0.00/0.00	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : app
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : kbo
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n120.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 07:16:38 CST 2018
10.80/10.97	% done 2269 iterations in 10.768s
10.80/10.97	% SZS status Theorem for 'stdin'
10.80/10.97	% SZS output start Refutation
10.80/10.97	tff(zf_stmt_60, axiom,
10.80/10.97	  (app_encode_app(bool,$o,pp,
10.80/10.97	                  app_encode_app(type,bool,
10.80/10.97	                                 app_encode_app(fun1(type,bool),
10.80/10.97	                                                app_encode_fun(type,bool),
10.80/10.97	                                                aa(type,bool),
10.80/10.97	                                                app_encode_app(dB,
10.80/10.97	                                                               fun1(type,bool),
10.80/10.97	                                                               app_encode_app(
10.80/10.97	                                                               fun1(dB,
10.80/10.97	                                                                    fun1(
10.80/10.97	                                                                    type,bool)),
10.80/10.97	                                                               app_encode_fun(
10.80/10.97	                                                               dB,
10.80/10.97	                                                               fun1(type,bool)),
10.80/10.97	                                                               aa(dB,
10.80/10.97	                                                                  fun1(
10.80/10.97	                                                                  type,bool)),
10.80/10.97	                                                               app_encode_app(
10.80/10.97	                                                               fun1(nat,type),
10.80/10.97	                                                               fun1(dB,
10.80/10.97	                                                                    fun1(
10.80/10.97	                                                                    type,bool)),
10.80/10.97	                                                               typing,e)),
10.80/10.97	                                                               app_encode_app(
10.80/10.97	                                                               nat,dB,
10.80/10.97	                                                               app_encode_app(
10.80/10.97	                                                               fun1(nat,dB),
10.80/10.97	                                                               app_encode_fun(
10.80/10.97	                                                               nat,dB),
10.80/10.97	                                                               aa(nat,dB),
10.80/10.97	                                                               app_encode_app(
10.80/10.97	                                                               dB,
10.80/10.97	                                                               fun1(nat,dB),
10.80/10.97	                                                               app_encode_app(
10.80/10.97	                                                               fun1(dB,
10.80/10.97	                                                                    fun1(
10.80/10.97	                                                                    nat,dB)),
10.80/10.97	                                                               app_encode_fun(
10.80/10.97	                                                               dB,
10.80/10.97	                                                               fun1(nat,dB)),
10.80/10.97	                                                               aa(dB,
10.80/10.97	                                                                  fun1(
10.80/10.97	                                                                  nat,dB)),
10.80/10.97	                                                               app_encode_app(
10.80/10.97	                                                               dB,
10.80/10.97	                                                               fun1(dB,
10.80/10.97	                                                                    fun1(
10.80/10.97	                                                                    nat,dB)),
10.80/10.97	                                                               app_encode_app(
10.80/10.97	                                                               fun1(dB,
10.80/10.97	                                                                    fun1(
10.80/10.97	                                                                    dB,
10.80/10.97	                                                                    fun1(
10.80/10.97	                                                                    nat,dB))),
10.80/10.97	                                                               app_encode_fun(
10.80/10.97	                                                               dB,
10.80/10.97	                                                               fun1(dB,
10.80/10.97	                                                                    fun1(
10.80/10.97	                                                                    nat,dB))),
10.80/10.97	                                                               aa(dB,
10.80/10.97	                                                                  fun1(
10.80/10.97	                                                                  dB,
10.80/10.97	                                                                  fun1(
10.80/10.97	                                                                  nat,dB))),
10.80/10.97	                                                               subst),a)),u)),
10.80/10.97	                                                               i))),
10.80/10.97	                                 t2)))).
10.80/10.97	tff('0', plain,
10.80/10.97	    app_encode_app(bool, $o, pp, 
10.80/10.97	      app_encode_app(type, bool, 
10.80/10.97	        app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
10.80/10.97	          aa(type, bool), 
10.80/10.97	          app_encode_app(dB, fun1(type, bool), 
10.80/10.97	            app_encode_app(fun1(dB, fun1(type, bool)), 
10.80/10.97	              app_encode_fun(dB, fun1(type, bool)), 
10.80/10.97	              aa(dB, fun1(type, bool)), 
10.80/10.97	              app_encode_app(fun1(nat, type), fun1(dB, fun1(type, bool)), 
10.80/10.97	                typing, e)), 
10.80/10.97	            app_encode_app(nat, dB, 
10.80/10.97	              app_encode_app(fun1(nat, dB), app_encode_fun(nat, dB), 
10.80/10.97	                aa(nat, dB), 
10.80/10.97	                app_encode_app(dB, fun1(nat, dB), 
10.80/10.97	                  app_encode_app(fun1(dB, fun1(nat, dB)), 
10.80/10.97	                    app_encode_fun(dB, fun1(nat, dB)), 
10.80/10.97	                    aa(dB, fun1(nat, dB)), 
10.80/10.97	                    app_encode_app(dB, fun1(dB, fun1(nat, dB)), 
10.80/10.97	                      app_encode_app(fun1(dB, fun1(dB, fun1(nat, dB))), 
10.80/10.97	                        app_encode_fun(dB, fun1(dB, fun1(nat, dB))), 
10.80/10.97	                        aa(dB, fun1(dB, fun1(nat, dB))), subst), a)), u)), i))), 
10.80/10.97	        t2)),
10.80/10.97	    inference('cnf', [status(esa)], [zf_stmt_60])).
