0.00/0.00	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : appext
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : kbo
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n110.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 06:37:24 CST 2018
107.59/107.78	% done 9179 iterations in 107.579s
107.59/107.78	% SZS status Theorem for 'stdin'
107.59/107.78	% SZS output start Refutation
107.59/107.78	tff(zf_stmt_49, axiom,
107.59/107.78	  (![Ss:list(dB),S2:dB,Ra:dB]:
107.59/107.78	     (app_encode_app(bool,$o,pp,
107.59/107.78	                     app_encode_app(dB,bool,
107.59/107.78	                                    app_encode_app(fun(dB,bool),
107.59/107.78	                                                   app_encode_fun(dB,bool),
107.59/107.78	                                                   aa(dB,bool),it),
107.59/107.78	                                    app_encode_app(list(dB),dB,
107.59/107.78	                                                   app_encode_app(dB,
107.59/107.78	                                                                  app_encode_fun(
107.59/107.78	                                                                  list(dB),dB),
107.59/107.78	                                                                  app_encode_app(
107.59/107.78	                                                                  fun(
107.59/107.78	                                                                  dB,
107.59/107.78	                                                                  fun(dB,dB)),
107.59/107.78	                                                                  app_encode_fun(
107.59/107.78	                                                                  dB,
107.59/107.80	                                                                  app_encode_fun(
107.59/107.80	                                                                  list(dB),dB)),
107.59/107.80	                                                                  foldl(
107.59/107.80	                                                                  dB,dB),app),
107.59/107.80	                                                                  app_encode_app(
107.59/107.80	                                                                  nat,dB,
107.59/107.80	                                                                  app_encode_app(
107.59/107.80	                                                                  fun(nat,dB),
107.59/107.80	                                                                  app_encode_fun(
107.59/107.80	                                                                  nat,dB),
107.59/107.80	                                                                  aa(nat,dB),
107.59/107.80	                                                                  app_encode_app(
107.59/107.80	                                                                  dB,
107.59/107.80	                                                                  fun(nat,dB),
107.59/107.80	                                                                  app_encode_app(
107.59/107.80	                                                                  fun(
107.59/107.80	                                                                  dB,
107.59/107.80	                                                                  fun(nat,dB)),
107.59/107.80	                                                                  app_encode_fun(
107.59/107.80	                                                                  dB,
107.59/107.80	                                                                  fun(nat,dB)),
107.59/107.80	                                                                  aa(
107.59/107.80	                                                                  dB,
107.59/107.80	                                                                  fun(nat,dB)),
107.59/107.80	                                                                  app_encode_app(
107.59/107.80	                                                                  dB,
107.59/107.80	                                                                  fun(
107.59/107.80	                                                                  dB,
107.59/107.80	                                                                  fun(nat,dB)),
107.59/107.80	                                                                  app_encode_app(
107.59/107.80	                                                                  fun(
107.59/107.80	                                                                  dB,
107.59/107.80	                                                                  fun(
107.59/107.80	                                                                  dB,
107.59/107.80	                                                                  fun(nat,dB))),
107.59/107.80	                                                                  app_encode_fun(
107.59/107.80	                                                                  dB,
107.59/107.80	                                                                  fun(
107.59/107.80	                                                                  dB,
107.59/107.80	                                                                  fun(nat,dB))),
107.59/107.80	                                                                  aa(
107.59/107.80	                                                                  dB,
107.59/107.80	                                                                  fun(
107.59/107.80	                                                                  dB,
107.59/107.80	                                                                  fun(nat,dB))),
107.59/107.80	                                                                  subst),Ra)),
107.59/107.80	                                                                  S2)),
107.59/107.80	                                                                  zero_zero(
107.59/107.80	                                                                  nat))),
107.59/107.80	                                                   Ss))) =>
107.59/107.80	      (app_encode_app(bool,$o,pp,
107.59/107.80	                      app_encode_app(dB,bool,
107.59/107.80	                                     app_encode_app(fun(dB,bool),
107.59/107.80	                                                    app_encode_fun(dB,bool),
107.59/107.80	                                                    aa(dB,bool),it),
107.59/107.80	                                     S2)) =>
107.59/107.80	       app_encode_app(bool,$o,pp,
107.59/107.80	                      app_encode_app(dB,bool,
107.59/107.80	                                     app_encode_app(fun(dB,bool),
107.59/107.80	                                                    app_encode_fun(dB,bool),
107.59/107.80	                                                    aa(dB,bool),it),
107.59/107.80	                                     app_encode_app(list(dB),dB,
107.59/107.80	                                                    app_encode_app(dB,
107.59/107.80	                                                                   app_encode_fun(
107.59/107.80	                                                                   list(dB),
107.59/107.80	                                                                   dB),
107.59/107.80	                                                                   app_encode_app(
107.59/107.80	                                                                   fun(
107.59/107.80	                                                                   dB,
107.59/107.80	                                                                   fun(dB,dB)),
107.59/107.80	                                                                   app_encode_fun(
107.59/107.80	                                                                   dB,
107.59/107.80	                                                                   app_encode_fun(
107.59/107.80	                                                                   list(dB),
107.59/107.80	                                                                   dB)),
107.59/107.80	                                                                   foldl(
107.59/107.80	                                                                   dB,dB),app),
107.59/107.80	                                                                   app_encode_app(
107.59/107.80	                                                                   dB,dB,
107.59/107.80	                                                                   app_encode_app(
107.59/107.80	                                                                   fun(dB,dB),
107.59/107.80	                                                                   app_encode_fun(
107.59/107.80	                                                                   dB,dB),
107.59/107.80	                                                                   aa(dB,dB),
107.59/107.80	                                                                   app_encode_app(
107.59/107.80	                                                                   dB,
107.59/107.80	                                                                   fun(dB,dB),
107.59/107.80	                                                                   app_encode_app(
107.59/107.80	                                                                   fun(
107.59/107.80	                                                                   dB,
107.59/107.80	                                                                   fun(dB,dB)),
107.59/107.80	                                                                   app_encode_fun(
107.59/107.80	                                                                   dB,
107.59/107.80	                                                                   fun(dB,dB)),
107.59/107.80	                                                                   aa(
107.59/107.80	                                                                   dB,
107.59/107.80	                                                                   fun(dB,dB)),
107.59/107.80	                                                                   app),
107.59/107.80	                                                                   app_encode_app(
107.59/107.80	                                                                   dB,dB,abs,
107.59/107.80	                                                                   Ra))),S2)),
107.59/107.80	                                                    Ss))))))).
107.59/107.80	tff('0', plain,
107.59/107.80	    ![X4 : dB, X5 : dB, X6 : list(dB)]:
107.59/107.80	      (~ app_encode_app(bool, $o, pp, 
107.59/107.80	           app_encode_app(dB, bool, 
107.59/107.80	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
107.59/107.80	               aa(dB, bool), it), X4))
107.59/107.80	       | ~ app_encode_app(bool, $o, pp, 
107.59/107.80	             app_encode_app(dB, bool, 
107.59/107.80	               app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
107.59/107.80	                 aa(dB, bool), it), 
107.59/107.80	               app_encode_app(list(dB), dB, 
107.59/107.80	                 app_encode_app(dB, app_encode_fun(list(dB), dB), 
107.59/107.80	                   app_encode_app(fun(dB, fun(dB, dB)), 
107.59/107.80	                     app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
107.59/107.80	                     foldl(dB, dB), app), 
107.59/107.80	                   app_encode_app(nat, dB, 
107.59/107.80	                     app_encode_app(fun(nat, dB), app_encode_fun(nat, dB), 
107.59/107.80	                       aa(nat, dB), 
107.59/107.80	                       app_encode_app(dB, fun(nat, dB), 
107.59/107.80	                         app_encode_app(fun(dB, fun(nat, dB)), 
107.59/107.80	                           app_encode_fun(dB, fun(nat, dB)), 
107.59/107.80	                           aa(dB, fun(nat, dB)), 
107.59/107.80	                           app_encode_app(dB, fun(dB, fun(nat, dB)), 
107.59/107.80	                             app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
107.59/107.80	                               app_encode_fun(dB, fun(dB, fun(nat, dB))), 
107.59/107.80	                               aa(dB, fun(dB, fun(nat, dB))), subst), X5)), 
107.59/107.80	                         X4)), zero_zero(nat))), X6)))
107.59/107.80	       | app_encode_app(bool, $o, pp, 
107.59/107.80	           app_encode_app(dB, bool, 
107.59/107.80	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
107.59/107.80	               aa(dB, bool), it), 
107.59/107.80	             app_encode_app(list(dB), dB, 
107.59/107.80	               app_encode_app(dB, app_encode_fun(list(dB), dB), 
107.59/107.80	                 app_encode_app(fun(dB, fun(dB, dB)), 
107.59/107.80	                   app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
107.59/107.80	                   foldl(dB, dB), app), 
107.59/107.80	                 app_encode_app(dB, dB, 
107.59/107.80	                   app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), 
107.59/107.80	                     aa(dB, dB), 
107.59/107.80	                     app_encode_app(dB, fun(dB, dB), 
107.59/107.80	                       app_encode_app(fun(dB, fun(dB, dB)), 
107.59/107.80	                         app_encode_fun(dB, fun(dB, dB)), 
107.59/107.80	                         aa(dB, fun(dB, dB)), app), 
107.59/107.80	                       app_encode_app(dB, dB, abs, X5))), X4)), X6)))),
107.59/107.80	    inference('cnf', [status(esa)], [zf_stmt_49])).
