                                   type,bool)),
99.05/99.22	                                                               typing,
99.05/99.22	                                                               app_encode_app(
99.05/99.22	                                                               type,
99.05/99.22	                                                               fun(nat,type),
99.05/99.22	                                                               app_encode_app(
99.05/99.22	                                                               nat,
99.05/99.22	                                                               app_encode_fun(
99.05/99.22	                                                               type,
99.05/99.22	                                                               fun(nat,type)),
99.05/99.22	                                                               app_encode_app(
99.05/99.22	                                                               fun(nat,type),
99.05/99.22	                                                               app_encode_fun(
99.05/99.22	                                                               nat,
99.05/99.22	                                                               app_encode_fun(
99.05/99.22	                                                               type,
99.05/99.22	                                                               fun(nat,type))),
99.05/99.22	                                                               shift(type),e),
99.05/99.22	                                                               zero_zero(nat)),
99.05/99.22	                                                               app_encode_app(
99.05/99.22	                                                               type,type,
99.05/99.22	                                                               app_encode_app(
99.05/99.22	                                                               list(type),
99.05/99.22	                                                               app_encode_fun(
99.05/99.22	                                                               type,type),
99.05/99.22	                                                               app_encode_app(
99.05/99.22	                                                               fun(type,
99.05/99.22	                                                                   fun(
99.05/99.22	                                                                   type,type)),
99.05/99.22	                                                               app_encode_fun(
99.05/99.22	                                                               list(type),
99.05/99.22	                                                               app_encode_fun(
99.05/99.22	                                                               type,type)),
99.05/99.22	                                                               foldr(
99.05/99.22	                                                               type,type),
99.05/99.22	                                                               fun1),ts),t)))),
99.05/99.22	                                                               app_encode_app(
99.05/99.22	                                                               list(dB),dB,
99.05/99.22	                                                               app_encode_app(
99.05/99.22	                                                               dB,
99.05/99.22	                                                               app_encode_fun(
99.05/99.22	                                                               list(dB),dB),
99.05/99.22	                                                               app_encode_app(
99.05/99.22	                                                               fun(dB,
99.05/99.22	                                                                   fun(dB,dB)),
99.05/99.22	                                                               app_encode_fun(
99.05/99.22	                                                               dB,
99.05/99.22	                                                               app_encode_fun(
99.05/99.22	                                                               list(dB),dB)),
99.05/99.22	                                                               foldl(dB,dB),
99.05/99.22	                                                               app),
99.05/99.22	                                                               app_encode_app(
99.05/99.22	                                                               nat,dB,var,
99.05/99.22	                                                               zero_zero(nat))),
99.05/99.22	                                                               app_encode_app(
99.05/99.22	                                                               list(dB),
99.05/99.22	                                                               list(dB),
99.05/99.22	                                                               app_encode_app(
99.05/99.22	                                                               fun(dB,dB),
99.05/99.22	                                                               app_encode_fun(
99.05/99.22	                                                               list(dB),
99.05/99.22	                                                               list(dB)),
99.05/99.22	                                                               map(dB,dB),
99.05/99.22	                                                               app_encode_app(
99.05/99.22	                                                               nat,
99.05/99.22	                                                               fun(dB,dB),
99.05/99.22	                                                               app_encode_app(
99.05/99.22	                                                               fun(dB,
99.05/99.22	                                                                   fun(
99.05/99.22	                                                                   nat,dB)),
99.05/99.22	                                                               app_encode_fun(
99.05/99.22	                                                               nat,fun(dB,dB)),
99.05/99.22	                                                               combc(
99.05/99.22	                                                               dB,nat,dB),
99.05/99.22	                                                               lift),
99.05/99.22	                                                               zero_zero(nat))),
99.05/99.22	                                                               app_encode_app(
99.05/99.22	                                                               list(dB),
99.05/99.22	                                                               list(dB),
99.05/99.22	                                                               app_encode_app(
99.05/99.22	                                                               fun(dB,dB),
99.05/99.22	                                                               app_encode_fun(
99.05/99.22	                                                               list(dB),
99.05/99.22	                                                               list(dB)),
99.05/99.22	                                                               map(dB,dB),
99.05/99.22	                                                               app_encode_app(
99.05/99.22	                                                               nat,
99.05/99.22	                                                               fun(dB,dB),
99.05/99.22	                                                               app_encode_app(
99.05/99.22	                                                               fun(dB,
99.05/99.22	                                                                   fun(
99.05/99.22	                                                                   nat,dB)),
99.05/99.22	                                                               app_encode_fun(
99.05/99.22	                                                               nat,fun(dB,dB)),
99.05/99.22	                                                               combc(
99.05/99.22	                                                               dB,nat,dB),
99.05/99.22	                                                               app_encode_app(
99.05/99.22	                                                               dB,
99.05/99.22	                                                               fun(dB,
99.05/99.22	                                                                   fun(
99.05/99.22	                                                                   nat,dB)),
99.05/99.22	                                                               app_encode_app(
99.05/99.22	                                                               fun(dB,
99.05/99.22	                                                                   fun(
99.05/99.22	                                                                   dB,
99.05/99.22	                                                                   fun(
99.05/99.22	                                                                   nat,dB))),
99.05/99.22	                                                               app_encode_fun(
99.05/99.22	                                                               dB,
99.05/99.22	                                                               fun(dB,
99.05/99.22	                                                                   fun(
99.05/99.22	                                                                   nat,dB))),
99.05/99.22	                                                               combc(
99.05/99.22	                                                               dB,dB,
99.05/99.22	                                                               fun(nat,dB)),
99.05/99.22	                                                               subst),u)),i)),
99.05/99.22	                                                               as))))),
99.05/99.22	                                 t)))).
