0.00/0.00	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : app
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : kbo
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.20	% Computer   : n030.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 06:47:54 CST 2018
191.51/191.72	% done 7464 iterations in 191.516s
191.51/191.72	% SZS status Theorem for 'stdin'
191.51/191.72	% SZS output start Refutation
191.51/191.73	tff(zf_stmt_143, axiom,
191.51/191.73	  (app_encode_app(bool,$o,pp,
191.51/191.73	                  app_encode_app(dB,bool,
191.51/191.73	                                 app_encode_app(fun(dB,bool),
191.51/191.73	                                                app_encode_fun(dB,bool),
191.51/191.73	                                                aa(dB,bool),it),
191.51/191.73	                                 app_encode_app(dB,dB,
191.51/191.73	                                                app_encode_app(fun(dB,dB),
191.51/191.73	                                                               app_encode_fun(
191.51/191.73	                                                               dB,dB),
191.51/191.73	                                                               aa(dB,dB),
191.51/191.73	                                                               app_encode_app(
191.51/191.73	                                                               dB,fun(dB,dB),
191.51/191.73	                                                               app_encode_app(
191.51/191.73	                                                               fun(dB,
191.51/191.73	                                                                   fun(dB,dB)),
191.51/191.73	                                                               app_encode_fun(
191.51/191.73	                                                               dB,fun(dB,dB)),
191.51/191.73	                                                               aa(dB,
191.51/191.73	                                                                  fun(dB,dB)),
191.51/191.73	                                                               app),
191.51/191.73	                                                               app_encode_app(
191.51/191.73	                                                               list(dB),dB,
191.51/191.73	                                                               app_encode_app(
191.51/191.73	                                                               dB,
191.51/191.73	                                                               app_encode_fun(
191.51/191.73	                                                               list(dB),dB),
191.51/191.73	                                                               app_encode_app(
191.51/191.73	                                                               fun(dB,
191.51/191.73	                                                                   fun(dB,dB)),
191.51/191.73	                                                               app_encode_fun(
191.51/191.73	                                                               dB,
191.51/191.73	                                                               app_encode_fun(
191.51/191.73	                                                               list(dB),dB)),
191.51/191.73	                                                               foldl(dB,dB),
191.51/191.73	                                                               app),
191.51/191.73	                                                               app_encode_app(
191.51/191.73	                                                               nat,dB,
191.51/191.73	                                                               app_encode_app(
191.51/191.73	                                                               dB,
191.51/191.73	                                                               app_encode_fun(
191.51/191.73	                                                               nat,dB),
191.51/191.73	                                                               app_encode_app(
191.51/191.73	                                                               dB,
191.51/191.73	                                                               app_encode_fun(
191.51/191.73	                                                               dB,
191.51/191.73	                                                               app_encode_fun(
191.51/191.73	                                                               nat,dB)),
191.51/191.73	                                                               subst,r),s),
191.51/191.73	                                                               zero_zero(nat))),
191.51/191.73	                                                               ss))),
191.51/191.73	                                                app_encode_app(nat,dB,var,i)))))).
191.51/191.73	tff('0', plain,
191.51/191.73	    app_encode_app(bool, $o, pp, 
191.51/191.73	      app_encode_app(dB, bool, 
191.51/191.73	        app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
191.51/191.73	          aa(dB, bool), it), 
191.51/191.73	        app_encode_app(dB, dB, 
191.51/191.73	          app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), aa(dB, dB), 
191.51/191.73	            app_encode_app(dB, fun(dB, dB), 
191.51/191.73	              app_encode_app(fun(dB, fun(dB, dB)), 
191.51/191.73	                app_encode_fun(dB, fun(dB, dB)), aa(dB, fun(dB, dB)), app), 
191.51/191.73	              app_encode_app(list(dB), dB, 
191.51/191.73	                app_encode_app(dB, app_encode_fun(list(dB), dB), 
191.51/191.73	                  app_encode_app(fun(dB, fun(dB, dB)), 
191.51/191.73	                    app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
191.51/191.73	                    foldl(dB, dB), app), 
191.51/191.73	                  app_encode_app(nat, dB, 
191.51/191.73	                    app_encode_app(dB, app_encode_fun(nat, dB), 
191.51/191.73	                      app_encode_app(dB, 
191.51/191.73	                        app_encode_fun(dB, app_encode_fun(nat, dB)), subst, 
191.51/191.73	                        r), s), zero_zero(nat))), ss))), 
191.51/191.73	          app_encode_app(nat, dB, var, i)))),
191.51/191.73	    inference('cnf', [status(esa)], [zf_stmt_143])).