107.59/107.80	tff(zf_stmt_157, axiom,
107.59/107.80	  (![A:$tType,C:$tType,B:$tType,R:A,Q:B,P:fun(A,fun(B,C))]:
107.59/107.80	     (app_encode_app(A,C,
107.59/107.80	                     app_encode_app(fun(A,C),app_encode_fun(A,C),aa(A,C),
107.59/107.80	                                    app_encode_app(B,fun(A,C),
107.59/107.80	                                                   app_encode_app(fun(
107.59/107.80	                                                                  A,fun(B,C)),
107.59/107.80	                                                                  app_encode_fun(
107.59/107.80	                                                                  B,fun(A,C)),
107.59/107.80	                                                                  combc(
107.59/107.80	                                                                  A,B,C),P),
107.59/107.80	                                                   Q)),
107.59/107.80	                     R) =
107.59/107.80	      app_encode_app(B,C,
107.59/107.80	                     app_encode_app(fun(B,C),app_encode_fun(B,C),aa(B,C),
107.59/107.80	                                    app_encode_app(A,fun(B,C),
107.59/107.80	                                                   app_encode_app(fun(
107.59/107.80	                                                                  A,fun(B,C)),
107.59/107.80	                                                                  app_encode_fun(
107.59/107.80	                                                                  A,fun(B,C)),
107.59/107.80	                                                                  aa(
107.59/107.80	                                                                  A,fun(B,C)),
107.59/107.80	                                                                  P),
107.59/107.80	                                                   R)),
107.59/107.80	                     Q)))).
107.59/107.80	tff('1', plain,
107.59/107.80	    ![X286 : $tType, X287 : $tType, X288 : $tType, 
107.59/107.80	      X289 : fun(X288, fun(X286, X287)), X290 : X288, X291 : X286]:
107.59/107.80	      app_encode_app(X288, X287, 
107.59/107.80	        app_encode_app(fun(X288, X287), app_encode_fun(X288, X287), 
107.59/107.80	          aa(X288, X287), 
107.59/107.80	          app_encode_app(X286, fun(X288, X287), 
107.59/107.80	            app_encode_app(fun(X288, fun(X286, X287)), 
107.59/107.80	              app_encode_fun(X286, fun(X288, X287)), 
107.59/107.80	              combc(X288, X286, X287), X289), X291)), X290)
107.59/107.80	       = app_encode_app(X286, X287, 
107.59/107.80	           app_encode_app(fun(X286, X287), app_encode_fun(X286, X287), 
107.59/107.80	             aa(X286, X287), 
107.59/107.80	             app_encode_app(X288, fun(X286, X287), 
107.59/107.80	               app_encode_app(fun(X288, fun(X286, X287)), 
107.59/107.80	                 app_encode_fun(X288, fun(X286, X287)), 
107.59/107.80	                 aa(X288, fun(X286, X287)), X289), X290)), X291),
107.59/107.80	    inference('cnf', [status(esa)], [zf_stmt_157])).
107.59/107.80	tff('2', plain,
107.59/107.80	    ![X4 : dB, X5 : dB, X6 : list(dB)]:
107.59/107.80	      (~ app_encode_app(bool, $o, pp, 
107.59/107.80	           app_encode_app(dB, bool, 
107.59/107.80	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
107.59/107.80	               aa(dB, bool), it), X4))
107.59/107.80	       | ~ app_encode_app(bool, $o, pp, 
107.59/107.80	             app_encode_app(dB, bool, 
107.59/107.80	               app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
107.59/107.80	                 aa(dB, bool), it), 
107.59/107.80	               app_encode_app(list(dB), dB, 
107.59/107.80	                 app_encode_app(dB, app_encode_fun(list(dB), dB), 
107.59/107.80	                   app_encode_app(fun(dB, fun(dB, dB)), 
107.59/107.80	                     app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
107.59/107.80	                     foldl(dB, dB), app), 
107.59/107.80	                   app_encode_app(dB, dB, 
107.59/107.80	                     app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), 
107.59/107.80	                       aa(dB, dB), 
107.59/107.80	                       app_encode_app(nat, fun(dB, dB), 
107.59/107.80	                         app_encode_app(fun(dB, fun(nat, dB)), 
107.59/107.80	                           app_encode_fun(nat, fun(dB, dB)), 
107.59/107.80	                           combc(dB, nat, dB), 
107.59/107.80	                           app_encode_app(dB, fun(dB, fun(nat, dB)), 
107.59/107.80	                             app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
107.59/107.80	                               app_encode_fun(dB, fun(dB, fun(nat, dB))), 
107.59/107.80	                               combc(dB, dB, fun(nat, dB)), subst), X4)), 
107.59/107.80	                         zero_zero(nat))), X5)), X6)))
107.59/107.80	       | app_encode_app(bool, $o, pp, 
107.59/107.80	           app_encode_app(dB, bool, 
107.59/107.80	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
107.59/107.80	               aa(dB, bool), it), 
107.59/107.80	             app_encode_app(list(dB), dB, 
107.59/107.80	               app_encode_app(dB, app_encode_fun(list(dB), dB), 
107.59/107.80	                 app_encode_app(fun(dB, fun(dB, dB)), 
107.59/107.80	                   app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
107.59/107.80	                   foldl(dB, dB), app), 
107.59/107.80	                 app_encode_app(dB, dB, 
107.59/107.80	                   app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), 
107.59/107.80	                     aa(dB, dB), 
107.59/107.80	                     app_encode_app(dB, fun(dB, dB), 
107.59/107.80	                       app_encode_app(fun(dB, fun(dB, dB)), 
107.59/107.80	                         app_encode_fun(dB, fun(dB, dB)), combc(dB, dB, dB), 
107.59/107.80	                         app), X4)), app_encode_app(dB, dB, abs, X5))), X6)))),
107.59/107.80	    inference('demod', [status(thm)], ['0', '1', '1', '1'])).
107.59/107.80	tff(zf_stmt_142, axiom,
107.59/107.80	  (![S:dB,T:dB]:
107.59/107.80	     (app_encode_app(nat,dB,
107.59/107.80	                     app_encode_app(dB,app_encode_fun(nat,dB),
107.59/107.80	                                    app_encode_app(dB,
107.59/107.80	                                                   app_encode_fun(dB,
107.59/107.80	                                                                  app_encode_fun(
107.59/107.80	                                                                  nat,dB)),
107.59/107.80	                                                   substn,T),
107.59/107.80	                                    S),
107.59/107.80	                     zero_zero(nat)) =
107.59/107.80	      app_encode_app(nat,dB,
107.59/107.80	                     app_encode_app(fun(nat,dB),app_encode_fun(nat,dB),
107.59/107.80	                                    aa(nat,dB),
107.59/107.80	                                    app_encode_app(dB,fun(nat,dB),
107.59/107.80	                                                   app_encode_app(fun(
107.59/107.80	                                                                  dB,
107.59/107.80	                                                                  fun(nat,dB)),
107.59/107.80	                                                                  app_encode_fun(
107.59/107.80	                                                                  dB,
107.59/107.80	                                                                  fun(nat,dB)),
107.59/107.80	                                                                  aa(
107.59/107.80	                                                                  dB,
107.59/107.80	                                                                  fun(nat,dB)),
107.59/107.80	                                                                  app_encode_app(
107.59/107.80	                                                                  dB,
107.59/107.80	                                                                  fun(
107.59/107.80	                                                                  dB,
107.59/107.80	                                                                  fun(nat,dB)),
107.59/107.80	                                                                  app_encode_app(
107.59/107.80	                                                                  fun(
107.59/107.80	                                                                  dB,
107.59/107.80	                                                                  fun(
107.59/107.80	                                                                  dB,
107.59/107.80	                                                                  fun(nat,dB))),
107.59/107.80	                                                                  app_encode_fun(
107.59/107.80	                                                                  dB,
107.59/107.80	                                                                  fun(
107.59/107.80	                                                                  dB,
107.59/107.80	                                                                  fun(nat,dB))),
107.59/107.80	                                                                  aa(
107.59/107.80	                                                                  dB,
107.59/107.80	                                                                  fun(
107.59/107.80	                                                                  dB,
107.59/107.80	                                                                  fun(nat,dB))),
107.59/107.80	                                                                  subst),T)),
107.59/107.80	                                                   S)),
107.59/107.80	                     zero_zero(nat))))).
107.59/107.80	tff('3', plain,
107.59/107.80	    ![X266 : dB, X267 : dB]:
107.59/107.80	      app_encode_app(nat, dB, 
107.59/107.80	        app_encode_app(dB, app_encode_fun(nat, dB), 
107.59/107.80	          app_encode_app(dB, app_encode_fun(dB, app_encode_fun(nat, dB)), 
107.59/107.80	            substn, X266), X267), zero_zero(nat))
107.59/107.80	       = app_encode_app(nat, dB, 
107.59/107.80	           app_encode_app(fun(nat, dB), app_encode_fun(nat, dB), 
107.59/107.80	             aa(nat, dB), 
107.59/107.80	             app_encode_app(dB, fun(nat, dB), 
107.59/107.80	               app_encode_app(fun(dB, fun(nat, dB)), 
107.59/107.80	                 app_encode_fun(dB, fun(nat, dB)), aa(dB, fun(nat, dB)), 
107.59/107.80	                 app_encode_app(dB, fun(dB, fun(nat, dB)), 
107.59/107.80	                   app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
107.59/107.80	                     app_encode_fun(dB, fun(dB, fun(nat, dB))), 
107.59/107.80	                     aa(dB, fun(dB, fun(nat, dB))), subst), X266)), X267)), 
107.59/107.80	           zero_zero(nat)),
107.59/107.80	    inference('cnf', [status(esa)], [zf_stmt_142])).
