0.00/0.00	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : appext
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : kbo
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n101.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 07:16:24 CST 2018
12.25/12.40	% done 2581 iterations in 12.205s
12.25/12.40	% SZS status Theorem for 'stdin'
12.25/12.40	% SZS output start Refutation
12.27/12.40	tff(zf_stmt_61, axiom,
12.27/12.40	  (app_encode_app(bool,$o,pp,
12.27/12.40	                  app_encode_app(type,bool,
12.27/12.40	                                 app_encode_app(fun1(type,bool),
12.27/12.40	                                                app_encode_fun(type,bool),
12.27/12.40	                                                aa(type,bool),
12.27/12.40	                                                app_encode_app(dB,
12.27/12.40	                                                               fun1(type,bool),
12.27/12.40	                                                               app_encode_app(
12.27/12.40	                                                               fun1(dB,
12.27/12.40	                                                                    fun1(
12.27/12.40	                                                                    type,bool)),
12.27/12.40	                                                               app_encode_fun(
12.27/12.40	                                                               dB,
12.27/12.40	                                                               fun1(type,bool)),
12.27/12.40	                                                               aa(dB,
12.27/12.40	                                                                  fun1(
12.27/12.40	                                                                  type,bool)),
12.27/12.40	                                                               app_encode_app(
12.27/12.40	                                                               fun1(nat,type),
12.27/12.40	                                                               fun1(dB,
12.27/12.40	                                                                    fun1(
12.27/12.40	                                                                    type,bool)),
12.27/12.40	                                                               typing,e)),
12.27/12.40	                                                               app_encode_app(
12.27/12.40	                                                               nat,dB,
12.27/12.40	                                                               app_encode_app(
12.27/12.40	                                                               fun1(nat,dB),
12.27/12.40	                                                               app_encode_fun(
12.27/12.40	                                                               nat,dB),
12.27/12.40	                                                               aa(nat,dB),
12.27/12.40	                                                               app_encode_app(
12.27/12.40	                                                               dB,
12.27/12.40	                                                               fun1(nat,dB),
12.27/12.40	                                                               app_encode_app(
12.27/12.40	                                                               fun1(dB,
12.27/12.40	                                                                    fun1(
12.27/12.40	                                                                    nat,dB)),
12.27/12.40	                                                               app_encode_fun(
12.27/12.40	                                                               dB,
12.27/12.40	                                                               fun1(nat,dB)),
12.27/12.40	                                                               aa(dB,
12.27/12.40	                                                                  fun1(
12.27/12.40	                                                                  nat,dB)),
12.27/12.40	                                                               app_encode_app(
12.27/12.40	                                                               dB,
12.27/12.40	                                                               fun1(dB,
12.27/12.40	                                                                    fun1(
12.27/12.40	                                                                    nat,dB)),
12.27/12.40	                                                               app_encode_app(
12.27/12.40	                                                               fun1(dB,
12.27/12.40	                                                                    fun1(
12.27/12.40	                                                                    dB,
12.27/12.40	                                                                    fun1(
12.27/12.40	                                                                    nat,dB))),
12.27/12.40	                                                               app_encode_fun(
12.27/12.40	                                                               dB,
12.27/12.40	                                                               fun1(dB,
12.27/12.40	                                                                    fun1(
12.27/12.40	                                                                    nat,dB))),
12.27/12.40	                                                               aa(dB,
12.27/12.40	                                                                  fun1(
12.27/12.40	                                                                  dB,
12.27/12.40	                                                                  fun1(
12.27/12.40	                                                                  nat,dB))),
12.27/12.40	                                                               subst),a)),u)),
12.27/12.40	                                                               i))),
12.27/12.40	                                 t2)))).
12.27/12.40	tff('0', plain,
12.27/12.40	    app_encode_app(bool, $o, pp, 
12.27/12.40	      app_encode_app(type, bool, 
12.27/12.40	        app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
12.27/12.40	          aa(type, bool), 
12.27/12.40	          app_encode_app(dB, fun1(type, bool), 
12.27/12.40	            app_encode_app(fun1(dB, fun1(type, bool)), 
12.27/12.40	              app_encode_fun(dB, fun1(type, bool)), 
12.27/12.40	              aa(dB, fun1(type, bool)), 
12.27/12.40	              app_encode_app(fun1(nat, type), fun1(dB, fun1(type, bool)), 
12.27/12.40	                typing, e)), 
12.27/12.40	            app_encode_app(nat, dB, 
12.27/12.40	              app_encode_app(fun1(nat, dB), app_encode_fun(nat, dB), 
12.27/12.40	                aa(nat, dB), 
12.27/12.40	                app_encode_app(dB, fun1(nat, dB), 
12.27/12.40	                  app_encode_app(fun1(dB, fun1(nat, dB)), 
12.27/12.40	                    app_encode_fun(dB, fun1(nat, dB)), 
12.27/12.40	                    aa(dB, fun1(nat, dB)), 
12.27/12.40	                    app_encode_app(dB, fun1(dB, fun1(nat, dB)), 
12.27/12.40	                      app_encode_app(fun1(dB, fun1(dB, fun1(nat, dB))), 
12.27/12.40	                        app_encode_fun(dB, fun1(dB, fun1(nat, dB))), 
12.27/12.40	                        aa(dB, fun1(dB, fun1(nat, dB))), subst), a)), u)), i))), 
12.27/12.40	        t2)),
12.27/12.40	    inference('cnf', [status(esa)], [zf_stmt_61])).