191.51/191.73	tff(zf_stmt_107, axiom,
191.51/191.73	  (![Ts:list(dB),Ta:dB,S:dB,R:dB]:
191.51/191.73	     ((app_encode_app(dB,dB,
191.51/191.73	                      app_encode_app(fun(dB,dB),app_encode_fun(dB,dB),
191.51/191.73	                                     aa(dB,dB),
191.51/191.73	                                     app_encode_app(dB,fun(dB,dB),
191.51/191.73	                                                    app_encode_app(fun(
191.51/191.73	                                                                   dB,
191.51/191.73	                                                                   fun(dB,dB)),
191.51/191.73	                                                                   app_encode_fun(
191.51/191.73	                                                                   dB,
191.51/191.73	                                                                   fun(dB,dB)),
191.51/191.73	                                                                   aa(
191.51/191.73	                                                                   dB,
191.51/191.73	                                                                   fun(dB,dB)),
191.51/191.73	                                                                   app),
191.51/191.73	                                                    R)),
191.51/191.73	                      S) =
191.51/191.73	       app_encode_app(list(dB),dB,
191.51/191.73	                      app_encode_app(dB,app_encode_fun(list(dB),dB),
191.51/191.73	                                     app_encode_app(fun(dB,fun(dB,dB)),
191.51/191.73	                                                    app_encode_fun(dB,
191.51/191.73	                                                                   app_encode_fun(
191.51/191.73	                                                                   list(dB),
191.51/191.73	                                                                   dB)),
191.51/191.73	                                                    foldl(dB,dB),app),
191.51/191.73	                                     Ta),
191.51/191.73	                      Ts)) <=>
191.51/191.73	      (((Ts = nil(dB)) =>
191.51/191.73	        (app_encode_app(dB,dB,
191.51/191.73	                        app_encode_app(fun(dB,dB),app_encode_fun(dB,dB),
191.51/191.73	                                       aa(dB,dB),
191.51/191.73	                                       app_encode_app(dB,fun(dB,dB),
191.51/191.73	                                                      app_encode_app(
191.51/191.73	                                                      fun(dB,fun(dB,dB)),
191.51/191.73	                                                      app_encode_fun(
191.51/191.73	                                                      dB,fun(dB,dB)),
191.51/191.73	                                                      aa(dB,fun(dB,dB)),app),
191.51/191.73	                                                      R)),
191.51/191.73	                        S) =
191.51/191.73	         Ta)) & 
191.51/191.73	       ((Ts != nil(dB)) =>
191.51/191.73	        (?[Ss:list(dB)]:
191.51/191.73	           ((Ts =
191.51/191.73	             app_encode_app(list(dB),list(dB),
191.51/191.73	                            app_encode_app(list(dB),
191.51/191.73	                                           app_encode_fun(list(dB),list(dB)),
191.51/191.73	                                           append(dB),Ss),
191.51/191.73	                            app_encode_app(list(dB),list(dB),
191.51/191.73	                                           app_encode_app(dB,
191.51/191.73	                                                          app_encode_fun(
191.51/191.73	                                                          list(dB),list(dB)),
191.51/191.73	                                                          cons(dB),S),
191.51/191.73	                                           nil(dB)))) & 
191.51/191.73	            (R =
191.51/191.73	             app_encode_app(list(dB),dB,
191.51/191.73	                            app_encode_app(dB,app_encode_fun(list(dB),dB),
191.51/191.73	                                           app_encode_app(fun(dB,fun(dB,dB)),
191.51/191.73	                                                          app_encode_fun(
191.51/191.73	                                                          dB,
191.51/191.73	                                                          app_encode_fun(
191.51/191.73	                                                          list(dB),dB)),
191.51/191.73	                                                          foldl(dB,dB),app),
191.51/191.73	                                           Ta),
191.51/191.73	                            Ss))))))))).
191.51/191.73	tff('1', plain,
191.51/191.73	    ![X253 : list(dB), X254 : dB, X256 : dB, X257 : dB, X258 : list(dB)]:
191.51/191.73	      (app_encode_app(dB, dB, 
191.51/191.73	         app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), aa(dB, dB), 
191.51/191.73	           app_encode_app(dB, fun(dB, dB), 
191.51/191.73	             app_encode_app(fun(dB, fun(dB, dB)), 
191.51/191.73	               app_encode_fun(dB, fun(dB, dB)), aa(dB, fun(dB, dB)), app), 
191.51/191.73	             X257)), X256)
191.51/191.73	        = app_encode_app(list(dB), dB, 
191.51/191.73	            app_encode_app(dB, app_encode_fun(list(dB), dB), 
191.51/191.73	              app_encode_app(fun(dB, fun(dB, dB)), 
191.51/191.73	                app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
191.51/191.73	                foldl(dB, dB), app), X254), X253)
191.51/191.73	       | X257
191.51/191.73	          != app_encode_app(list(dB), dB, 
191.51/191.73	               app_encode_app(dB, app_encode_fun(list(dB), dB), 
191.51/191.73	                 app_encode_app(fun(dB, fun(dB, dB)), 
191.51/191.73	                   app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
191.51/191.73	                   foldl(dB, dB), app), X254), X258)
191.51/191.73	       | X253
191.51/191.73	          != app_encode_app(list(dB), list(dB), 
191.51/191.73	               app_encode_app(list(dB), app_encode_fun(list(dB), list(dB)), 
191.51/191.73	                 append(dB), X258), 
191.51/191.73	               app_encode_app(list(dB), list(dB), 
191.51/191.73	                 app_encode_app(dB, app_encode_fun(list(dB), list(dB)), 
191.51/191.73	                   cons(dB), X256), nil(dB)))
191.51/191.73	       | X253 = nil(dB)),
191.51/191.73	    inference('cnf', [status(esa)], [zf_stmt_107])).