107.59/107.80	tff('4', plain,
107.59/107.80	    ![X266 : dB, X267 : dB]:
107.59/107.80	      app_encode_app(nat, dB, 
107.59/107.80	        app_encode_app(dB, app_encode_fun(nat, dB), 
107.59/107.80	          app_encode_app(dB, app_encode_fun(dB, app_encode_fun(nat, dB)), 
107.59/107.80	            substn, X266), X267), zero_zero(nat))
107.59/107.80	       = app_encode_app(dB, dB, 
107.59/107.80	           app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), aa(dB, dB), 
107.59/107.80	             app_encode_app(nat, fun(dB, dB), 
107.59/107.80	               app_encode_app(fun(dB, fun(nat, dB)), 
107.59/107.80	                 app_encode_fun(nat, fun(dB, dB)), combc(dB, nat, dB), 
107.59/107.80	                 app_encode_app(dB, fun(dB, fun(nat, dB)), 
107.59/107.80	                   app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
107.59/107.80	                     app_encode_fun(dB, fun(dB, fun(nat, dB))), 
107.59/107.80	                     combc(dB, dB, fun(nat, dB)), subst), X267)), 
107.59/107.80	               zero_zero(nat))), X266),
107.59/107.80	    inference('demod', [status(thm)], ['3', '1', '1'])).
107.59/107.80	tff('5', plain,
107.59/107.80	    ![X4 : dB, X5 : dB, X6 : list(dB)]:
107.59/107.80	      (~ app_encode_app(bool, $o, pp, 
107.59/107.80	           app_encode_app(dB, bool, 
107.59/107.80	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
107.59/107.80	               aa(dB, bool), it), X4))
107.59/107.80	       | ~ app_encode_app(bool, $o, pp, 
107.59/107.80	             app_encode_app(dB, bool, 
107.59/107.80	               app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
107.59/107.80	                 aa(dB, bool), it), 
107.59/107.80	               app_encode_app(list(dB), dB, 
107.59/107.80	                 app_encode_app(dB, app_encode_fun(list(dB), dB), 
107.59/107.80	                   app_encode_app(fun(dB, fun(dB, dB)), 
107.59/107.80	                     app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
107.59/107.80	                     foldl(dB, dB), app), 
107.59/107.80	                   app_encode_app(nat, dB, 
107.59/107.80	                     app_encode_app(dB, app_encode_fun(nat, dB), 
107.59/107.80	                       app_encode_app(dB, 
107.59/107.80	                         app_encode_fun(dB, app_encode_fun(nat, dB)), 
107.59/107.80	                         substn, X5), X4), zero_zero(nat))), X6)))
107.59/107.80	       | app_encode_app(bool, $o, pp, 
107.59/107.80	           app_encode_app(dB, bool, 
107.59/107.80	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
107.59/107.80	               aa(dB, bool), it), 
107.59/107.80	             app_encode_app(list(dB), dB, 
107.59/107.80	               app_encode_app(dB, app_encode_fun(list(dB), dB), 
107.59/107.80	                 app_encode_app(fun(dB, fun(dB, dB)), 
107.59/107.80	                   app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
107.59/107.80	                   foldl(dB, dB), app), 
107.59/107.80	                 app_encode_app(dB, dB, 
107.59/107.80	                   app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), 
107.59/107.80	                     aa(dB, dB), 
107.59/107.80	                     app_encode_app(dB, fun(dB, dB), 
107.59/107.80	                       app_encode_app(fun(dB, fun(dB, dB)), 
107.59/107.80	                         app_encode_fun(dB, fun(dB, dB)), combc(dB, dB, dB), 
107.59/107.80	                         app), X4)), app_encode_app(dB, dB, abs, X5))), X6)))),
107.59/107.80	    inference('demod', [status(thm)], ['2', '4'])).
107.59/107.80	tff(zf_stmt_167, conjecture,
107.59/107.80	  (app_encode_app(bool,$o,pp,
107.59/107.80	                  app_encode_app(dB,bool,
107.59/107.80	                                 app_encode_app(fun(dB,bool),
107.59/107.80	                                                app_encode_fun(dB,bool),
107.59/107.80	                                                aa(dB,bool),it),
107.59/107.80	                                 app_encode_app(list(dB),dB,
107.59/107.80	                                                app_encode_app(dB,
107.59/107.80	                                                               app_encode_fun(
107.59/107.80	                                                               list(dB),dB),
107.59/107.80	                                                               app_encode_app(
107.59/107.80	                                                               fun(dB,
107.59/107.80	                                                                   fun(dB,dB)),
107.59/107.80	                                                               app_encode_fun(
107.59/107.80	                                                               dB,
107.59/107.80	                                                               app_encode_fun(
107.59/107.80	                                                               list(dB),dB)),
107.59/107.80	                                                               foldl(dB,dB),
107.59/107.80	                                                               app),
107.59/107.80	                                                               app_encode_app(
107.59/107.80	                                                               dB,dB,
107.59/107.80	                                                               app_encode_app(
107.59/107.80	                                                               fun(dB,dB),
107.59/107.80	                                                               app_encode_fun(
107.59/107.80	                                                               dB,dB),
107.59/107.80	                                                               aa(dB,dB),
107.59/107.80	                                                               app_encode_app(
107.59/107.80	                                                               dB,fun(dB,dB),
107.59/107.80	                                                               app_encode_app(
107.59/107.80	                                                               fun(dB,
107.59/107.80	                                                                   fun(dB,dB)),
107.59/107.80	                                                               app_encode_fun(
107.59/107.80	                                                               dB,fun(dB,dB)),
107.59/107.80	                                                               aa(dB,
107.59/107.80	                                                                  fun(dB,dB)),
107.59/107.80	                                                               app),
107.59/107.80	                                                               app_encode_app(
107.59/107.80	                                                               dB,dB,abs,
107.59/107.80	                                                               app_encode_app(
107.59/107.80	                                                               nat,dB,
107.59/107.80	                                                               app_encode_app(
107.59/107.80	                                                               fun(nat,dB),
107.59/107.80	                                                               app_encode_fun(
107.59/107.80	                                                               nat,dB),
107.59/107.80	                                                               aa(nat,dB),
107.59/107.80	                                                               app_encode_app(
107.59/107.80	                                                               dB,
107.59/107.80	                                                               fun(nat,dB),
107.59/107.80	                                                               app_encode_app(
107.59/107.80	                                                               fun(dB,
107.59/107.80	                                                                   fun(
107.59/107.80	                                                                   nat,dB)),
107.59/107.80	                                                               app_encode_fun(
107.59/107.80	                                                               dB,fun(nat,dB)),
107.59/107.80	                                                               aa(dB,
107.59/107.80	                                                                  fun(nat,dB)),
107.59/107.80	                                                               app_encode_app(
107.59/107.80	                                                               dB,
107.59/107.80	                                                               fun(dB,
107.59/107.80	                                                                   fun(
107.59/107.80	                                                                   nat,dB)),
107.59/107.80	                                                               app_encode_app(
107.59/107.80	                                                               fun(dB,
107.59/107.80	                                                                   fun(
107.59/107.80	                                                                   dB,
107.59/107.80	                                                                   fun(
107.59/107.80	                                                                   nat,dB))),
107.59/107.80	                                                               app_encode_fun(
107.59/107.80	                                                               dB,
107.59/107.80	                                                               fun(dB,
107.59/107.80	                                                                   fun(
107.59/107.80	                                                                   nat,dB))),
107.59/107.80	                                                               aa(dB,
107.59/107.80	                                                                  fun(
107.59/107.80	                                                                  dB,
107.59/107.80	                                                                  fun(nat,dB))),
107.59/107.80	                                                               subst),ra)),
107.59/107.80	                                                               app_encode_app(
107.59/107.80	                                                               nat,dB,var,
107.59/107.80	                                                               app_encode_app(
107.59/107.80	                                                               nat,nat,suc,ia)))),
107.59/107.80	                                                               app_encode_app(
107.59/107.80	                                                               nat,nat,suc,ja))))),
107.59/107.80	                                                               app_encode_app(
107.59/107.80	                                                               nat,dB,
107.59/107.80	                                                               app_encode_app(
107.59/107.80	                                                               fun(nat,dB),
107.59/107.80	                                                               app_encode_fun(
107.59/107.80	                                                               nat,dB),
107.59/107.80	                                                               aa(nat,dB),
107.59/107.80	                                                               app_encode_app(
107.59/107.80	                                                               dB,
107.59/107.80	                                                               fun(nat,dB),
107.59/107.80	                                                               app_encode_app(
107.59/107.80	                                                               fun(dB,
107.59/107.80	                                                                   fun(
107.59/107.80	                                                                   nat,dB)),
107.59/107.80	                                                               app_encode_fun(
107.59/107.80	                                                               dB,fun(nat,dB)),
107.59/107.80	                                                               aa(dB,
107.59/107.80	                                                                  fun(nat,dB)),
107.59/107.80	                                                               app_encode_app(
107.59/107.80	                                                               dB,
107.59/107.80	                                                               fun(dB,
107.59/107.80	                                                                   fun(
107.59/107.80	                                                                   nat,dB)),
107.59/107.80	                                                               app_encode_app(
107.59/107.80	                                                               fun(dB,
107.59/107.80	                                                                   fun(
107.59/107.80	                                                                   dB,
107.59/107.80	                                                                   fun(
107.59/107.80	                                                                   nat,dB))),
107.59/107.80	                                                               app_encode_fun(
107.59/107.80	                                                               dB,
107.59/107.80	                                                               fun(dB,
107.59/107.80	                                                                   fun(
107.59/107.80	                                                                   nat,dB))),
107.59/107.80	                                                               aa(dB,
107.59/107.80	                                                                  fun(
107.59/107.80	                                                                  dB,
107.59/107.80	                                                                  fun(nat,dB))),
107.59/107.80	                                                               subst),s)),
107.59/107.80	                                                               app_encode_app(
107.59/107.80	                                                               nat,dB,var,ia))),
107.59/107.80	                                                               ja))),
107.59/107.80	                                                app_encode_app(list(dB),
107.59/107.80	                                                               list(dB),
107.59/107.80	                                                               app_encode_app(
107.59/107.80	                                                               fun(dB,dB),
107.59/107.80	                                                               app_encode_fun(
107.59/107.80	                                                               list(dB),
107.59/107.80	                                                               list(dB)),
107.59/107.80	                                                               map(dB,dB),
107.59/107.80	                                                               app_encode_app(
107.59/107.80	                                                               nat,
107.59/107.80	                                                               fun(dB,dB),
107.59/107.80	                                                               app_encode_app(
107.59/107.80	                                                               fun(dB,
107.59/107.80	                                                                   fun(
107.59/107.80	                                                                   nat,dB)),
107.59/107.80	                                                               app_encode_fun(
107.59/107.80	                                                               nat,fun(dB,dB)),
107.59/107.80	                                                               combc(
107.59/107.80	                                                               dB,nat,dB),
107.59/107.80	                                                               app_encode_app(
107.59/107.80	                                                               dB,
107.59/107.80	                                                               fun(dB,
107.59/107.80	                                                                   fun(
107.59/107.80	                                                                   nat,dB)),
107.59/107.80	                                                               app_encode_app(
107.59/107.80	                                                               fun(dB,
107.59/107.80	                                                                   fun(
107.59/107.80	                                                                   dB,
107.59/107.80	                                                                   fun(
107.59/107.80	                                                                   nat,dB))),
107.59/107.80	                                                               app_encode_fun(
107.59/107.80	                                                               dB,
107.59/107.80	                                                               fun(dB,
107.59/107.80	                                                                   fun(
107.59/107.80	                                                                   nat,dB))),
107.59/107.80	                                                               combc(
107.59/107.80	                                                               dB,dB,
107.59/107.80	                                                               fun(nat,dB)),
107.59/107.80	                                                               subst),
107.59/107.80	                                                               app_encode_app(
107.59/107.80	                                                               nat,dB,var,ia))),
107.59/107.80	                                                               ja)),ss)))))).
