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 $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.20	% Computer   : n173.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 07:18:25 CST 2018
23.10/23.28	% done 1664 iterations in 23.077s
23.10/23.28	% SZS status Theorem for 'stdin'
23.10/23.28	% SZS output start Refutation
23.10/23.29	tff(zf_stmt_174, conjecture,
23.10/23.29	  (![E:fun(nat,type),T:type,U:dB,I:nat]:
23.10/23.29	     ((~
23.10/23.29	        app_encode_app(bool,$o,pp,
23.10/23.29	                       app_encode_app(type,bool,
23.10/23.29	                                      app_encode_app(fun(type,bool),
23.10/23.29	                                                     app_encode_fun(type,bool),
23.10/23.29	                                                     aa(type,bool),
23.10/23.29	                                                     app_encode_app(dB,
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    type,bool),
23.10/23.29	                                                                    app_encode_app(
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    dB,
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    type,bool)),
23.10/23.29	                                                                    app_encode_fun(
23.10/23.29	                                                                    dB,
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    type,bool)),
23.10/23.29	                                                                    aa(
23.10/23.29	                                                                    dB,
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    type,bool)),
23.10/23.29	                                                                    app_encode_app(
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    nat,type),
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    dB,
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    type,bool)),
23.10/23.29	                                                                    app_encode_app(
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    nat,type),
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    dB,
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    type,bool))),
23.10/23.29	                                                                    app_encode_fun(
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    nat,type),
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    dB,
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    type,bool))),
23.10/23.29	                                                                    aa(
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    nat,type),
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    dB,
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    type,bool))),
23.10/23.29	                                                                    typing),
23.10/23.29	                                                                    app_encode_app(
23.10/23.29	                                                                    type,
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    nat,type),
23.10/23.29	                                                                    app_encode_app(
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    type,
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    nat,type)),
23.10/23.29	                                                                    app_encode_fun(
23.10/23.29	                                                                    type,
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    nat,type)),
23.10/23.29	                                                                    aa(
23.10/23.29	                                                                    type,
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    nat,type)),
23.10/23.29	                                                                    app_encode_app(
23.10/23.29	                                                                    nat,
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    type,
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    nat,type)),
23.10/23.29	                                                                    app_encode_app(
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    nat,
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    type,
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    nat,type))),
23.10/23.29	                                                                    app_encode_fun(
23.10/23.29	                                                                    nat,
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    type,
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    nat,type))),
23.10/23.29	                                                                    aa(
23.10/23.29	                                                                    nat,
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    type,
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    nat,type))),
23.10/23.29	                                                                    app_encode_app(
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    nat,type),
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    nat,
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    type,
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    nat,type))),
23.10/23.29	                                                                    app_encode_app(
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    nat,type),
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    nat,
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    type,
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    nat,type)))),
23.10/23.29	                                                                    app_encode_fun(
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    nat,type),
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    nat,
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    type,
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    nat,type)))),
23.10/23.29	                                                                    aa(
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    nat,type),
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    nat,
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    type,
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    nat,type)))),
23.10/23.29	                                                                    shift(
23.10/23.29	                                                                    type)),E)),
23.10/23.29	                                                                    I)),t))),
23.10/23.29	                                                                    a)),
23.10/23.29	                                      T))) | 
23.10/23.29	      (~
23.10/23.29	        app_encode_app(bool,$o,pp,
23.10/23.29	                       app_encode_app(dB,bool,
23.10/23.29	                                      app_encode_app(fun(dB,bool),
23.10/23.29	                                                     app_encode_fun(dB,bool),
23.10/23.29	                                                     aa(dB,bool),it),
23.10/23.29	                                      U))) | 
23.10/23.29	      (~
23.10/23.29	        app_encode_app(bool,$o,pp,
23.10/23.29	                       app_encode_app(type,bool,
23.10/23.29	                                      app_encode_app(fun(type,bool),
23.10/23.29	                                                     app_encode_fun(type,bool),
23.10/23.29	                                                     aa(type,bool),
23.10/23.29	                                                     app_encode_app(dB,
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    type,bool),
23.10/23.29	                                                                    app_encode_app(
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    dB,
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    type,bool)),
23.10/23.29	                                                                    app_encode_fun(
23.10/23.29	                                                                    dB,
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    type,bool)),
23.10/23.29	                                                                    aa(
23.10/23.29	                                                                    dB,
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    type,bool)),
23.10/23.29	                                                                    app_encode_app(
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    nat,type),
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    dB,
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    type,bool)),
23.10/23.29	                                                                    app_encode_app(
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    nat,type),
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    dB,
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    type,bool))),
23.10/23.29	                                                                    app_encode_fun(
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    nat,type),
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    dB,
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    type,bool))),
23.10/23.29	                                                                    aa(
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    nat,type),
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    dB,
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    type,bool))),
23.10/23.29	                                                                    typing),E)),
23.10/23.29	                                                                    U)),
23.10/23.29	                                      t))) | 
23.10/23.29	      app_encode_app(bool,$o,pp,
23.10/23.29	                     app_encode_app(dB,bool,
23.10/23.29	                                    app_encode_app(fun(dB,bool),
23.10/23.29	                                                   app_encode_fun(dB,bool),
23.10/23.29	                                                   aa(dB,bool),it),
23.10/23.29	                                    app_encode_app(nat,dB,
23.10/23.29	                                                   app_encode_app(fun(nat,dB),
23.10/23.29	                                                                  app_encode_fun(
23.10/23.29	                                                                  nat,dB),
23.10/23.29	                                                                  aa(nat,dB),
23.10/23.29	                                                                  app_encode_app(
23.10/23.29	                                                                  dB,
23.10/23.29	                                                                  fun(nat,dB),
23.10/23.29	                                                                  app_encode_app(
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  dB,
23.10/23.29	                                                                  fun(nat,dB)),
23.10/23.29	                                                                  app_encode_fun(
23.10/23.29	                                                                  dB,
23.10/23.29	                                                                  fun(nat,dB)),
23.10/23.29	                                                                  aa(
23.10/23.29	                                                                  dB,
23.10/23.29	                                                                  fun(nat,dB)),
23.10/23.29	                                                                  app_encode_app(
23.10/23.29	                                                                  dB,
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  dB,
23.10/23.29	                                                                  fun(nat,dB)),
23.10/23.29	                                                                  app_encode_app(
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  dB,
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  dB,
23.10/23.29	                                                                  fun(nat,dB))),
23.10/23.29	                                                                  app_encode_fun(
23.10/23.29	                                                                  dB,
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  dB,
23.10/23.29	                                                                  fun(nat,dB))),
23.10/23.29	                                                                  aa(
23.10/23.29	                                                                  dB,
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  dB,
23.10/23.29	                                                                  fun(nat,dB))),
23.10/23.29	                                                                  subst),a)),
23.10/23.29	                                                                  U)),
23.10/23.29	                                                   I)))))).