191.51/191.73	tff('2', plain,
191.51/191.73	    ![X254 : dB, X256 : dB, X258 : list(dB)]:
191.51/191.73	      (app_encode_app(list(dB), list(dB), 
191.51/191.73	         app_encode_app(list(dB), app_encode_fun(list(dB), list(dB)), 
191.51/191.73	           append(dB), X258), 
191.51/191.73	         app_encode_app(list(dB), list(dB), 
191.51/191.73	           app_encode_app(dB, app_encode_fun(list(dB), list(dB)), cons(dB), 
191.51/191.73	             X256), nil(dB)))
191.51/191.73	        = nil(dB)
191.51/191.73	       | app_encode_app(dB, dB, 
191.51/191.73	           app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), aa(dB, dB), 
191.51/191.73	             app_encode_app(dB, fun(dB, dB), 
191.51/191.73	               app_encode_app(fun(dB, fun(dB, dB)), 
191.51/191.73	                 app_encode_fun(dB, fun(dB, dB)), aa(dB, fun(dB, dB)), app), 
191.51/191.73	               app_encode_app(list(dB), dB, 
191.51/191.73	                 app_encode_app(dB, app_encode_fun(list(dB), dB), 
191.51/191.73	                   app_encode_app(fun(dB, fun(dB, dB)), 
191.51/191.73	                     app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
191.51/191.73	                     foldl(dB, dB), app), X254), X258))), X256)
191.51/191.73	          = app_encode_app(list(dB), dB, 
191.51/191.73	              app_encode_app(dB, app_encode_fun(list(dB), dB), 
191.51/191.73	                app_encode_app(fun(dB, fun(dB, dB)), 
191.51/191.73	                  app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
191.51/191.73	                  foldl(dB, dB), app), X254), 
191.51/191.73	              app_encode_app(list(dB), list(dB), 
191.51/191.73	                app_encode_app(list(dB), app_encode_fun(list(dB), list(dB)), 
191.51/191.73	                  append(dB), X258), 
191.51/191.73	                app_encode_app(list(dB), list(dB), 
191.51/191.73	                  app_encode_app(dB, app_encode_fun(list(dB), list(dB)), 
191.51/191.73	                    cons(dB), X256), nil(dB))))),
191.51/191.73	    inference('simplify', [status(thm)], ['1'])).
191.51/191.73	tff(zf_stmt_138, axiom,
191.51/191.73	  (![A:$tType,B:$tType,Xs:list(B),X:B]:
191.51/191.73	     ((app_encode_app(list(A),list(A),rotate1(A),nil(A)) = nil(A)) & 
191.51/191.73	      (app_encode_app(list(B),list(B),rotate1(B),
191.51/191.73	                      app_encode_app(list(B),list(B),
191.51/191.73	                                     app_encode_app(B,
191.51/191.73	                                                    app_encode_fun(list(B),
191.51/191.73	                                                                   list(B)),
191.51/191.73	                                                    cons(B),X),
191.51/191.73	                                     Xs)) =
191.51/191.73	       app_encode_app(list(B),list(B),
191.51/191.73	                      app_encode_app(list(B),app_encode_fun(list(B),list(B)),
191.51/191.73	                                     append(B),Xs),
191.51/191.73	                      app_encode_app(list(B),list(B),
191.51/191.73	                                     app_encode_app(B,
191.51/191.73	                                                    app_encode_fun(list(B),
191.51/191.73	                                                                   list(B)),
191.51/191.73	                                                    cons(B),X),
191.51/191.73	                                     nil(B))))))).