107.59/107.80	tff(zf_stmt_0, negated_conjecture,
107.59/107.80	  (~
107.59/107.80	    app_encode_app(bool,$o,pp,
107.59/107.80	                   app_encode_app(dB,bool,
107.59/107.80	                                  app_encode_app(fun(dB,bool),
107.59/107.80	                                                 app_encode_fun(dB,bool),
107.59/107.80	                                                 aa(dB,bool),it),
107.59/107.80	                                  app_encode_app(list(dB),dB,
107.59/107.80	                                                 app_encode_app(dB,
107.59/107.80	                                                                app_encode_fun(
107.59/107.80	                                                                list(dB),dB),
107.59/107.80	                                                                app_encode_app(
107.59/107.80	                                                                fun(dB,
107.59/107.80	                                                                    fun(
107.59/107.80	                                                                    dB,dB)),
107.59/107.80	                                                                app_encode_fun(
107.59/107.80	                                                                dB,
107.59/107.80	                                                                app_encode_fun(
107.59/107.80	                                                                list(dB),dB)),
107.59/107.80	                                                                foldl(dB,dB),
107.59/107.80	                                                                app),
107.59/107.80	                                                                app_encode_app(
107.59/107.80	                                                                dB,dB,
107.59/107.80	                                                                app_encode_app(
107.59/107.80	                                                                fun(dB,dB),
107.59/107.80	                                                                app_encode_fun(
107.59/107.80	                                                                dB,dB),
107.59/107.80	                                                                aa(dB,dB),
107.59/107.80	                                                                app_encode_app(
107.59/107.80	                                                                dB,
107.59/107.80	                                                                fun(dB,dB),
107.59/107.80	                                                                app_encode_app(
107.59/107.80	                                                                fun(dB,
107.59/107.80	                                                                    fun(
107.59/107.80	                                                                    dB,dB)),
107.59/107.80	                                                                app_encode_fun(
107.59/107.80	                                                                dB,fun(dB,dB)),
107.59/107.80	                                                                aa(dB,
107.59/107.80	                                                                   fun(dB,dB)),
107.59/107.80	                                                                app),
107.59/107.80	                                                                app_encode_app(
107.59/107.80	                                                                dB,dB,abs,
107.59/107.80	                                                                app_encode_app(
107.59/107.80	                                                                nat,dB,
107.59/107.80	                                                                app_encode_app(
107.59/107.80	                                                                fun(nat,dB),
107.59/107.80	                                                                app_encode_fun(
107.59/107.80	                                                                nat,dB),
107.59/107.80	                                                                aa(nat,dB),
107.59/107.80	                                                                app_encode_app(
107.59/107.80	                                                                dB,
107.59/107.80	                                                                fun(nat,dB),
107.59/107.80	                                                                app_encode_app(
107.59/107.80	                                                                fun(dB,
107.59/107.80	                                                                    fun(
107.59/107.80	                                                                    nat,dB)),
107.59/107.80	                                                                app_encode_fun(
107.59/107.80	                                                                dB,
107.59/107.80	                                                                fun(nat,dB)),
107.59/107.80	                                                                aa(dB,
107.59/107.80	                                                                   fun(
107.59/107.80	                                                                   nat,dB)),
107.59/107.80	                                                                app_encode_app(
107.59/107.80	                                                                dB,
107.59/107.80	                                                                fun(dB,
107.59/107.80	                                                                    fun(
107.59/107.80	                                                                    nat,dB)),
107.59/107.80	                                                                app_encode_app(
107.59/107.80	                                                                fun(dB,
107.59/107.80	                                                                    fun(
107.59/107.80	                                                                    dB,
107.59/107.80	                                                                    fun(
107.59/107.80	                                                                    nat,dB))),
107.59/107.80	                                                                app_encode_fun(
107.59/107.80	                                                                dB,
107.59/107.80	                                                                fun(dB,
107.59/107.80	                                                                    fun(
107.59/107.80	                                                                    nat,dB))),
107.59/107.80	                                                                aa(dB,
107.59/107.80	                                                                   fun(
107.59/107.80	                                                                   dB,
107.59/107.80	                                                                   fun(
107.59/107.80	                                                                   nat,dB))),
107.59/107.80	                                                                subst),ra)),
107.59/107.80	                                                                app_encode_app(
107.59/107.80	                                                                nat,dB,var,
107.59/107.80	                                                                app_encode_app(
107.59/107.80	                                                                nat,nat,suc,
107.59/107.80	                                                                ia)))),
107.59/107.80	                                                                app_encode_app(
107.59/107.80	                                                                nat,nat,suc,
107.59/107.80	                                                                ja))))),
107.59/107.80	                                                                app_encode_app(
107.59/107.80	                                                                nat,dB,
107.59/107.80	                                                                app_encode_app(
107.59/107.80	                                                                fun(nat,dB),
107.59/107.80	                                                                app_encode_fun(
107.59/107.80	                                                                nat,dB),
107.59/107.80	                                                                aa(nat,dB),
107.59/107.80	                                                                app_encode_app(
107.59/107.80	                                                                dB,
107.59/107.80	                                                                fun(nat,dB),
107.59/107.80	                                                                app_encode_app(
107.59/107.80	                                                                fun(dB,
107.59/107.80	                                                                    fun(
107.59/107.80	                                                                    nat,dB)),
107.59/107.80	                                                                app_encode_fun(
107.59/107.80	                                                                dB,
107.59/107.80	                                                                fun(nat,dB)),
107.59/107.80	                                                                aa(dB,
107.59/107.80	                                                                   fun(
107.59/107.80	                                                                   nat,dB)),
107.59/107.80	                                                                app_encode_app(
107.59/107.80	                                                                dB,
107.59/107.80	                                                                fun(dB,
107.59/107.80	                                                                    fun(
107.59/107.80	                                                                    nat,dB)),
107.59/107.80	                                                                app_encode_app(
107.59/107.80	                                                                fun(dB,
107.59/107.80	                                                                    fun(
107.59/107.80	                                                                    dB,
107.59/107.80	                                                                    fun(
107.59/107.80	                                                                    nat,dB))),
107.59/107.80	                                                                app_encode_fun(
107.59/107.80	                                                                dB,
107.59/107.80	                                                                fun(dB,
107.59/107.80	                                                                    fun(
107.59/107.80	                                                                    nat,dB))),
107.59/107.80	                                                                aa(dB,
107.59/107.80	                                                                   fun(
107.59/107.80	                                                                   dB,
107.59/107.80	                                                                   fun(
107.59/107.80	                                                                   nat,dB))),
107.59/107.80	                                                                subst),s)),
107.59/107.80	                                                                app_encode_app(
107.59/107.80	                                                                nat,dB,var,ia))),
107.59/107.80	                                                                ja))),
107.59/107.80	                                                 app_encode_app(list(dB),
107.59/107.80	                                                                list(dB),
107.59/107.80	                                                                app_encode_app(
107.59/107.80	                                                                fun(dB,dB),
107.59/107.80	                                                                app_encode_fun(
107.59/107.80	                                                                list(dB),
107.59/107.80	                                                                list(dB)),
107.59/107.80	                                                                map(dB,dB),
107.59/107.80	                                                                app_encode_app(
107.59/107.80	                                                                nat,
107.59/107.80	                                                                fun(dB,dB),
107.59/107.80	                                                                app_encode_app(
107.59/107.80	                                                                fun(dB,
107.59/107.80	                                                                    fun(
107.59/107.80	                                                                    nat,dB)),
107.59/107.80	                                                                app_encode_fun(
107.59/107.80	                                                                nat,
107.59/107.80	                                                                fun(dB,dB)),
107.59/107.80	                                                                combc(
107.59/107.80	                                                                dB,nat,dB),
107.59/107.80	                                                                app_encode_app(
107.59/107.80	                                                                dB,
107.59/107.80	                                                                fun(dB,
107.59/107.80	                                                                    fun(
107.59/107.80	                                                                    nat,dB)),
107.59/107.80	                                                                app_encode_app(
107.59/107.80	                                                                fun(dB,
107.59/107.80	                                                                    fun(
107.59/107.80	                                                                    dB,
107.59/107.80	                                                                    fun(
107.59/107.80	                                                                    nat,dB))),
107.59/107.80	                                                                app_encode_fun(
107.59/107.80	                                                                dB,
107.59/107.80	                                                                fun(dB,
107.59/107.80	                                                                    fun(
107.59/107.80	                                                                    nat,dB))),
107.59/107.80	                                                                combc(
107.59/107.80	                                                                dB,dB,
107.59/107.80	                                                                fun(nat,dB)),
107.59/107.80	                                                                subst),
107.59/107.80	                                                                app_encode_app(
107.59/107.80	                                                                nat,dB,var,ia))),
107.59/107.80	                                                                ja)),ss)))))).