12.27/12.40	tff(zf_stmt_66, axiom,
12.27/12.40	  (![Ta:dB,Ua:type,Ta1:type,S1:dB,Env:fun1(nat,type)]:
12.27/12.40	     (app_encode_app(bool,$o,pp,
12.27/12.40	                     app_encode_app(type,bool,
12.27/12.40	                                    app_encode_app(fun1(type,bool),
12.27/12.40	                                                   app_encode_fun(type,bool),
12.27/12.40	                                                   aa(type,bool),
12.27/12.40	                                                   app_encode_app(dB,
12.27/12.40	                                                                  fun1(
12.27/12.40	                                                                  type,bool),
12.27/12.40	                                                                  app_encode_app(
12.27/12.40	                                                                  fun1(
12.27/12.40	                                                                  dB,
12.27/12.40	                                                                  fun1(
12.27/12.40	                                                                  type,bool)),
12.27/12.40	                                                                  app_encode_fun(
12.27/12.40	                                                                  dB,
12.27/12.40	                                                                  fun1(
12.27/12.40	                                                                  type,bool)),
12.27/12.40	                                                                  aa(
12.27/12.40	                                                                  dB,
12.27/12.40	                                                                  fun1(
12.27/12.40	                                                                  type,bool)),
12.27/12.40	                                                                  app_encode_app(
12.27/12.40	                                                                  fun1(
12.27/12.40	                                                                  nat,type),
12.27/12.40	                                                                  fun1(
12.27/12.40	                                                                  dB,
12.27/12.40	                                                                  fun1(
12.27/12.40	                                                                  type,bool)),
12.27/12.40	                                                                  typing,Env)),
12.27/12.40	                                                                  S1)),
12.27/12.40	                                    app_encode_app(type,type,
12.27/12.40	                                                   app_encode_app(fun1(
12.27/12.40	                                                                  type,type),
12.27/12.40	                                                                  app_encode_fun(
12.27/12.40	                                                                  type,type),
12.27/12.40	                                                                  aa(
12.27/12.40	                                                                  type,type),
12.27/12.40	                                                                  app_encode_app(
12.27/12.40	                                                                  type,
12.27/12.40	                                                                  fun1(
12.27/12.40	                                                                  type,type),
12.27/12.40	                                                                  app_encode_app(
12.27/12.40	                                                                  fun1(
12.27/12.40	                                                                  type,
12.27/12.40	                                                                  fun1(
12.27/12.40	                                                                  type,type)),
12.27/12.40	                                                                  app_encode_fun(
12.27/12.40	                                                                  type,
12.27/12.40	                                                                  fun1(
12.27/12.40	                                                                  type,type)),
12.27/12.40	                                                                  aa(
12.27/12.40	                                                                  type,
12.27/12.40	                                                                  fun1(
12.27/12.40	                                                                  type,type)),
12.27/12.40	                                                                  fun),Ta1)),
12.27/12.40	                                                   Ua))) =>
12.27/12.40	      (app_encode_app(bool,$o,pp,
12.27/12.40	                      app_encode_app(type,bool,
12.27/12.40	                                     app_encode_app(fun1(type,bool),
12.27/12.40	                                                    app_encode_fun(type,bool),
12.27/12.40	                                                    aa(type,bool),
12.27/12.40	                                                    app_encode_app(dB,
12.27/12.40	                                                                   fun1(
12.27/12.40	                                                                   type,bool),
12.27/12.40	                                                                   app_encode_app(
12.27/12.40	                                                                   fun1(
12.27/12.40	                                                                   dB,
12.27/12.40	                                                                   fun1(
12.27/12.40	                                                                   type,bool)),
12.27/12.40	                                                                   app_encode_fun(
12.27/12.40	                                                                   dB,
12.27/12.40	                                                                   fun1(
12.27/12.40	                                                                   type,bool)),
12.27/12.40	                                                                   aa(
12.27/12.40	                                                                   dB,
12.27/12.40	                                                                   fun1(
12.27/12.40	                                                                   type,bool)),
12.27/12.40	                                                                   app_encode_app(
12.27/12.40	                                                                   fun1(
12.27/12.40	                                                                   nat,type),
12.27/12.40	                                                                   fun1(
12.27/12.40	                                                                   dB,
12.27/12.40	                                                                   fun1(
12.27/12.40	                                                                   type,bool)),
12.27/12.40	                                                                   typing,Env)),
12.27/12.40	                                                                   Ta)),
12.27/12.40	                                     Ta1)) =>
12.27/12.40	       app_encode_app(bool,$o,pp,
12.27/12.40	                      app_encode_app(type,bool,
12.27/12.40	                                     app_encode_app(fun1(type,bool),
12.27/12.40	                                                    app_encode_fun(type,bool),
12.27/12.40	                                                    aa(type,bool),
12.27/12.40	                                                    app_encode_app(dB,
12.27/12.40	                                                                   fun1(
12.27/12.40	                                                                   type,bool),
12.27/12.40	                                                                   app_encode_app(
12.27/12.40	                                                                   fun1(
12.27/12.40	                                                                   dB,
12.27/12.40	                                                                   fun1(
12.27/12.40	                                                                   type,bool)),
12.27/12.40	                                                                   app_encode_fun(
12.27/12.40	                                                                   dB,
12.27/12.40	                                                                   fun1(
12.27/12.40	                                                                   type,bool)),
12.27/12.40	                                                                   aa(
12.27/12.40	                                                                   dB,
12.27/12.40	                                                                   fun1(
12.27/12.40	                                                                   type,bool)),
12.27/12.40	                                                                   app_encode_app(
12.27/12.40	                                                                   fun1(
12.27/12.40	                                                                   nat,type),
12.27/12.40	                                                                   fun1(
12.27/12.40	                                                                   dB,
12.27/12.40	                                                                   fun1(
12.27/12.40	                                                                   type,bool)),
12.27/12.40	                                                                   typing,Env)),
12.27/12.40	                                                                   app_encode_app(
12.27/12.40	                                                                   dB,dB,
12.27/12.40	                                                                   app_encode_app(
12.27/12.40	                                                                   fun1(
12.27/12.40	                                                                   dB,dB),
12.27/12.40	                                                                   app_encode_fun(
12.27/12.40	                                                                   dB,dB),
12.27/12.40	                                                                   aa(dB,dB),
12.27/12.40	                                                                   app_encode_app(
12.27/12.40	                                                                   dB,
12.27/12.40	                                                                   fun1(
12.27/12.40	                                                                   dB,dB),
12.27/12.40	                                                                   app_encode_app(
12.27/12.40	                                                                   fun1(
12.27/12.40	                                                                   dB,
12.27/12.40	                                                                   fun1(
12.27/12.40	                                                                   dB,dB)),
12.27/12.40	                                                                   app_encode_fun(
12.27/12.40	                                                                   dB,
12.27/12.40	                                                                   fun1(
12.27/12.40	                                                                   dB,dB)),
12.27/12.40	                                                                   aa(
12.27/12.40	                                                                   dB,
12.27/12.40	                                                                   fun1(
12.27/12.40	                                                                   dB,dB)),
12.27/12.40	                                                                   app),S1)),
12.27/12.40	                                                                   Ta))),
12.27/12.40	                                     Ua)))))).
12.27/12.40	tff('1', plain,
12.27/12.40	    ![X4 : fun1(nat, type), X5 : dB, X6 : type, X7 : dB, X8 : type]:
12.27/12.40	      (~ app_encode_app(bool, $o, pp, 
12.27/12.40	           app_encode_app(type, bool, 
12.27/12.40	             app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
12.27/12.40	               aa(type, bool), 
12.27/12.40	               app_encode_app(dB, fun1(type, bool), 
12.27/12.40	                 app_encode_app(fun1(dB, fun1(type, bool)), 
12.27/12.40	                   app_encode_fun(dB, fun1(type, bool)), 
12.27/12.40	                   aa(dB, fun1(type, bool)), 
12.27/12.40	                   app_encode_app(fun1(nat, type), 
12.27/12.40	                     fun1(dB, fun1(type, bool)), typing, X4)), X5)), X6))
12.27/12.40	       | app_encode_app(bool, $o, pp, 
12.27/12.40	           app_encode_app(type, bool, 
12.27/12.40	             app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
12.27/12.40	               aa(type, bool), 
12.27/12.40	               app_encode_app(dB, fun1(type, bool), 
12.27/12.40	                 app_encode_app(fun1(dB, fun1(type, bool)), 
12.27/12.40	                   app_encode_fun(dB, fun1(type, bool)), 
12.27/12.40	                   aa(dB, fun1(type, bool)), 
12.27/12.40	                   app_encode_app(fun1(nat, type), 
12.27/12.40	                     fun1(dB, fun1(type, bool)), typing, X4)), 
12.27/12.40	                 app_encode_app(dB, dB, 
12.27/12.40	                   app_encode_app(fun1(dB, dB), app_encode_fun(dB, dB), 
12.27/12.40	                     aa(dB, dB), 
12.27/12.40	                     app_encode_app(dB, fun1(dB, dB), 
12.27/12.40	                       app_encode_app(fun1(dB, fun1(dB, dB)), 
12.27/12.40	                         app_encode_fun(dB, fun1(dB, dB)), 
12.27/12.40	                         aa(dB, fun1(dB, dB)), app), X7)), X5))), X8))
12.27/12.40	       | ~ app_encode_app(bool, $o, pp, 
12.27/12.40	             app_encode_app(type, bool, 
12.27/12.40	               app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
12.27/12.40	                 aa(type, bool), 
12.27/12.40	                 app_encode_app(dB, fun1(type, bool), 
12.27/12.40	                   app_encode_app(fun1(dB, fun1(type, bool)), 
12.27/12.40	                     app_encode_fun(dB, fun1(type, bool)), 
12.27/12.40	                     aa(dB, fun1(type, bool)), 
12.27/12.40	                     app_encode_app(fun1(nat, type), 
12.27/12.40	                       fun1(dB, fun1(type, bool)), typing, X4)), X7)), 
12.27/12.40	               app_encode_app(type, type, 
12.27/12.40	                 app_encode_app(fun1(type, type), 
12.27/12.40	                   app_encode_fun(type, type), aa(type, type), 
12.27/12.40	                   app_encode_app(type, fun1(type, type), 
12.27/12.40	                     app_encode_app(fun1(type, fun1(type, type)), 
12.27/12.40	                       app_encode_fun(type, fun1(type, type)), 
12.27/12.40	                       aa(type, fun1(type, type)), fun), X6)), X8)))),
12.27/12.40	    inference('cnf', [status(esa)], [zf_stmt_66])).