191.51/191.73	tff('3', plain,
191.51/191.73	    ![X397 : $tType, X398 : list(X397), X399 : X397]:
191.51/191.73	      app_encode_app(list(X397), list(X397), rotate1(X397), 
191.51/191.73	        app_encode_app(list(X397), list(X397), 
191.51/191.73	          app_encode_app(X397, app_encode_fun(list(X397), list(X397)), 
191.51/191.73	            cons(X397), X399), X398))
191.51/191.73	       = app_encode_app(list(X397), list(X397), 
191.51/191.73	           app_encode_app(list(X397), 
191.51/191.73	             app_encode_fun(list(X397), list(X397)), append(X397), X398), 
191.51/191.73	           app_encode_app(list(X397), list(X397), 
191.51/191.73	             app_encode_app(X397, app_encode_fun(list(X397), list(X397)), 
191.51/191.73	               cons(X397), X399), nil(X397))),
191.51/191.73	    inference('cnf', [status(esa)], [zf_stmt_138])).
191.51/191.73	tff('4', plain,
191.51/191.73	    ![X254 : dB, X256 : dB, X258 : list(dB)]:
191.51/191.73	      (app_encode_app(list(dB), list(dB), rotate1(dB), 
191.51/191.73	         app_encode_app(list(dB), list(dB), 
191.51/191.73	           app_encode_app(dB, app_encode_fun(list(dB), list(dB)), cons(dB), 
191.51/191.73	             X256), X258))
191.51/191.73	        = nil(dB)
191.51/191.73	       | app_encode_app(dB, dB, 
191.51/191.73	           app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), aa(dB, dB), 
191.51/191.73	             app_encode_app(dB, fun(dB, dB), 
191.51/191.73	               app_encode_app(fun(dB, fun(dB, dB)), 
191.51/191.73	                 app_encode_fun(dB, fun(dB, dB)), aa(dB, fun(dB, dB)), app), 
191.51/191.73	               app_encode_app(list(dB), dB, 
191.51/191.73	                 app_encode_app(dB, app_encode_fun(list(dB), dB), 
191.51/191.73	                   app_encode_app(fun(dB, fun(dB, dB)), 
191.51/191.73	                     app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
191.51/191.73	                     foldl(dB, dB), app), X254), X258))), X256)
191.51/191.73	          = app_encode_app(list(dB), dB, 
191.51/191.73	              app_encode_app(dB, app_encode_fun(list(dB), dB), 
191.51/191.73	                app_encode_app(fun(dB, fun(dB, dB)), 
191.51/191.73	                  app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
191.51/191.73	                  foldl(dB, dB), app), X254), 
191.51/191.73	              app_encode_app(list(dB), list(dB), rotate1(dB), 
191.51/191.73	                app_encode_app(list(dB), list(dB), 
191.51/191.73	                  app_encode_app(dB, app_encode_fun(list(dB), list(dB)), 
191.51/191.73	                    cons(dB), X256), X258)))),
191.51/191.73	    inference('demod', [status(thm)], ['2', '3', '3'])).
191.51/191.73	tff(zf_stmt_112, axiom,
191.51/191.73	  (![A:$tType,Ys1:list(A),Xs1:list(A)]:
191.51/191.73	     ((nil(A) =
191.51/191.73	       app_encode_app(list(A),list(A),
191.51/191.73	                      app_encode_app(list(A),app_encode_fun(list(A),list(A)),
191.51/191.73	                                     append(A),Xs1),
191.51/191.73	                      Ys1)) <=>
191.51/191.73	      ((Xs1 = nil(A)) & (Ys1 = nil(A)))))).
191.51/191.73	tff('5', plain,
191.51/191.73	    ![X277 : $tType, X278 : list(X277), X279 : list(X277)]:
191.51/191.73	      (X279 = nil(X277)
191.51/191.73	       | nil(X277)
191.51/191.73	          != app_encode_app(list(X277), list(X277), 
191.51/191.73	               app_encode_app(list(X277), 
191.51/191.73	                 app_encode_fun(list(X277), list(X277)), append(X277), X278), 
191.51/191.73	               X279)),
191.51/191.73	    inference('cnf', [status(esa)], [zf_stmt_112])).
191.51/191.73	tff('6', plain,
191.51/191.73	    ![X0 : $tType, X1 : list(X0), X2 : X0]:
191.51/191.73	      (nil(X0)
191.51/191.73	        != app_encode_app(list(X0), list(X0), rotate1(X0), 
191.51/191.73	             app_encode_app(list(X0), list(X0), 
191.51/191.73	               app_encode_app(X0, app_encode_fun(list(X0), list(X0)), 
191.51/191.73	                 cons(X0), X2), X1))
191.51/191.73	       | app_encode_app(list(X0), list(X0), 
191.51/191.73	           app_encode_app(X0, app_encode_fun(list(X0), list(X0)), cons(X0), 
191.51/191.73	             X2), nil(X0))
191.51/191.73	          = nil(X0)),
191.51/191.73	    inference('sup-', [status(thm)], ['3', '5'])).