107.59/107.80	tff('6', plain,
107.59/107.80	    ~ app_encode_app(bool, $o, pp, 
107.59/107.80	        app_encode_app(dB, bool, 
107.59/107.80	          app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
107.59/107.80	            aa(dB, bool), it), 
107.59/107.80	          app_encode_app(list(dB), dB, 
107.59/107.80	            app_encode_app(dB, app_encode_fun(list(dB), dB), 
107.59/107.80	              app_encode_app(fun(dB, fun(dB, dB)), 
107.59/107.80	                app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
107.59/107.80	                foldl(dB, dB), app), 
107.59/107.80	              app_encode_app(dB, dB, 
107.59/107.80	                app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), 
107.59/107.80	                  aa(dB, dB), 
107.59/107.80	                  app_encode_app(dB, fun(dB, dB), 
107.59/107.80	                    app_encode_app(fun(dB, fun(dB, dB)), 
107.59/107.80	                      app_encode_fun(dB, fun(dB, dB)), aa(dB, fun(dB, dB)), 
107.59/107.80	                      app), 
107.59/107.80	                    app_encode_app(dB, dB, abs, 
107.59/107.80	                      app_encode_app(nat, dB, 
107.59/107.80	                        app_encode_app(fun(nat, dB), 
107.59/107.80	                          app_encode_fun(nat, dB), aa(nat, dB), 
107.59/107.80	                          app_encode_app(dB, fun(nat, dB), 
107.59/107.80	                            app_encode_app(fun(dB, fun(nat, dB)), 
107.59/107.80	                              app_encode_fun(dB, fun(nat, dB)), 
107.59/107.80	                              aa(dB, fun(nat, dB)), 
107.59/107.80	                              app_encode_app(dB, fun(dB, fun(nat, dB)), 
107.59/107.80	                                app_encode_app(
107.59/107.80	                                  fun(dB, fun(dB, fun(nat, dB))), 
107.59/107.80	                                  app_encode_fun(dB, fun(dB, fun(nat, dB))), 
107.59/107.80	                                  aa(dB, fun(dB, fun(nat, dB))), subst), ra)), 
107.59/107.80	                            app_encode_app(nat, dB, var, 
107.59/107.80	                              app_encode_app(nat, nat, suc, ia)))), 
107.59/107.80	                        app_encode_app(nat, nat, suc, ja))))), 
107.59/107.80	                app_encode_app(nat, dB, 
107.59/107.80	                  app_encode_app(fun(nat, dB), app_encode_fun(nat, dB), 
107.59/107.80	                    aa(nat, dB), 
107.59/107.80	                    app_encode_app(dB, fun(nat, dB), 
107.59/107.80	                      app_encode_app(fun(dB, fun(nat, dB)), 
107.59/107.80	                        app_encode_fun(dB, fun(nat, dB)), 
107.59/107.80	                        aa(dB, fun(nat, dB)), 
107.59/107.80	                        app_encode_app(dB, fun(dB, fun(nat, dB)), 
107.59/107.80	                          app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
107.59/107.80	                            app_encode_fun(dB, fun(dB, fun(nat, dB))), 
107.59/107.80	                            aa(dB, fun(dB, fun(nat, dB))), subst), s)), 
107.59/107.80	                      app_encode_app(nat, dB, var, ia))), ja))), 
107.59/107.80	            app_encode_app(list(dB), list(dB), 
107.59/107.80	              app_encode_app(fun(dB, dB), 
107.59/107.80	                app_encode_fun(list(dB), list(dB)), map(dB, dB), 
107.59/107.80	                app_encode_app(nat, fun(dB, dB), 
107.59/107.80	                  app_encode_app(fun(dB, fun(nat, dB)), 
107.59/107.80	                    app_encode_fun(nat, fun(dB, dB)), combc(dB, nat, dB), 
107.59/107.80	                    app_encode_app(dB, fun(dB, fun(nat, dB)), 
107.59/107.80	                      app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
107.59/107.80	                        app_encode_fun(dB, fun(dB, fun(nat, dB))), 
107.59/107.80	                        combc(dB, dB, fun(nat, dB)), subst), 
107.59/107.80	                      app_encode_app(nat, dB, var, ia))), ja)), ss)))),
107.59/107.80	    inference('cnf', [status(esa)], [zf_stmt_0])).
107.59/107.80	tff('7', plain,
107.59/107.80	    ~ app_encode_app(bool, $o, pp, 
107.59/107.80	        app_encode_app(dB, bool, 
107.59/107.80	          app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
107.59/107.80	            aa(dB, bool), it), 
107.59/107.80	          app_encode_app(list(dB), dB, 
107.59/107.80	            app_encode_app(dB, app_encode_fun(list(dB), dB), 
107.59/107.80	              app_encode_app(fun(dB, fun(dB, dB)), 
107.59/107.80	                app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
107.59/107.80	                foldl(dB, dB), app), 
107.59/107.80	              app_encode_app(dB, dB, 
107.59/107.80	                app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), 
107.59/107.80	                  aa(dB, dB), 
107.59/107.80	                  app_encode_app(dB, fun(dB, dB), 
107.59/107.80	                    app_encode_app(fun(dB, fun(dB, dB)), 
107.59/107.80	                      app_encode_fun(dB, fun(dB, dB)), combc(dB, dB, dB), 
107.59/107.80	                      app), 
107.59/107.80	                    app_encode_app(dB, dB, 
107.59/107.80	                      app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), 
107.59/107.80	                        aa(dB, dB), 
107.59/107.80	                        app_encode_app(nat, fun(dB, dB), 
107.59/107.80	                          app_encode_app(fun(dB, fun(nat, dB)), 
107.59/107.80	                            app_encode_fun(nat, fun(dB, dB)), 
107.59/107.80	                            combc(dB, nat, dB), 
107.59/107.80	                            app_encode_app(dB, fun(dB, fun(nat, dB)), 
107.59/107.80	                              app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
107.59/107.80	                                app_encode_fun(dB, fun(dB, fun(nat, dB))), 
107.59/107.80	                                combc(dB, dB, fun(nat, dB)), subst), 
107.59/107.80	                              app_encode_app(nat, dB, var, ia))), ja)), s))), 
107.59/107.80	                app_encode_app(dB, dB, abs, 
107.59/107.80	                  app_encode_app(dB, dB, 
107.59/107.80	                    app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), 
107.59/107.80	                      aa(dB, dB), 
107.59/107.80	                      app_encode_app(nat, fun(dB, dB), 
107.59/107.80	                        app_encode_app(fun(dB, fun(nat, dB)), 
107.59/107.80	                          app_encode_fun(nat, fun(dB, dB)), 
107.59/107.80	                          combc(dB, nat, dB), 
107.59/107.80	                          app_encode_app(dB, fun(dB, fun(nat, dB)), 
107.59/107.80	                            app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
107.59/107.80	                              app_encode_fun(dB, fun(dB, fun(nat, dB))), 
107.59/107.80	                              combc(dB, dB, fun(nat, dB)), subst), 
107.59/107.80	                            app_encode_app(nat, dB, var, 
107.59/107.80	                              app_encode_app(nat, nat, suc, ia)))), 
107.59/107.80	                        app_encode_app(nat, nat, suc, ja))), ra)))), 
107.59/107.80	            app_encode_app(list(dB), list(dB), 
107.59/107.80	              app_encode_app(fun(dB, dB), 
107.59/107.80	                app_encode_fun(list(dB), list(dB)), map(dB, dB), 
107.59/107.80	                app_encode_app(nat, fun(dB, dB), 
107.59/107.80	                  app_encode_app(fun(dB, fun(nat, dB)), 
107.59/107.80	                    app_encode_fun(nat, fun(dB, dB)), combc(dB, nat, dB), 
107.59/107.80	                    app_encode_app(dB, fun(dB, fun(nat, dB)), 
107.59/107.80	                      app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
107.59/107.80	                        app_encode_fun(dB, fun(dB, fun(nat, dB))), 
107.59/107.80	                        combc(dB, dB, fun(nat, dB)), subst), 
107.59/107.80	                      app_encode_app(nat, dB, var, ia))), ja)), ss)))),
107.59/107.80	    inference('demod', [status(thm)], ['6', '1', '1', '1', '1', '1'])).