12.27/12.40	tff('2', plain,
12.27/12.40	    ![X0 : type, X1 : dB]:
12.27/12.40	      (~ $true
12.27/12.40	       | ~ app_encode_app(bool, $o, pp, 
12.27/12.40	             app_encode_app(type, bool, 
12.27/12.40	               app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
12.27/12.40	                 aa(type, bool), 
12.27/12.40	                 app_encode_app(dB, fun1(type, bool), 
12.27/12.40	                   app_encode_app(fun1(dB, fun1(type, bool)), 
12.27/12.40	                     app_encode_fun(dB, fun1(type, bool)), 
12.27/12.40	                     aa(dB, fun1(type, bool)), 
12.27/12.40	                     app_encode_app(fun1(nat, type), 
12.27/12.40	                       fun1(dB, fun1(type, bool)), typing, e)), X1)), 
12.27/12.40	               app_encode_app(type, type, 
12.27/12.40	                 app_encode_app(fun1(type, type), 
12.27/12.40	                   app_encode_fun(type, type), aa(type, type), 
12.27/12.40	                   app_encode_app(type, fun1(type, type), 
12.27/12.40	                     app_encode_app(fun1(type, fun1(type, type)), 
12.27/12.40	                       app_encode_fun(type, fun1(type, type)), 
12.27/12.40	                       aa(type, fun1(type, type)), fun), t2)), X0)))
12.27/12.40	       | app_encode_app(bool, $o, pp, 
12.27/12.40	           app_encode_app(type, bool, 
12.27/12.40	             app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
12.27/12.40	               aa(type, bool), 
12.27/12.40	               app_encode_app(dB, fun1(type, bool), 
12.27/12.40	                 app_encode_app(fun1(dB, fun1(type, bool)), 
12.27/12.40	                   app_encode_fun(dB, fun1(type, bool)), 
12.27/12.40	                   aa(dB, fun1(type, bool)), 
12.27/12.40	                   app_encode_app(fun1(nat, type), 
12.27/12.40	                     fun1(dB, fun1(type, bool)), typing, e)), 
12.27/12.40	                 app_encode_app(dB, dB, 
12.27/12.40	                   app_encode_app(fun1(dB, dB), app_encode_fun(dB, dB), 
12.27/12.40	                     aa(dB, dB), 
12.27/12.40	                     app_encode_app(dB, fun1(dB, dB), 
12.27/12.40	                       app_encode_app(fun1(dB, fun1(dB, dB)), 
12.27/12.40	                         app_encode_fun(dB, fun1(dB, dB)), 
12.27/12.40	                         aa(dB, fun1(dB, dB)), app), X1)), 
12.27/12.40	                   app_encode_app(nat, dB, 
12.27/12.40	                     app_encode_app(fun1(nat, dB), app_encode_fun(nat, dB), 
12.27/12.40	                       aa(nat, dB), 
12.27/12.40	                       app_encode_app(dB, fun1(nat, dB), 
12.27/12.40	                         app_encode_app(fun1(dB, fun1(nat, dB)), 
12.27/12.40	                           app_encode_fun(dB, fun1(nat, dB)), 
12.27/12.40	                           aa(dB, fun1(nat, dB)), 
12.27/12.40	                           app_encode_app(dB, fun1(dB, fun1(nat, dB)), 
12.27/12.40	                             app_encode_app(
12.27/12.40	                               fun1(dB, fun1(dB, fun1(nat, dB))), 
12.27/12.40	                               app_encode_fun(dB, fun1(dB, fun1(nat, dB))), 
12.27/12.40	                               aa(dB, fun1(dB, fun1(nat, dB))), subst), a)), 
12.27/12.40	                         u)), i)))), X0))),
12.27/12.40	    inference('sup-', [status(thm)], ['0', '1'])).
12.27/12.40	tff('3', plain,
12.27/12.40	    ![X0 : type, X1 : dB]:
12.27/12.40	      (app_encode_app(bool, $o, pp, 
12.27/12.40	         app_encode_app(type, bool, 
12.27/12.40	           app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
12.27/12.40	             aa(type, bool), 
12.27/12.40	             app_encode_app(dB, fun1(type, bool), 
12.27/12.40	               app_encode_app(fun1(dB, fun1(type, bool)), 
12.27/12.40	                 app_encode_fun(dB, fun1(type, bool)), 
12.27/12.40	                 aa(dB, fun1(type, bool)), 
12.27/12.40	                 app_encode_app(fun1(nat, type), fun1(dB, fun1(type, bool)), 
12.27/12.40	                   typing, e)), 
12.27/12.40	               app_encode_app(dB, dB, 
12.27/12.40	                 app_encode_app(fun1(dB, dB), app_encode_fun(dB, dB), 
12.27/12.40	                   aa(dB, dB), 
12.27/12.40	                   app_encode_app(dB, fun1(dB, dB), 
12.27/12.40	                     app_encode_app(fun1(dB, fun1(dB, dB)), 
12.27/12.40	                       app_encode_fun(dB, fun1(dB, dB)), 
12.27/12.40	                       aa(dB, fun1(dB, dB)), app), X1)), 
12.27/12.40	                 app_encode_app(nat, dB, 
12.27/12.40	                   app_encode_app(fun1(nat, dB), app_encode_fun(nat, dB), 
12.27/12.40	                     aa(nat, dB), 
12.27/12.40	                     app_encode_app(dB, fun1(nat, dB), 
12.27/12.40	                       app_encode_app(fun1(dB, fun1(nat, dB)), 
12.27/12.40	                         app_encode_fun(dB, fun1(nat, dB)), 
12.27/12.40	                         aa(dB, fun1(nat, dB)), 
12.27/12.40	                         app_encode_app(dB, fun1(dB, fun1(nat, dB)), 
12.27/12.40	                           app_encode_app(fun1(dB, fun1(dB, fun1(nat, dB))), 
12.27/12.40	                             app_encode_fun(dB, fun1(dB, fun1(nat, dB))), 
12.27/12.40	                             aa(dB, fun1(dB, fun1(nat, dB))), subst), a)), u)), 
12.27/12.40	                   i)))), X0))
12.27/12.40	       | ~ app_encode_app(bool, $o, pp, 
12.27/12.40	             app_encode_app(type, bool, 
12.27/12.40	               app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
12.27/12.40	                 aa(type, bool), 
12.27/12.40	                 app_encode_app(dB, fun1(type, bool), 
12.27/12.40	                   app_encode_app(fun1(dB, fun1(type, bool)), 
12.27/12.40	                     app_encode_fun(dB, fun1(type, bool)), 
12.27/12.40	                     aa(dB, fun1(type, bool)), 
12.27/12.40	                     app_encode_app(fun1(nat, type), 
12.27/12.40	                       fun1(dB, fun1(type, bool)), typing, e)), X1)), 
12.27/12.40	               app_encode_app(type, type, 
12.27/12.40	                 app_encode_app(fun1(type, type), 
12.27/12.40	                   app_encode_fun(type, type), aa(type, type), 
12.27/12.40	                   app_encode_app(type, fun1(type, type), 
12.27/12.40	                     app_encode_app(fun1(type, fun1(type, type)), 
12.27/12.40	                       app_encode_fun(type, fun1(type, type)), 
12.27/12.40	                       aa(type, fun1(type, type)), fun), t2)), X0)))),
12.27/12.40	    inference('simplify', [status(thm)], ['2'])).