10.80/10.97	tff(zf_stmt_65, axiom,
10.80/10.97	  (![Ta:dB,Ua:type,Ta1:type,S1:dB,Env:fun1(nat,type)]:
10.80/10.97	     (app_encode_app(bool,$o,pp,
10.80/10.97	                     app_encode_app(type,bool,
10.80/10.97	                                    app_encode_app(fun1(type,bool),
10.80/10.97	                                                   app_encode_fun(type,bool),
10.80/10.97	                                                   aa(type,bool),
10.80/10.97	                                                   app_encode_app(dB,
10.80/10.97	                                                                  fun1(
10.80/10.97	                                                                  type,bool),
10.80/10.97	                                                                  app_encode_app(
10.80/10.97	                                                                  fun1(
10.80/10.97	                                                                  dB,
10.80/10.97	                                                                  fun1(
10.80/10.97	                                                                  type,bool)),
10.80/10.97	                                                                  app_encode_fun(
10.80/10.97	                                                                  dB,
10.80/10.97	                                                                  fun1(
10.80/10.97	                                                                  type,bool)),
10.80/10.97	                                                                  aa(
10.80/10.97	                                                                  dB,
10.80/10.97	                                                                  fun1(
10.80/10.97	                                                                  type,bool)),
10.80/10.97	                                                                  app_encode_app(
10.80/10.97	                                                                  fun1(
10.80/10.97	                                                                  nat,type),
10.80/10.97	                                                                  fun1(
10.80/10.97	                                                                  dB,
10.80/10.97	                                                                  fun1(
10.80/10.97	                                                                  type,bool)),
10.80/10.97	                                                                  typing,Env)),
10.80/10.97	                                                                  S1)),
10.80/10.97	                                    app_encode_app(type,type,
10.80/10.97	                                                   app_encode_app(fun1(
10.80/10.97	                                                                  type,type),
10.80/10.97	                                                                  app_encode_fun(
10.80/10.97	                                                                  type,type),
10.80/10.97	                                                                  aa(
10.80/10.97	                                                                  type,type),
10.80/10.97	                                                                  app_encode_app(
10.80/10.97	                                                                  type,
10.80/10.97	                                                                  fun1(
10.80/10.97	                                                                  type,type),
10.80/10.97	                                                                  app_encode_app(
10.80/10.97	                                                                  fun1(
10.80/10.97	                                                                  type,
10.80/10.97	                                                                  fun1(
10.80/10.97	                                                                  type,type)),
10.80/10.97	                                                                  app_encode_fun(
10.80/10.97	                                                                  type,
10.80/10.97	                                                                  fun1(
10.80/10.97	                                                                  type,type)),
10.80/10.97	                                                                  aa(
10.80/10.97	                                                                  type,
10.80/10.97	                                                                  fun1(
10.80/10.97	                                                                  type,type)),
10.80/10.97	                                                                  fun),Ta1)),
10.80/10.97	                                                   Ua))) =>
10.80/10.97	      (app_encode_app(bool,$o,pp,
10.80/10.97	                      app_encode_app(type,bool,
10.80/10.97	                                     app_encode_app(fun1(type,bool),
10.80/10.97	                                                    app_encode_fun(type,bool),
10.80/10.97	                                                    aa(type,bool),
10.80/10.97	                                                    app_encode_app(dB,
10.80/10.97	                                                                   fun1(
10.80/10.97	                                                                   type,bool),
10.80/10.97	                                                                   app_encode_app(
10.80/10.97	                                                                   fun1(
10.80/10.97	                                                                   dB,
10.80/10.97	                                                                   fun1(
10.80/10.97	                                                                   type,bool)),
10.80/10.97	                                                                   app_encode_fun(
10.80/10.97	                                                                   dB,
10.80/10.97	                                                                   fun1(
10.80/10.97	                                                                   type,bool)),
10.80/10.97	                                                                   aa(
10.80/10.97	                                                                   dB,
10.80/10.97	                                                                   fun1(
10.80/10.97	                                                                   type,bool)),
10.80/10.97	                                                                   app_encode_app(
10.80/10.97	                                                                   fun1(
10.80/10.97	                                                                   nat,type),
10.80/10.97	                                                                   fun1(
10.80/10.97	                                                                   dB,
10.80/10.97	                                                                   fun1(
10.80/10.97	                                                                   type,bool)),
10.80/10.97	                                                                   typing,Env)),
10.80/10.97	                                                                   Ta)),
10.80/10.97	                                     Ta1)) =>
10.80/10.97	       app_encode_app(bool,$o,pp,
10.80/10.97	                      app_encode_app(type,bool,
10.80/10.97	                                     app_encode_app(fun1(type,bool),
10.80/10.97	                                                    app_encode_fun(type,bool),
10.80/10.97	                                                    aa(type,bool),
10.80/10.97	                                                    app_encode_app(dB,
10.80/10.97	                                                                   fun1(
10.80/10.97	                                                                   type,bool),
10.80/10.97	                                                                   app_encode_app(
10.80/10.97	                                                                   fun1(
10.80/10.97	                                                                   dB,
10.80/10.97	                                                                   fun1(
10.80/10.97	                                                                   type,bool)),
10.80/10.97	                                                                   app_encode_fun(
10.80/10.97	                                                                   dB,
10.80/10.97	                                                                   fun1(
10.80/10.97	                                                                   type,bool)),
10.80/10.97	                                                                   aa(
10.80/10.97	                                                                   dB,
10.80/10.97	                                                                   fun1(
10.80/10.97	                                                                   type,bool)),
10.80/10.97	                                                                   app_encode_app(
10.80/10.97	                                                                   fun1(
10.80/10.97	                                                                   nat,type),
10.80/10.97	                                                                   fun1(
10.80/10.97	                                                                   dB,
10.80/10.97	                                                                   fun1(
10.80/10.97	                                                                   type,bool)),
10.80/10.97	                                                                   typing,Env)),
10.80/10.97	                                                                   app_encode_app(
10.80/10.97	                                                                   dB,dB,
10.80/10.97	                                                                   app_encode_app(
10.80/10.97	                                                                   fun1(
10.80/10.97	                                                                   dB,dB),
10.80/10.97	                                                                   app_encode_fun(
10.80/10.97	                                                                   dB,dB),
10.80/10.97	                                                                   aa(dB,dB),
10.80/10.97	                                                                   app_encode_app(
10.80/10.97	                                                                   dB,
10.80/10.97	                                                                   fun1(
10.80/10.97	                                                                   dB,dB),
10.80/10.97	                                                                   app_encode_app(
10.80/10.97	                                                                   fun1(
10.80/10.97	                                                                   dB,
10.80/10.97	                                                                   fun1(
10.80/10.97	                                                                   dB,dB)),
10.80/10.97	                                                                   app_encode_fun(
10.80/10.97	                                                                   dB,
10.80/10.97	                                                                   fun1(
10.80/10.97	                                                                   dB,dB)),
10.80/10.97	                                                                   aa(
10.80/10.97	                                                                   dB,
10.80/10.97	                                                                   fun1(
10.80/10.97	                                                                   dB,dB)),
10.80/10.97	                                                                   app),S1)),
10.80/10.97	                                                                   Ta))),
10.80/10.97	                                     Ua)))))).
10.80/10.97	tff('1', plain,
10.80/10.97	    ![X0 : fun1(nat, type), X1 : dB, X2 : type, X3 : dB, X4 : type]:
10.80/10.97	      (~ app_encode_app(bool, $o, pp, 
10.80/10.97	           app_encode_app(type, bool, 
10.80/10.97	             app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
10.80/10.97	               aa(type, bool), 
10.80/10.97	               app_encode_app(dB, fun1(type, bool), 
10.80/10.97	                 app_encode_app(fun1(dB, fun1(type, bool)), 
10.80/10.97	                   app_encode_fun(dB, fun1(type, bool)), 
10.80/10.97	                   aa(dB, fun1(type, bool)), 
10.80/10.97	                   app_encode_app(fun1(nat, type), 
10.80/10.97	                     fun1(dB, fun1(type, bool)), typing, X0)), X1)), X2))
10.80/10.97	       | app_encode_app(bool, $o, pp, 
10.80/10.97	           app_encode_app(type, bool, 
10.80/10.97	             app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
10.80/10.97	               aa(type, bool), 
10.80/10.97	               app_encode_app(dB, fun1(type, bool), 
10.80/10.97	                 app_encode_app(fun1(dB, fun1(type, bool)), 
10.80/10.97	                   app_encode_fun(dB, fun1(type, bool)), 
10.80/10.97	                   aa(dB, fun1(type, bool)), 
10.80/10.97	                   app_encode_app(fun1(nat, type), 
10.80/10.97	                     fun1(dB, fun1(type, bool)), typing, X0)), 
10.80/10.97	                 app_encode_app(dB, dB, 
10.80/10.97	                   app_encode_app(fun1(dB, dB), app_encode_fun(dB, dB), 
10.80/10.97	                     aa(dB, dB), 
10.80/10.97	                     app_encode_app(dB, fun1(dB, dB), 
10.80/10.97	                       app_encode_app(fun1(dB, fun1(dB, dB)), 
10.80/10.97	                         app_encode_fun(dB, fun1(dB, dB)), 
10.80/10.97	                         aa(dB, fun1(dB, dB)), app), X3)), X1))), X4))
10.80/10.97	       | ~ app_encode_app(bool, $o, pp, 
10.80/10.97	             app_encode_app(type, bool, 
10.80/10.97	               app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
10.80/10.97	                 aa(type, bool), 
10.80/10.97	                 app_encode_app(dB, fun1(type, bool), 
10.80/10.97	                   app_encode_app(fun1(dB, fun1(type, bool)), 
10.80/10.97	                     app_encode_fun(dB, fun1(type, bool)), 
10.80/10.97	                     aa(dB, fun1(type, bool)), 
10.80/10.97	                     app_encode_app(fun1(nat, type), 
10.80/10.97	                       fun1(dB, fun1(type, bool)), typing, X0)), X3)), 
10.80/10.97	               app_encode_app(type, type, 
10.80/10.97	                 app_encode_app(fun1(type, type), 
10.80/10.97	                   app_encode_fun(type, type), aa(type, type), 
10.80/10.97	                   app_encode_app(type, fun1(type, type), 
10.80/10.97	                     app_encode_app(fun1(type, fun1(type, type)), 
10.80/10.97	                       app_encode_fun(type, fun1(type, type)), 
10.80/10.97	                       aa(type, fun1(type, type)), fun), X2)), X4)))),
10.80/10.97	    inference('cnf', [status(esa)], [zf_stmt_65])).
