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    : rpo6
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 $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n152.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 06:54:53 CST 2018
33.15/33.39	% done 2268 iterations in 33.192s
33.15/33.39	% SZS status Theorem for 'stdin'
33.15/33.39	% SZS output start Refutation
33.15/33.39	tff(zf_stmt_161, conjecture,
33.15/33.39	  (app_encode_app(bool,$o,pp,
33.15/33.39	                  app_encode_app(type,bool,
33.15/33.39	                                 app_encode_app(fun(type,bool),
33.15/33.39	                                                app_encode_fun(type,bool),
33.15/33.39	                                                aa(type,bool),
33.15/33.39	                                                app_encode_app(dB,
33.15/33.39	                                                               fun(type,bool),
33.15/33.39	                                                               app_encode_app(
33.15/33.39	                                                               fun(nat,type),
33.15/33.39	                                                               app_encode_fun(
33.15/33.39	                                                               dB,
33.15/33.39	                                                               fun(type,bool)),
33.15/33.39	                                                               typing,
33.15/33.39	                                                               app_encode_app(
33.15/33.39	                                                               type,
33.15/33.39	                                                               fun(nat,type),
33.15/33.39	                                                               app_encode_app(
33.15/33.39	                                                               nat,
33.15/33.39	                                                               app_encode_fun(
33.15/33.39	                                                               type,
33.15/33.39	                                                               fun(nat,type)),
33.15/33.39	                                                               app_encode_app(
33.15/33.39	                                                               fun(nat,type),
33.15/33.39	                                                               app_encode_fun(
33.15/33.39	                                                               nat,
33.15/33.39	                                                               app_encode_fun(
33.15/33.39	                                                               type,
33.15/33.39	                                                               fun(nat,type))),
33.15/33.39	                                                               shift(type),e),
33.15/33.39	                                                               i),t1)),
33.15/33.39	                                                               app_encode_app(
33.15/33.39	                                                               list(dB),dB,
33.15/33.39	                                                               app_encode_app(
33.15/33.39	                                                               dB,
33.15/33.39	                                                               app_encode_fun(
33.15/33.39	                                                               list(dB),dB),
33.15/33.39	                                                               app_encode_app(
33.15/33.39	                                                               fun(dB,
33.15/33.39	                                                                   fun(dB,dB)),
33.15/33.39	                                                               app_encode_fun(
33.15/33.39	                                                               dB,
33.15/33.39	                                                               app_encode_fun(
33.15/33.39	                                                               list(dB),dB)),
33.15/33.39	                                                               foldl(dB,dB),
33.15/33.39	                                                               app),
33.15/33.39	                                                               app_encode_app(
33.15/33.39	                                                               dB,dB,
33.15/33.39	                                                               app_encode_app(
33.15/33.39	                                                               fun(dB,dB),
33.15/33.39	                                                               app_encode_fun(
33.15/33.39	                                                               dB,dB),
33.15/33.39	                                                               aa(dB,dB),
33.15/33.39	                                                               app_encode_app(
33.15/33.39	                                                               dB,fun(dB,dB),
33.15/33.39	                                                               app_encode_app(
33.15/33.39	                                                               fun(dB,
33.15/33.39	                                                                   fun(dB,dB)),
33.15/33.39	                                                               app_encode_fun(
33.15/33.39	                                                               dB,fun(dB,dB)),
33.15/33.39	                                                               aa(dB,
33.15/33.39	                                                                  fun(dB,dB)),
33.15/33.39	                                                               app),
33.15/33.39	                                                               app_encode_app(
33.15/33.39	                                                               nat,dB,var,n))),
33.15/33.39	                                                               a)),as))),
33.15/33.39	                                 t)))).