23.10/23.29	tff(zf_stmt_0, negated_conjecture,
23.10/23.29	  (~
23.10/23.29	    (![E:fun(nat,type),T:type,U:dB,I:nat]:
23.10/23.29	       ((~
23.10/23.29	          app_encode_app(bool,$o,pp,
23.10/23.29	                         app_encode_app(type,bool,
23.10/23.29	                                        app_encode_app(fun(type,bool),
23.10/23.29	                                                       app_encode_fun(
23.10/23.29	                                                       type,bool),
23.10/23.29	                                                       aa(type,bool),
23.10/23.29	                                                       app_encode_app(
23.10/23.29	                                                       dB,fun(type,bool),
23.10/23.29	                                                       app_encode_app(
23.10/23.29	                                                       fun(dB,fun(type,bool)),
23.10/23.29	                                                       app_encode_fun(
23.10/23.29	                                                       dB,fun(type,bool)),
23.10/23.29	                                                       aa(dB,fun(type,bool)),
23.10/23.29	                                                       app_encode_app(
23.10/23.29	                                                       fun(nat,type),
23.10/23.29	                                                       fun(dB,fun(type,bool)),
23.10/23.29	                                                       app_encode_app(
23.10/23.29	                                                       fun(fun(nat,type),
23.10/23.29	                                                           fun(dB,
23.10/23.29	                                                               fun(type,bool))),
23.10/23.29	                                                       app_encode_fun(
23.10/23.29	                                                       fun(nat,type),
23.10/23.29	                                                       fun(dB,fun(type,bool))),
23.10/23.29	                                                       aa(fun(nat,type),
23.10/23.29	                                                          fun(dB,
23.10/23.29	                                                              fun(type,bool))),
23.10/23.29	                                                       typing),
23.10/23.29	                                                       app_encode_app(
23.10/23.29	                                                       type,fun(nat,type),
23.10/23.29	                                                       app_encode_app(
23.10/23.29	                                                       fun(type,fun(nat,type)),
23.10/23.29	                                                       app_encode_fun(
23.10/23.29	                                                       type,fun(nat,type)),
23.10/23.29	                                                       aa(type,fun(nat,type)),
23.10/23.29	                                                       app_encode_app(
23.10/23.29	                                                       nat,
23.10/23.29	                                                       fun(type,fun(nat,type)),
23.10/23.29	                                                       app_encode_app(
23.10/23.29	                                                       fun(nat,
23.10/23.29	                                                           fun(type,
23.10/23.29	                                                               fun(nat,type))),
23.10/23.29	                                                       app_encode_fun(
23.10/23.29	                                                       nat,
23.10/23.29	                                                       fun(type,fun(nat,type))),
23.10/23.29	                                                       aa(nat,
23.10/23.29	                                                          fun(type,
23.10/23.29	                                                              fun(nat,type))),
23.10/23.29	                                                       app_encode_app(
23.10/23.29	                                                       fun(nat,type),
23.10/23.29	                                                       fun(nat,
23.10/23.29	                                                           fun(type,
23.10/23.29	                                                               fun(nat,type))),
23.10/23.29	                                                       app_encode_app(
23.10/23.29	                                                       fun(fun(nat,type),
23.10/23.29	                                                           fun(nat,
23.10/23.29	                                                               fun(type,
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   nat,type)))),
23.10/23.29	                                                       app_encode_fun(
23.10/23.29	                                                       fun(nat,type),
23.10/23.29	                                                       fun(nat,
23.10/23.29	                                                           fun(type,
23.10/23.29	                                                               fun(nat,type)))),
23.10/23.29	                                                       aa(fun(nat,type),
23.10/23.29	                                                          fun(nat,
23.10/23.29	                                                              fun(type,
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  nat,type)))),
23.10/23.29	                                                       shift(type)),E)),I)),t))),
23.10/23.29	                                                       a)),
23.10/23.29	                                        T))) | 
23.10/23.29	        (~
23.10/23.29	          app_encode_app(bool,$o,pp,
23.10/23.29	                         app_encode_app(dB,bool,
23.10/23.29	                                        app_encode_app(fun(dB,bool),
23.10/23.29	                                                       app_encode_fun(
23.10/23.29	                                                       dB,bool),aa(dB,bool),
23.10/23.29	                                                       it),
23.10/23.29	                                        U))) | 
23.10/23.29	        (~
23.10/23.29	          app_encode_app(bool,$o,pp,
23.10/23.29	                         app_encode_app(type,bool,
23.10/23.29	                                        app_encode_app(fun(type,bool),
23.10/23.29	                                                       app_encode_fun(
23.10/23.29	                                                       type,bool),
23.10/23.29	                                                       aa(type,bool),
23.10/23.29	                                                       app_encode_app(
23.10/23.29	                                                       dB,fun(type,bool),
23.10/23.29	                                                       app_encode_app(
23.10/23.29	                                                       fun(dB,fun(type,bool)),
23.10/23.29	                                                       app_encode_fun(
23.10/23.29	                                                       dB,fun(type,bool)),
23.10/23.29	                                                       aa(dB,fun(type,bool)),
23.10/23.29	                                                       app_encode_app(
23.10/23.29	                                                       fun(nat,type),
23.10/23.29	                                                       fun(dB,fun(type,bool)),