10.80/10.97	tff('2', plain,
10.80/10.97	    ![X0 : type, X1 : dB]:
10.80/10.97	      (~ $true
10.80/10.97	       | ~ app_encode_app(bool, $o, pp, 
10.80/10.97	             app_encode_app(type, bool, 
10.80/10.97	               app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
10.80/10.97	                 aa(type, bool), 
10.80/10.97	                 app_encode_app(dB, fun1(type, bool), 
10.80/10.97	                   app_encode_app(fun1(dB, fun1(type, bool)), 
10.80/10.97	                     app_encode_fun(dB, fun1(type, bool)), 
10.80/10.97	                     aa(dB, fun1(type, bool)), 
10.80/10.97	                     app_encode_app(fun1(nat, type), 
10.80/10.97	                       fun1(dB, fun1(type, bool)), typing, e)), X1)), 
10.80/10.97	               app_encode_app(type, type, 
10.80/10.97	                 app_encode_app(fun1(type, type), 
10.80/10.97	                   app_encode_fun(type, type), aa(type, type), 
10.80/10.97	                   app_encode_app(type, fun1(type, type), 
10.80/10.97	                     app_encode_app(fun1(type, fun1(type, type)), 
10.80/10.97	                       app_encode_fun(type, fun1(type, type)), 
10.80/10.97	                       aa(type, fun1(type, type)), fun), t2)), X0)))
10.80/10.97	       | app_encode_app(bool, $o, pp, 
10.80/10.97	           app_encode_app(type, bool, 
10.80/10.97	             app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
10.80/10.97	               aa(type, bool), 
10.80/10.97	               app_encode_app(dB, fun1(type, bool), 
10.80/10.97	                 app_encode_app(fun1(dB, fun1(type, bool)), 
10.80/10.97	                   app_encode_fun(dB, fun1(type, bool)), 
10.80/10.97	                   aa(dB, fun1(type, bool)), 
10.80/10.97	                   app_encode_app(fun1(nat, type), 
10.80/10.97	                     fun1(dB, fun1(type, bool)), typing, e)), 
10.80/10.97	                 app_encode_app(dB, dB, 
10.80/10.97	                   app_encode_app(fun1(dB, dB), app_encode_fun(dB, dB), 
10.80/10.97	                     aa(dB, dB), 
10.80/10.97	                     app_encode_app(dB, fun1(dB, dB), 
10.80/10.97	                       app_encode_app(fun1(dB, fun1(dB, dB)), 
10.80/10.97	                         app_encode_fun(dB, fun1(dB, dB)), 
10.80/10.97	                         aa(dB, fun1(dB, dB)), app), X1)), 
10.80/10.97	                   app_encode_app(nat, dB, 
10.80/10.97	                     app_encode_app(fun1(nat, dB), app_encode_fun(nat, dB), 
10.80/10.97	                       aa(nat, dB), 
10.80/10.97	                       app_encode_app(dB, fun1(nat, dB), 
10.80/10.97	                         app_encode_app(fun1(dB, fun1(nat, dB)), 
10.80/10.97	                           app_encode_fun(dB, fun1(nat, dB)), 
10.80/10.97	                           aa(dB, fun1(nat, dB)), 
10.80/10.97	                           app_encode_app(dB, fun1(dB, fun1(nat, dB)), 
10.80/10.97	                             app_encode_app(
10.80/10.97	                               fun1(dB, fun1(dB, fun1(nat, dB))), 
10.80/10.97	                               app_encode_fun(dB, fun1(dB, fun1(nat, dB))), 
10.80/10.97	                               aa(dB, fun1(dB, fun1(nat, dB))), subst), a)), 
10.80/10.97	                         u)), i)))), X0))),
10.80/10.97	    inference('sup-', [status(thm)], ['0', '1'])).
10.80/10.97	tff('3', plain,
10.80/10.97	    ![X0 : type, X1 : dB]:
10.80/10.97	      (app_encode_app(bool, $o, pp, 
10.80/10.97	         app_encode_app(type, bool, 
10.80/10.97	           app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
10.80/10.97	             aa(type, bool), 
10.80/10.97	             app_encode_app(dB, fun1(type, bool), 
10.80/10.97	               app_encode_app(fun1(dB, fun1(type, bool)), 
10.80/10.97	                 app_encode_fun(dB, fun1(type, bool)), 
10.80/10.97	                 aa(dB, fun1(type, bool)), 
10.80/10.97	                 app_encode_app(fun1(nat, type), fun1(dB, fun1(type, bool)), 
10.80/10.97	                   typing, e)), 
10.80/10.97	               app_encode_app(dB, dB, 
10.80/10.97	                 app_encode_app(fun1(dB, dB), app_encode_fun(dB, dB), 
10.80/10.97	                   aa(dB, dB), 
10.80/10.97	                   app_encode_app(dB, fun1(dB, dB), 
10.80/10.97	                     app_encode_app(fun1(dB, fun1(dB, dB)), 
10.80/10.97	                       app_encode_fun(dB, fun1(dB, dB)), 
10.80/10.97	                       aa(dB, fun1(dB, dB)), app), X1)), 
10.80/10.97	                 app_encode_app(nat, dB, 
10.80/10.97	                   app_encode_app(fun1(nat, dB), app_encode_fun(nat, dB), 
10.80/10.97	                     aa(nat, dB), 
10.80/10.97	                     app_encode_app(dB, fun1(nat, dB), 
10.80/10.97	                       app_encode_app(fun1(dB, fun1(nat, dB)), 
10.80/10.97	                         app_encode_fun(dB, fun1(nat, dB)), 
10.80/10.97	                         aa(dB, fun1(nat, dB)), 
10.80/10.97	                         app_encode_app(dB, fun1(dB, fun1(nat, dB)), 
10.80/10.97	                           app_encode_app(fun1(dB, fun1(dB, fun1(nat, dB))), 
10.80/10.97	                             app_encode_fun(dB, fun1(dB, fun1(nat, dB))), 
10.80/10.97	                             aa(dB, fun1(dB, fun1(nat, dB))), subst), a)), u)), 
10.80/10.97	                   i)))), X0))
10.80/10.97	       | ~ app_encode_app(bool, $o, pp, 
10.80/10.97	             app_encode_app(type, bool, 
10.80/10.97	               app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
10.80/10.97	                 aa(type, bool), 
10.80/10.97	                 app_encode_app(dB, fun1(type, bool), 
10.80/10.97	                   app_encode_app(fun1(dB, fun1(type, bool)), 
10.80/10.97	                     app_encode_fun(dB, fun1(type, bool)), 
10.80/10.97	                     aa(dB, fun1(type, bool)), 
10.80/10.97	                     app_encode_app(fun1(nat, type), 
10.80/10.97	                       fun1(dB, fun1(type, bool)), typing, e)), X1)), 
10.80/10.97	               app_encode_app(type, type, 
10.80/10.97	                 app_encode_app(fun1(type, type), 
10.80/10.97	                   app_encode_fun(type, type), aa(type, type), 
10.80/10.97	                   app_encode_app(type, fun1(type, type), 
10.80/10.97	                     app_encode_app(fun1(type, fun1(type, type)), 
10.80/10.97	                       app_encode_fun(type, fun1(type, type)), 
10.80/10.97	                       aa(type, fun1(type, type)), fun), t2)), X0)))),
10.80/10.97	    inference('simplify', [status(thm)], ['2'])).