33.15/33.39	tff(zf_stmt_0, negated_conjecture,
33.15/33.39	  (~
33.15/33.39	    app_encode_app(bool,$o,pp,
33.15/33.39	                   app_encode_app(type,bool,
33.15/33.39	                                  app_encode_app(fun(type,bool),
33.15/33.39	                                                 app_encode_fun(type,bool),
33.15/33.39	                                                 aa(type,bool),
33.15/33.39	                                                 app_encode_app(dB,
33.15/33.39	                                                                fun(type,bool),
33.15/33.39	                                                                app_encode_app(
33.15/33.39	                                                                fun(nat,type),
33.15/33.39	                                                                app_encode_fun(
33.15/33.39	                                                                dB,
33.15/33.39	                                                                fun(type,bool)),
33.15/33.39	                                                                typing,
33.15/33.39	                                                                app_encode_app(
33.15/33.39	                                                                type,
33.15/33.39	                                                                fun(nat,type),
33.15/33.39	                                                                app_encode_app(
33.15/33.39	                                                                nat,
33.15/33.39	                                                                app_encode_fun(
33.15/33.39	                                                                type,
33.15/33.39	                                                                fun(nat,type)),
33.15/33.39	                                                                app_encode_app(
33.15/33.39	                                                                fun(nat,type),
33.15/33.39	                                                                app_encode_fun(
33.15/33.39	                                                                nat,
33.15/33.39	                                                                app_encode_fun(
33.15/33.39	                                                                type,
33.15/33.39	                                                                fun(nat,type))),
33.15/33.39	                                                                shift(type),e),
33.15/33.39	                                                                i),t1)),
33.15/33.39	                                                                app_encode_app(
33.15/33.39	                                                                list(dB),dB,
33.15/33.39	                                                                app_encode_app(
33.15/33.39	                                                                dB,
33.15/33.39	                                                                app_encode_fun(
33.15/33.39	                                                                list(dB),dB),
33.15/33.39	                                                                app_encode_app(
33.15/33.39	                                                                fun(dB,
33.15/33.39	                                                                    fun(
33.15/33.39	                                                                    dB,dB)),
33.15/33.39	                                                                app_encode_fun(
33.15/33.39	                                                                dB,
33.15/33.39	                                                                app_encode_fun(
33.15/33.39	                                                                list(dB),dB)),
33.15/33.39	                                                                foldl(dB,dB),
33.15/33.39	                                                                app),
33.15/33.39	                                                                app_encode_app(
33.15/33.39	                                                                dB,dB,
33.15/33.39	                                                                app_encode_app(
33.15/33.39	                                                                fun(dB,dB),
33.15/33.39	                                                                app_encode_fun(
33.15/33.39	                                                                dB,dB),
33.15/33.39	                                                                aa(dB,dB),
33.15/33.39	                                                                app_encode_app(
33.15/33.39	                                                                dB,
33.15/33.39	                                                                fun(dB,dB),
33.15/33.39	                                                                app_encode_app(
33.15/33.39	                                                                fun(dB,
33.15/33.39	                                                                    fun(
33.15/33.39	                                                                    dB,dB)),
33.15/33.39	                                                                app_encode_fun(
33.15/33.39	                                                                dB,fun(dB,dB)),
33.15/33.39	                                                                aa(dB,
33.15/33.39	                                                                   fun(dB,dB)),
33.15/33.39	                                                                app),
33.15/33.39	                                                                app_encode_app(
33.15/33.39	                                                                nat,dB,var,n))),
33.15/33.39	                                                                a)),as))),
33.15/33.39	                                  t)))).
33.15/33.39	tff('0', plain,
33.15/33.39	    ~ app_encode_app(bool, $o, pp, 
33.15/33.39	        app_encode_app(type, bool, 
33.15/33.39	          app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
33.15/33.39	            aa(type, bool), 
33.15/33.39	            app_encode_app(dB, fun(type, bool), 
33.15/33.39	              app_encode_app(fun(nat, type), 
33.15/33.39	                app_encode_fun(dB, fun(type, bool)), typing, 
33.15/33.39	                app_encode_app(type, fun(nat, type), 
33.15/33.39	                  app_encode_app(nat, app_encode_fun(type, fun(nat, type)), 
33.15/33.39	                    app_encode_app(fun(nat, type), 
33.15/33.39	                      app_encode_fun(nat, 
33.15/33.39	                        app_encode_fun(type, fun(nat, type))), shift(type), 
33.15/33.39	                      e), i), t1)), 
33.15/33.39	              app_encode_app(list(dB), dB, 
33.15/33.39	                app_encode_app(dB, app_encode_fun(list(dB), dB), 
33.15/33.39	                  app_encode_app(fun(dB, fun(dB, dB)), 
33.15/33.39	                    app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
33.15/33.39	                    foldl(dB, dB), app), 
33.15/33.39	                  app_encode_app(dB, dB, 
33.15/33.39	                    app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), 
33.15/33.39	                      aa(dB, dB), 
33.15/33.39	                      app_encode_app(dB, fun(dB, dB), 
33.15/33.39	                        app_encode_app(fun(dB, fun(dB, dB)), 
33.15/33.39	                          app_encode_fun(dB, fun(dB, dB)), 
33.15/33.39	                          aa(dB, fun(dB, dB)), app), 
33.15/33.39	                        app_encode_app(nat, dB, var, n))), a)), as))), t)),
33.15/33.39	    inference('cnf', [status(esa)], [zf_stmt_0])).