12.27/12.40	tff(zf_stmt_163, axiom,
12.27/12.40	  (![A:$tType,C:$tType,B:$tType,R:A,Q:B,P:fun1(A,fun1(B,C))]:
12.27/12.40	     (app_encode_app(A,C,
12.27/12.40	                     app_encode_app(fun1(A,C),app_encode_fun(A,C),aa(A,C),
12.27/12.40	                                    app_encode_app(B,fun1(A,C),
12.27/12.40	                                                   app_encode_app(fun1(
12.27/12.40	                                                                  A,fun1(B,C)),
12.27/12.40	                                                                  app_encode_fun(
12.27/12.40	                                                                  B,fun1(A,C)),
12.27/12.40	                                                                  combc(
12.27/12.40	                                                                  A,B,C),P),
12.27/12.40	                                                   Q)),
12.27/12.40	                     R) =
12.27/12.40	      app_encode_app(B,C,
12.27/12.40	                     app_encode_app(fun1(B,C),app_encode_fun(B,C),aa(B,C),
12.27/12.40	                                    app_encode_app(A,fun1(B,C),
12.27/12.40	                                                   app_encode_app(fun1(
12.27/12.40	                                                                  A,fun1(B,C)),
12.27/12.40	                                                                  app_encode_fun(
12.27/12.40	                                                                  A,fun1(B,C)),
12.27/12.40	                                                                  aa(
12.27/12.40	                                                                  A,fun1(B,C)),
12.27/12.40	                                                                  P),
12.27/12.40	                                                   R)),
12.27/12.40	                     Q)))).
12.27/12.40	tff('4', plain,
12.27/12.40	    ![X307 : $tType, X308 : $tType, X309 : $tType, 
12.27/12.40	      X310 : fun1(X309, fun1(X307, X308)), X311 : X309, X312 : X307]:
12.27/12.40	      app_encode_app(X309, X308, 
12.27/12.40	        app_encode_app(fun1(X309, X308), app_encode_fun(X309, X308), 
12.27/12.40	          aa(X309, X308), 
12.27/12.40	          app_encode_app(X307, fun1(X309, X308), 
12.27/12.40	            app_encode_app(fun1(X309, fun1(X307, X308)), 
12.27/12.40	              app_encode_fun(X307, fun1(X309, X308)), 
12.27/12.40	              combc(X309, X307, X308), X310), X312)), X311)
12.27/12.40	       = app_encode_app(X307, X308, 
12.27/12.40	           app_encode_app(fun1(X307, X308), app_encode_fun(X307, X308), 
12.27/12.40	             aa(X307, X308), 
12.27/12.40	             app_encode_app(X309, fun1(X307, X308), 
12.27/12.40	               app_encode_app(fun1(X309, fun1(X307, X308)), 
12.27/12.40	                 app_encode_fun(X309, fun1(X307, X308)), 
12.27/12.40	                 aa(X309, fun1(X307, X308)), X310), X311)), X312),
12.27/12.40	    inference('cnf', [status(esa)], [zf_stmt_163])).
12.27/12.40	tff('5', plain,
12.27/12.40	    ![X0 : type, X1 : dB]:
12.27/12.40	      (app_encode_app(bool, $o, pp, 
12.27/12.40	         app_encode_app(dB, bool, 
12.27/12.40	           app_encode_app(fun1(dB, bool), app_encode_fun(dB, bool), 
12.27/12.40	             aa(dB, bool), 
12.27/12.40	             app_encode_app(type, fun1(dB, bool), 
12.27/12.40	               app_encode_app(fun1(dB, fun1(type, bool)), 
12.27/12.40	                 app_encode_fun(type, fun1(dB, bool)), 
12.27/12.40	                 combc(dB, type, bool), 
12.27/12.40	                 app_encode_app(fun1(nat, type), fun1(dB, fun1(type, bool)), 
12.27/12.40	                   typing, e)), X0)), 
12.27/12.40	           app_encode_app(dB, dB, 
12.27/12.40	             app_encode_app(fun1(dB, dB), app_encode_fun(dB, dB), 
12.27/12.40	               aa(dB, dB), 
12.27/12.40	               app_encode_app(dB, fun1(dB, dB), 
12.27/12.40	                 app_encode_app(fun1(dB, fun1(dB, dB)), 
12.27/12.40	                   app_encode_fun(dB, fun1(dB, dB)), combc(dB, dB, dB), app), 
12.27/12.40	                 app_encode_app(dB, dB, 
12.27/12.40	                   app_encode_app(fun1(dB, dB), app_encode_fun(dB, dB), 
12.27/12.40	                     aa(dB, dB), 
12.27/12.40	                     app_encode_app(nat, fun1(dB, dB), 
12.27/12.40	                       app_encode_app(fun1(dB, fun1(nat, dB)), 
12.27/12.40	                         app_encode_fun(nat, fun1(dB, dB)), 
12.27/12.40	                         combc(dB, nat, dB), 
12.27/12.40	                         app_encode_app(dB, fun1(dB, fun1(nat, dB)), 
12.27/12.40	                           app_encode_app(fun1(dB, fun1(dB, fun1(nat, dB))), 
12.27/12.40	                             app_encode_fun(dB, fun1(dB, fun1(nat, dB))), 
12.27/12.40	                             combc(dB, dB, fun1(nat, dB)), subst), u)), i)), 
12.27/12.40	                   a))), X1)))
12.27/12.40	       | ~ app_encode_app(bool, $o, pp, 
12.27/12.40	             app_encode_app(dB, bool, 
12.27/12.40	               app_encode_app(fun1(dB, bool), app_encode_fun(dB, bool), 
12.27/12.40	                 aa(dB, bool), 
12.27/12.40	                 app_encode_app(type, fun1(dB, bool), 
12.27/12.40	                   app_encode_app(fun1(dB, fun1(type, bool)), 
12.27/12.40	                     app_encode_fun(type, fun1(dB, bool)), 
12.27/12.40	                     combc(dB, type, bool), 
12.27/12.40	                     app_encode_app(fun1(nat, type), 
12.27/12.40	                       fun1(dB, fun1(type, bool)), typing, e)), 
12.27/12.40	                   app_encode_app(type, type, 
12.27/12.40	                     app_encode_app(fun1(type, type), 
12.27/12.40	                       app_encode_fun(type, type), aa(type, type), 
12.27/12.40	                       app_encode_app(type, fun1(type, type), 
12.27/12.40	                         app_encode_app(fun1(type, fun1(type, type)), 
12.27/12.40	                           app_encode_fun(type, fun1(type, type)), 
12.27/12.40	                           combc(type, type, type), fun), X0)), t2))), X1))),
12.27/12.40	    inference('demod', [status(thm)], ['3', '4', '4', '4', '4', '4', '4'])).