10.80/10.97	tff(zf_stmt_162, axiom,
10.80/10.97	  (![A:$tType,C:$tType,B:$tType,R:A,Q:B,P:fun1(A,fun1(B,C))]:
10.80/10.97	     (app_encode_app(A,C,
10.80/10.97	                     app_encode_app(fun1(A,C),app_encode_fun(A,C),aa(A,C),
10.80/10.97	                                    app_encode_app(B,fun1(A,C),
10.80/10.97	                                                   app_encode_app(fun1(
10.80/10.97	                                                                  A,fun1(B,C)),
10.80/10.97	                                                                  app_encode_fun(
10.80/10.97	                                                                  B,fun1(A,C)),
10.80/10.97	                                                                  combc(
10.80/10.97	                                                                  A,B,C),P),
10.80/10.97	                                                   Q)),
10.80/10.97	                     R) =
10.80/10.97	      app_encode_app(B,C,
10.80/10.97	                     app_encode_app(fun1(B,C),app_encode_fun(B,C),aa(B,C),
10.80/10.97	                                    app_encode_app(A,fun1(B,C),
10.80/10.97	                                                   app_encode_app(fun1(
10.80/10.97	                                                                  A,fun1(B,C)),
10.80/10.97	                                                                  app_encode_fun(
10.80/10.97	                                                                  A,fun1(B,C)),
10.80/10.97	                                                                  aa(
10.80/10.97	                                                                  A,fun1(B,C)),
10.80/10.97	                                                                  P),
10.80/10.97	                                                   R)),
10.80/10.97	                     Q)))).
10.80/10.97	tff('4', plain,
10.80/10.97	    ![X303 : $tType, X304 : $tType, X305 : $tType, 
10.80/10.97	      X306 : fun1(X305, fun1(X303, X304)), X307 : X305, X308 : X303]:
10.80/10.97	      app_encode_app(X305, X304, 
10.80/10.97	        app_encode_app(fun1(X305, X304), app_encode_fun(X305, X304), 
10.80/10.97	          aa(X305, X304), 
10.80/10.97	          app_encode_app(X303, fun1(X305, X304), 
10.80/10.97	            app_encode_app(fun1(X305, fun1(X303, X304)), 
10.80/10.97	              app_encode_fun(X303, fun1(X305, X304)), 
10.80/10.97	              combc(X305, X303, X304), X306), X308)), X307)
10.80/10.97	       = app_encode_app(X303, X304, 
10.80/10.97	           app_encode_app(fun1(X303, X304), app_encode_fun(X303, X304), 
10.80/10.97	             aa(X303, X304), 
10.80/10.97	             app_encode_app(X305, fun1(X303, X304), 
10.80/10.97	               app_encode_app(fun1(X305, fun1(X303, X304)), 
10.80/10.97	                 app_encode_fun(X305, fun1(X303, X304)), 
10.80/10.97	                 aa(X305, fun1(X303, X304)), X306), X307)), X308),
10.80/10.97	    inference('cnf', [status(esa)], [zf_stmt_162])).
10.80/10.97	tff('5', plain,
10.80/10.97	    ![X0 : type, X1 : dB]:
10.80/10.97	      (app_encode_app(bool, $o, pp, 
10.80/10.97	         app_encode_app(dB, bool, 
10.80/10.97	           app_encode_app(fun1(dB, bool), app_encode_fun(dB, bool), 
10.80/10.97	             aa(dB, bool), 
10.80/10.97	             app_encode_app(type, fun1(dB, bool), 
10.80/10.97	               app_encode_app(fun1(dB, fun1(type, bool)), 
10.80/10.97	                 app_encode_fun(type, fun1(dB, bool)), 
10.80/10.97	                 combc(dB, type, bool), 
10.80/10.97	                 app_encode_app(fun1(nat, type), fun1(dB, fun1(type, bool)), 
10.80/10.97	                   typing, e)), X0)), 
10.80/10.97	           app_encode_app(dB, dB, 
10.80/10.97	             app_encode_app(fun1(dB, dB), app_encode_fun(dB, dB), 
10.80/10.97	               aa(dB, dB), 
10.80/10.97	               app_encode_app(dB, fun1(dB, dB), 
10.80/10.97	                 app_encode_app(fun1(dB, fun1(dB, dB)), 
10.80/10.97	                   app_encode_fun(dB, fun1(dB, dB)), combc(dB, dB, dB), app), 
10.80/10.97	                 app_encode_app(dB, dB, 
10.80/10.97	                   app_encode_app(fun1(dB, dB), app_encode_fun(dB, dB), 
10.80/10.97	                     aa(dB, dB), 
10.80/10.97	                     app_encode_app(nat, fun1(dB, dB), 
10.80/10.97	                       app_encode_app(fun1(dB, fun1(nat, dB)), 
10.80/10.97	                         app_encode_fun(nat, fun1(dB, dB)), 
10.80/10.97	                         combc(dB, nat, dB), 
10.80/10.97	                         app_encode_app(dB, fun1(dB, fun1(nat, dB)), 
10.80/10.97	                           app_encode_app(fun1(dB, fun1(dB, fun1(nat, dB))), 
10.80/10.97	                             app_encode_fun(dB, fun1(dB, fun1(nat, dB))), 
10.80/10.97	                             combc(dB, dB, fun1(nat, dB)), subst), u)), i)), 
10.80/10.97	                   a))), X1)))
10.80/10.97	       | ~ app_encode_app(bool, $o, pp, 
10.80/10.97	             app_encode_app(dB, bool, 
10.80/10.97	               app_encode_app(fun1(dB, bool), app_encode_fun(dB, bool), 
10.80/10.97	                 aa(dB, bool), 
10.80/10.97	                 app_encode_app(type, fun1(dB, bool), 
10.80/10.97	                   app_encode_app(fun1(dB, fun1(type, bool)), 
10.80/10.97	                     app_encode_fun(type, fun1(dB, bool)), 
10.80/10.97	                     combc(dB, type, bool), 
10.80/10.97	                     app_encode_app(fun1(nat, type), 
10.80/10.97	                       fun1(dB, fun1(type, bool)), typing, e)), 
10.80/10.97	                   app_encode_app(type, type, 
10.80/10.97	                     app_encode_app(fun1(type, type), 
10.80/10.97	                       app_encode_fun(type, type), aa(type, type), 
10.80/10.97	                       app_encode_app(type, fun1(type, type), 
10.80/10.97	                         app_encode_app(fun1(type, fun1(type, type)), 
10.80/10.97	                           app_encode_fun(type, fun1(type, type)), 
10.80/10.97	                           combc(type, type, type), fun), X0)), t2))), X1))),
10.80/10.97	    inference('demod', [status(thm)], ['3', '4', '4', '4', '4', '4', '4'])).