107.59/107.80	tff('8', plain,
107.59/107.80	    (~ $true
107.59/107.80	     | ~ app_encode_app(bool, $o, pp, 
107.59/107.80	           app_encode_app(dB, bool, 
107.59/107.80	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
107.59/107.80	               aa(dB, bool), it), 
107.59/107.80	             app_encode_app(list(dB), dB, 
107.59/107.80	               app_encode_app(dB, app_encode_fun(list(dB), dB), 
107.59/107.80	                 app_encode_app(fun(dB, fun(dB, dB)), 
107.59/107.80	                   app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
107.59/107.80	                   foldl(dB, dB), app), 
107.59/107.80	                 app_encode_app(nat, dB, 
107.59/107.80	                   app_encode_app(dB, app_encode_fun(nat, dB), 
107.59/107.80	                     app_encode_app(dB, 
107.59/107.80	                       app_encode_fun(dB, app_encode_fun(nat, dB)), substn, 
107.59/107.80	                       app_encode_app(dB, dB, 
107.59/107.80	                         app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), 
107.59/107.80	                           aa(dB, dB), 
107.59/107.80	                           app_encode_app(nat, fun(dB, dB), 
107.59/107.80	                             app_encode_app(fun(dB, fun(nat, dB)), 
107.59/107.80	                               app_encode_fun(nat, fun(dB, dB)), 
107.59/107.80	                               combc(dB, nat, dB), 
107.59/107.80	                               app_encode_app(dB, fun(dB, fun(nat, dB)), 
107.59/107.80	                                 app_encode_app(
107.59/107.80	                                   fun(dB, fun(dB, fun(nat, dB))), 
107.59/107.80	                                   app_encode_fun(dB, fun(dB, fun(nat, dB))), 
107.59/107.80	                                   combc(dB, dB, fun(nat, dB)), subst), 
107.59/107.80	                                 app_encode_app(nat, dB, var, 
107.59/107.80	                                   app_encode_app(nat, nat, suc, ia)))), 
107.59/107.80	                             app_encode_app(nat, nat, suc, ja))), ra)), 
107.59/107.80	                     app_encode_app(dB, dB, 
107.59/107.80	                       app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), 
107.59/107.80	                         aa(dB, dB), 
107.59/107.80	                         app_encode_app(nat, fun(dB, dB), 
107.59/107.80	                           app_encode_app(fun(dB, fun(nat, dB)), 
107.59/107.80	                             app_encode_fun(nat, fun(dB, dB)), 
107.59/107.80	                             combc(dB, nat, dB), 
107.59/107.80	                             app_encode_app(dB, fun(dB, fun(nat, dB)), 
107.59/107.80	                               app_encode_app(
107.59/107.80	                                 fun(dB, fun(dB, fun(nat, dB))), 
107.59/107.80	                                 app_encode_fun(dB, fun(dB, fun(nat, dB))), 
107.59/107.80	                                 combc(dB, dB, fun(nat, dB)), subst), 
107.59/107.80	                               app_encode_app(nat, dB, var, ia))), ja)), s)), 
107.59/107.80	                   zero_zero(nat))), 
107.59/107.80	               app_encode_app(list(dB), list(dB), 
107.59/107.80	                 app_encode_app(fun(dB, dB), 
107.59/107.80	                   app_encode_fun(list(dB), list(dB)), map(dB, dB), 
107.59/107.80	                   app_encode_app(nat, fun(dB, dB), 
107.59/107.80	                     app_encode_app(fun(dB, fun(nat, dB)), 
107.59/107.80	                       app_encode_fun(nat, fun(dB, dB)), combc(dB, nat, dB), 
107.59/107.80	                       app_encode_app(dB, fun(dB, fun(nat, dB)), 
107.59/107.80	                         app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
107.59/107.80	                           app_encode_fun(dB, fun(dB, fun(nat, dB))), 
107.59/107.80	                           combc(dB, dB, fun(nat, dB)), subst), 
107.59/107.80	                         app_encode_app(nat, dB, var, ia))), ja)), ss))))
107.59/107.80	     | ~ app_encode_app(bool, $o, pp, 
107.59/107.80	           app_encode_app(dB, bool, 
107.59/107.80	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
107.59/107.80	               aa(dB, bool), it), 
107.59/107.80	             app_encode_app(dB, dB, 
107.59/107.80	               app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), 
107.59/107.80	                 aa(dB, dB), 
107.59/107.80	                 app_encode_app(nat, fun(dB, dB), 
107.59/107.80	                   app_encode_app(fun(dB, fun(nat, dB)), 
107.59/107.80	                     app_encode_fun(nat, fun(dB, dB)), combc(dB, nat, dB), 
107.59/107.80	                     app_encode_app(dB, fun(dB, fun(nat, dB)), 
107.59/107.80	                       app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
107.59/107.80	                         app_encode_fun(dB, fun(dB, fun(nat, dB))), 
107.59/107.80	                         combc(dB, dB, fun(nat, dB)), subst), 
107.59/107.80	                       app_encode_app(nat, dB, var, ia))), ja)), s)))),
107.59/107.80	    inference('sup-', [status(thm)], ['5', '7'])).
107.59/107.80	tff(zf_stmt_164, axiom,
107.59/107.80	  (![I:nat,J:nat]:
107.59/107.80	     app_encode_app(bool,$o,pp,
107.59/107.80	                    app_encode_app(dB,bool,
107.59/107.80	                                   app_encode_app(fun(dB,bool),
107.59/107.80	                                                  app_encode_fun(dB,bool),
107.59/107.80	                                                  aa(dB,bool),it),
107.59/107.80	                                   app_encode_app(list(dB),dB,
107.59/107.80	                                                  app_encode_app(dB,
107.59/107.80	                                                                 app_encode_fun(
107.59/107.80	                                                                 list(dB),dB),
107.59/107.80	                                                                 app_encode_app(
107.59/107.80	                                                                 fun(
107.59/107.80	                                                                 dB,
107.59/107.80	                                                                 fun(dB,dB)),
107.59/107.80	                                                                 app_encode_fun(
107.59/107.80	                                                                 dB,
107.59/107.80	                                                                 app_encode_fun(
107.59/107.80	                                                                 list(dB),dB)),
107.59/107.80	                                                                 foldl(dB,dB),
107.59/107.80	                                                                 app),
107.59/107.80	                                                                 app_encode_app(
107.59/107.80	                                                                 nat,dB,
107.59/107.80	                                                                 app_encode_app(
107.59/107.80	                                                                 fun(nat,dB),
107.59/107.80	                                                                 app_encode_fun(
107.59/107.80	                                                                 nat,dB),
107.59/107.80	                                                                 aa(nat,dB),
107.59/107.80	                                                                 app_encode_app(
107.59/107.80	                                                                 dB,
107.59/107.80	                                                                 fun(nat,dB),
107.59/107.80	                                                                 app_encode_app(
107.59/107.80	                                                                 fun(
107.59/107.80	                                                                 dB,
107.59/107.80	                                                                 fun(nat,dB)),
107.59/107.80	                                                                 app_encode_fun(
107.59/107.80	                                                                 dB,
107.59/107.80	                                                                 fun(nat,dB)),
107.59/107.80	                                                                 aa(dB,
107.59/107.80	                                                                    fun(
107.59/107.80	                                                                    nat,dB)),
107.59/107.80	                                                                 app_encode_app(
107.59/107.80	                                                                 dB,
107.59/107.80	                                                                 fun(
107.59/107.80	                                                                 dB,
107.59/107.80	                                                                 fun(nat,dB)),
107.59/107.80	                                                                 app_encode_app(
107.59/107.80	                                                                 fun(
107.59/107.80	                                                                 dB,
107.59/107.80	                                                                 fun(
107.59/107.80	                                                                 dB,
107.59/107.80	                                                                 fun(nat,dB))),
107.59/107.80	                                                                 app_encode_fun(
107.59/107.80	                                                                 dB,
107.59/107.80	                                                                 fun(
107.59/107.80	                                                                 dB,
107.59/107.80	                                                                 fun(nat,dB))),
107.59/107.80	                                                                 aa(dB,
107.59/107.80	                                                                    fun(
107.59/107.80	                                                                    dB,
107.59/107.80	                                                                    fun(
107.59/107.80	                                                                    nat,dB))),
107.59/107.80	                                                                 subst),
107.59/107.80	                                                                 app_encode_app(
107.59/107.80	                                                                 nat,dB,
107.59/107.80	                                                                 app_encode_app(
107.59/107.80	                                                                 fun(nat,dB),
107.59/107.80	                                                                 app_encode_fun(
107.59/107.80	                                                                 nat,dB),
107.59/107.80	                                                                 aa(nat,dB),
107.59/107.80	                                                                 app_encode_app(
107.59/107.80	                                                                 dB,
107.59/107.80	                                                                 fun(nat,dB),
107.59/107.80	                                                                 app_encode_app(
107.59/107.80	                                                                 fun(
107.59/107.80	                                                                 dB,
107.59/107.80	                                                                 fun(nat,dB)),
107.59/107.80	                                                                 app_encode_fun(
107.59/107.80	                                                                 dB,
107.59/107.80	                                                                 fun(nat,dB)),
107.59/107.80	                                                                 aa(dB,
107.59/107.80	                                                                    fun(
107.59/107.80	                                                                    nat,dB)),
107.59/107.80	                                                                 app_encode_app(
107.59/107.80	                                                                 dB,
107.59/107.80	                                                                 fun(
107.59/107.80	                                                                 dB,
107.59/107.80	                                                                 fun(nat,dB)),
107.59/107.80	                                                                 app_encode_app(
107.59/107.80	                                                                 fun(
107.59/107.80	                                                                 dB,
107.59/107.80	                                                                 fun(
107.59/107.80	                                                                 dB,
107.59/107.80	                                                                 fun(nat,dB))),
107.59/107.80	                                                                 app_encode_fun(
107.59/107.80	                                                                 dB,
107.59/107.80	                                                                 fun(
107.59/107.80	                                                                 dB,
107.59/107.80	                                                                 fun(nat,dB))),
107.59/107.80	                                                                 aa(dB,