191.51/191.73	tff(zf_stmt_96, axiom,
191.51/191.73	  (![A:$tType,Xs:list(A),X:A]:
191.51/191.73	     (app_encode_app(list(A),list(A),
191.51/191.73	                     app_encode_app(A,app_encode_fun(list(A),list(A)),
191.51/191.73	                                    cons(A),X),
191.51/191.73	                     Xs) !=
191.51/191.73	      Xs))).
191.51/191.73	tff('7', plain,
191.51/191.73	    ![X204 : $tType, X205 : list(X204), X206 : X204]:
191.51/191.73	      app_encode_app(list(X204), list(X204), 
191.51/191.73	        app_encode_app(X204, app_encode_fun(list(X204), list(X204)), 
191.51/191.73	          cons(X204), X206), X205)
191.51/191.73	       != X205,
191.51/191.73	    inference('cnf', [status(esa)], [zf_stmt_96])).
191.51/191.73	tff('8', plain,
191.51/191.73	    ![X0 : $tType, X1 : list(X0), X2 : X0]:
191.51/191.73	      nil(X0)
191.51/191.73	       != app_encode_app(list(X0), list(X0), rotate1(X0), 
191.51/191.73	            app_encode_app(list(X0), list(X0), 
191.51/191.73	              app_encode_app(X0, app_encode_fun(list(X0), list(X0)), 
191.51/191.73	                cons(X0), X2), X1)),
191.51/191.73	    inference('simplify_reflect-', [status(thm)], ['6', '7'])).
191.51/191.73	tff('9', plain,
191.51/191.73	    ![X254 : dB, X256 : dB, X258 : list(dB)]:
191.51/191.73	      app_encode_app(dB, dB, 
191.51/191.73	        app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), aa(dB, dB), 
191.51/191.73	          app_encode_app(dB, fun(dB, dB), 
191.51/191.73	            app_encode_app(fun(dB, fun(dB, dB)), 
191.51/191.73	              app_encode_fun(dB, fun(dB, dB)), aa(dB, fun(dB, dB)), app), 
191.51/191.73	            app_encode_app(list(dB), dB, 
191.51/191.73	              app_encode_app(dB, app_encode_fun(list(dB), dB), 
191.51/191.73	                app_encode_app(fun(dB, fun(dB, dB)), 
191.51/191.73	                  app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
191.51/191.73	                  foldl(dB, dB), app), X254), X258))), X256)
191.51/191.73	       = app_encode_app(list(dB), dB, 
191.51/191.73	           app_encode_app(dB, app_encode_fun(list(dB), dB), 
191.51/191.73	             app_encode_app(fun(dB, fun(dB, dB)), 
191.51/191.73	               app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
191.51/191.73	               foldl(dB, dB), app), X254), 
191.51/191.73	           app_encode_app(list(dB), list(dB), rotate1(dB), 
191.51/191.73	             app_encode_app(list(dB), list(dB), 
191.51/191.73	               app_encode_app(dB, app_encode_fun(list(dB), list(dB)), 
191.51/191.73	                 cons(dB), X256), X258))),
191.51/191.73	    inference('clc', [status(thm)], ['4', '8'])).
191.51/191.73	tff('10', plain,
191.51/191.73	    app_encode_app(bool, $o, pp, 
191.51/191.73	      app_encode_app(dB, bool, 
191.51/191.73	        app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
191.51/191.73	          aa(dB, bool), it), 
191.51/191.73	        app_encode_app(list(dB), dB, 
191.51/191.73	          app_encode_app(dB, app_encode_fun(list(dB), dB), 
191.51/191.73	            app_encode_app(fun(dB, fun(dB, dB)), 
191.51/191.73	              app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
191.51/191.73	              foldl(dB, dB), app), 
191.51/191.73	            app_encode_app(nat, dB, 
191.51/191.73	              app_encode_app(dB, app_encode_fun(nat, dB), 
191.51/191.73	                app_encode_app(dB, 
191.51/191.73	                  app_encode_fun(dB, app_encode_fun(nat, dB)), subst, r), s), 
191.51/191.73	              zero_zero(nat))), 
191.51/191.73	          app_encode_app(list(dB), list(dB), rotate1(dB), 
191.51/191.73	            app_encode_app(list(dB), list(dB), 
191.51/191.73	              app_encode_app(dB, app_encode_fun(list(dB), list(dB)), 
191.51/191.73	                cons(dB), app_encode_app(nat, dB, var, i)), ss))))),
191.51/191.73	    inference('demod', [status(thm)], ['0', '9'])).