33.15/33.39	tff(zf_stmt_52, axiom, (n = i)).
33.15/33.39	tff('1', plain, n = i, inference('cnf', [status(esa)], [zf_stmt_52])).
33.15/33.39	tff('2', plain,
33.15/33.39	    ~ app_encode_app(bool, $o, pp, 
33.15/33.39	        app_encode_app(type, bool, 
33.15/33.39	          app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
33.15/33.39	            aa(type, bool), 
33.15/33.39	            app_encode_app(dB, fun(type, bool), 
33.15/33.39	              app_encode_app(fun(nat, type), 
33.15/33.39	                app_encode_fun(dB, fun(type, bool)), typing, 
33.15/33.39	                app_encode_app(type, fun(nat, type), 
33.15/33.39	                  app_encode_app(nat, app_encode_fun(type, fun(nat, type)), 
33.15/33.39	                    app_encode_app(fun(nat, type), 
33.15/33.39	                      app_encode_fun(nat, 
33.15/33.39	                        app_encode_fun(type, fun(nat, type))), shift(type), 
33.15/33.39	                      e), n), t1)), 
33.15/33.39	              app_encode_app(list(dB), dB, 
33.15/33.39	                app_encode_app(dB, app_encode_fun(list(dB), dB), 
33.15/33.39	                  app_encode_app(fun(dB, fun(dB, dB)), 
33.15/33.39	                    app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
33.15/33.39	                    foldl(dB, dB), app), 
33.15/33.39	                  app_encode_app(dB, dB, 
33.15/33.39	                    app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), 
33.15/33.39	                      aa(dB, dB), 
33.15/33.39	                      app_encode_app(dB, fun(dB, dB), 
33.15/33.39	                        app_encode_app(fun(dB, fun(dB, dB)), 
33.15/33.39	                          app_encode_fun(dB, fun(dB, dB)), 
33.15/33.39	                          aa(dB, fun(dB, dB)), app), 
33.15/33.39	                        app_encode_app(nat, dB, var, n))), a)), as))), t)),
33.15/33.39	    inference('demod', [status(thm)], ['0', '1'])).
33.15/33.39	tff(zf_stmt_53, axiom,
33.15/33.39	  (rs =
33.15/33.39	   app_encode_app(list(dB),list(dB),
33.15/33.39	                  app_encode_app(fun(list(dB),list(dB)),
33.15/33.39	                                 app_encode_fun(list(dB),list(dB)),
33.15/33.39	                                 aa(list(dB),list(dB)),
33.15/33.39	                                 app_encode_app(dB,fun(list(dB),list(dB)),
33.15/33.39	                                                app_encode_app(fun(dB,
33.15/33.39	                                                                   fun(
33.15/33.39	                                                                   list(dB),
33.15/33.39	                                                                   list(dB))),
33.15/33.39	                                                               app_encode_fun(
33.15/33.39	                                                               dB,
33.15/33.39	                                                               fun(list(dB),
33.15/33.39	                                                                   list(dB))),
33.15/33.39	                                                               aa(dB,
33.15/33.39	                                                                  fun(
33.15/33.39	                                                                  list(dB),
33.15/33.39	                                                                  list(dB))),
33.15/33.39	                                                               cons(dB)),
33.15/33.39	                                                a)),
33.15/33.39	                  as))).
33.15/33.39	tff('3', plain,
33.15/33.39	    rs
33.15/33.39	     = app_encode_app(list(dB), list(dB), 
33.15/33.39	         app_encode_app(fun(list(dB), list(dB)), 
33.15/33.39	           app_encode_fun(list(dB), list(dB)), aa(list(dB), list(dB)), 
33.15/33.39	           app_encode_app(dB, fun(list(dB), list(dB)), 
33.15/33.39	             app_encode_app(fun(dB, fun(list(dB), list(dB))), 
33.15/33.39	               app_encode_fun(dB, fun(list(dB), list(dB))), 
33.15/33.39	               aa(dB, fun(list(dB), list(dB))), cons(dB)), a)), as),
33.15/33.39	    inference('cnf', [status(esa)], [zf_stmt_53])).