99.05/99.22	tff(zf_stmt_0, negated_conjecture,
99.05/99.22	  (~
99.05/99.22	    app_encode_app(bool,$o,pp,
99.05/99.22	                   app_encode_app(type,bool,
99.05/99.22	                                  app_encode_app(fun(type,bool),
99.05/99.22	                                                 app_encode_fun(type,bool),
99.05/99.22	                                                 aa(type,bool),
99.05/99.22	                                                 app_encode_app(dB,
99.05/99.22	                                                                fun(type,bool),
99.05/99.22	                                                                app_encode_app(
99.05/99.22	                                                                fun(dB,
99.05/99.22	                                                                    fun(
99.05/99.22	                                                                    type,bool)),
99.05/99.22	                                                                app_encode_fun(
99.05/99.22	                                                                dB,
99.05/99.22	                                                                fun(type,bool)),
99.05/99.22	                                                                aa(dB,
99.05/99.22	                                                                   fun(
99.05/99.22	                                                                   type,bool)),
99.05/99.22	                                                                app_encode_app(
99.05/99.22	                                                                fun(nat,type),
99.05/99.22	                                                                fun(dB,
99.05/99.22	                                                                    fun(
99.05/99.22	                                                                    type,bool)),
99.05/99.22	                                                                typing,
99.05/99.22	                                                                app_encode_app(
99.05/99.22	                                                                type,
99.05/99.22	                                                                fun(nat,type),
99.05/99.22	                                                                app_encode_app(
99.05/99.22	                                                                nat,
99.05/99.22	                                                                app_encode_fun(
99.05/99.22	                                                                type,
99.05/99.22	                                                                fun(nat,type)),
99.05/99.22	                                                                app_encode_app(
99.05/99.22	                                                                fun(nat,type),
99.05/99.22	                                                                app_encode_fun(
99.05/99.22	                                                                nat,
99.05/99.22	                                                                app_encode_fun(
99.05/99.22	                                                                type,
99.05/99.22	                                                                fun(nat,type))),
99.05/99.22	                                                                shift(type),e),
99.05/99.22	                                                                zero_zero(
99.05/99.22	                                                                nat)),
99.05/99.22	                                                                app_encode_app(
99.05/99.22	                                                                type,type,
99.05/99.22	                                                                app_encode_app(
99.05/99.22	                                                                list(type),
99.05/99.22	                                                                app_encode_fun(
99.05/99.22	                                                                type,type),
99.05/99.22	                                                                app_encode_app(
99.05/99.22	                                                                fun(type,
99.05/99.22	                                                                    fun(
99.05/99.22	                                                                    type,type)),
99.05/99.22	                                                                app_encode_fun(
99.05/99.22	                                                                list(type),
99.05/99.22	                                                                app_encode_fun(
99.05/99.22	                                                                type,type)),
99.05/99.22	                                                                foldr(
99.05/99.22	                                                                type,type),
99.05/99.22	                                                                fun1),ts),t)))),
99.05/99.22	                                                                app_encode_app(
99.05/99.22	                                                                list(dB),dB,
99.05/99.22	                                                                app_encode_app(
99.05/99.22	                                                                dB,
99.05/99.22	                                                                app_encode_fun(
99.05/99.22	                                                                list(dB),dB),
99.05/99.22	                                                                app_encode_app(
99.05/99.22	                                                                fun(dB,
99.05/99.22	                                                                    fun(
99.05/99.22	                                                                    dB,dB)),
99.05/99.22	                                                                app_encode_fun(
99.05/99.22	                                                                dB,
99.05/99.22	                                                                app_encode_fun(
99.05/99.22	                                                                list(dB),dB)),