191.51/191.73	tff(zf_stmt_42, axiom,
191.51/191.73	  (![Ss2:list(dB),S:dB,R:dB]:
191.51/191.73	     (app_encode_app(bool,$o,pp,
191.51/191.73	                     app_encode_app(dB,bool,
191.51/191.73	                                    app_encode_app(fun(dB,bool),
191.51/191.73	                                                   app_encode_fun(dB,bool),
191.51/191.73	                                                   aa(dB,bool),it),
191.51/191.73	                                    app_encode_app(list(dB),dB,
191.51/191.73	                                                   app_encode_app(dB,
191.51/191.73	                                                                  app_encode_fun(
191.51/191.73	                                                                  list(dB),dB),
191.51/191.73	                                                                  app_encode_app(
191.51/191.73	                                                                  fun(
191.51/191.73	                                                                  dB,
191.51/191.73	                                                                  fun(dB,dB)),
191.51/191.73	                                                                  app_encode_fun(
191.51/191.73	                                                                  dB,
191.51/191.73	                                                                  app_encode_fun(
191.51/191.73	                                                                  list(dB),dB)),
191.51/191.73	                                                                  foldl(
191.51/191.73	                                                                  dB,dB),app),
191.51/191.73	                                                                  app_encode_app(
191.51/191.73	                                                                  nat,dB,
191.51/191.73	                                                                  app_encode_app(
191.51/191.73	                                                                  dB,
191.51/191.73	                                                                  app_encode_fun(
191.51/191.73	                                                                  nat,dB),
191.51/191.73	                                                                  app_encode_app(
191.51/191.73	                                                                  dB,
191.51/191.73	                                                                  app_encode_fun(
191.51/191.73	                                                                  dB,
191.51/191.73	                                                                  app_encode_fun(
191.51/191.73	                                                                  nat,dB)),
191.51/191.73	                                                                  subst,R),S),
191.51/191.73	                                                                  zero_zero(
191.51/191.73	                                                                  nat))),
191.51/191.73	                                                   Ss2))) =>
191.51/191.73	      (app_encode_app(bool,$o,pp,
191.51/191.73	                      app_encode_app(dB,bool,
191.51/191.73	                                     app_encode_app(fun(dB,bool),
191.51/191.73	                                                    app_encode_fun(dB,bool),
191.51/191.73	                                                    aa(dB,bool),it),
191.51/191.73	                                     S)) =>
191.51/191.73	       app_encode_app(bool,$o,pp,
191.51/191.73	                      app_encode_app(dB,bool,
191.51/191.73	                                     app_encode_app(fun(dB,bool),
191.51/191.73	                                                    app_encode_fun(dB,bool),
191.51/191.73	                                                    aa(dB,bool),it),
191.51/191.73	                                     app_encode_app(list(dB),dB,
191.51/191.73	                                                    app_encode_app(dB,
191.51/191.73	                                                                   app_encode_fun(
191.51/191.73	                                                                   list(dB),
191.51/191.73	                                                                   dB),
191.51/191.73	                                                                   app_encode_app(
191.51/191.73	                                                                   fun(
191.51/191.73	                                                                   dB,
191.51/191.73	                                                                   fun(dB,dB)),
191.51/191.73	                                                                   app_encode_fun(
191.51/191.73	                                                                   dB,
191.51/191.73	                                                                   app_encode_fun(
191.51/191.73	                                                                   list(dB),
191.51/191.73	                                                                   dB)),
191.51/191.73	                                                                   foldl(
191.51/191.73	                                                                   dB,dB),app),
191.51/191.73	                                                                   app_encode_app(
191.51/191.73	                                                                   dB,dB,
191.51/191.73	                                                                   app_encode_app(
191.51/191.73	                                                                   fun(dB,dB),
191.51/191.73	                                                                   app_encode_fun(
191.51/191.73	                                                                   dB,dB),
191.51/191.73	                                                                   aa(dB,dB),
191.51/191.73	                                                                   app_encode_app(
191.51/191.73	                                                                   dB,
191.51/191.73	                                                                   fun(dB,dB),
191.51/191.73	                                                                   app_encode_app(
191.51/191.73	                                                                   fun(
191.51/191.73	                                                                   dB,
191.51/191.73	                                                                   fun(dB,dB)),
191.51/191.73	                                                                   app_encode_fun(
191.51/191.73	                                                                   dB,
191.51/191.73	                                                                   fun(dB,dB)),
191.51/191.73	                                                                   aa(
191.51/191.73	                                                                   dB,
191.51/191.73	                                                                   fun(dB,dB)),
191.51/191.73	                                                                   app),
191.51/191.73	                                                                   app_encode_app(
191.51/191.73	                                                                   dB,dB,abs,
191.51/191.73	                                                                   R))),S)),
191.51/191.73	                                                    Ss2))))))).