33.15/33.39	tff(zf_stmt_73, axiom,
33.15/33.39	  (![A:$tType,B:$tType,Xs:list(B),X:B,Aa:A,F:fun(A,fun(B,A))]:
33.15/33.39	     (app_encode_app(list(B),A,
33.15/33.39	                     app_encode_app(A,app_encode_fun(list(B),A),
33.15/33.39	                                    app_encode_app(fun(A,fun(B,A)),
33.15/33.39	                                                   app_encode_fun(A,
33.15/33.39	                                                                  app_encode_fun(
33.15/33.39	                                                                  list(B),A)),
33.15/33.39	                                                   foldl(A,B),F),
33.15/33.39	                                    Aa),
33.15/33.39	                     app_encode_app(list(B),list(B),
33.15/33.39	                                    app_encode_app(fun(list(B),list(B)),
33.15/33.39	                                                   app_encode_fun(list(B),
33.15/33.39	                                                                  list(B)),
33.15/33.39	                                                   aa(list(B),list(B)),
33.15/33.39	                                                   app_encode_app(B,
33.15/33.39	                                                                  fun(
33.15/33.39	                                                                  list(B),
33.15/33.39	                                                                  list(B)),
33.15/33.39	                                                                  app_encode_app(
33.15/33.39	                                                                  fun(
33.15/33.39	                                                                  B,
33.15/33.39	                                                                  fun(
33.15/33.39	                                                                  list(B),
33.15/33.39	                                                                  list(B))),
33.15/33.39	                                                                  app_encode_fun(
33.15/33.39	                                                                  B,
33.15/33.39	                                                                  fun(
33.15/33.39	                                                                  list(B),
33.15/33.39	                                                                  list(B))),
33.15/33.39	                                                                  aa(
33.15/33.39	                                                                  B,
33.15/33.39	                                                                  fun(
33.15/33.39	                                                                  list(B),
33.15/33.39	                                                                  list(B))),
33.15/33.39	                                                                  cons(B)),X)),
33.15/33.39	                                    Xs)) =
33.15/33.39	      app_encode_app(list(B),A,
33.15/33.39	                     app_encode_app(A,app_encode_fun(list(B),A),
33.15/33.39	                                    app_encode_app(fun(A,fun(B,A)),
33.15/33.39	                                                   app_encode_fun(A,
33.15/33.39	                                                                  app_encode_fun(
33.15/33.39	                                                                  list(B),A)),
33.15/33.39	                                                   foldl(A,B),F),
33.15/33.39	                                    app_encode_app(B,A,
33.15/33.39	                                                   app_encode_app(fun(B,A),
33.15/33.39	                                                                  app_encode_fun(
33.15/33.39	                                                                  B,A),
33.15/33.39	                                                                  aa(B,A),
33.15/33.39	                                                                  app_encode_app(
33.15/33.39	                                                                  A,fun(B,A),
33.15/33.39	                                                                  app_encode_app(
33.15/33.39	                                                                  fun(
33.15/33.39	                                                                  A,fun(B,A)),
33.15/33.39	                                                                  app_encode_fun(
33.15/33.39	                                                                  A,fun(B,A)),
33.15/33.39	                                                                  aa(
33.15/33.39	                                                                  A,fun(B,A)),
33.15/33.39	                                                                  F),Aa)),
33.15/33.39	                                                   X)),
33.15/33.39	                     Xs)))).