107.59/107.80	                                                                    fun(
107.59/107.80	                                                                    dB,
107.59/107.80	                                                                    fun(
107.59/107.80	                                                                    nat,dB))),
107.59/107.80	                                                                 subst),ra)),
107.59/107.80	                                                                 app_encode_app(
107.59/107.80	                                                                 nat,dB,var,
107.59/107.80	                                                                 app_encode_app(
107.59/107.80	                                                                 nat,nat,suc,
107.59/107.80	                                                                 I)))),
107.59/107.80	                                                                 app_encode_app(
107.59/107.80	                                                                 nat,nat,suc,
107.59/107.80	                                                                 J)))),
107.59/107.80	                                                                 app_encode_app(
107.59/107.80	                                                                 nat,dB,
107.59/107.80	                                                                 app_encode_app(
107.59/107.80	                                                                 fun(nat,dB),
107.59/107.80	                                                                 app_encode_fun(
107.59/107.80	                                                                 nat,dB),
107.59/107.80	                                                                 aa(nat,dB),
107.59/107.80	                                                                 app_encode_app(
107.59/107.80	                                                                 dB,
107.59/107.80	                                                                 fun(nat,dB),
107.59/107.80	                                                                 app_encode_app(
107.59/107.80	                                                                 fun(
107.59/107.80	                                                                 dB,
107.59/107.80	                                                                 fun(nat,dB)),
107.59/107.80	                                                                 app_encode_fun(
107.59/107.80	                                                                 dB,
107.59/107.80	                                                                 fun(nat,dB)),
107.59/107.80	                                                                 aa(dB,
107.59/107.80	                                                                    fun(
107.59/107.80	                                                                    nat,dB)),
107.59/107.80	                                                                 app_encode_app(
107.59/107.80	                                                                 dB,
107.59/107.80	                                                                 fun(
107.59/107.80	                                                                 dB,
107.59/107.80	                                                                 fun(nat,dB)),
107.59/107.80	                                                                 app_encode_app(
107.59/107.80	                                                                 fun(
107.59/107.80	                                                                 dB,
107.59/107.80	                                                                 fun(
107.59/107.80	                                                                 dB,
107.59/107.80	                                                                 fun(nat,dB))),
107.59/107.80	                                                                 app_encode_fun(
107.59/107.80	                                                                 dB,
107.59/107.80	                                                                 fun(
107.59/107.80	                                                                 dB,
107.59/107.80	                                                                 fun(nat,dB))),
107.59/107.80	                                                                 aa(dB,
107.59/107.80	                                                                    fun(
107.59/107.80	                                                                    dB,
107.59/107.80	                                                                    fun(
107.59/107.80	                                                                    nat,dB))),
107.59/107.80	                                                                 subst),s)),
107.59/107.80	                                                                 app_encode_app(
107.59/107.80	                                                                 nat,dB,var,I))),
107.59/107.80	                                                                 J))),
107.59/107.80	                                                                 zero_zero(
107.59/107.80	                                                                 nat))),
107.59/107.80	                                                  app_encode_app(list(dB),
107.59/107.80	                                                                 list(dB),
107.59/107.80	                                                                 app_encode_app(
107.59/107.80	                                                                 fun(dB,dB),
107.59/107.80	                                                                 app_encode_fun(
107.59/107.80	                                                                 list(dB),
107.59/107.80	                                                                 list(dB)),
107.59/107.80	                                                                 map(dB,dB),
107.59/107.80	                                                                 app_encode_app(
107.59/107.80	                                                                 nat,
107.59/107.80	                                                                 fun(dB,dB),
107.59/107.80	                                                                 app_encode_app(
107.59/107.80	                                                                 fun(
107.59/107.80	                                                                 dB,
107.59/107.80	                                                                 fun(nat,dB)),
107.59/107.80	                                                                 app_encode_fun(
107.59/107.80	                                                                 nat,
107.59/107.80	                                                                 fun(dB,dB)),
107.59/107.80	                                                                 combc(
107.59/107.80	                                                                 dB,nat,dB),
107.59/107.80	                                                                 app_encode_app(
107.59/107.80	                                                                 dB,
107.59/107.80	                                                                 fun(
107.59/107.80	                                                                 dB,
107.59/107.80	                                                                 fun(nat,dB)),
107.59/107.80	                                                                 app_encode_app(
107.59/107.80	                                                                 fun(
107.59/107.80	                                                                 dB,
107.59/107.80	                                                                 fun(
107.59/107.80	                                                                 dB,
107.59/107.80	                                                                 fun(nat,dB))),
107.59/107.80	                                                                 app_encode_fun(
107.59/107.80	                                                                 dB,
107.59/107.80	                                                                 fun(
107.59/107.80	                                                                 dB,
107.59/107.80	                                                                 fun(nat,dB))),
107.59/107.80	                                                                 combc(
107.59/107.80	                                                                 dB,dB,
107.59/107.80	                                                                 fun(nat,dB)),
107.59/107.80	                                                                 subst),
107.59/107.80	                                                                 app_encode_app(
107.59/107.80	                                                                 nat,dB,var,I))),
107.59/107.80	                                                                 J)),ss)))))).
107.59/107.80	tff('9', plain,
107.59/107.80	    ![X306 : nat, X307 : nat]:
107.59/107.80	      app_encode_app(bool, $o, pp, 
107.59/107.80	        app_encode_app(dB, bool, 
107.59/107.80	          app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
107.59/107.80	            aa(dB, bool), it), 
107.59/107.80	          app_encode_app(list(dB), dB, 
107.59/107.80	            app_encode_app(dB, app_encode_fun(list(dB), dB), 
107.59/107.80	              app_encode_app(fun(dB, fun(dB, dB)), 
107.59/107.80	                app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
107.59/107.80	                foldl(dB, dB), app), 
107.59/107.80	              app_encode_app(nat, dB, 
107.59/107.80	                app_encode_app(fun(nat, dB), app_encode_fun(nat, dB), 
107.59/107.80	                  aa(nat, dB), 
107.59/107.80	                  app_encode_app(dB, fun(nat, dB), 
107.59/107.80	                    app_encode_app(fun(dB, fun(nat, dB)), 
107.59/107.80	                      app_encode_fun(dB, fun(nat, dB)), 
107.59/107.80	                      aa(dB, fun(nat, dB)), 
107.59/107.80	                      app_encode_app(dB, fun(dB, fun(nat, dB)), 
107.59/107.80	                        app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
107.59/107.80	                          app_encode_fun(dB, fun(dB, fun(nat, dB))), 
107.59/107.80	                          aa(dB, fun(dB, fun(nat, dB))), subst), 
107.59/107.80	                        app_encode_app(nat, dB, 
107.59/107.80	                          app_encode_app(fun(nat, dB), 
107.59/107.80	                            app_encode_fun(nat, dB), aa(nat, dB), 
107.59/107.80	                            app_encode_app(dB, fun(nat, dB), 
107.59/107.80	                              app_encode_app(fun(dB, fun(nat, dB)), 
107.59/107.80	                                app_encode_fun(dB, fun(nat, dB)), 
107.59/107.80	                                aa(dB, fun(nat, dB)), 
107.59/107.80	                                app_encode_app(dB, fun(dB, fun(nat, dB)), 
107.59/107.80	                                  app_encode_app(
107.59/107.80	                                    fun(dB, fun(dB, fun(nat, dB))), 
107.59/107.80	                                    app_encode_fun(dB, fun(dB, fun(nat, dB))), 
107.59/107.80	                                    aa(dB, fun(dB, fun(nat, dB))), subst), 
107.59/107.80	                                  ra)), 
107.59/107.80	                              app_encode_app(nat, dB, var, 
107.59/107.80	                                app_encode_app(nat, nat, suc, X306)))), 
107.59/107.80	                          app_encode_app(nat, nat, suc, X307)))), 
107.59/107.80	                    app_encode_app(nat, dB, 
107.59/107.80	                      app_encode_app(fun(nat, dB), app_encode_fun(nat, dB), 
107.59/107.80	                        aa(nat, dB), 
107.59/107.80	                        app_encode_app(dB, fun(nat, dB), 
107.59/107.80	                          app_encode_app(fun(dB, fun(nat, dB)), 
107.59/107.80	                            app_encode_fun(dB, fun(nat, dB)), 
107.59/107.80	                            aa(dB, fun(nat, dB)), 
107.59/107.80	                            app_encode_app(dB, fun(dB, fun(nat, dB)), 
107.59/107.80	                              app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
107.59/107.80	                                app_encode_fun(dB, fun(dB, fun(nat, dB))), 
107.59/107.80	                                aa(dB, fun(dB, fun(nat, dB))), subst), s)), 
107.59/107.80	                          app_encode_app(nat, dB, var, X306))), X307))), 
107.59/107.80	                zero_zero(nat))), 
107.59/107.80	            app_encode_app(list(dB), list(dB), 
107.59/107.80	              app_encode_app(fun(dB, dB), 
107.59/107.80	                app_encode_fun(list(dB), list(dB)), map(dB, dB), 
107.59/107.80	                app_encode_app(nat, fun(dB, dB), 
107.59/107.80	                  app_encode_app(fun(dB, fun(nat, dB)), 
107.59/107.80	                    app_encode_fun(nat, fun(dB, dB)), combc(dB, nat, dB), 
107.59/107.80	                    app_encode_app(dB, fun(dB, fun(nat, dB)), 
107.59/107.80	                      app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
107.59/107.80	                        app_encode_fun(dB, fun(dB, fun(nat, dB))), 
107.59/107.80	                        combc(dB, dB, fun(nat, dB)), subst), 
107.59/107.80	                      app_encode_app(nat, dB, var, X306))), X307)), ss)))),
107.59/107.80	    inference('cnf', [status(esa)], [zf_stmt_164])).