12.27/12.40	tff(zf_stmt_173, conjecture,
12.27/12.40	  (app_encode_app(bool,$o,pp,
12.27/12.40	                  app_encode_app(type,bool,
12.27/12.40	                                 app_encode_app(fun1(type,bool),
12.27/12.40	                                                app_encode_fun(type,bool),
12.27/12.40	                                                aa(type,bool),
12.27/12.40	                                                app_encode_app(dB,
12.27/12.40	                                                               fun1(type,bool),
12.27/12.40	                                                               app_encode_app(
12.27/12.40	                                                               fun1(dB,
12.27/12.40	                                                                    fun1(
12.27/12.40	                                                                    type,bool)),
12.27/12.40	                                                               app_encode_fun(
12.27/12.40	                                                               dB,
12.27/12.40	                                                               fun1(type,bool)),
12.27/12.40	                                                               aa(dB,
12.27/12.40	                                                                  fun1(
12.27/12.40	                                                                  type,bool)),
12.27/12.40	                                                               app_encode_app(
12.27/12.40	                                                               fun1(nat,type),
12.27/12.40	                                                               fun1(dB,
12.27/12.40	                                                                    fun1(
12.27/12.40	                                                                    type,bool)),
12.27/12.40	                                                               typing,e)),
12.27/12.40	                                                               app_encode_app(
12.27/12.40	                                                               dB,dB,
12.27/12.40	                                                               app_encode_app(
12.27/12.40	                                                               fun1(dB,dB),
12.27/12.40	                                                               app_encode_fun(
12.27/12.40	                                                               dB,dB),
12.27/12.40	                                                               aa(dB,dB),
12.27/12.40	                                                               app_encode_app(
12.27/12.40	                                                               dB,
12.27/12.40	                                                               fun1(dB,dB),
12.27/12.40	                                                               app_encode_app(
12.27/12.40	                                                               fun1(dB,
12.27/12.40	                                                                    fun1(
12.27/12.40	                                                                    dB,dB)),
12.27/12.40	                                                               app_encode_fun(
12.27/12.40	                                                               dB,fun1(dB,dB)),
12.27/12.40	                                                               aa(dB,
12.27/12.40	                                                                  fun1(dB,dB)),
12.27/12.40	                                                               app),u)),
12.27/12.40	                                                               app_encode_app(
12.27/12.40	                                                               nat,dB,
12.27/12.40	                                                               app_encode_app(
12.27/12.40	                                                               fun1(nat,dB),
12.27/12.40	                                                               app_encode_fun(
12.27/12.40	                                                               nat,dB),
12.27/12.40	                                                               aa(nat,dB),
12.27/12.40	                                                               app_encode_app(
12.27/12.40	                                                               dB,
12.27/12.40	                                                               fun1(nat,dB),
12.27/12.40	                                                               app_encode_app(
12.27/12.40	                                                               fun1(dB,
12.27/12.40	                                                                    fun1(
12.27/12.40	                                                                    nat,dB)),
12.27/12.40	                                                               app_encode_fun(
12.27/12.40	                                                               dB,
12.27/12.40	                                                               fun1(nat,dB)),
12.27/12.40	                                                               aa(dB,
12.27/12.40	                                                                  fun1(
12.27/12.40	                                                                  nat,dB)),
12.27/12.40	                                                               app_encode_app(
12.27/12.40	                                                               dB,
12.27/12.40	                                                               fun1(dB,
12.27/12.40	                                                                    fun1(
12.27/12.40	                                                                    nat,dB)),
12.27/12.40	                                                               app_encode_app(
12.27/12.40	                                                               fun1(dB,
12.27/12.40	                                                                    fun1(
12.27/12.40	                                                                    dB,
12.27/12.40	                                                                    fun1(
12.27/12.40	                                                                    nat,dB))),
12.27/12.40	                                                               app_encode_fun(
12.27/12.40	                                                               dB,
12.27/12.40	                                                               fun1(dB,
12.27/12.40	                                                                    fun1(
12.27/12.40	                                                                    nat,dB))),
12.27/12.40	                                                               aa(dB,
12.27/12.40	                                                                  fun1(
12.27/12.40	                                                                  dB,
12.27/12.40	                                                                  fun1(
12.27/12.40	                                                                  nat,dB))),
12.27/12.40	                                                               subst),a)),u)),
12.27/12.40	                                                               i)))),
12.27/12.40	                                 app_encode_app(type,type,
12.27/12.40	                                                app_encode_app(list(type),
12.27/12.40	                                                               app_encode_fun(
12.27/12.40	                                                               type,type),
12.27/12.40	                                                               app_encode_app(
12.27/12.40	                                                               fun1(type,
12.27/12.40	                                                                    fun1(
12.27/12.40	                                                                    type,type)),
12.27/12.40	                                                               app_encode_fun(
12.27/12.40	                                                               list(type),
12.27/12.40	                                                               app_encode_fun(
12.27/12.40	                                                               type,type)),
12.27/12.40	                                                               foldr(
12.27/12.40	                                                               type,type),fun),
12.27/12.40	                                                               ts),
12.27/12.40	                                                t))))).