191.51/191.73	tff('11', plain,
191.51/191.73	    ![X4 : dB, X5 : dB, X6 : list(dB)]:
191.51/191.73	      (~ app_encode_app(bool, $o, pp, 
191.51/191.73	           app_encode_app(dB, bool, 
191.51/191.73	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
191.51/191.73	               aa(dB, bool), it), X4))
191.51/191.73	       | ~ app_encode_app(bool, $o, pp, 
191.51/191.73	             app_encode_app(dB, bool, 
191.51/191.73	               app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
191.51/191.73	                 aa(dB, bool), it), 
191.51/191.73	               app_encode_app(list(dB), dB, 
191.51/191.73	                 app_encode_app(dB, app_encode_fun(list(dB), dB), 
191.51/191.73	                   app_encode_app(fun(dB, fun(dB, dB)), 
191.51/191.73	                     app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
191.51/191.73	                     foldl(dB, dB), app), 
191.51/191.73	                   app_encode_app(nat, dB, 
191.51/191.73	                     app_encode_app(dB, app_encode_fun(nat, dB), 
191.51/191.73	                       app_encode_app(dB, 
191.51/191.73	                         app_encode_fun(dB, app_encode_fun(nat, dB)), subst, 
191.51/191.73	                         X5), X4), zero_zero(nat))), X6)))
191.51/191.73	       | app_encode_app(bool, $o, pp, 
191.51/191.73	           app_encode_app(dB, bool, 
191.51/191.73	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
191.51/191.73	               aa(dB, bool), it), 
191.51/191.73	             app_encode_app(list(dB), dB, 
191.51/191.73	               app_encode_app(dB, app_encode_fun(list(dB), dB), 
191.51/191.73	                 app_encode_app(fun(dB, fun(dB, dB)), 
191.51/191.73	                   app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
191.51/191.73	                   foldl(dB, dB), app), 
191.51/191.73	                 app_encode_app(dB, dB, 
191.51/191.73	                   app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), 
191.51/191.73	                     aa(dB, dB), 
191.51/191.73	                     app_encode_app(dB, fun(dB, dB), 
191.51/191.73	                       app_encode_app(fun(dB, fun(dB, dB)), 
191.51/191.73	                         app_encode_fun(dB, fun(dB, dB)), 
191.51/191.73	                         aa(dB, fun(dB, dB)), app), 
191.51/191.73	                       app_encode_app(dB, dB, abs, X5))), X4)), X6)))),
191.51/191.73	    inference('cnf', [status(esa)], [zf_stmt_42])).
191.51/191.73	tff(zf_stmt_115, axiom,
191.51/191.73	  (![A:$tType,A1:fun(A,bool),X2:A]:
191.51/191.73	     (app_encode_app(fun(A,bool),$o,
191.51/191.73	                     app_encode_app(A,app_encode_fun(fun(A,bool),$o),
191.51/191.73	                                    member(A),X2),
191.51/191.73	                     A1) <=>
191.51/191.73	      app_encode_app(bool,$o,pp,
191.51/191.73	                     app_encode_app(A,bool,
191.51/191.73	                                    app_encode_app(fun(A,bool),
191.51/191.73	                                                   app_encode_fun(A,bool),
191.51/191.73	                                                   aa(A,bool),A1),
191.51/191.73	                                    X2))))).
191.51/191.73	tff('12', plain,
191.51/191.73	    ![X289 : $tType, X290 : fun(X289, bool), X292 : X289]:
191.51/191.73	      (app_encode_app(fun(X289, bool), $o, 
191.51/191.73	         app_encode_app(X289, app_encode_fun(fun(X289, bool), $o), 
191.51/191.73	           member(X289), X292), X290)
191.51/191.73	       | ~ app_encode_app(bool, $o, pp, 
191.51/191.73	             app_encode_app(X289, bool, 
191.51/191.73	               app_encode_app(fun(X289, bool), app_encode_fun(X289, bool), 
191.51/191.73	                 aa(X289, bool), X290), X292))),
191.51/191.73	    inference('cnf', [status(esa)], [zf_stmt_115])).