107.59/107.80	tff('10', plain,
107.59/107.80	    ![X306 : nat, X307 : nat]:
107.59/107.80	      app_encode_app(bool, $o, pp, 
107.59/107.80	        app_encode_app(dB, bool, 
107.59/107.80	          app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
107.59/107.80	            aa(dB, bool), it), 
107.59/107.80	          app_encode_app(list(dB), dB, 
107.59/107.80	            app_encode_app(dB, app_encode_fun(list(dB), dB), 
107.59/107.80	              app_encode_app(fun(dB, fun(dB, dB)), 
107.59/107.80	                app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
107.59/107.80	                foldl(dB, dB), app), 
107.59/107.80	              app_encode_app(nat, dB, 
107.59/107.80	                app_encode_app(dB, app_encode_fun(nat, dB), 
107.59/107.80	                  app_encode_app(dB, 
107.59/107.80	                    app_encode_fun(dB, app_encode_fun(nat, dB)), substn, 
107.59/107.80	                    app_encode_app(dB, dB, 
107.59/107.80	                      app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), 
107.59/107.80	                        aa(dB, dB), 
107.59/107.80	                        app_encode_app(nat, fun(dB, dB), 
107.59/107.80	                          app_encode_app(fun(dB, fun(nat, dB)), 
107.59/107.80	                            app_encode_fun(nat, fun(dB, dB)), 
107.59/107.80	                            combc(dB, nat, dB), 
107.59/107.80	                            app_encode_app(dB, fun(dB, fun(nat, dB)), 
107.59/107.80	                              app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
107.59/107.80	                                app_encode_fun(dB, fun(dB, fun(nat, dB))), 
107.59/107.80	                                combc(dB, dB, fun(nat, dB)), subst), 
107.59/107.80	                              app_encode_app(nat, dB, var, 
107.59/107.80	                                app_encode_app(nat, nat, suc, X306)))), 
107.59/107.80	                          app_encode_app(nat, nat, suc, X307))), ra)), 
107.59/107.80	                  app_encode_app(dB, dB, 
107.59/107.80	                    app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), 
107.59/107.80	                      aa(dB, dB), 
107.59/107.80	                      app_encode_app(nat, fun(dB, dB), 
107.59/107.80	                        app_encode_app(fun(dB, fun(nat, dB)), 
107.59/107.80	                          app_encode_fun(nat, fun(dB, dB)), 
107.59/107.80	                          combc(dB, nat, dB), 
107.59/107.80	                          app_encode_app(dB, fun(dB, fun(nat, dB)), 
107.59/107.80	                            app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
107.59/107.80	                              app_encode_fun(dB, fun(dB, fun(nat, dB))), 
107.59/107.80	                              combc(dB, dB, fun(nat, dB)), subst), 
107.59/107.80	                            app_encode_app(nat, dB, var, X306))), X307)), s)), 
107.59/107.80	                zero_zero(nat))), 
107.59/107.80	            app_encode_app(list(dB), list(dB), 
107.59/107.80	              app_encode_app(fun(dB, dB), 
107.59/107.80	                app_encode_fun(list(dB), list(dB)), map(dB, dB), 
107.59/107.80	                app_encode_app(nat, fun(dB, dB), 
107.59/107.80	                  app_encode_app(fun(dB, fun(nat, dB)), 
107.59/107.80	                    app_encode_fun(nat, fun(dB, dB)), combc(dB, nat, dB), 
107.59/107.80	                    app_encode_app(dB, fun(dB, fun(nat, dB)), 
107.59/107.80	                      app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
107.59/107.80	                        app_encode_fun(dB, fun(dB, fun(nat, dB))), 
107.59/107.80	                        combc(dB, dB, fun(nat, dB)), subst), 
107.59/107.80	                      app_encode_app(nat, dB, var, X306))), X307)), ss)))),
107.59/107.80	    inference('demod', [status(thm)],
107.59/107.80	              ['9', '1', '1', '1', '1', '1', '1', '4'])).
107.59/107.80	tff(zf_stmt_166, axiom,
107.59/107.80	  (![I:nat,J:nat]:
107.59/107.80	     app_encode_app(bool,$o,pp,
107.59/107.80	                    app_encode_app(dB,bool,
107.59/107.80	                                   app_encode_app(fun(dB,bool),
107.59/107.80	                                                  app_encode_fun(dB,bool),
107.59/107.80	                                                  aa(dB,bool),it),
107.59/107.80	                                   app_encode_app(nat,dB,
107.59/107.80	                                                  app_encode_app(fun(nat,dB),
107.59/107.80	                                                                 app_encode_fun(
107.59/107.80	                                                                 nat,dB),
107.59/107.80	                                                                 aa(nat,dB),
107.59/107.80	                                                                 app_encode_app(
107.59/107.80	                                                                 dB,
107.59/107.80	                                                                 fun(nat,dB),
107.59/107.80	                                                                 app_encode_app(
107.59/107.80	                                                                 fun(
107.59/107.80	                                                                 dB,
107.59/107.80	                                                                 fun(nat,dB)),
107.59/107.80	                                                                 app_encode_fun(
107.59/107.80	                                                                 dB,
107.59/107.80	                                                                 fun(nat,dB)),
107.59/107.80	                                                                 aa(dB,
107.59/107.80	                                                                    fun(
107.59/107.80	                                                                    nat,dB)),
107.59/107.80	                                                                 app_encode_app(
107.59/107.80	                                                                 dB,
107.59/107.80	                                                                 fun(
107.59/107.80	                                                                 dB,
107.59/107.80	                                                                 fun(nat,dB)),
107.59/107.80	                                                                 app_encode_app(
107.59/107.80	                                                                 fun(
107.59/107.80	                                                                 dB,
107.59/107.80	                                                                 fun(
107.59/107.80	                                                                 dB,
107.59/107.80	                                                                 fun(nat,dB))),
107.59/107.80	                                                                 app_encode_fun(
107.59/107.80	                                                                 dB,
107.59/107.80	                                                                 fun(
107.59/107.80	                                                                 dB,
107.59/107.80	                                                                 fun(nat,dB))),
107.59/107.80	                                                                 aa(dB,
107.59/107.80	                                                                    fun(
107.59/107.80	                                                                    dB,
107.59/107.80	                                                                    fun(
107.59/107.80	                                                                    nat,dB))),
107.59/107.80	                                                                 subst),s)),
107.59/107.80	                                                                 app_encode_app(
107.59/107.80	                                                                 nat,dB,var,I))),
107.59/107.80	                                                  J))))).
107.59/107.80	tff('11', plain,
107.59/107.80	    ![X308 : nat, X309 : nat]:
107.59/107.80	      app_encode_app(bool, $o, pp, 
107.59/107.80	        app_encode_app(dB, bool, 
107.59/107.80	          app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
107.59/107.80	            aa(dB, bool), it), 
107.59/107.80	          app_encode_app(nat, dB, 
107.59/107.80	            app_encode_app(fun(nat, dB), app_encode_fun(nat, dB), 
107.59/107.80	              aa(nat, dB), 
107.59/107.80	              app_encode_app(dB, fun(nat, dB), 
107.59/107.80	                app_encode_app(fun(dB, fun(nat, dB)), 
107.59/107.80	                  app_encode_fun(dB, fun(nat, dB)), aa(dB, fun(nat, dB)), 
107.59/107.80	                  app_encode_app(dB, fun(dB, fun(nat, dB)), 
107.59/107.80	                    app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
107.59/107.80	                      app_encode_fun(dB, fun(dB, fun(nat, dB))), 
107.59/107.80	                      aa(dB, fun(dB, fun(nat, dB))), subst), s)), 
107.59/107.80	                app_encode_app(nat, dB, var, X308))), X309))),
107.59/107.80	    inference('cnf', [status(esa)], [zf_stmt_166])).
107.59/107.80	tff('12', plain,
107.59/107.80	    ![X308 : nat, X309 : nat]:
107.59/107.80	      app_encode_app(bool, $o, pp, 
107.59/107.80	        app_encode_app(dB, bool, 
107.59/107.80	          app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
107.59/107.80	            aa(dB, bool), it), 
107.59/107.80	          app_encode_app(dB, dB, 
107.59/107.80	            app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), aa(dB, dB), 
107.59/107.80	              app_encode_app(nat, fun(dB, dB), 
107.59/107.80	                app_encode_app(fun(dB, fun(nat, dB)), 
107.59/107.80	                  app_encode_fun(nat, fun(dB, dB)), combc(dB, nat, dB), 
107.59/107.80	                  app_encode_app(dB, fun(dB, fun(nat, dB)), 
107.59/107.80	                    app_encode_app(fun(dB, fun(dB, fun(nat, dB))), 
107.59/107.80	                      app_encode_fun(dB, fun(dB, fun(nat, dB))), 
107.59/107.80	                      combc(dB, dB, fun(nat, dB)), subst), 
107.59/107.80	                    app_encode_app(nat, dB, var, X308))), X309)), s))),
107.59/107.80	    inference('demod', [status(thm)], ['11', '1', '1'])).
107.59/107.80	tff('13', plain, (~ $true | ~ $true | ~ $true),
107.59/107.80	    inference('demod', [status(thm)], ['8', '10', '12'])).
107.59/107.80	tff('14', plain, $false, inference('simplify', [status(thm)], ['13'])).
107.59/107.80	
107.59/107.80	% SZS output end Refutation
107.59/107.81	EOF