12.27/12.40	tff(zf_stmt_0, negated_conjecture,
12.27/12.40	  (~
12.27/12.40	    app_encode_app(bool,$o,pp,
12.27/12.40	                   app_encode_app(type,bool,
12.27/12.40	                                  app_encode_app(fun1(type,bool),
12.27/12.40	                                                 app_encode_fun(type,bool),
12.27/12.40	                                                 aa(type,bool),
12.27/12.40	                                                 app_encode_app(dB,
12.27/12.40	                                                                fun1(
12.27/12.40	                                                                type,bool),
12.27/12.40	                                                                app_encode_app(
12.27/12.40	                                                                fun1(
12.27/12.40	                                                                dB,
12.27/12.40	                                                                fun1(
12.27/12.40	                                                                type,bool)),
12.27/12.40	                                                                app_encode_fun(
12.27/12.40	                                                                dB,
12.27/12.40	                                                                fun1(
12.27/12.40	                                                                type,bool)),
12.27/12.40	                                                                aa(dB,
12.27/12.40	                                                                   fun1(
12.27/12.40	                                                                   type,bool)),
12.27/12.40	                                                                app_encode_app(
12.27/12.40	                                                                fun1(
12.27/12.40	                                                                nat,type),
12.27/12.40	                                                                fun1(
12.27/12.40	                                                                dB,
12.27/12.40	                                                                fun1(
12.27/12.40	                                                                type,bool)),
12.27/12.40	                                                                typing,e)),
12.27/12.40	                                                                app_encode_app(
12.27/12.40	                                                                dB,dB,
12.27/12.40	                                                                app_encode_app(
12.27/12.40	                                                                fun1(dB,dB),
12.27/12.40	                                                                app_encode_fun(
12.27/12.40	                                                                dB,dB),
12.27/12.40	                                                                aa(dB,dB),
12.27/12.40	                                                                app_encode_app(
12.27/12.40	                                                                dB,
12.27/12.40	                                                                fun1(dB,dB),
12.27/12.40	                                                                app_encode_app(
12.27/12.40	                                                                fun1(
12.27/12.40	                                                                dB,
12.27/12.40	                                                                fun1(dB,dB)),
12.27/12.40	                                                                app_encode_fun(
12.27/12.40	                                                                dB,
12.27/12.40	                                                                fun1(dB,dB)),
12.27/12.40	                                                                aa(dB,
12.27/12.40	                                                                   fun1(
12.27/12.40	                                                                   dB,dB)),
12.27/12.40	                                                                app),u)),
12.27/12.40	                                                                app_encode_app(
12.27/12.40	                                                                nat,dB,
12.27/12.40	                                                                app_encode_app(
12.27/12.40	                                                                fun1(nat,dB),
12.27/12.40	                                                                app_encode_fun(
12.27/12.40	                                                                nat,dB),
12.27/12.40	                                                                aa(nat,dB),
12.27/12.40	                                                                app_encode_app(
12.27/12.40	                                                                dB,
12.27/12.40	                                                                fun1(nat,dB),
12.27/12.40	                                                                app_encode_app(
12.27/12.40	                                                                fun1(
12.27/12.40	                                                                dB,
12.27/12.40	                                                                fun1(nat,dB)),
12.27/12.40	                                                                app_encode_fun(
12.27/12.40	                                                                dB,
12.27/12.40	                                                                fun1(nat,dB)),
12.27/12.40	                                                                aa(dB,
12.27/12.40	                                                                   fun1(
12.27/12.40	                                                                   nat,dB)),
12.27/12.40	                                                                app_encode_app(
12.27/12.40	                                                                dB,
12.27/12.40	                                                                fun1(
12.27/12.40	                                                                dB,
12.27/12.40	                                                                fun1(nat,dB)),
12.27/12.40	                                                                app_encode_app(
12.27/12.40	                                                                fun1(
12.27/12.40	                                                                dB,
12.27/12.40	                                                                fun1(
12.27/12.40	                                                                dB,
12.27/12.41	                                                                fun1(nat,dB))),
12.27/12.41	                                                                app_encode_fun(
12.27/12.41	                                                                dB,
12.27/12.41	                                                                fun1(
12.27/12.41	                                                                dB,
12.27/12.41	                                                                fun1(nat,dB))),
12.27/12.41	                                                                aa(dB,
12.27/12.41	                                                                   fun1(
12.27/12.41	                                                                   dB,
12.27/12.41	                                                                   fun1(
12.27/12.41	                                                                   nat,dB))),
12.27/12.41	                                                                subst),a)),u)),
12.27/12.41	                                                                i)))),
12.27/12.41	                                  app_encode_app(type,type,
12.27/12.41	                                                 app_encode_app(list(type),
12.27/12.41	                                                                app_encode_fun(
12.27/12.41	                                                                type,type),
12.27/12.41	                                                                app_encode_app(
12.27/12.41	                                                                fun1(
12.27/12.41	                                                                type,
12.27/12.41	                                                                fun1(
12.27/12.41	                                                                type,type)),
12.27/12.41	                                                                app_encode_fun(
12.27/12.41	                                                                list(type),
12.27/12.41	                                                                app_encode_fun(
12.27/12.41	                                                                type,type)),
12.27/12.41	                                                                foldr(
12.27/12.41	                                                                type,type),
12.27/12.41	                                                                fun),ts),
12.27/12.41	                                                 t))))).
12.27/12.41	tff('6', plain,
12.27/12.41	    ~ app_encode_app(bool, $o, pp, 
12.27/12.41	        app_encode_app(type, bool, 
12.27/12.41	          app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
12.27/12.41	            aa(type, bool), 
12.27/12.41	            app_encode_app(dB, fun1(type, bool), 
12.27/12.41	              app_encode_app(fun1(dB, fun1(type, bool)), 
12.27/12.41	                app_encode_fun(dB, fun1(type, bool)), 
12.27/12.41	                aa(dB, fun1(type, bool)), 
12.27/12.41	                app_encode_app(fun1(nat, type), fun1(dB, fun1(type, bool)), 
12.27/12.41	                  typing, e)), 
12.27/12.41	              app_encode_app(dB, dB, 
12.27/12.41	                app_encode_app(fun1(dB, dB), app_encode_fun(dB, dB), 
12.27/12.41	                  aa(dB, dB), 
12.27/12.41	                  app_encode_app(dB, fun1(dB, dB), 
12.27/12.41	                    app_encode_app(fun1(dB, fun1(dB, dB)), 
12.27/12.41	                      app_encode_fun(dB, fun1(dB, dB)), 
12.27/12.41	                      aa(dB, fun1(dB, dB)), app), u)), 
12.27/12.41	                app_encode_app(nat, dB, 
12.27/12.41	                  app_encode_app(fun1(nat, dB), app_encode_fun(nat, dB), 
12.27/12.41	                    aa(nat, dB), 
12.27/12.41	                    app_encode_app(dB, fun1(nat, dB), 
12.27/12.41	                      app_encode_app(fun1(dB, fun1(nat, dB)), 
12.27/12.41	                        app_encode_fun(dB, fun1(nat, dB)), 
12.27/12.41	                        aa(dB, fun1(nat, dB)), 
12.27/12.41	                        app_encode_app(dB, fun1(dB, fun1(nat, dB)), 
12.27/12.41	                          app_encode_app(fun1(dB, fun1(dB, fun1(nat, dB))), 
12.27/12.41	                            app_encode_fun(dB, fun1(dB, fun1(nat, dB))), 
12.27/12.41	                            aa(dB, fun1(dB, fun1(nat, dB))), subst), a)), u)), 
12.27/12.41	                  i)))), 
12.27/12.41	          app_encode_app(type, type, 
12.27/12.41	            app_encode_app(list(type), app_encode_fun(type, type), 
12.27/12.41	              app_encode_app(fun1(type, fun1(type, type)), 
12.27/12.41	                app_encode_fun(list(type), app_encode_fun(type, type)), 
12.27/12.41	                foldr(type, type), fun), ts), t))),
12.27/12.41	    inference('cnf', [status(esa)], [zf_stmt_0])).