33.15/33.39	tff('4', plain,
33.15/33.39	    ![X48 : $tType, X49 : $tType, X50 : fun(X49, fun(X48, X49)), X51 : X49, 
33.15/33.39	      X52 : X48, X53 : list(X48)]:
33.15/33.39	      app_encode_app(list(X48), X49, 
33.15/33.39	        app_encode_app(X49, app_encode_fun(list(X48), X49), 
33.15/33.39	          app_encode_app(fun(X49, fun(X48, X49)), 
33.15/33.39	            app_encode_fun(X49, app_encode_fun(list(X48), X49)), 
33.15/33.39	            foldl(X49, X48), X50), X51), 
33.15/33.39	        app_encode_app(list(X48), list(X48), 
33.15/33.39	          app_encode_app(fun(list(X48), list(X48)), 
33.15/33.39	            app_encode_fun(list(X48), list(X48)), aa(list(X48), list(X48)), 
33.15/33.39	            app_encode_app(X48, fun(list(X48), list(X48)), 
33.15/33.39	              app_encode_app(fun(X48, fun(list(X48), list(X48))), 
33.15/33.39	                app_encode_fun(X48, fun(list(X48), list(X48))), 
33.15/33.39	                aa(X48, fun(list(X48), list(X48))), cons(X48)), X52)), X53))
33.15/33.39	       = app_encode_app(list(X48), X49, 
33.15/33.39	           app_encode_app(X49, app_encode_fun(list(X48), X49), 
33.15/33.39	             app_encode_app(fun(X49, fun(X48, X49)), 
33.15/33.39	               app_encode_fun(X49, app_encode_fun(list(X48), X49)), 
33.15/33.39	               foldl(X49, X48), X50), 
33.15/33.39	             app_encode_app(X48, X49, 
33.15/33.39	               app_encode_app(fun(X48, X49), app_encode_fun(X48, X49), 
33.15/33.39	                 aa(X48, X49), 
33.15/33.39	                 app_encode_app(X49, fun(X48, X49), 
33.15/33.39	                   app_encode_app(fun(X49, fun(X48, X49)), 
33.15/33.39	                     app_encode_fun(X49, fun(X48, X49)), 
33.15/33.39	                     aa(X49, fun(X48, X49)), X50), X51)), X52)), X53),
33.15/33.39	    inference('cnf', [status(esa)], [zf_stmt_73])).
33.15/33.39	tff('5', plain,
33.15/33.39	    ![X0 : $tType, X1 : X0, X2 : fun(X0, fun(dB, X0))]:
33.15/33.39	      app_encode_app(list(dB), X0, 
33.15/33.39	        app_encode_app(X0, app_encode_fun(list(dB), X0), 
33.15/33.39	          app_encode_app(fun(X0, fun(dB, X0)), 
33.15/33.39	            app_encode_fun(X0, app_encode_fun(list(dB), X0)), foldl(X0, dB), 
33.15/33.39	            X2), X1), rs)
33.15/33.39	       = app_encode_app(list(dB), X0, 
33.15/33.39	           app_encode_app(X0, app_encode_fun(list(dB), X0), 
33.15/33.39	             app_encode_app(fun(X0, fun(dB, X0)), 
33.15/33.39	               app_encode_fun(X0, app_encode_fun(list(dB), X0)), 
33.15/33.39	               foldl(X0, dB), X2), 
33.15/33.39	             app_encode_app(dB, X0, 
33.15/33.39	               app_encode_app(fun(dB, X0), app_encode_fun(dB, X0), 
33.15/33.39	                 aa(dB, X0), 
33.15/33.39	                 app_encode_app(X0, fun(dB, X0), 
33.15/33.39	                   app_encode_app(fun(X0, fun(dB, X0)), 
33.15/33.39	                     app_encode_fun(X0, fun(dB, X0)), aa(X0, fun(dB, X0)), 
33.15/33.39	                     X2), X1)), a)), as),
33.15/33.39	    inference('sup+', [status(thm)], ['3', '4'])).