10.80/10.97	tff(zf_stmt_172, conjecture,
10.80/10.97	  (app_encode_app(bool,$o,pp,
10.80/10.97	                  app_encode_app(type,bool,
10.80/10.97	                                 app_encode_app(fun1(type,bool),
10.80/10.97	                                                app_encode_fun(type,bool),
10.80/10.97	                                                aa(type,bool),
10.80/10.97	                                                app_encode_app(dB,
10.80/10.97	                                                               fun1(type,bool),
10.80/10.97	                                                               app_encode_app(
10.80/10.97	                                                               fun1(dB,
10.80/10.97	                                                                    fun1(
10.80/10.97	                                                                    type,bool)),
10.80/10.97	                                                               app_encode_fun(
10.80/10.97	                                                               dB,
10.80/10.97	                                                               fun1(type,bool)),
10.80/10.97	                                                               aa(dB,
10.80/10.97	                                                                  fun1(
10.80/10.97	                                                                  type,bool)),
10.80/10.97	                                                               app_encode_app(
10.80/10.97	                                                               fun1(nat,type),
10.80/10.97	                                                               fun1(dB,
10.80/10.97	                                                                    fun1(
10.80/10.97	                                                                    type,bool)),
10.80/10.97	                                                               typing,e)),
10.80/10.97	                                                               app_encode_app(
10.80/10.97	                                                               dB,dB,
10.80/10.97	                                                               app_encode_app(
10.80/10.97	                                                               fun1(dB,dB),
10.80/10.97	                                                               app_encode_fun(
10.80/10.97	                                                               dB,dB),
10.80/10.97	                                                               aa(dB,dB),
10.80/10.97	                                                               app_encode_app(
10.80/10.97	                                                               dB,
10.80/10.97	                                                               fun1(dB,dB),
10.80/10.97	                                                               app_encode_app(
10.80/10.97	                                                               fun1(dB,
10.80/10.97	                                                                    fun1(
10.80/10.97	                                                                    dB,dB)),
10.80/10.97	                                                               app_encode_fun(
10.80/10.97	                                                               dB,fun1(dB,dB)),
10.80/10.97	                                                               aa(dB,
10.80/10.97	                                                                  fun1(dB,dB)),
10.80/10.97	                                                               app),u)),
10.80/10.97	                                                               app_encode_app(
10.80/10.97	                                                               nat,dB,
10.80/10.97	                                                               app_encode_app(
10.80/10.97	                                                               fun1(nat,dB),
10.80/10.97	                                                               app_encode_fun(
10.80/10.97	                                                               nat,dB),
10.80/10.97	                                                               aa(nat,dB),
10.80/10.97	                                                               app_encode_app(
10.80/10.97	                                                               dB,
10.80/10.97	                                                               fun1(nat,dB),
10.80/10.97	                                                               app_encode_app(
10.80/10.97	                                                               fun1(dB,
10.80/10.97	                                                                    fun1(
10.80/10.97	                                                                    nat,dB)),
10.80/10.97	                                                               app_encode_fun(
10.80/10.97	                                                               dB,
10.80/10.97	                                                               fun1(nat,dB)),
10.80/10.97	                                                               aa(dB,
10.80/10.97	                                                                  fun1(
10.80/10.97	                                                                  nat,dB)),
10.80/10.97	                                                               app_encode_app(
10.80/10.97	                                                               dB,
10.80/10.97	                                                               fun1(dB,
10.80/10.97	                                                                    fun1(
10.80/10.97	                                                                    nat,dB)),
10.80/10.97	                                                               app_encode_app(
10.80/10.97	                                                               fun1(dB,
10.80/10.97	                                                                    fun1(
10.80/10.97	                                                                    dB,
10.80/10.97	                                                                    fun1(
10.80/10.97	                                                                    nat,dB))),
10.80/10.97	                                                               app_encode_fun(
10.80/10.97	                                                               dB,
10.80/10.97	                                                               fun1(dB,
10.80/10.97	                                                                    fun1(
10.80/10.97	                                                                    nat,dB))),
10.80/10.97	                                                               aa(dB,
10.80/10.97	                                                                  fun1(
10.80/10.97	                                                                  dB,
10.80/10.97	                                                                  fun1(
10.80/10.97	                                                                  nat,dB))),
10.80/10.97	                                                               subst),a)),u)),
10.80/10.97	                                                               i)))),
10.80/10.97	                                 app_encode_app(type,type,
10.80/10.97	                                                app_encode_app(list(type),
10.80/10.97	                                                               app_encode_fun(
10.80/10.97	                                                               type,type),
10.80/10.97	                                                               app_encode_app(
10.80/10.97	                                                               fun1(type,
10.80/10.97	                                                                    fun1(
10.80/10.97	                                                                    type,type)),
10.80/10.97	                                                               app_encode_fun(
10.80/10.97	                                                               list(type),
10.80/10.97	                                                               app_encode_fun(
10.80/10.97	                                                               type,type)),
10.80/10.97	                                                               foldr(
10.80/10.97	                                                               type,type),fun),
10.80/10.97	                                                               ts),
10.80/10.97	                                                t))))).