23.10/23.29	                                                       app_encode_app(
23.10/23.29	                                                       fun(fun(nat,type),
23.10/23.29	                                                           fun(dB,
23.10/23.29	                                                               fun(type,bool))),
23.10/23.29	                                                       app_encode_fun(
23.10/23.29	                                                       fun(nat,type),
23.10/23.29	                                                       fun(dB,fun(type,bool))),
23.10/23.29	                                                       aa(fun(nat,type),
23.10/23.29	                                                          fun(dB,
23.10/23.29	                                                              fun(type,bool))),
23.10/23.29	                                                       typing),E)),U)),
23.10/23.29	                                        t))) | 
23.10/23.29	        app_encode_app(bool,$o,pp,
23.10/23.29	                       app_encode_app(dB,bool,
23.10/23.29	                                      app_encode_app(fun(dB,bool),
23.10/23.29	                                                     app_encode_fun(dB,bool),
23.10/23.29	                                                     aa(dB,bool),it),
23.10/23.29	                                      app_encode_app(nat,dB,
23.10/23.29	                                                     app_encode_app(fun(
23.10/23.29	                                                                    nat,dB),
23.10/23.29	                                                                    app_encode_fun(
23.10/23.29	                                                                    nat,dB),
23.10/23.29	                                                                    aa(
23.10/23.29	                                                                    nat,dB),
23.10/23.29	                                                                    app_encode_app(
23.10/23.29	                                                                    dB,
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    nat,dB),
23.10/23.29	                                                                    app_encode_app(
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    dB,
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    nat,dB)),
23.10/23.29	                                                                    app_encode_fun(
23.10/23.29	                                                                    dB,
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    nat,dB)),
23.10/23.29	                                                                    aa(
23.10/23.29	                                                                    dB,
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    nat,dB)),
23.10/23.29	                                                                    app_encode_app(
23.10/23.29	                                                                    dB,
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    dB,
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    nat,dB)),
23.10/23.29	                                                                    app_encode_app(
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    dB,
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    dB,
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    nat,dB))),
23.10/23.29	                                                                    app_encode_fun(
23.10/23.29	                                                                    dB,
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    dB,
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    nat,dB))),
23.10/23.29	                                                                    aa(
23.10/23.29	                                                                    dB,
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    dB,
23.10/23.29	                                                                    fun(
23.10/23.29	                                                                    nat,dB))),
23.10/23.29	                                                                    subst),a)),
23.10/23.29	                                                                    U)),
23.10/23.29	                                                     I))))))).
23.10/23.29	tff('0', plain,
23.10/23.29	    app_encode_app(bool, $o, pp, 
23.10/23.29	      app_encode_app(type, bool, 
23.10/23.29	        app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
23.10/23.29	          aa(type, bool), 
23.10/23.29	          app_encode_app(dB, fun(type, bool), 
23.10/23.29	            app_encode_app(fun(dB, fun(type, bool)), 
23.10/23.29	              app_encode_fun(dB, fun(type, bool)), aa(dB, fun(type, bool)), 
23.10/23.29	              app_encode_app(fun(nat, type), fun(dB, fun(type, bool)), 
23.10/23.29	                app_encode_app(
23.10/23.29	                  fun(fun(nat, type), fun(dB, fun(type, bool))), 
23.10/23.29	                  app_encode_fun(fun(nat, type), fun(dB, fun(type, bool))), 
23.10/23.29	                  aa(fun(nat, type), fun(dB, fun(type, bool))), typing), 
23.10/23.29	                app_encode_app(type, fun(nat, type), 
23.10/23.29	                  app_encode_app(fun(type, fun(nat, type)), 
23.10/23.29	                    app_encode_fun(type, fun(nat, type)), 
23.10/23.29	                    aa(type, fun(nat, type)), 
23.10/23.29	                    app_encode_app(nat, fun(type, fun(nat, type)), 
23.10/23.29	                      app_encode_app(fun(nat, fun(type, fun(nat, type))), 
23.10/23.29	                        app_encode_fun(nat, fun(type, fun(nat, type))), 
23.10/23.29	                        aa(nat, fun(type, fun(nat, type))), 
23.10/23.29	                        app_encode_app(fun(nat, type), 
23.10/23.29	                          fun(nat, fun(type, fun(nat, type))), 
23.10/23.29	                          app_encode_app(
23.10/23.29	                            fun(fun(nat, type), 
23.10/23.29	                              fun(nat, fun(type, fun(nat, type)))), 
23.10/23.29	                            app_encode_fun(fun(nat, type), 
23.10/23.29	                              fun(nat, fun(type, fun(nat, type)))), 
23.10/23.29	                            aa(fun(nat, type), 
23.10/23.29	                              fun(nat, fun(type, fun(nat, type)))), 
23.10/23.29	                            shift(type)), sk_E)), sk_I)), t))), a)), sk_T)),
23.10/23.29	    inference('cnf', [status(esa)], [zf_stmt_0])).
23.10/23.29	tff('1', plain,
23.10/23.29	    app_encode_app(bool, $o, pp, 
23.10/23.29	      app_encode_app(type, bool, 
23.10/23.29	        app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
23.10/23.29	          aa(type, bool), 
23.10/23.29	          app_encode_app(dB, fun(type, bool), 
23.10/23.29	            app_encode_app(fun(dB, fun(type, bool)), 
23.10/23.29	              app_encode_fun(dB, fun(type, bool)), aa(dB, fun(type, bool)), 
23.10/23.29	              app_encode_app(fun(nat, type), fun(dB, fun(type, bool)), 
23.10/23.29	                app_encode_app(
23.10/23.29	                  fun(fun(nat, type), fun(dB, fun(type, bool))), 
23.10/23.29	                  app_encode_fun(fun(nat, type), fun(dB, fun(type, bool))), 
23.10/23.29	                  aa(fun(nat, type), fun(dB, fun(type, bool))), typing), 
23.10/23.29	                sk_E)), sk_U1)), t)),
23.10/23.29	    inference('cnf', [status(esa)], [zf_stmt_0])).