99.05/99.22	                                                                foldl(dB,dB),
99.05/99.22	                                                                app),
99.05/99.22	                                                                app_encode_app(
99.05/99.22	                                                                nat,dB,var,
99.05/99.22	                                                                zero_zero(
99.05/99.22	                                                                nat))),
99.05/99.22	                                                                app_encode_app(
99.05/99.22	                                                                list(dB),
99.05/99.22	                                                                list(dB),
99.05/99.22	                                                                app_encode_app(
99.05/99.22	                                                                fun(dB,dB),
99.05/99.22	                                                                app_encode_fun(
99.05/99.22	                                                                list(dB),
99.05/99.22	                                                                list(dB)),
99.05/99.22	                                                                map(dB,dB),
99.05/99.22	                                                                app_encode_app(
99.05/99.22	                                                                nat,
99.05/99.22	                                                                fun(dB,dB),
99.05/99.22	                                                                app_encode_app(
99.05/99.22	                                                                fun(dB,
99.05/99.22	                                                                    fun(
99.05/99.22	                                                                    nat,dB)),
99.05/99.22	                                                                app_encode_fun(
99.05/99.22	                                                                nat,
99.05/99.22	                                                                fun(dB,dB)),
99.05/99.22	                                                                combc(
99.05/99.22	                                                                dB,nat,dB),
99.05/99.22	                                                                lift),
99.05/99.22	                                                                zero_zero(
99.05/99.22	                                                                nat))),
99.05/99.22	                                                                app_encode_app(
99.05/99.22	                                                                list(dB),
99.05/99.22	                                                                list(dB),
99.05/99.22	                                                                app_encode_app(
99.05/99.22	                                                                fun(dB,dB),
99.05/99.22	                                                                app_encode_fun(
99.05/99.22	                                                                list(dB),
99.05/99.22	                                                                list(dB)),
99.05/99.22	                                                                map(dB,dB),
99.05/99.22	                                                                app_encode_app(
99.05/99.22	                                                                nat,
99.05/99.22	                                                                fun(dB,dB),
99.05/99.22	                                                                app_encode_app(
99.05/99.22	                                                                fun(dB,
99.05/99.22	                                                                    fun(
99.05/99.22	                                                                    nat,dB)),
99.05/99.22	                                                                app_encode_fun(
99.05/99.22	                                                                nat,
99.05/99.22	                                                                fun(dB,dB)),
99.05/99.22	                                                                combc(
99.05/99.22	                                                                dB,nat,dB),
99.05/99.22	                                                                app_encode_app(
99.05/99.22	                                                                dB,
99.05/99.22	                                                                fun(dB,
99.05/99.22	                                                                    fun(
99.05/99.22	                                                                    nat,dB)),
99.05/99.22	                                                                app_encode_app(
99.05/99.22	                                                                fun(dB,
99.05/99.22	                                                                    fun(
99.05/99.22	                                                                    dB,
99.05/99.22	                                                                    fun(
99.05/99.22	                                                                    nat,dB))),
99.05/99.22	                                                                app_encode_fun(
99.05/99.22	                                                                dB,
99.05/99.22	                                                                fun(dB,
99.05/99.22	                                                                    fun(
99.05/99.22	                                                                    nat,dB))),
99.05/99.22	                                                                combc(
99.05/99.22	                                                                dB,dB,
99.05/99.22	                                                                fun(nat,dB)),
99.05/99.22	                                                                subst),u)),i)),
99.05/99.22	                                                                as))))),
99.05/99.22	                                  t)))).