10.80/10.97	tff(zf_stmt_0, negated_conjecture,
10.80/10.97	  (~
10.80/10.97	    app_encode_app(bool,$o,pp,
10.80/10.97	                   app_encode_app(type,bool,
10.80/10.97	                                  app_encode_app(fun1(type,bool),
10.80/10.97	                                                 app_encode_fun(type,bool),
10.80/10.97	                                                 aa(type,bool),
10.80/10.97	                                                 app_encode_app(dB,
10.80/10.97	                                                                fun1(
10.80/10.97	                                                                type,bool),
10.80/10.97	                                                                app_encode_app(
10.80/10.97	                                                                fun1(
10.80/10.97	                                                                dB,
10.80/10.97	                                                                fun1(
10.80/10.97	                                                                type,bool)),
10.80/10.97	                                                                app_encode_fun(
10.80/10.97	                                                                dB,
10.80/10.97	                                                                fun1(
10.80/10.97	                                                                type,bool)),
10.80/10.97	                                                                aa(dB,
10.80/10.97	                                                                   fun1(
10.80/10.97	                                                                   type,bool)),
10.80/10.97	                                                                app_encode_app(
10.80/10.97	                                                                fun1(
10.80/10.97	                                                                nat,type),
10.80/10.97	                                                                fun1(
10.80/10.97	                                                                dB,
10.80/10.97	                                                                fun1(
10.80/10.97	                                                                type,bool)),
10.80/10.97	                                                                typing,e)),
10.80/10.97	                                                                app_encode_app(
10.80/10.97	                                                                dB,dB,
10.80/10.97	                                                                app_encode_app(
10.80/10.97	                                                                fun1(dB,dB),
10.80/10.97	                                                                app_encode_fun(
10.80/10.97	                                                                dB,dB),
10.80/10.97	                                                                aa(dB,dB),
10.80/10.97	                                                                app_encode_app(
10.80/10.97	                                                                dB,
10.80/10.97	                                                                fun1(dB,dB),
10.80/10.97	                                                                app_encode_app(
10.80/10.97	                                                                fun1(
10.80/10.97	                                                                dB,
10.80/10.97	                                                                fun1(dB,dB)),
10.80/10.97	                                                                app_encode_fun(
10.80/10.97	                                                                dB,
10.80/10.97	                                                                fun1(dB,dB)),
10.80/10.97	                                                                aa(dB,
10.80/10.97	                                                                   fun1(
10.80/10.97	                                                                   dB,dB)),
10.80/10.97	                                                                app),u)),
10.80/10.97	                                                                app_encode_app(
10.80/10.97	                                                                nat,dB,
10.80/10.97	                                                                app_encode_app(
10.80/10.97	                                                                fun1(nat,dB),
10.80/10.97	                                                                app_encode_fun(
10.80/10.97	                                                                nat,dB),
10.80/10.97	                                                                aa(nat,dB),
10.80/10.97	                                                                app_encode_app(
10.80/10.97	                                                                dB,
10.80/10.97	                                                                fun1(nat,dB),
10.80/10.97	                                                                app_encode_app(
10.80/10.97	                                                                fun1(
10.80/10.97	                                                                dB,
10.80/10.97	                                                                fun1(nat,dB)),
10.80/10.97	                                                                app_encode_fun(
10.80/10.97	                                                                dB,
10.80/10.97	                                                                fun1(nat,dB)),
10.80/10.97	                                                                aa(dB,
10.80/10.97	                                                                   fun1(
10.80/10.97	                                                                   nat,dB)),
10.80/10.97	                                                                app_encode_app(
10.80/10.97	                                                                dB,
10.80/10.97	                                                                fun1(
10.80/10.97	                                                                dB,
10.80/10.97	                                                                fun1(nat,dB)),
10.80/10.97	                                                                app_encode_app(
10.80/10.97	                                                                fun1(
10.80/10.97	                                                                dB,
10.80/10.97	                                                                fun1(
10.80/10.97	                                                                dB,
10.80/10.97	                                                                fun1(nat,dB))),
10.80/10.97	                                                                app_encode_fun(
10.80/10.97	                                                                dB,
10.80/10.97	                                                                fun1(
10.80/10.97	                                                                dB,
10.80/10.97	                                                                fun1(nat,dB))),
10.80/10.97	                                                                aa(dB,
10.80/10.97	                                                                   fun1(
10.80/10.97	                                                                   dB,
10.80/10.97	                                                                   fun1(
10.80/10.97	                                                                   nat,dB))),
10.80/10.97	                                                                subst),a)),u)),
10.80/10.97	                                                                i)))),
10.80/10.97	                                  app_encode_app(type,type,
10.80/10.97	                                                 app_encode_app(list(type),
10.80/10.97	                                                                app_encode_fun(
10.80/10.97	                                                                type,type),
10.80/10.97	                                                                app_encode_app(
10.80/10.97	                                                                fun1(
10.80/10.97	                                                                type,
10.80/10.97	                                                                fun1(
10.80/10.97	                                                                type,type)),
10.80/10.97	                                                                app_encode_fun(
10.80/10.97	                                                                list(type),
10.80/10.97	                                                                app_encode_fun(
10.80/10.97	                                                                type,type)),
10.80/10.97	                                                                foldr(
10.80/10.97	                                                                type,type),
10.80/10.97	                                                                fun),ts),
10.80/10.97	                                                 t))))).
10.80/10.97	tff('6', plain,
10.80/10.97	    ~ app_encode_app(bool, $o, pp, 
10.80/10.97	        app_encode_app(type, bool, 
10.80/10.97	          app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
10.80/10.97	            aa(type, bool), 
10.80/10.97	            app_encode_app(dB, fun1(type, bool), 
10.80/10.97	              app_encode_app(fun1(dB, fun1(type, bool)), 
10.80/10.97	                app_encode_fun(dB, fun1(type, bool)), 
10.80/10.97	                aa(dB, fun1(type, bool)), 
10.80/10.97	                app_encode_app(fun1(nat, type), fun1(dB, fun1(type, bool)), 
10.80/10.97	                  typing, e)), 
10.80/10.97	              app_encode_app(dB, dB, 
10.80/10.97	                app_encode_app(fun1(dB, dB), app_encode_fun(dB, dB), 
10.80/10.97	                  aa(dB, dB), 
10.80/10.97	                  app_encode_app(dB, fun1(dB, dB), 
10.80/10.97	                    app_encode_app(fun1(dB, fun1(dB, dB)), 
10.80/10.97	                      app_encode_fun(dB, fun1(dB, dB)), 
10.80/10.97	                      aa(dB, fun1(dB, dB)), app), u)), 
10.80/10.97	                app_encode_app(nat, dB, 
10.80/10.97	                  app_encode_app(fun1(nat, dB), app_encode_fun(nat, dB), 
10.80/10.97	                    aa(nat, dB), 
10.80/10.97	                    app_encode_app(dB, fun1(nat, dB), 
10.80/10.97	                      app_encode_app(fun1(dB, fun1(nat, dB)), 
10.80/10.97	                        app_encode_fun(dB, fun1(nat, dB)), 
10.80/10.97	                        aa(dB, fun1(nat, dB)), 
10.80/10.97	                        app_encode_app(dB, fun1(dB, fun1(nat, dB)), 
10.80/10.97	                          app_encode_app(fun1(dB, fun1(dB, fun1(nat, dB))), 
10.80/10.97	                            app_encode_fun(dB, fun1(dB, fun1(nat, dB))), 
10.80/10.97	                            aa(dB, fun1(dB, fun1(nat, dB))), subst), a)), u)), 
10.80/10.97	                  i)))), 
10.80/10.97	          app_encode_app(type, type, 
10.80/10.97	            app_encode_app(list(type), app_encode_fun(type, type), 
10.80/10.97	              app_encode_app(fun1(type, fun1(type, type)), 
10.80/10.97	                app_encode_fun(list(type), app_encode_fun(type, type)), 
10.80/10.97	                foldr(type, type), fun), ts), t))),
10.80/10.97	    inference('cnf', [status(esa)], [zf_stmt_0])).