23.10/23.29	tff(zf_stmt_65, axiom,
23.10/23.29	  ((![E2:fun(nat,type),T5:type,U3:dB,I2:nat]:
23.10/23.29	      (app_encode_app(bool,$o,pp,
23.10/23.29	                      app_encode_app(type,bool,
23.10/23.29	                                     app_encode_app(fun(type,bool),
23.10/23.29	                                                    app_encode_fun(type,bool),
23.10/23.29	                                                    aa(type,bool),
23.10/23.29	                                                    app_encode_app(dB,
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   type,bool),
23.10/23.29	                                                                   app_encode_app(
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   dB,
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   type,bool)),
23.10/23.29	                                                                   app_encode_fun(
23.10/23.29	                                                                   dB,
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   type,bool)),
23.10/23.29	                                                                   aa(
23.10/23.29	                                                                   dB,
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   type,bool)),
23.10/23.29	                                                                   app_encode_app(
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   nat,type),
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   dB,
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   type,bool)),
23.10/23.29	                                                                   app_encode_app(
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   nat,type),
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   dB,
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   type,bool))),
23.10/23.29	                                                                   app_encode_fun(
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   nat,type),
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   dB,
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   type,bool))),
23.10/23.29	                                                                   aa(
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   nat,type),
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   dB,
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   type,bool))),
23.10/23.29	                                                                   typing),
23.10/23.29	                                                                   app_encode_app(
23.10/23.29	                                                                   type,
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   nat,type),
23.10/23.29	                                                                   app_encode_app(
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   type,
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   nat,type)),
23.10/23.29	                                                                   app_encode_fun(
23.10/23.29	                                                                   type,
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   nat,type)),
23.10/23.29	                                                                   aa(
23.10/23.29	                                                                   type,
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   nat,type)),
23.10/23.29	                                                                   app_encode_app(
23.10/23.29	                                                                   nat,
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   type,
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   nat,type)),
23.10/23.29	                                                                   app_encode_app(
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   nat,
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   type,
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   nat,type))),
23.10/23.29	                                                                   app_encode_fun(
23.10/23.29	                                                                   nat,
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   type,
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   nat,type))),
23.10/23.29	                                                                   aa(
23.10/23.29	                                                                   nat,
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   type,
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   nat,type))),
23.10/23.29	                                                                   app_encode_app(
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   nat,type),
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   nat,
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   type,
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   nat,type))),
23.10/23.29	                                                                   app_encode_app(
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   nat,type),
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   nat,
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   type,
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   nat,type)))),
23.10/23.29	                                                                   app_encode_fun(
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   nat,type),
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   nat,
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   type,
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   nat,type)))),
23.10/23.29	                                                                   aa(
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   nat,type),
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   nat,
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   type,
23.10/23.29	                                                                   fun(
23.10/23.29	                                                                   nat,type)))),
23.10/23.29	                                                                   shift(
23.10/23.29	                                                                   type)),E2)),
23.10/23.29	                                                                   I2)),t))),
23.10/23.29	                                                                   a)),
23.10/23.29	                                     T5)) =>
23.10/23.29	       (app_encode_app(bool,$o,pp,
23.10/23.29	                       app_encode_app(dB,bool,
23.10/23.29	                                      app_encode_app(fun(dB,bool),
23.10/23.29	                                                     app_encode_fun(dB,bool),
23.10/23.29	                                                     aa(dB,bool),it),
23.10/23.29	                                      U3)) =>
23.10/23.29	        (app_encode_app(bool,$o,pp,
23.10/23.29	                        app_encode_app(type,bool,
23.10/23.29	                                       app_encode_app(fun(type,bool),
23.10/23.29	                                                      app_encode_fun(
23.10/23.29	                                                      type,bool),
23.10/23.29	                                                      aa(type,bool),
23.10/23.29	                                                      app_encode_app(
23.10/23.29	                                                      dB,fun(type,bool),
23.10/23.29	                                                      app_encode_app(
23.10/23.29	                                                      fun(dB,fun(type,bool)),
23.10/23.29	                                                      app_encode_fun(
23.10/23.29	                                                      dB,fun(type,bool)),
23.10/23.29	                                                      aa(dB,fun(type,bool)),
23.10/23.29	                                                      app_encode_app(
23.10/23.29	                                                      fun(nat,type),
23.10/23.29	                                                      fun(dB,fun(type,bool)),
23.10/23.29	                                                      app_encode_app(
23.10/23.29	                                                      fun(fun(nat,type),
23.10/23.29	                                                          fun(dB,
23.10/23.29	                                                              fun(type,bool))),
23.10/23.29	                                                      app_encode_fun(
23.10/23.29	                                                      fun(nat,type),
23.10/23.29	                                                      fun(dB,fun(type,bool))),