12.27/12.41	tff('7', plain,
12.27/12.41	    ~ app_encode_app(bool, $o, pp, 
12.27/12.41	        app_encode_app(dB, bool, 
12.27/12.41	          app_encode_app(fun1(dB, bool), app_encode_fun(dB, bool), 
12.27/12.41	            aa(dB, bool), 
12.27/12.41	            app_encode_app(type, fun1(dB, bool), 
12.27/12.41	              app_encode_app(fun1(dB, fun1(type, bool)), 
12.27/12.41	                app_encode_fun(type, fun1(dB, bool)), combc(dB, type, bool), 
12.27/12.41	                app_encode_app(fun1(nat, type), fun1(dB, fun1(type, bool)), 
12.27/12.41	                  typing, e)), 
12.27/12.41	              app_encode_app(type, type, 
12.27/12.41	                app_encode_app(list(type), app_encode_fun(type, type), 
12.27/12.41	                  app_encode_app(fun1(type, fun1(type, type)), 
12.27/12.41	                    app_encode_fun(list(type), app_encode_fun(type, type)), 
12.27/12.41	                    foldr(type, type), fun), ts), t))), 
12.27/12.41	          app_encode_app(dB, dB, 
12.27/12.41	            app_encode_app(fun1(dB, dB), app_encode_fun(dB, dB), aa(dB, dB), 
12.27/12.41	              app_encode_app(dB, fun1(dB, dB), 
12.27/12.41	                app_encode_app(fun1(dB, fun1(dB, dB)), 
12.27/12.41	                  app_encode_fun(dB, fun1(dB, dB)), combc(dB, dB, dB), app), 
12.27/12.41	                app_encode_app(dB, dB, 
12.27/12.41	                  app_encode_app(fun1(dB, dB), app_encode_fun(dB, dB), 
12.27/12.41	                    aa(dB, dB), 
12.27/12.41	                    app_encode_app(nat, fun1(dB, dB), 
12.27/12.41	                      app_encode_app(fun1(dB, fun1(nat, dB)), 
12.27/12.41	                        app_encode_fun(nat, fun1(dB, dB)), 
12.27/12.41	                        combc(dB, nat, dB), 
12.27/12.41	                        app_encode_app(dB, fun1(dB, fun1(nat, dB)), 
12.27/12.41	                          app_encode_app(fun1(dB, fun1(dB, fun1(nat, dB))), 
12.27/12.41	                            app_encode_fun(dB, fun1(dB, fun1(nat, dB))), 
12.27/12.41	                            combc(dB, dB, fun1(nat, dB)), subst), u)), i)), 
12.27/12.41	                  a))), u))),
12.27/12.41	    inference('demod', [status(thm)], ['6', '4', '4', '4', '4'])).
12.27/12.41	tff('8', plain,
12.27/12.41	    (~ $true
12.27/12.41	     | ~ app_encode_app(bool, $o, pp, 
12.27/12.41	           app_encode_app(dB, bool, 
12.27/12.41	             app_encode_app(fun1(dB, bool), app_encode_fun(dB, bool), 
12.27/12.41	               aa(dB, bool), 
12.27/12.41	               app_encode_app(type, fun1(dB, bool), 
12.27/12.41	                 app_encode_app(fun1(dB, fun1(type, bool)), 
12.27/12.41	                   app_encode_fun(type, fun1(dB, bool)), 
12.27/12.41	                   combc(dB, type, bool), 
12.27/12.41	                   app_encode_app(fun1(nat, type), 
12.27/12.41	                     fun1(dB, fun1(type, bool)), typing, e)), 
12.27/12.41	                 app_encode_app(type, type, 
12.27/12.41	                   app_encode_app(fun1(type, type), 
12.27/12.41	                     app_encode_fun(type, type), aa(type, type), 
12.27/12.41	                     app_encode_app(type, fun1(type, type), 
12.27/12.41	                       app_encode_app(fun1(type, fun1(type, type)), 
12.27/12.41	                         app_encode_fun(type, fun1(type, type)), 
12.27/12.41	                         combc(type, type, type), fun), 
12.27/12.41	                       app_encode_app(type, type, 
12.27/12.41	                         app_encode_app(list(type), 
12.27/12.41	                           app_encode_fun(type, type), 
12.27/12.41	                           app_encode_app(fun1(type, fun1(type, type)), 
12.27/12.41	                             app_encode_fun(list(type), 
12.27/12.41	                               app_encode_fun(type, type)), 
12.27/12.41	                             foldr(type, type), fun), ts), t))), t2))), u))),
12.27/12.41	    inference('sup-', [status(thm)], ['5', '7'])).
12.27/12.41	tff(zf_stmt_62, axiom,
12.27/12.41	  (app_encode_app(bool,$o,pp,
12.27/12.41	                  app_encode_app(type,bool,
12.27/12.41	                                 app_encode_app(fun1(type,bool),
12.27/12.41	                                                app_encode_fun(type,bool),
12.27/12.41	                                                aa(type,bool),
12.27/12.41	                                                app_encode_app(dB,
12.27/12.41	                                                               fun1(type,bool),
12.27/12.41	                                                               app_encode_app(
12.27/12.41	                                                               fun1(dB,
12.27/12.41	                                                                    fun1(
12.27/12.41	                                                                    type,bool)),
12.27/12.41	                                                               app_encode_fun(
12.27/12.41	                                                               dB,
12.27/12.41	                                                               fun1(type,bool)),
12.27/12.41	                                                               aa(dB,
12.27/12.41	                                                                  fun1(
12.27/12.41	                                                                  type,bool)),
12.27/12.41	                                                               app_encode_app(
12.27/12.41	                                                               fun1(nat,type),
12.27/12.41	                                                               fun1(dB,
12.27/12.41	                                                                    fun1(
12.27/12.41	                                                                    type,bool)),
12.27/12.41	                                                               typing,e)),u)),
12.27/12.41	                                 app_encode_app(type,type,
12.27/12.41	                                                app_encode_app(fun1(type,type),
12.27/12.41	                                                               app_encode_fun(
12.27/12.41	                                                               type,type),
12.27/12.41	                                                               aa(type,type),
12.27/12.41	                                                               app_encode_app(
12.27/12.41	                                                               type,
12.27/12.41	                                                               fun1(type,type),
12.27/12.41	                                                               app_encode_app(
12.27/12.41	                                                               fun1(type,
12.27/12.41	                                                                    fun1(
12.27/12.41	                                                                    type,type)),
12.27/12.41	                                                               app_encode_fun(
12.27/12.41	                                                               type,
12.27/12.41	                                                               fun1(type,type)),
12.27/12.41	                                                               aa(type,
12.27/12.41	                                                                  fun1(
12.27/12.41	                                                                  type,type)),
12.27/12.41	                                                               fun),t2)),
12.27/12.41	                                                app_encode_app(type,type,
12.27/12.41	                                                               app_encode_app(
12.27/12.41	                                                               list(type),
12.27/12.41	                                                               app_encode_fun(
12.27/12.41	                                                               type,type),
12.27/12.41	                                                               app_encode_app(
12.27/12.41	                                                               fun1(type,
12.27/12.41	                                                                    fun1(
12.27/12.41	                                                                    type,type)),
12.27/12.41	                                                               app_encode_fun(
12.27/12.41	                                                               list(type),
12.27/12.41	                                                               app_encode_fun(
12.27/12.41	                                                               type,type)),
12.27/12.41	                                                               foldr(
12.27/12.41	                                                               type,type),fun),
12.27/12.41	                                                               ts),t)))))).