33.15/33.39	tff(zf_stmt_55, axiom,
33.15/33.39	  (app_encode_app(bool,$o,pp,
33.15/33.39	                  app_encode_app(type,bool,
33.15/33.39	                                 app_encode_app(fun(type,bool),
33.15/33.39	                                                app_encode_fun(type,bool),
33.15/33.39	                                                aa(type,bool),
33.15/33.39	                                                app_encode_app(dB,
33.15/33.39	                                                               fun(type,bool),
33.15/33.39	                                                               app_encode_app(
33.15/33.39	                                                               fun(nat,type),
33.15/33.39	                                                               app_encode_fun(
33.15/33.39	                                                               dB,
33.15/33.39	                                                               fun(type,bool)),
33.15/33.39	                                                               typing,
33.15/33.39	                                                               app_encode_app(
33.15/33.39	                                                               type,
33.15/33.39	                                                               fun(nat,type),
33.15/33.39	                                                               app_encode_app(
33.15/33.39	                                                               nat,
33.15/33.39	                                                               app_encode_fun(
33.15/33.39	                                                               type,
33.15/33.39	                                                               fun(nat,type)),
33.15/33.39	                                                               app_encode_app(
33.15/33.39	                                                               fun(nat,type),
33.15/33.39	                                                               app_encode_fun(
33.15/33.39	                                                               nat,
33.15/33.39	                                                               app_encode_fun(
33.15/33.39	                                                               type,
33.15/33.39	                                                               fun(nat,type))),
33.15/33.39	                                                               shift(type),e),
33.15/33.39	                                                               i),t1)),
33.15/33.39	                                                               app_encode_app(
33.15/33.39	                                                               list(dB),dB,
33.15/33.39	                                                               app_encode_app(
33.15/33.39	                                                               dB,
33.15/33.39	                                                               app_encode_fun(
33.15/33.39	                                                               list(dB),dB),
33.15/33.39	                                                               app_encode_app(
33.15/33.39	                                                               fun(dB,
33.15/33.39	                                                                   fun(dB,dB)),
33.15/33.39	                                                               app_encode_fun(
33.15/33.39	                                                               dB,
33.15/33.39	                                                               app_encode_fun(
33.15/33.39	                                                               list(dB),dB)),
33.15/33.39	                                                               foldl(dB,dB),
33.15/33.39	                                                               app),
33.15/33.39	                                                               app_encode_app(
33.15/33.39	                                                               nat,dB,var,n)),
33.15/33.39	                                                               rs))),
33.15/33.39	                                 t)))).
33.15/33.39	tff('6', plain,
33.15/33.39	    app_encode_app(bool, $o, pp, 
33.15/33.39	      app_encode_app(type, bool, 
33.15/33.39	        app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
33.15/33.39	          aa(type, bool), 
33.15/33.39	          app_encode_app(dB, fun(type, bool), 
33.15/33.39	            app_encode_app(fun(nat, type), 
33.15/33.39	              app_encode_fun(dB, fun(type, bool)), typing, 
33.15/33.39	              app_encode_app(type, fun(nat, type), 
33.15/33.39	                app_encode_app(nat, app_encode_fun(type, fun(nat, type)), 
33.15/33.39	                  app_encode_app(fun(nat, type), 
33.15/33.39	                    app_encode_fun(nat, app_encode_fun(type, fun(nat, type))), 
33.15/33.39	                    shift(type), e), i), t1)), 
33.15/33.39	            app_encode_app(list(dB), dB, 
33.15/33.39	              app_encode_app(dB, app_encode_fun(list(dB), dB), 
33.15/33.39	                app_encode_app(fun(dB, fun(dB, dB)), 
33.15/33.39	                  app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
33.15/33.39	                  foldl(dB, dB), app), app_encode_app(nat, dB, var, n)), rs))), 
33.15/33.39	        t)),
33.15/33.39	    inference('cnf', [status(esa)], [zf_stmt_55])).
33.15/33.39	tff('7', plain,
33.15/33.39	    app_encode_app(bool, $o, pp, 
33.15/33.39	      app_encode_app(type, bool, 
33.15/33.39	        app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
33.15/33.39	          aa(type, bool), 
33.15/33.39	          app_encode_app(dB, fun(type, bool), 
33.15/33.39	            app_encode_app(fun(nat, type), 
33.15/33.39	              app_encode_fun(dB, fun(type, bool)), typing, 
33.15/33.39	              app_encode_app(type, fun(nat, type), 
33.15/33.39	                app_encode_app(nat, app_encode_fun(type, fun(nat, type)), 
33.15/33.39	                  app_encode_app(fun(nat, type), 
33.15/33.39	                    app_encode_fun(nat, app_encode_fun(type, fun(nat, type))), 
33.15/33.39	                    shift(type), e), n), t1)), 
33.15/33.39	            app_encode_app(list(dB), dB, 
33.15/33.39	              app_encode_app(dB, app_encode_fun(list(dB), dB), 
33.15/33.39	                app_encode_app(fun(dB, fun(dB, dB)), 
33.15/33.39	                  app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
33.15/33.39	                  foldl(dB, dB), app), app_encode_app(nat, dB, var, n)), rs))), 
33.15/33.39	        t)),
33.15/33.39	    inference('demod', [status(thm)], ['6', '1'])).