99.05/99.22	tff('6', plain,
99.05/99.22	    ~ app_encode_app(bool, $o, pp, 
99.05/99.22	        app_encode_app(type, bool, 
99.05/99.22	          app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
99.05/99.22	            aa(type, bool), 
99.05/99.22	            app_encode_app(dB, fun(type, bool), 
99.05/99.22	              app_encode_app(fun(dB, fun(type, bool)), 
99.05/99.22	                app_encode_fun(dB, fun(type, bool)), 
99.05/99.22	                aa(dB, fun(type, bool)), 
99.05/99.22	                app_encode_app(fun(nat, type), fun(dB, fun(type, bool)), 
99.05/99.22	                  typing, 
99.05/99.22	                  app_encode_app(type, fun(nat, type), 
99.05/99.22	                    app_encode_app(nat, 
99.05/99.22	                      app_encode_fun(type, fun(nat, type)), 
99.05/99.22	                      app_encode_app(fun(nat, type), 
99.05/99.22	                        app_encode_fun(nat, 
99.05/99.22	                          app_encode_fun(type, fun(nat, type))), 
99.05/99.22	                        shift(type), e), zero_zero(nat)), 
99.05/99.22	                    app_encode_app(type, type, 
99.05/99.22	                      app_encode_app(list(type), app_encode_fun(type, type), 
99.05/99.22	                        app_encode_app(fun(type, fun(type, type)), 
99.05/99.22	                          app_encode_fun(list(type), 
99.05/99.22	                            app_encode_fun(type, type)), foldr(type, type), 
99.05/99.22	                          fun1), ts), t)))), 
99.05/99.22	              app_encode_app(list(dB), dB, 
99.05/99.22	                app_encode_app(dB, app_encode_fun(list(dB), dB), 
99.05/99.22	                  app_encode_app(fun(dB, fun(dB, dB)), 
99.05/99.22	                    app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
99.05/99.22	                    foldl(dB, dB), app), 
99.05/99.22	                  app_encode_app(nat, dB, var, zero_zero(nat))), 
99.05/99.22	                app_encode_app(list(dB), list(dB), 
99.05/99.22	                  app_encode_app(fun(dB, dB), 
99.05/99.22	                    app_encode_fun(list(dB), list(dB)), map(dB, dB), 
99.05/99.22	                    app_encode_app(nat, fun(dB, dB), 
99.05/99.22	                      app_encode_app(fun(dB, fun(nat, dB)), 
99.05/99.22	                        app_encode_fun(nat, fun(dB, dB)), 
99.05/99.22	                        combc(dB, nat, dB), lift), zero_zero(nat))), 
99.05/99.22	                  app_encode_app(list(dB), list(dB), 
99.05/99.22	                    app_encode_app(fun(dB, dB), 
99.05/99.22	                      app_encode_fun(list(dB), list(dB)), map(dB, dB), 
99.05/99.22	                      app_encode_app(nat, fun(dB, dB), 
99.05/99.22	                        app_encode_app(fun(dB, fun(nat, dB)), 
99.05/99.22	                          app_encode_fun(nat, fun(dB, dB)), 
99.05/99.22	                          combc(dB, nat, dB), 
99.05/99.22	                          app_encode_app(dB, fun(dB, fun(nat, dB)), 
99.05/99.22	                            app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
99.05/99.22	                              app_encode_fun(dB, fun(dB, fun(nat, dB))), 
99.05/99.22	                              combc(dB, dB, fun(nat, dB)), subst), u)), i)), 
99.05/99.22	                    as))))), t)),
99.05/99.22	    inference('cnf', [status(esa)], [zf_stmt_0])).
99.05/99.22	tff('7', plain,
99.05/99.22	    ~ app_encode_app(bool, $o, pp, 
99.05/99.22	        app_encode_app(dB, bool, 
99.05/99.22	          app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
99.05/99.22	            aa(dB, bool), 
99.05/99.22	            app_encode_app(type, fun(dB, bool), 
99.05/99.22	              app_encode_app(fun(dB, fun(type, bool)), 
99.05/99.22	                app_encode_fun(type, fun(dB, bool)), combc(dB, type, bool), 
99.05/99.22	                app_encode_app(fun(nat, type), fun(dB, fun(type, bool)), 
99.05/99.22	                  typing, 
99.05/99.22	                  app_encode_app(type, fun(nat, type), 
99.05/99.22	                    app_encode_app(nat, 
99.05/99.22	                      app_encode_fun(type, fun(nat, type)), 
99.05/99.22	                      app_encode_app(fun(nat, type), 
99.05/99.22	                        app_encode_fun(nat, 
99.05/99.22	                          app_encode_fun(type, fun(nat, type))), 