12.27/12.41	tff('9', plain,
12.27/12.41	    app_encode_app(bool, $o, pp, 
12.27/12.41	      app_encode_app(type, bool, 
12.27/12.41	        app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
12.27/12.41	          aa(type, bool), 
12.27/12.41	          app_encode_app(dB, fun1(type, bool), 
12.27/12.41	            app_encode_app(fun1(dB, fun1(type, bool)), 
12.27/12.41	              app_encode_fun(dB, fun1(type, bool)), 
12.27/12.41	              aa(dB, fun1(type, bool)), 
12.27/12.41	              app_encode_app(fun1(nat, type), fun1(dB, fun1(type, bool)), 
12.27/12.41	                typing, e)), u)), 
12.27/12.41	        app_encode_app(type, type, 
12.27/12.41	          app_encode_app(fun1(type, type), app_encode_fun(type, type), 
12.27/12.41	            aa(type, type), 
12.27/12.41	            app_encode_app(type, fun1(type, type), 
12.27/12.41	              app_encode_app(fun1(type, fun1(type, type)), 
12.27/12.41	                app_encode_fun(type, fun1(type, type)), 
12.27/12.41	                aa(type, fun1(type, type)), fun), t2)), 
12.27/12.41	          app_encode_app(type, type, 
12.27/12.41	            app_encode_app(list(type), app_encode_fun(type, type), 
12.27/12.41	              app_encode_app(fun1(type, fun1(type, type)), 
12.27/12.41	                app_encode_fun(list(type), app_encode_fun(type, type)), 
12.27/12.41	                foldr(type, type), fun), ts), t)))),
12.27/12.41	    inference('cnf', [status(esa)], [zf_stmt_62])).
12.27/12.41	tff(zf_stmt_170, axiom, (![P:bool]: ((P = fTrue) | (P = fFalse)))).
12.27/12.41	tff('10', plain, ![X327 : bool]: (X327 = fTrue | X327 = fFalse),
12.27/12.41	    inference('cnf', [status(esa)], [zf_stmt_170])).
12.27/12.41	tff(zf_stmt_159, axiom, (~app_encode_app(bool,$o,pp,fFalse))).
12.27/12.41	tff('11', plain, ~ app_encode_app(bool, $o, pp, fFalse),
12.27/12.41	    inference('cnf', [status(esa)], [zf_stmt_159])).
12.27/12.41	tff('12', plain,
12.27/12.41	    ![X0 : bool]: (~ app_encode_app(bool, $o, pp, X0) | X0 = fTrue),
12.27/12.41	    inference('sup-', [status(thm)], ['10', '11'])).
12.27/12.41	tff('13', plain,
12.27/12.41	    (~ $true
12.27/12.41	     | app_encode_app(type, bool, 
12.27/12.41	         app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
12.27/12.41	           aa(type, bool), 
12.27/12.41	           app_encode_app(dB, fun1(type, bool), 
12.27/12.41	             app_encode_app(fun1(dB, fun1(type, bool)), 
12.27/12.41	               app_encode_fun(dB, fun1(type, bool)), 
12.27/12.41	               aa(dB, fun1(type, bool)), 
12.27/12.41	               app_encode_app(fun1(nat, type), fun1(dB, fun1(type, bool)), 
12.27/12.41	                 typing, e)), u)), 
12.27/12.41	         app_encode_app(type, type, 
12.27/12.41	           app_encode_app(fun1(type, type), app_encode_fun(type, type), 
12.27/12.41	             aa(type, type), 
12.27/12.41	             app_encode_app(type, fun1(type, type), 
12.27/12.41	               app_encode_app(fun1(type, fun1(type, type)), 
12.27/12.41	                 app_encode_fun(type, fun1(type, type)), 
12.27/12.41	                 aa(type, fun1(type, type)), fun), t2)), 
12.27/12.41	           app_encode_app(type, type, 
12.27/12.41	             app_encode_app(list(type), app_encode_fun(type, type), 
12.27/12.41	               app_encode_app(fun1(type, fun1(type, type)), 
12.27/12.41	                 app_encode_fun(list(type), app_encode_fun(type, type)), 
12.27/12.41	                 foldr(type, type), fun), ts), t)))
12.27/12.41	        = fTrue),
12.27/12.41	    inference('sup-', [status(thm)], ['9', '12'])).
12.27/12.41	tff('14', plain,
12.27/12.41	    app_encode_app(type, bool, 
12.27/12.41	      app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
12.27/12.41	        aa(type, bool), 
12.27/12.41	        app_encode_app(dB, fun1(type, bool), 
12.27/12.41	          app_encode_app(fun1(dB, fun1(type, bool)), 
12.27/12.41	            app_encode_fun(dB, fun1(type, bool)), aa(dB, fun1(type, bool)), 
12.27/12.41	            app_encode_app(fun1(nat, type), fun1(dB, fun1(type, bool)), 
12.27/12.41	              typing, e)), u)), 
12.27/12.41	      app_encode_app(type, type, 
12.27/12.41	        app_encode_app(fun1(type, type), app_encode_fun(type, type), 
12.27/12.41	          aa(type, type), 
12.27/12.41	          app_encode_app(type, fun1(type, type), 
12.27/12.41	            app_encode_app(fun1(type, fun1(type, type)), 
12.27/12.41	              app_encode_fun(type, fun1(type, type)), 
12.27/12.41	              aa(type, fun1(type, type)), fun), t2)), 
12.27/12.41	        app_encode_app(type, type, 
12.27/12.41	          app_encode_app(list(type), app_encode_fun(type, type), 
12.27/12.41	            app_encode_app(fun1(type, fun1(type, type)), 
12.27/12.41	              app_encode_fun(list(type), app_encode_fun(type, type)), 
12.27/12.41	              foldr(type, type), fun), ts), t)))
12.27/12.41	     = fTrue,
12.27/12.41	    inference('simplify', [status(thm)], ['13'])).
12.27/12.41	tff('15', plain,
12.27/12.41	    app_encode_app(dB, bool, 
12.27/12.41	      app_encode_app(fun1(dB, bool), app_encode_fun(dB, bool), aa(dB, bool), 
12.27/12.41	        app_encode_app(type, fun1(dB, bool), 
12.27/12.41	          app_encode_app(fun1(dB, fun1(type, bool)), 
12.27/12.41	            app_encode_fun(type, fun1(dB, bool)), combc(dB, type, bool), 
12.27/12.41	            app_encode_app(fun1(nat, type), fun1(dB, fun1(type, bool)), 
12.27/12.41	              typing, e)), 
12.27/12.41	          app_encode_app(type, type, 
12.27/12.41	            app_encode_app(fun1(type, type), app_encode_fun(type, type), 
12.27/12.41	              aa(type, type), 
12.27/12.41	              app_encode_app(type, fun1(type, type), 
12.27/12.41	                app_encode_app(fun1(type, fun1(type, type)), 
12.27/12.41	                  app_encode_fun(type, fun1(type, type)), 
12.27/12.41	                  combc(type, type, type), fun), 
12.27/12.41	                app_encode_app(type, type, 
12.27/12.41	                  app_encode_app(list(type), app_encode_fun(type, type), 
12.27/12.41	                    app_encode_app(fun1(type, fun1(type, type)), 
12.27/12.41	                      app_encode_fun(list(type), app_encode_fun(type, type)), 
12.27/12.41	                      foldr(type, type), fun), ts), t))), t2))), u)
12.27/12.41	     = fTrue,
12.27/12.41	    inference('demod', [status(thm)], ['14', '4', '4'])).
12.27/12.41	tff(zf_stmt_160, axiom, (app_encode_app(bool,$o,pp,fTrue))).
12.27/12.41	tff('16', plain, app_encode_app(bool, $o, pp, fTrue),
12.27/12.41	    inference('cnf', [status(esa)], [zf_stmt_160])).
12.27/12.41	tff('17', plain, (~ $true | ~ $true),
12.27/12.41	    inference('demod', [status(thm)], ['8', '15', '16'])).
12.27/12.41	tff('18', plain, $false, inference('simplify', [status(thm)], ['17'])).
12.27/12.41	
12.27/12.41	% SZS output end Refutation
12.27/12.41	EOF