33.15/33.39	tff(zf_stmt_160, axiom, (![P:bool]: ((P = fTrue) | (P = fFalse)))).
33.15/33.39	tff('8', plain, ![X410 : bool]: (X410 = fTrue | X410 = fFalse),
33.15/33.39	    inference('cnf', [status(esa)], [zf_stmt_160])).
33.15/33.39	tff(zf_stmt_151, axiom, (~app_encode_app(bool,$o,pp,fFalse))).
33.15/33.39	tff('9', plain, ~ app_encode_app(bool, $o, pp, fFalse),
33.15/33.39	    inference('cnf', [status(esa)], [zf_stmt_151])).
33.15/33.39	tff('10', plain,
33.15/33.39	    ![X0 : bool]: (~ app_encode_app(bool, $o, pp, X0) | X0 = fTrue),
33.15/33.39	    inference('sup-', [status(thm)], ['8', '9'])).
33.15/33.39	tff('11', plain,
33.15/33.39	    (~ $true
33.15/33.39	     | app_encode_app(type, bool, 
33.15/33.39	         app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
33.15/33.39	           aa(type, bool), 
33.15/33.39	           app_encode_app(dB, fun(type, bool), 
33.15/33.39	             app_encode_app(fun(nat, type), 
33.15/33.39	               app_encode_fun(dB, fun(type, bool)), typing, 
33.15/33.39	               app_encode_app(type, fun(nat, type), 
33.15/33.39	                 app_encode_app(nat, app_encode_fun(type, fun(nat, type)), 
33.15/33.39	                   app_encode_app(fun(nat, type), 
33.15/33.39	                     app_encode_fun(nat, 
33.15/33.39	                       app_encode_fun(type, fun(nat, type))), shift(type), e), 
33.15/33.39	                   n), t1)), 
33.15/33.39	             app_encode_app(list(dB), dB, 
33.15/33.39	               app_encode_app(dB, app_encode_fun(list(dB), dB), 
33.15/33.39	                 app_encode_app(fun(dB, fun(dB, dB)), 
33.15/33.39	                   app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
33.15/33.39	                   foldl(dB, dB), app), app_encode_app(nat, dB, var, n)), rs))), 
33.15/33.39	         t)
33.15/33.39	        = fTrue),
33.15/33.39	    inference('sup-', [status(thm)], ['7', '10'])).
33.15/33.39	tff('12', plain,
33.15/33.39	    app_encode_app(type, bool, 
33.15/33.39	      app_encode_app(fun(type, bool), app_encode_fun(type, bool), 
33.15/33.39	        aa(type, bool), 
33.15/33.39	        app_encode_app(dB, fun(type, bool), 
33.15/33.39	          app_encode_app(fun(nat, type), 
33.15/33.39	            app_encode_fun(dB, fun(type, bool)), typing, 
33.15/33.39	            app_encode_app(type, fun(nat, type), 
33.15/33.39	              app_encode_app(nat, app_encode_fun(type, fun(nat, type)), 
33.15/33.39	                app_encode_app(fun(nat, type), 
33.15/33.39	                  app_encode_fun(nat, app_encode_fun(type, fun(nat, type))), 
33.15/33.39	                  shift(type), e), n), t1)), 
33.15/33.39	          app_encode_app(list(dB), dB, 
33.15/33.39	            app_encode_app(dB, app_encode_fun(list(dB), dB), 
33.15/33.39	              app_encode_app(fun(dB, fun(dB, dB)), 
33.15/33.39	                app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
33.15/33.39	                foldl(dB, dB), app), app_encode_app(nat, dB, var, n)), rs))), 
33.15/33.39	      t)
33.15/33.39	     = fTrue,
33.15/33.39	    inference('simplify', [status(thm)], ['11'])).
33.15/33.39	tff(zf_stmt_152, axiom, (app_encode_app(bool,$o,pp,fTrue))).
33.15/33.39	tff('13', plain, app_encode_app(bool, $o, pp, fTrue),
33.15/33.39	    inference('cnf', [status(esa)], [zf_stmt_152])).
33.15/33.39	tff('14', plain, ~ $true,
33.15/33.39	    inference('demod', [status(thm)], ['2', '5', '12', '13'])).
33.15/33.39	tff('15', plain, $false, inference('simplify', [status(thm)], ['14'])).
33.15/33.39	
33.15/33.39	% SZS output end Refutation
33.23/33.39	EOF