99.05/99.22	                        shift(type), e), zero_zero(nat)), 
99.05/99.22	                    app_encode_app(type, type, 
99.05/99.22	                      app_encode_app(list(type), app_encode_fun(type, type), 
99.05/99.22	                        app_encode_app(fun(type, fun(type, type)), 
99.05/99.22	                          app_encode_fun(list(type), 
99.05/99.22	                            app_encode_fun(type, type)), foldr(type, type), 
99.05/99.22	                          fun1), ts), t)))), t)), 
99.05/99.22	          app_encode_app(list(dB), dB, 
99.05/99.22	            app_encode_app(dB, app_encode_fun(list(dB), dB), 
99.05/99.22	              app_encode_app(fun(dB, fun(dB, dB)), 
99.05/99.22	                app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
99.05/99.22	                foldl(dB, dB), app), 
99.05/99.22	              app_encode_app(nat, dB, var, zero_zero(nat))), 
99.05/99.22	            app_encode_app(list(dB), list(dB), 
99.05/99.22	              app_encode_app(fun(dB, dB), 
99.05/99.22	                app_encode_fun(list(dB), list(dB)), map(dB, dB), 
99.05/99.22	                app_encode_app(nat, fun(dB, dB), 
99.05/99.22	                  app_encode_app(fun(dB, fun(nat, dB)), 
99.05/99.22	                    app_encode_fun(nat, fun(dB, dB)), combc(dB, nat, dB), 
99.05/99.22	                    lift), zero_zero(nat))), 
99.05/99.22	              app_encode_app(list(dB), list(dB), 
99.05/99.22	                app_encode_app(fun(dB, dB), 
99.05/99.22	                  app_encode_fun(list(dB), list(dB)), map(dB, dB), 
99.05/99.22	                  app_encode_app(nat, fun(dB, dB), 
99.05/99.22	                    app_encode_app(fun(dB, fun(nat, dB)), 
99.05/99.22	                      app_encode_fun(nat, fun(dB, dB)), combc(dB, nat, dB), 
99.05/99.22	                      app_encode_app(dB, fun(dB, fun(nat, dB)), 
99.05/99.22	                        app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
99.05/99.22	                          app_encode_fun(dB, fun(dB, fun(nat, dB))), 
99.05/99.22	                          combc(dB, dB, fun(nat, dB)), subst), u)), i)), as))))),
99.05/99.22	    inference('demod', [status(thm)], ['6', '4'])).
99.05/99.22	tff('8', plain,
99.05/99.22	    (~ $true
99.05/99.22	     | ~ app_encode_app(bool, $o, pp, 
99.05/99.22	           app_encode_app(dB, bool, 
99.05/99.22	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
99.05/99.22	               aa(dB, bool), 
99.05/99.22	               app_encode_app(type, fun(dB, bool), 
99.05/99.22	                 app_encode_app(fun(dB, fun(type, bool)), 
99.05/99.22	                   app_encode_fun(type, fun(dB, bool)), 
99.05/99.22	                   combc(dB, type, bool), 
99.05/99.22	                   app_encode_app(fun(nat, type), fun(dB, fun(type, bool)), 
99.05/99.22	                     typing, 
99.05/99.22	                     app_encode_app(type, fun(nat, type), 
99.05/99.22	                       app_encode_app(nat, 
99.05/99.22	                         app_encode_fun(type, fun(nat, type)), 
99.05/99.22	                         app_encode_app(fun(nat, type), 
99.05/99.22	                           app_encode_fun(nat, 
99.05/99.22	                             app_encode_fun(type, fun(nat, type))), 
99.05/99.22	                           shift(type), e), zero_zero(nat)), 
99.05/99.22	                       app_encode_app(type, type, 
99.05/99.22	                         app_encode_app(list(type), 
99.05/99.22	                           app_encode_fun(type, type), 
99.05/99.22	                           app_encode_app(fun(type, fun(type, type)), 
99.05/99.22	                             app_encode_fun(list(type), 
99.05/99.22	                               app_encode_fun(type, type)), 
99.05/99.22	                             foldr(type, type), fun1), ts), t)))), 
99.05/99.22	                 app_encode_app(type, type, 
99.05/99.22	                   app_encode_app(list(type), app_encode_fun(type, type), 
99.05/99.22	                     app_encode_app(fun(type, fun(type, type)), 
99.05/99.22	                       app_encode_fun(list(type), app_encode_fun(type, type)), 
99.05/99.22	                       foldr(type, type), fun1), ts), t))), 
99.05/99.22	             app_encode_app(nat, dB, var, zero_zero(nat))))),
99.05/99.22	    inference('sup-', [status(thm)], ['5', '7'])).