23.10/23.29	                                                      aa(fun(nat,type),
23.10/23.29	                                                         fun(dB,
23.10/23.29	                                                             fun(type,bool))),
23.10/23.29	                                                      typing),E2)),U3)),
23.10/23.29	                                       t)) =>
23.10/23.29	         app_encode_app(bool,$o,pp,
23.10/23.29	                        app_encode_app(dB,bool,
23.10/23.29	                                       app_encode_app(fun(dB,bool),
23.10/23.29	                                                      app_encode_fun(dB,bool),
23.10/23.29	                                                      aa(dB,bool),it),
23.10/23.29	                                       app_encode_app(nat,dB,
23.10/23.29	                                                      app_encode_app(
23.10/23.29	                                                      fun(nat,dB),
23.10/23.29	                                                      app_encode_fun(nat,dB),
23.10/23.29	                                                      aa(nat,dB),
23.10/23.29	                                                      app_encode_app(
23.10/23.29	                                                      dB,fun(nat,dB),
23.10/23.29	                                                      app_encode_app(
23.10/23.29	                                                      fun(dB,fun(nat,dB)),
23.10/23.29	                                                      app_encode_fun(
23.10/23.29	                                                      dB,fun(nat,dB)),
23.10/23.29	                                                      aa(dB,fun(nat,dB)),
23.10/23.29	                                                      app_encode_app(
23.10/23.29	                                                      dB,fun(dB,fun(nat,dB)),
23.10/23.29	                                                      app_encode_app(
23.10/23.29	                                                      fun(dB,
23.10/23.29	                                                          fun(dB,fun(nat,dB))),
23.10/23.29	                                                      app_encode_fun(
23.10/23.29	                                                      dB,fun(dB,fun(nat,dB))),
23.10/23.29	                                                      aa(dB,
23.10/23.29	                                                         fun(dB,fun(nat,dB))),
23.10/23.29	                                                      subst),a)),U3)),I2))))))) & 
23.10/23.29	   (?[X11:type]:
23.10/23.29	      app_encode_app(bool,$o,pp,
23.10/23.29	                     app_encode_app(type,bool,
23.10/23.29	                                    app_encode_app(fun(type,bool),
23.10/23.29	                                                   app_encode_fun(type,bool),
23.10/23.29	                                                   aa(type,bool),
23.10/23.29	                                                   app_encode_app(dB,
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  type,bool),
23.10/23.29	                                                                  app_encode_app(
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  dB,
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  type,bool)),
23.10/23.29	                                                                  app_encode_fun(
23.10/23.29	                                                                  dB,
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  type,bool)),
23.10/23.29	                                                                  aa(
23.10/23.29	                                                                  dB,
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  type,bool)),
23.10/23.29	                                                                  app_encode_app(
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  nat,type),
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  dB,
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  type,bool)),
23.10/23.29	                                                                  app_encode_app(
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  nat,type),
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  dB,
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  type,bool))),
23.10/23.29	                                                                  app_encode_fun(
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  nat,type),
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  dB,
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  type,bool))),
23.10/23.29	                                                                  aa(
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  nat,type),
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  dB,
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  type,bool))),
23.10/23.29	                                                                  typing),
23.10/23.29	                                                                  app_encode_app(
23.10/23.29	                                                                  type,
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  nat,type),
23.10/23.29	                                                                  app_encode_app(
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  type,
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  nat,type)),
23.10/23.29	                                                                  app_encode_fun(
23.10/23.29	                                                                  type,
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  nat,type)),
23.10/23.29	                                                                  aa(
23.10/23.29	                                                                  type,
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  nat,type)),
23.10/23.29	                                                                  app_encode_app(
23.10/23.29	                                                                  nat,
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  type,
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  nat,type)),
23.10/23.29	                                                                  app_encode_app(
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  nat,
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  type,
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  nat,type))),
23.10/23.29	                                                                  app_encode_fun(
23.10/23.29	                                                                  nat,
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  type,
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  nat,type))),
23.10/23.29	                                                                  aa(
23.10/23.29	                                                                  nat,
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  type,
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  nat,type))),
23.10/23.29	                                                                  app_encode_app(
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  nat,type),
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  nat,
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  type,
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  nat,type))),
23.10/23.29	                                                                  app_encode_app(
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  nat,type),
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  nat,
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  type,
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  nat,type)))),
23.10/23.29	                                                                  app_encode_fun(
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  nat,type),
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  nat,
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  type,
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  nat,type)))),
23.10/23.29	                                                                  aa(
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  nat,type),
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  nat,
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  type,
23.10/23.29	                                                                  fun(
23.10/23.29	                                                                  nat,type)))),
23.10/23.29	                                                                  shift(type)),
23.10/23.29	                                                                  e)),i)),t))),
23.10/23.29	                                                                  a)),