10.80/10.97	tff('7', plain,
10.80/10.97	    ~ app_encode_app(bool, $o, pp, 
10.80/10.97	        app_encode_app(dB, bool, 
10.80/10.97	          app_encode_app(fun1(dB, bool), app_encode_fun(dB, bool), 
10.80/10.97	            aa(dB, bool), 
10.80/10.97	            app_encode_app(type, fun1(dB, bool), 
10.80/10.97	              app_encode_app(fun1(dB, fun1(type, bool)), 
10.80/10.97	                app_encode_fun(type, fun1(dB, bool)), combc(dB, type, bool), 
10.80/10.97	                app_encode_app(fun1(nat, type), fun1(dB, fun1(type, bool)), 
10.80/10.97	                  typing, e)), 
10.80/10.97	              app_encode_app(type, type, 
10.80/10.97	                app_encode_app(list(type), app_encode_fun(type, type), 
10.80/10.97	                  app_encode_app(fun1(type, fun1(type, type)), 
10.80/10.97	                    app_encode_fun(list(type), app_encode_fun(type, type)), 
10.80/10.97	                    foldr(type, type), fun), ts), t))), 
10.80/10.97	          app_encode_app(dB, dB, 
10.80/10.97	            app_encode_app(fun1(dB, dB), app_encode_fun(dB, dB), aa(dB, dB), 
10.80/10.97	              app_encode_app(dB, fun1(dB, dB), 
10.80/10.97	                app_encode_app(fun1(dB, fun1(dB, dB)), 
10.80/10.97	                  app_encode_fun(dB, fun1(dB, dB)), combc(dB, dB, dB), app), 
10.80/10.97	                app_encode_app(dB, dB, 
10.80/10.97	                  app_encode_app(fun1(dB, dB), app_encode_fun(dB, dB), 
10.80/10.97	                    aa(dB, dB), 
10.80/10.97	                    app_encode_app(nat, fun1(dB, dB), 
10.80/10.97	                      app_encode_app(fun1(dB, fun1(nat, dB)), 
10.80/10.97	                        app_encode_fun(nat, fun1(dB, dB)), 
10.80/10.97	                        combc(dB, nat, dB), 
10.80/10.97	                        app_encode_app(dB, fun1(dB, fun1(nat, dB)), 
10.80/10.97	                          app_encode_app(fun1(dB, fun1(dB, fun1(nat, dB))), 
10.80/10.97	                            app_encode_fun(dB, fun1(dB, fun1(nat, dB))), 
10.80/10.97	                            combc(dB, dB, fun1(nat, dB)), subst), u)), i)), 
10.80/10.97	                  a))), u))),
10.80/10.97	    inference('demod', [status(thm)], ['6', '4', '4', '4', '4'])).
10.80/10.97	tff('8', plain,
10.80/10.97	    (~ $true
10.80/10.97	     | ~ app_encode_app(bool, $o, pp, 
10.80/10.97	           app_encode_app(dB, bool, 
10.80/10.97	             app_encode_app(fun1(dB, bool), app_encode_fun(dB, bool), 
10.80/10.97	               aa(dB, bool), 
10.80/10.97	               app_encode_app(type, fun1(dB, bool), 
10.80/10.97	                 app_encode_app(fun1(dB, fun1(type, bool)), 
10.80/10.97	                   app_encode_fun(type, fun1(dB, bool)), 
10.80/10.97	                   combc(dB, type, bool), 
10.80/10.97	                   app_encode_app(fun1(nat, type), 
10.80/10.97	                     fun1(dB, fun1(type, bool)), typing, e)), 
10.80/10.97	                 app_encode_app(type, type, 
10.80/10.97	                   app_encode_app(fun1(type, type), 
10.80/10.97	                     app_encode_fun(type, type), aa(type, type), 
10.80/10.97	                     app_encode_app(type, fun1(type, type), 
10.80/10.97	                       app_encode_app(fun1(type, fun1(type, type)), 
10.80/10.97	                         app_encode_fun(type, fun1(type, type)), 
10.80/10.97	                         combc(type, type, type), fun), 
10.80/10.97	                       app_encode_app(type, type, 
10.80/10.97	                         app_encode_app(list(type), 
10.80/10.97	                           app_encode_fun(type, type), 
10.80/10.97	                           app_encode_app(fun1(type, fun1(type, type)), 
10.80/10.97	                             app_encode_fun(list(type), 
10.80/10.97	                               app_encode_fun(type, type)), 
10.80/10.97	                             foldr(type, type), fun), ts), t))), t2))), u))),
10.80/10.97	    inference('sup-', [status(thm)], ['5', '7'])).
10.80/10.97	tff(zf_stmt_61, axiom,
10.80/10.97	  (app_encode_app(bool,$o,pp,
10.80/10.97	                  app_encode_app(type,bool,
10.80/10.97	                                 app_encode_app(fun1(type,bool),
10.80/10.97	                                                app_encode_fun(type,bool),
10.80/10.97	                                                aa(type,bool),
10.80/10.97	                                                app_encode_app(dB,
10.80/10.97	                                                               fun1(type,bool),
10.80/10.97	                                                               app_encode_app(
10.80/10.97	                                                               fun1(dB,
10.80/10.97	                                                                    fun1(
10.80/10.97	                                                                    type,bool)),
10.80/10.97	                                                               app_encode_fun(
10.80/10.97	                                                               dB,
10.80/10.97	                                                               fun1(type,bool)),
10.80/10.97	                                                               aa(dB,
10.80/10.97	                                                                  fun1(
10.80/10.97	                                                                  type,bool)),
10.80/10.97	                                                               app_encode_app(
10.80/10.97	                                                               fun1(nat,type),
10.80/10.97	                                                               fun1(dB,
10.80/10.97	                                                                    fun1(
10.80/10.97	                                                                    type,bool)),
10.80/10.97	                                                               typing,e)),u)),
10.80/10.97	                                 app_encode_app(type,type,
10.80/10.97	                                                app_encode_app(fun1(type,type),
10.80/10.97	                                                               app_encode_fun(
10.80/10.97	                                                               type,type),
10.80/10.97	                                                               aa(type,type),
10.80/10.97	                                                               app_encode_app(
10.80/10.97	                                                               type,
10.80/10.97	                                                               fun1(type,type),
10.80/10.97	                                                               app_encode_app(
10.80/10.97	                                                               fun1(type,
10.80/10.97	                                                                    fun1(
10.80/10.97	                                                                    type,type)),
10.80/10.97	                                                               app_encode_fun(
10.80/10.97	                                                               type,
10.80/10.97	                                                               fun1(type,type)),
10.80/10.97	                                                               aa(type,
10.80/10.97	                                                                  fun1(
10.80/10.97	                                                                  type,type)),
10.80/10.97	                                                               fun),t2)),
10.80/10.97	                                                app_encode_app(type,type,
10.80/10.97	                                                               app_encode_app(
10.80/10.97	                                                               list(type),
10.80/10.97	                                                               app_encode_fun(
10.80/10.97	                                                               type,type),
10.80/10.97	                                                               app_encode_app(
10.80/10.97	                                                               fun1(type,
10.80/10.97	                                                                    fun1(
10.80/10.97	                                                                    type,type)),
10.80/10.97	                                                               app_encode_fun(
10.80/10.97	                                                               list(type),
10.80/10.97	                                                               app_encode_fun(
10.80/10.97	                                                               type,type)),
10.80/10.97	                                                               foldr(
10.80/10.97	                                                               type,type),fun),
10.80/10.97	                                                               ts),t)))))).
10.80/10.97	tff('9', plain,
10.80/10.97	    app_encode_app(bool, $o, pp, 
10.80/10.97	      app_encode_app(type, bool, 
10.80/10.97	        app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
10.80/10.97	          aa(type, bool), 
10.80/10.97	          app_encode_app(dB, fun1(type, bool), 
10.80/10.97	            app_encode_app(fun1(dB, fun1(type, bool)), 
10.80/10.97	              app_encode_fun(dB, fun1(type, bool)), 
10.80/10.97	              aa(dB, fun1(type, bool)), 
10.80/10.97	              app_encode_app(fun1(nat, type), fun1(dB, fun1(type, bool)), 
10.80/10.97	                typing, e)), u)), 
10.80/10.97	        app_encode_app(type, type, 
10.80/10.97	          app_encode_app(fun1(type, type), app_encode_fun(type, type), 
10.80/10.97	            aa(type, type), 
10.80/10.97	            app_encode_app(type, fun1(type, type), 
10.80/10.97	              app_encode_app(fun1(type, fun1(type, type)), 
10.80/10.97	                app_encode_fun(type, fun1(type, type)), 
10.80/10.97	                aa(type, fun1(type, type)), fun), t2)), 
10.80/10.97	          app_encode_app(type, type, 
10.80/10.97	            app_encode_app(list(type), app_encode_fun(type, type), 
10.80/10.97	              app_encode_app(fun1(type, fun1(type, type)), 
10.80/10.97	                app_encode_fun(list(type), app_encode_fun(type, type)), 
10.80/10.97	                foldr(type, type), fun), ts), t)))),
10.80/10.97	    inference('cnf', [status(esa)], [zf_stmt_61])).