99.05/99.22	tff(zf_stmt_95, axiom,
99.05/99.22	  (![A:$tType,Ta1:A,Eb:fun(nat,A),J:nat,Ib:nat]:
99.05/99.22	     ((Ib = J) =>
99.05/99.22	      (app_encode_app(nat,A,
99.05/99.22	                      app_encode_app(fun(nat,A),app_encode_fun(nat,A),
99.05/99.22	                                     aa(nat,A),
99.05/99.22	                                     app_encode_app(A,fun(nat,A),
99.05/99.22	                                                    app_encode_app(nat,
99.05/99.22	                                                                   app_encode_fun(
99.05/99.22	                                                                   A,
99.05/99.22	                                                                   fun(nat,A)),
99.05/99.22	                                                                   app_encode_app(
99.05/99.22	                                                                   fun(nat,A),
99.05/99.22	                                                                   app_encode_fun(
99.05/99.22	                                                                   nat,
99.05/99.22	                                                                   app_encode_fun(
99.05/99.22	                                                                   A,
99.05/99.22	                                                                   fun(nat,A))),
99.05/99.22	                                                                   shift(A),
99.05/99.22	                                                                   Eb),Ib),
99.05/99.22	                                                    Ta1)),
99.05/99.22	                      J) =
99.05/99.22	       Ta1)))).
99.05/99.22	tff('9', plain,
99.05/99.22	    ![X74 : $tType, X75 : X74, X76 : fun(nat, X74), X77 : nat, X78 : nat]:
99.05/99.22	      (app_encode_app(nat, X74, 
99.05/99.22	         app_encode_app(fun(nat, X74), app_encode_fun(nat, X74), 
99.05/99.22	           aa(nat, X74), 
99.05/99.22	           app_encode_app(X74, fun(nat, X74), 
99.05/99.22	             app_encode_app(nat, app_encode_fun(X74, fun(nat, X74)), 
99.05/99.22	               app_encode_app(fun(nat, X74), 
99.05/99.22	                 app_encode_fun(nat, app_encode_fun(X74, fun(nat, X74))), 
99.05/99.22	                 shift(X74), X76), X77), X75)), X78)
99.05/99.22	        = X75
99.05/99.22	       | X77 != X78),
99.05/99.22	    inference('cnf', [status(esa)], [zf_stmt_95])).
99.05/99.22	tff('10', plain,
99.05/99.22	    ![X74 : $tType, X75 : X74, X76 : fun(nat, X74), X78 : nat]:
99.05/99.22	      app_encode_app(nat, X74, 
99.05/99.22	        app_encode_app(fun(nat, X74), app_encode_fun(nat, X74), 
99.05/99.22	          aa(nat, X74), 
99.05/99.22	          app_encode_app(X74, fun(nat, X74), 
99.05/99.22	            app_encode_app(nat, app_encode_fun(X74, fun(nat, X74)), 
99.05/99.22	              app_encode_app(fun(nat, X74), 
99.05/99.22	                app_encode_fun(nat, app_encode_fun(X74, fun(nat, X74))), 
99.05/99.22	                shift(X74), X76), X78), X75)), X78)
99.05/99.22	       = X75,
99.05/99.22	    inference('simplify', [status(thm)], ['9'])).
99.05/99.22	tff(zf_stmt_75, axiom,
99.05/99.22	  (![Ta1:type,X1:nat,Env:fun(nat,type)]:
99.05/99.22	     ((app_encode_app(nat,type,
99.05/99.22	                      app_encode_app(fun(nat,type),app_encode_fun(nat,type),
99.05/99.22	                                     aa(nat,type),Env),
99.05/99.22	                      X1) =
99.05/99.22	       Ta1) =>
99.05/99.22	      app_encode_app(bool,$o,pp,
99.05/99.22	                     app_encode_app(type,bool,
99.05/99.22	                                    app_encode_app(fun(type,bool),
99.05/99.22	                                                   app_encode_fun(type,bool),
99.05/99.22	                                                   aa(type,bool),
99.05/99.22	                                                   app_encode_app(dB,
99.05/99.22	                                                                  fun(
99.05/99.22	                                                                  type,bool),
99.05/99.22	                                                                  app_encode_app(
99.05/99.22	                                                                  fun(
99.05/99.22	                                                                  dB,
99.05/99.22	                                                                  fun(
99.05/99.22	                                                                  type,bool)),
99.05/99.22	                                                                  app_encode_fun(
99.05/99.22	                                                                  dB,
99.05/99.22	                                                                  fun(
99.05/99.22	                                                                  type,bool)),
99.05/99.22	                                                                  aa(
99.05/99.22	                                                                  dB,
99.05/99.22	                                                                  fun(
99.05/99.22	                                                                  type,bool)),
99.05/99.22	                                                                  app_encode_app(
99.05/99.22	                                                                  fun(
99.05/99.22	                                                                  nat,type),
99.05/99.22	                                                                  fun(
99.05/99.22	                                                                  dB,
99.05/99.22	                                                                  fun(
99.05/99.22	                                                                  type,bool)),
99.05/99.22	                                                                  typing,Env)),
99.05/99.22	                                                                  app_encode_app(
99.05/99.22	                                                                  nat,dB,var,
99.05/99.22	                                                                  X1))),
99.05/99.22	                                    Ta1))))).