23.10/23.29	                                    X11))))).
23.10/23.29	tff('2', plain,
23.10/23.29	    ![X0 : dB, X1 : fun(nat, type), X2 : nat, X3 : type]:
23.10/23.29	      (~ app_encode_app(bool, $o, pp, 
23.10/23.29	           app_encode_app(dB, bool, 
23.10/23.29	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
23.10/23.29	               aa(dB, bool), it), X0))
23.10/23.29	       | ~ app_encode_app(bool, $o, pp, 
23.10/23.29	             app_encode_app(type, bool, 
23.10/23.29	               app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
23.10/23.29	                 aa(type, bool), 
23.10/23.29	                 app_encode_app(dB, fun(type, bool), 
23.10/23.29	                   app_encode_app(fun(dB, fun(type, bool)), 
23.10/23.29	                     app_encode_fun(dB, fun(type, bool)), 
23.10/23.29	                     aa(dB, fun(type, bool)), 
23.10/23.29	                     app_encode_app(fun(nat, type), 
23.10/23.29	                       fun(dB, fun(type, bool)), 
23.10/23.29	                       app_encode_app(
23.10/23.29	                         fun(fun(nat, type), fun(dB, fun(type, bool))), 
23.10/23.29	                         app_encode_fun(fun(nat, type), 
23.10/23.29	                           fun(dB, fun(type, bool))), 
23.10/23.29	                         aa(fun(nat, type), fun(dB, fun(type, bool))), 
23.10/23.29	                         typing), X1)), X0)), t))
23.10/23.29	       | ~ app_encode_app(bool, $o, pp, 
23.10/23.29	             app_encode_app(type, bool, 
23.10/23.29	               app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
23.10/23.29	                 aa(type, bool), 
23.10/23.29	                 app_encode_app(dB, fun(type, bool), 
23.10/23.29	                   app_encode_app(fun(dB, fun(type, bool)), 
23.10/23.29	                     app_encode_fun(dB, fun(type, bool)), 
23.10/23.29	                     aa(dB, fun(type, bool)), 
23.10/23.29	                     app_encode_app(fun(nat, type), 
23.10/23.29	                       fun(dB, fun(type, bool)), 
23.10/23.29	                       app_encode_app(
23.10/23.29	                         fun(fun(nat, type), fun(dB, fun(type, bool))), 
23.10/23.29	                         app_encode_fun(fun(nat, type), 
23.10/23.29	                           fun(dB, fun(type, bool))), 
23.10/23.29	                         aa(fun(nat, type), fun(dB, fun(type, bool))), 
23.10/23.29	                         typing), 
23.10/23.29	                       app_encode_app(type, fun(nat, type), 
23.10/23.29	                         app_encode_app(fun(type, fun(nat, type)), 
23.10/23.29	                           app_encode_fun(type, fun(nat, type)), 
23.10/23.29	                           aa(type, fun(nat, type)), 
23.10/23.29	                           app_encode_app(nat, fun(type, fun(nat, type)), 
23.10/23.29	                             app_encode_app(
23.10/23.29	                               fun(nat, fun(type, fun(nat, type))), 
23.10/23.29	                               app_encode_fun(nat, fun(type, fun(nat, type))), 
23.10/23.29	                               aa(nat, fun(type, fun(nat, type))), 
23.10/23.29	                               app_encode_app(fun(nat, type), 
23.10/23.29	                                 fun(nat, fun(type, fun(nat, type))), 
23.10/23.29	                                 app_encode_app(
23.10/23.29	                                   fun(fun(nat, type), 
23.10/23.29	                                     fun(nat, fun(type, fun(nat, type)))), 
23.10/23.29	                                   app_encode_fun(fun(nat, type), 
23.10/23.29	                                     fun(nat, fun(type, fun(nat, type)))), 
23.10/23.29	                                   aa(fun(nat, type), 
23.10/23.29	                                     fun(nat, fun(type, fun(nat, type)))), 
23.10/23.29	                                   shift(type)), X1)), X2)), t))), a)), X3))
23.10/23.29	       | app_encode_app(bool, $o, pp, 
23.10/23.29	           app_encode_app(dB, bool, 
23.10/23.29	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
23.10/23.29	               aa(dB, bool), it), 
23.10/23.29	             app_encode_app(nat, dB, 
23.10/23.29	               app_encode_app(fun(nat, dB), app_encode_fun(nat, dB), 
23.10/23.29	                 aa(nat, dB), 
23.10/23.29	                 app_encode_app(dB, fun(nat, dB), 
23.10/23.29	                   app_encode_app(fun(dB, fun(nat, dB)), 
23.10/23.29	                     app_encode_fun(dB, fun(nat, dB)), aa(dB, fun(nat, dB)), 
23.10/23.29	                     app_encode_app(dB, fun(dB, fun(nat, dB)), 
23.10/23.29	                       app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
23.10/23.29	                         app_encode_fun(dB, fun(dB, fun(nat, dB))), 
23.10/23.29	                         aa(dB, fun(dB, fun(nat, dB))), subst), a)), X0)), 
23.10/23.29	               X2)))),
23.10/23.29	    inference('cnf', [status(esa)], [zf_stmt_65])).
23.10/23.29	tff('3', plain,
23.10/23.29	    ![X0 : nat, X1 : type]:
23.10/23.29	      (~ $true
23.10/23.29	       | app_encode_app(bool, $o, pp, 
23.10/23.29	           app_encode_app(dB, bool, 
23.10/23.29	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
23.10/23.29	               aa(dB, bool), it), 
23.10/23.29	             app_encode_app(nat, dB, 
23.10/23.29	               app_encode_app(fun(nat, dB), app_encode_fun(nat, dB), 
23.10/23.29	                 aa(nat, dB), 
23.10/23.29	                 app_encode_app(dB, fun(nat, dB), 
23.10/23.29	                   app_encode_app(fun(dB, fun(nat, dB)), 
23.10/23.29	                     app_encode_fun(dB, fun(nat, dB)), aa(dB, fun(nat, dB)), 
23.10/23.29	                     app_encode_app(dB, fun(dB, fun(nat, dB)), 
23.10/23.29	                       app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
23.10/23.29	                         app_encode_fun(dB, fun(dB, fun(nat, dB))), 
23.10/23.29	                         aa(dB, fun(dB, fun(nat, dB))), subst), a)), sk_U1)), 
23.10/23.29	               X0)))
23.10/23.29	       | ~ app_encode_app(bool, $o, pp, 
23.10/23.29	             app_encode_app(type, bool, 
23.10/23.29	               app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
23.10/23.29	                 aa(type, bool), 
23.10/23.29	                 app_encode_app(dB, fun(type, bool), 
23.10/23.29	                   app_encode_app(fun(dB, fun(type, bool)), 
23.10/23.29	                     app_encode_fun(dB, fun(type, bool)), 
23.10/23.29	                     aa(dB, fun(type, bool)), 
23.10/23.29	                     app_encode_app(fun(nat, type), 
23.10/23.29	                       fun(dB, fun(type, bool)), 
23.10/23.29	                       app_encode_app(
23.10/23.29	                         fun(fun(nat, type), fun(dB, fun(type, bool))), 
23.10/23.29	                         app_encode_fun(fun(nat, type), 
23.10/23.29	                           fun(dB, fun(type, bool))), 
23.10/23.29	                         aa(fun(nat, type), fun(dB, fun(type, bool))), 
23.10/23.29	                         typing), 
23.10/23.29	                       app_encode_app(type, fun(nat, type), 
23.10/23.29	                         app_encode_app(fun(type, fun(nat, type)), 
23.10/23.29	                           app_encode_fun(type, fun(nat, type)), 
23.10/23.29	                           aa(type, fun(nat, type)), 
23.10/23.29	                           app_encode_app(nat, fun(type, fun(nat, type)), 
23.10/23.29	                             app_encode_app(
23.10/23.29	                               fun(nat, fun(type, fun(nat, type))), 
23.10/23.29	                               app_encode_fun(nat, fun(type, fun(nat, type))), 
23.10/23.29	                               aa(nat, fun(type, fun(nat, type))), 
23.10/23.29	                               app_encode_app(fun(nat, type), 
23.10/23.29	                                 fun(nat, fun(type, fun(nat, type))), 
23.10/23.29	                                 app_encode_app(
23.10/23.29	                                   fun(fun(nat, type), 
23.10/23.29	                                     fun(nat, fun(type, fun(nat, type)))), 
23.10/23.29	                                   app_encode_fun(fun(nat, type), 
23.10/23.29	                                     fun(nat, fun(type, fun(nat, type)))), 
23.10/23.29	                                   aa(fun(nat, type), 
23.10/23.29	                                     fun(nat, fun(type, fun(nat, type)))), 
23.10/23.29	                                   shift(type)), sk_E)), X0)), t))), a)), X1))
23.10/23.29	       | ~ app_encode_app(bool, $o, pp, 
23.10/23.29	             app_encode_app(dB, bool, 
23.10/23.29	               app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
23.10/23.29	                 aa(dB, bool), it), sk_U1))),
23.10/23.29	    inference('sup-', [status(thm)], ['1', '2'])).