10.80/10.97	tff(zf_stmt_169, axiom, (![P:bool]: ((P = fTrue) | (P = fFalse)))).
10.80/10.97	tff('10', plain, ![X323 : bool]: (X323 = fTrue | X323 = fFalse),
10.80/10.97	    inference('cnf', [status(esa)], [zf_stmt_169])).
10.80/10.97	tff(zf_stmt_158, axiom, (~app_encode_app(bool,$o,pp,fFalse))).
10.80/10.97	tff('11', plain, ~ app_encode_app(bool, $o, pp, fFalse),
10.80/10.97	    inference('cnf', [status(esa)], [zf_stmt_158])).
10.80/10.97	tff('12', plain,
10.80/10.97	    ![X0 : bool]: (~ app_encode_app(bool, $o, pp, X0) | X0 = fTrue),
10.80/10.97	    inference('sup-', [status(thm)], ['10', '11'])).
10.80/10.97	tff('13', plain,
10.80/10.97	    (~ $true
10.80/10.97	     | app_encode_app(type, bool, 
10.80/10.97	         app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
10.80/10.97	           aa(type, bool), 
10.80/10.97	           app_encode_app(dB, fun1(type, bool), 
10.80/10.97	             app_encode_app(fun1(dB, fun1(type, bool)), 
10.80/10.97	               app_encode_fun(dB, fun1(type, bool)), 
10.80/10.97	               aa(dB, fun1(type, bool)), 
10.80/10.97	               app_encode_app(fun1(nat, type), fun1(dB, fun1(type, bool)), 
10.80/10.97	                 typing, e)), u)), 
10.80/10.97	         app_encode_app(type, type, 
10.80/10.97	           app_encode_app(fun1(type, type), app_encode_fun(type, type), 
10.80/10.97	             aa(type, type), 
10.80/10.97	             app_encode_app(type, fun1(type, type), 
10.80/10.97	               app_encode_app(fun1(type, fun1(type, type)), 
10.80/10.97	                 app_encode_fun(type, fun1(type, type)), 
10.80/10.97	                 aa(type, fun1(type, type)), fun), t2)), 
10.80/10.97	           app_encode_app(type, type, 
10.80/10.97	             app_encode_app(list(type), app_encode_fun(type, type), 
10.80/10.97	               app_encode_app(fun1(type, fun1(type, type)), 
10.80/10.97	                 app_encode_fun(list(type), app_encode_fun(type, type)), 
10.80/10.97	                 foldr(type, type), fun), ts), t)))
10.80/10.97	        = fTrue),
10.80/10.97	    inference('sup-', [status(thm)], ['9', '12'])).
10.80/10.97	tff('14', plain,
10.80/10.97	    app_encode_app(type, bool, 
10.80/10.97	      app_encode_app(fun1(type, bool), app_encode_fun(type, bool), 
10.80/10.97	        aa(type, bool), 
10.80/10.97	        app_encode_app(dB, fun1(type, bool), 
10.80/10.97	          app_encode_app(fun1(dB, fun1(type, bool)), 
10.80/10.97	            app_encode_fun(dB, fun1(type, bool)), aa(dB, fun1(type, bool)), 
10.80/10.97	            app_encode_app(fun1(nat, type), fun1(dB, fun1(type, bool)), 
10.80/10.97	              typing, e)), u)), 
10.80/10.97	      app_encode_app(type, type, 
10.80/10.97	        app_encode_app(fun1(type, type), app_encode_fun(type, type), 
10.80/10.97	          aa(type, type), 
10.80/10.97	          app_encode_app(type, fun1(type, type), 
10.80/10.97	            app_encode_app(fun1(type, fun1(type, type)), 
10.80/10.97	              app_encode_fun(type, fun1(type, type)), 
10.80/10.97	              aa(type, fun1(type, type)), fun), t2)), 
10.80/10.97	        app_encode_app(type, type, 
10.80/10.97	          app_encode_app(list(type), app_encode_fun(type, type), 
10.80/10.97	            app_encode_app(fun1(type, fun1(type, type)), 
10.80/10.97	              app_encode_fun(list(type), app_encode_fun(type, type)), 
10.80/10.97	              foldr(type, type), fun), ts), t)))
10.80/10.97	     = fTrue,
10.80/10.97	    inference('simplify', [status(thm)], ['13'])).
10.80/10.97	tff('15', plain,
10.80/10.97	    app_encode_app(dB, bool, 
10.80/10.97	      app_encode_app(fun1(dB, bool), app_encode_fun(dB, bool), aa(dB, bool), 
10.80/10.97	        app_encode_app(type, fun1(dB, bool), 
10.80/10.97	          app_encode_app(fun1(dB, fun1(type, bool)), 
10.80/10.97	            app_encode_fun(type, fun1(dB, bool)), combc(dB, type, bool), 
10.80/10.97	            app_encode_app(fun1(nat, type), fun1(dB, fun1(type, bool)), 
10.80/10.97	              typing, e)), 
10.80/10.97	          app_encode_app(type, type, 
10.80/10.97	            app_encode_app(fun1(type, type), app_encode_fun(type, type), 
10.80/10.97	              aa(type, type), 
10.80/10.97	              app_encode_app(type, fun1(type, type), 
10.80/10.97	                app_encode_app(fun1(type, fun1(type, type)), 
10.80/10.97	                  app_encode_fun(type, fun1(type, type)), 
10.80/10.97	                  combc(type, type, type), fun), 
10.80/10.97	                app_encode_app(type, type, 
10.80/10.97	                  app_encode_app(list(type), app_encode_fun(type, type), 
10.80/10.97	                    app_encode_app(fun1(type, fun1(type, type)), 
10.80/10.97	                      app_encode_fun(list(type), app_encode_fun(type, type)), 
10.80/10.97	                      foldr(type, type), fun), ts), t))), t2))), u)
10.80/10.97	     = fTrue,
10.80/10.97	    inference('demod', [status(thm)], ['14', '4', '4'])).
10.80/10.97	tff(zf_stmt_159, axiom, (app_encode_app(bool,$o,pp,fTrue))).
10.80/10.97	tff('16', plain, app_encode_app(bool, $o, pp, fTrue),
10.80/10.97	    inference('cnf', [status(esa)], [zf_stmt_159])).
10.80/10.97	tff('17', plain, (~ $true | ~ $true),
10.80/10.97	    inference('demod', [status(thm)], ['8', '15', '16'])).
10.80/10.97	tff('18', plain, $false, inference('simplify', [status(thm)], ['17'])).
10.80/10.97	
10.80/10.97	% SZS output end Refutation
10.80/10.97	EOF