99.05/99.22	tff('11', plain,
99.05/99.22	    ![X25 : fun(nat, type), X26 : nat, X27 : type]:
99.05/99.22	      (app_encode_app(bool, $o, pp, 
99.05/99.22	         app_encode_app(type, bool, 
99.05/99.22	           app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
99.05/99.22	             aa(type, bool), 
99.05/99.22	             app_encode_app(dB, fun(type, bool), 
99.05/99.22	               app_encode_app(fun(dB, fun(type, bool)), 
99.05/99.22	                 app_encode_fun(dB, fun(type, bool)), 
99.05/99.22	                 aa(dB, fun(type, bool)), 
99.05/99.22	                 app_encode_app(fun(nat, type), fun(dB, fun(type, bool)), 
99.05/99.22	                   typing, X25)), app_encode_app(nat, dB, var, X26))), X27))
99.05/99.22	       | app_encode_app(nat, type, 
99.05/99.22	           app_encode_app(fun(nat, type), app_encode_fun(nat, type), 
99.05/99.22	             aa(nat, type), X25), X26)
99.05/99.22	          != X27),
99.05/99.22	    inference('cnf', [status(esa)], [zf_stmt_75])).
99.05/99.22	tff('12', plain,
99.05/99.22	    ![X25 : fun(nat, type), X26 : nat]:
99.05/99.22	      app_encode_app(bool, $o, pp, 
99.05/99.22	        app_encode_app(type, bool, 
99.05/99.22	          app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
99.05/99.22	            aa(type, bool), 
99.05/99.22	            app_encode_app(dB, fun(type, bool), 
99.05/99.22	              app_encode_app(fun(dB, fun(type, bool)), 
99.05/99.22	                app_encode_fun(dB, fun(type, bool)), 
99.05/99.22	                aa(dB, fun(type, bool)), 
99.05/99.22	                app_encode_app(fun(nat, type), fun(dB, fun(type, bool)), 
99.05/99.22	                  typing, X25)), app_encode_app(nat, dB, var, X26))), 
99.05/99.22	          app_encode_app(nat, type, 
99.05/99.22	            app_encode_app(fun(nat, type), app_encode_fun(nat, type), 
99.05/99.22	              aa(nat, type), X25), X26))),
99.05/99.22	    inference('simplify', [status(thm)], ['11'])).
99.05/99.22	tff(zf_stmt_170, axiom, (![P:bool]: ((P = fTrue) | (P = fFalse)))).
99.05/99.22	tff('13', plain, ![X328 : bool]: (X328 = fTrue | X328 = fFalse),
99.05/99.22	    inference('cnf', [status(esa)], [zf_stmt_170])).
99.05/99.22	tff(zf_stmt_159, axiom, (~app_encode_app(bool,$o,pp,fFalse))).
99.05/99.22	tff('14', plain, ~ app_encode_app(bool, $o, pp, fFalse),
99.05/99.22	    inference('cnf', [status(esa)], [zf_stmt_159])).
99.05/99.22	tff('15', plain,
99.05/99.22	    ![X0 : bool]: (~ app_encode_app(bool, $o, pp, X0) | X0 = fTrue),
99.05/99.22	    inference('sup-', [status(thm)], ['13', '14'])).
99.05/99.22	tff('16', plain,
99.05/99.22	    ![X0 : nat, X1 : fun(nat, type)]:
99.05/99.22	      (~ $true
99.05/99.22	       | app_encode_app(type, bool, 
99.05/99.22	           app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
99.05/99.22	             aa(type, bool), 
99.05/99.22	             app_encode_app(dB, fun(type, bool), 
99.05/99.22	               app_encode_app(fun(dB, fun(type, bool)), 
99.05/99.22	                 app_encode_fun(dB, fun(type, bool)), 
99.05/99.22	                 aa(dB, fun(type, bool)), 
99.05/99.22	                 app_encode_app(fun(nat, type), fun(dB, fun(type, bool)), 
99.05/99.22	                   typing, X1)), app_encode_app(nat, dB, var, X0))), 
99.05/99.22	           app_encode_app(nat, type, 
99.05/99.22	             app_encode_app(fun(nat, type), app_encode_fun(nat, type), 
99.05/99.22	               aa(nat, type), X1), X0))
99.05/99.22	          = fTrue),
99.05/99.22	    inference('sup-', [status(thm)], ['12', '15'])).