23.10/23.29	tff('4', plain,
23.10/23.29	    app_encode_app(bool, $o, pp, 
23.10/23.29	      app_encode_app(dB, bool, 
23.10/23.29	        app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
23.10/23.29	          aa(dB, bool), it), sk_U1)),
23.10/23.29	    inference('cnf', [status(esa)], [zf_stmt_0])).
23.10/23.29	tff('5', plain,
23.10/23.29	    ![X0 : nat, X1 : type]:
23.10/23.29	      (~ $true
23.10/23.29	       | app_encode_app(bool, $o, pp, 
23.10/23.29	           app_encode_app(dB, bool, 
23.10/23.29	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
23.10/23.29	               aa(dB, bool), it), 
23.10/23.29	             app_encode_app(nat, dB, 
23.10/23.29	               app_encode_app(fun(nat, dB), app_encode_fun(nat, dB), 
23.10/23.29	                 aa(nat, dB), 
23.10/23.29	                 app_encode_app(dB, fun(nat, dB), 
23.10/23.29	                   app_encode_app(fun(dB, fun(nat, dB)), 
23.10/23.29	                     app_encode_fun(dB, fun(nat, dB)), aa(dB, fun(nat, dB)), 
23.10/23.29	                     app_encode_app(dB, fun(dB, fun(nat, dB)), 
23.10/23.29	                       app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
23.10/23.29	                         app_encode_fun(dB, fun(dB, fun(nat, dB))), 
23.10/23.29	                         aa(dB, fun(dB, fun(nat, dB))), subst), a)), sk_U1)), 
23.10/23.29	               X0)))
23.10/23.29	       | ~ app_encode_app(bool, $o, pp, 
23.10/23.29	             app_encode_app(type, bool, 
23.10/23.29	               app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
23.10/23.29	                 aa(type, bool), 
23.10/23.29	                 app_encode_app(dB, fun(type, bool), 
23.10/23.29	                   app_encode_app(fun(dB, fun(type, bool)), 
23.10/23.29	                     app_encode_fun(dB, fun(type, bool)), 
23.10/23.29	                     aa(dB, fun(type, bool)), 
23.10/23.29	                     app_encode_app(fun(nat, type), 
23.10/23.29	                       fun(dB, fun(type, bool)), 
23.10/23.29	                       app_encode_app(
23.10/23.29	                         fun(fun(nat, type), fun(dB, fun(type, bool))), 
23.10/23.29	                         app_encode_fun(fun(nat, type), 
23.10/23.29	                           fun(dB, fun(type, bool))), 
23.10/23.29	                         aa(fun(nat, type), fun(dB, fun(type, bool))), 
23.10/23.29	                         typing), 
23.10/23.29	                       app_encode_app(type, fun(nat, type), 
23.10/23.29	                         app_encode_app(fun(type, fun(nat, type)), 
23.10/23.29	                           app_encode_fun(type, fun(nat, type)), 
23.10/23.29	                           aa(type, fun(nat, type)), 
23.10/23.29	                           app_encode_app(nat, fun(type, fun(nat, type)), 
23.10/23.29	                             app_encode_app(
23.10/23.29	                               fun(nat, fun(type, fun(nat, type))), 
23.10/23.29	                               app_encode_fun(nat, fun(type, fun(nat, type))), 
23.10/23.29	                               aa(nat, fun(type, fun(nat, type))), 
23.10/23.29	                               app_encode_app(fun(nat, type), 
23.10/23.29	                                 fun(nat, fun(type, fun(nat, type))), 
23.10/23.29	                                 app_encode_app(
23.10/23.29	                                   fun(fun(nat, type), 
23.10/23.29	                                     fun(nat, fun(type, fun(nat, type)))), 
23.10/23.29	                                   app_encode_fun(fun(nat, type), 
23.10/23.29	                                     fun(nat, fun(type, fun(nat, type)))), 
23.10/23.29	                                   aa(fun(nat, type), 
23.10/23.29	                                     fun(nat, fun(type, fun(nat, type)))), 
23.10/23.29	                                   shift(type)), sk_E)), X0)), t))), a)), X1))
23.10/23.29	       | ~ $true),
23.10/23.29	    inference('demod', [status(thm)], ['3', '4'])).