99.05/99.22	tff('17', plain,
99.05/99.22	    ![X0 : nat, X1 : fun(nat, type)]:
99.05/99.22	      app_encode_app(type, bool, 
99.05/99.22	        app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
99.05/99.22	          aa(type, bool), 
99.05/99.22	          app_encode_app(dB, fun(type, bool), 
99.05/99.22	            app_encode_app(fun(dB, fun(type, bool)), 
99.05/99.22	              app_encode_fun(dB, fun(type, bool)), aa(dB, fun(type, bool)), 
99.05/99.22	              app_encode_app(fun(nat, type), fun(dB, fun(type, bool)), 
99.05/99.22	                typing, X1)), app_encode_app(nat, dB, var, X0))), 
99.05/99.22	        app_encode_app(nat, type, 
99.05/99.22	          app_encode_app(fun(nat, type), app_encode_fun(nat, type), 
99.05/99.22	            aa(nat, type), X1), X0))
99.05/99.22	       = fTrue,
99.05/99.22	    inference('simplify', [status(thm)], ['16'])).
99.05/99.22	tff('18', plain,
99.05/99.22	    ![X0 : nat, X1 : fun(nat, type)]:
99.05/99.22	      app_encode_app(dB, bool, 
99.05/99.22	        app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
99.05/99.22	          aa(dB, bool), 
99.05/99.22	          app_encode_app(type, fun(dB, bool), 
99.05/99.22	            app_encode_app(fun(dB, fun(type, bool)), 
99.05/99.22	              app_encode_fun(type, fun(dB, bool)), combc(dB, type, bool), 
99.05/99.22	              app_encode_app(fun(nat, type), fun(dB, fun(type, bool)), 
99.05/99.22	                typing, X1)), 
99.05/99.22	            app_encode_app(nat, type, 
99.05/99.22	              app_encode_app(fun(nat, type), app_encode_fun(nat, type), 
99.05/99.22	                aa(nat, type), X1), X0))), app_encode_app(nat, dB, var, X0))
99.05/99.22	       = fTrue,
99.05/99.22	    inference('demod', [status(thm)], ['17', '4'])).
99.05/99.22	tff('19', plain,
99.05/99.22	    ![X0 : type, X1 : nat, X2 : fun(nat, type)]:
99.05/99.22	      app_encode_app(dB, bool, 
99.05/99.22	        app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
99.05/99.22	          aa(dB, bool), 
99.05/99.22	          app_encode_app(type, fun(dB, bool), 
99.05/99.22	            app_encode_app(fun(dB, fun(type, bool)), 
99.05/99.22	              app_encode_fun(type, fun(dB, bool)), combc(dB, type, bool), 
99.05/99.22	              app_encode_app(fun(nat, type), fun(dB, fun(type, bool)), 
99.05/99.22	                typing, 
99.05/99.22	                app_encode_app(type, fun(nat, type), 
99.05/99.22	                  app_encode_app(nat, app_encode_fun(type, fun(nat, type)), 
99.05/99.22	                    app_encode_app(fun(nat, type), 
99.05/99.22	                      app_encode_fun(nat, 
99.05/99.22	                        app_encode_fun(type, fun(nat, type))), shift(type), 
99.05/99.22	                      X2), X1), X0))), X0)), 
99.05/99.22	        app_encode_app(nat, dB, var, X1))
99.05/99.22	       = fTrue,
99.05/99.22	    inference('sup+', [status(thm)], ['10', '18'])).
99.05/99.22	tff(zf_stmt_160, axiom, (app_encode_app(bool,$o,pp,fTrue))).
99.05/99.22	tff('20', plain, app_encode_app(bool, $o, pp, fTrue),
99.05/99.22	    inference('cnf', [status(esa)], [zf_stmt_160])).
99.05/99.22	tff('21', plain, (~ $true | ~ $true),
99.05/99.22	    inference('demod', [status(thm)], ['8', '19', '20'])).
99.05/99.22	tff('22', plain, $false, inference('simplify', [status(thm)], ['21'])).
99.05/99.22	
99.05/99.22	% SZS output end Refutation
99.05/99.23	EOF