23.10/23.29	tff('6', plain,
23.10/23.29	    ![X0 : nat, X1 : type]:
23.10/23.29	      (~ app_encode_app(bool, $o, pp, 
23.10/23.29	           app_encode_app(type, bool, 
23.10/23.29	             app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
23.10/23.29	               aa(type, bool), 
23.10/23.29	               app_encode_app(dB, fun(type, bool), 
23.10/23.29	                 app_encode_app(fun(dB, fun(type, bool)), 
23.10/23.29	                   app_encode_fun(dB, fun(type, bool)), 
23.10/23.29	                   aa(dB, fun(type, bool)), 
23.10/23.29	                   app_encode_app(fun(nat, type), fun(dB, fun(type, bool)), 
23.10/23.29	                     app_encode_app(
23.10/23.29	                       fun(fun(nat, type), fun(dB, fun(type, bool))), 
23.10/23.29	                       app_encode_fun(fun(nat, type), 
23.10/23.29	                         fun(dB, fun(type, bool))), 
23.10/23.29	                       aa(fun(nat, type), fun(dB, fun(type, bool))), typing), 
23.10/23.29	                     app_encode_app(type, fun(nat, type), 
23.10/23.29	                       app_encode_app(fun(type, fun(nat, type)), 
23.10/23.29	                         app_encode_fun(type, fun(nat, type)), 
23.10/23.29	                         aa(type, fun(nat, type)), 
23.10/23.29	                         app_encode_app(nat, fun(type, fun(nat, type)), 
23.10/23.29	                           app_encode_app(
23.10/23.29	                             fun(nat, fun(type, fun(nat, type))), 
23.10/23.29	                             app_encode_fun(nat, fun(type, fun(nat, type))), 
23.10/23.29	                             aa(nat, fun(type, fun(nat, type))), 
23.10/23.29	                             app_encode_app(fun(nat, type), 
23.10/23.29	                               fun(nat, fun(type, fun(nat, type))), 
23.10/23.29	                               app_encode_app(
23.10/23.29	                                 fun(fun(nat, type), 
23.10/23.29	                                   fun(nat, fun(type, fun(nat, type)))), 
23.10/23.29	                                 app_encode_fun(fun(nat, type), 
23.10/23.29	                                   fun(nat, fun(type, fun(nat, type)))), 
23.10/23.29	                                 aa(fun(nat, type), 
23.10/23.29	                                   fun(nat, fun(type, fun(nat, type)))), 
23.10/23.29	                                 shift(type)), sk_E)), X0)), t))), a)), X1))
23.10/23.29	       | app_encode_app(bool, $o, pp, 
23.10/23.29	           app_encode_app(dB, bool, 
23.10/23.29	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
23.10/23.29	               aa(dB, bool), it), 
23.10/23.29	             app_encode_app(nat, dB, 
23.10/23.29	               app_encode_app(fun(nat, dB), app_encode_fun(nat, dB), 
23.10/23.29	                 aa(nat, dB), 
23.10/23.29	                 app_encode_app(dB, fun(nat, dB), 
23.10/23.29	                   app_encode_app(fun(dB, fun(nat, dB)), 
23.10/23.29	                     app_encode_fun(dB, fun(nat, dB)), aa(dB, fun(nat, dB)), 
23.10/23.29	                     app_encode_app(dB, fun(dB, fun(nat, dB)), 
23.10/23.29	                       app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
23.10/23.29	                         app_encode_fun(dB, fun(dB, fun(nat, dB))), 
23.10/23.29	                         aa(dB, fun(dB, fun(nat, dB))), subst), a)), sk_U1)), 
23.10/23.29	               X0)))),
23.10/23.29	    inference('simplify', [status(thm)], ['5'])).
23.10/23.29	tff('7', plain,
23.10/23.29	    (~ $true
23.10/23.29	     | app_encode_app(bool, $o, pp, 
23.10/23.29	         app_encode_app(dB, bool, 
23.10/23.29	           app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
23.10/23.29	             aa(dB, bool), it), 
23.10/23.29	           app_encode_app(nat, dB, 
23.10/23.29	             app_encode_app(fun(nat, dB), app_encode_fun(nat, dB), 
23.10/23.29	               aa(nat, dB), 
23.10/23.29	               app_encode_app(dB, fun(nat, dB), 
23.10/23.29	                 app_encode_app(fun(dB, fun(nat, dB)), 
23.10/23.29	                   app_encode_fun(dB, fun(nat, dB)), aa(dB, fun(nat, dB)), 
23.10/23.29	                   app_encode_app(dB, fun(dB, fun(nat, dB)), 
23.10/23.29	                     app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
23.10/23.29	                       app_encode_fun(dB, fun(dB, fun(nat, dB))), 
23.10/23.29	                       aa(dB, fun(dB, fun(nat, dB))), subst), a)), sk_U1)), 
23.10/23.29	             sk_I)))),
23.10/23.29	    inference('sup-', [status(thm)], ['0', '6'])).
23.10/23.29	tff('8', plain,
23.10/23.29	    app_encode_app(bool, $o, pp, 
23.10/23.29	      app_encode_app(dB, bool, 
23.10/23.29	        app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
23.10/23.29	          aa(dB, bool), it), 
23.10/23.29	        app_encode_app(nat, dB, 
23.10/23.29	          app_encode_app(fun(nat, dB), app_encode_fun(nat, dB), aa(nat, dB), 
23.10/23.29	            app_encode_app(dB, fun(nat, dB), 
23.10/23.29	              app_encode_app(fun(dB, fun(nat, dB)), 
23.10/23.29	                app_encode_fun(dB, fun(nat, dB)), aa(dB, fun(nat, dB)), 
23.10/23.29	                app_encode_app(dB, fun(dB, fun(nat, dB)), 
23.10/23.29	                  app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
23.10/23.29	                    app_encode_fun(dB, fun(dB, fun(nat, dB))), 
23.10/23.29	                    aa(dB, fun(dB, fun(nat, dB))), subst), a)), sk_U1)), 
23.10/23.29	          sk_I))),
23.10/23.29	    inference('simplify', [status(thm)], ['7'])).
23.10/23.29	tff('9', plain,
23.10/23.29	    ~ app_encode_app(bool, $o, pp, 
23.10/23.29	        app_encode_app(dB, bool, 
23.10/23.29	          app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
23.10/23.29	            aa(dB, bool), it), 
23.10/23.29	          app_encode_app(nat, dB, 
23.10/23.29	            app_encode_app(fun(nat, dB), app_encode_fun(nat, dB), 
23.10/23.29	              aa(nat, dB), 
23.10/23.29	              app_encode_app(dB, fun(nat, dB), 
23.10/23.29	                app_encode_app(fun(dB, fun(nat, dB)), 
23.10/23.29	                  app_encode_fun(dB, fun(nat, dB)), aa(dB, fun(nat, dB)), 
23.10/23.29	                  app_encode_app(dB, fun(dB, fun(nat, dB)), 
23.10/23.29	                    app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
23.10/23.29	                      app_encode_fun(dB, fun(dB, fun(nat, dB))), 
23.10/23.29	                      aa(dB, fun(dB, fun(nat, dB))), subst), a)), sk_U1)), 
23.10/23.29	            sk_I))),
23.10/23.29	    inference('cnf', [status(esa)], [zf_stmt_0])).
23.10/23.29	tff('10', plain, ~ $true, inference('sup-', [status(thm)], ['8', '9'])).
23.10/23.29	tff('11', plain, $false, inference('simplify', [status(thm)], ['10'])).
23.10/23.29	
23.10/23.29	% SZS output end Refutation
23.20/23.29	EOF