191.51/191.73	tff('13', plain,
191.51/191.73	    ![X0 : list(dB), X1 : dB, X2 : dB]:
191.51/191.73	      (~ $true
191.51/191.73	       | ~ app_encode_app(bool, $o, pp, 
191.51/191.73	             app_encode_app(dB, bool, 
191.51/191.73	               app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
191.51/191.73	                 aa(dB, bool), it), 
191.51/191.73	               app_encode_app(list(dB), dB, 
191.51/191.73	                 app_encode_app(dB, app_encode_fun(list(dB), dB), 
191.51/191.73	                   app_encode_app(fun(dB, fun(dB, dB)), 
191.51/191.73	                     app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
191.51/191.73	                     foldl(dB, dB), app), 
191.51/191.73	                   app_encode_app(nat, dB, 
191.51/191.73	                     app_encode_app(dB, app_encode_fun(nat, dB), 
191.51/191.73	                       app_encode_app(dB, 
191.51/191.73	                         app_encode_fun(dB, app_encode_fun(nat, dB)), subst, 
191.51/191.73	                         X2), X1), zero_zero(nat))), X0)))
191.51/191.73	       | ~ app_encode_app(bool, $o, pp, 
191.51/191.73	             app_encode_app(dB, bool, 
191.51/191.73	               app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
191.51/191.73	                 aa(dB, bool), it), X1))
191.51/191.73	       | app_encode_app(fun(dB, bool), $o, 
191.51/191.73	           app_encode_app(dB, app_encode_fun(fun(dB, bool), $o), member(dB), 
191.51/191.73	             app_encode_app(list(dB), dB, 
191.51/191.73	               app_encode_app(dB, app_encode_fun(list(dB), dB), 
191.51/191.73	                 app_encode_app(fun(dB, fun(dB, dB)), 
191.51/191.73	                   app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
191.51/191.73	                   foldl(dB, dB), app), 
191.51/191.73	                 app_encode_app(dB, dB, 
191.51/191.73	                   app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), 
191.51/191.73	                     aa(dB, dB), 
191.51/191.73	                     app_encode_app(dB, fun(dB, dB), 
191.51/191.73	                       app_encode_app(fun(dB, fun(dB, dB)), 
191.51/191.73	                         app_encode_fun(dB, fun(dB, dB)), 
191.51/191.73	                         aa(dB, fun(dB, dB)), app), 
191.51/191.73	                       app_encode_app(dB, dB, abs, X2))), X1)), X0)), it)),
191.51/191.73	    inference('sup-', [status(thm)], ['11', '12'])).
191.51/191.73	tff('14', plain,
191.51/191.73	    ![X0 : list(dB), X1 : dB, X2 : dB]:
191.51/191.73	      (app_encode_app(fun(dB, bool), $o, 
191.51/191.73	         app_encode_app(dB, app_encode_fun(fun(dB, bool), $o), member(dB), 
191.51/191.73	           app_encode_app(list(dB), dB, 
191.51/191.73	             app_encode_app(dB, app_encode_fun(list(dB), dB), 
191.51/191.73	               app_encode_app(fun(dB, fun(dB, dB)), 
191.51/191.73	                 app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
191.51/191.73	                 foldl(dB, dB), app), 
191.51/191.73	               app_encode_app(dB, dB, 
191.51/191.73	                 app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), 
191.51/191.73	                   aa(dB, dB), 
191.51/191.73	                   app_encode_app(dB, fun(dB, dB), 
191.51/191.73	                     app_encode_app(fun(dB, fun(dB, dB)), 
191.51/191.73	                       app_encode_fun(dB, fun(dB, dB)), aa(dB, fun(dB, dB)), 
191.51/191.73	                       app), app_encode_app(dB, dB, abs, X2))), X1)), X0)), 
191.51/191.73	         it)
191.51/191.73	       | ~ app_encode_app(bool, $o, pp, 
191.51/191.73	             app_encode_app(dB, bool, 
191.51/191.73	               app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
191.51/191.73	                 aa(dB, bool), it), X1))
191.51/191.73	       | ~ app_encode_app(bool, $o, pp, 
191.51/191.73	             app_encode_app(dB, bool, 
191.51/191.73	               app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
191.51/191.73	                 aa(dB, bool), it), 
191.51/191.73	               app_encode_app(list(dB), dB, 
191.51/191.73	                 app_encode_app(dB, app_encode_fun(list(dB), dB), 
191.51/191.73	                   app_encode_app(fun(dB, fun(dB, dB)), 
191.51/191.73	                     app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
191.51/191.73	                     foldl(dB, dB), app), 
191.51/191.73	                   app_encode_app(nat, dB, 
191.51/191.73	                     app_encode_app(dB, app_encode_fun(nat, dB), 
191.51/191.73	                       app_encode_app(dB, 
191.51/191.73	                         app_encode_fun(dB, app_encode_fun(nat, dB)), subst, 
191.51/191.73	                         X2), X1), zero_zero(nat))), X0)))),
191.51/191.73	    inference('simplify', [status(thm)], ['13'])).
191.51/191.73	tff(zf_stmt_98, axiom,
191.51/191.73	  (![A:$tType,B:$tType,Xs1:list(B),X2:B,A2:A,F:fun(A,fun(B,A))]:
191.51/191.73	     (app_encode_app(list(B),A,
191.51/191.73	                     app_encode_app(A,app_encode_fun(list(B),A),
191.51/191.73	                                    app_encode_app(fun(A,fun(B,A)),
191.51/191.73	                                                   app_encode_fun(A,
191.51/191.73	                                                                  app_encode_fun(
191.51/191.73	                                                                  list(B),A)),
191.51/191.73	                                                   foldl(A,B),F),
191.51/191.73	                                    A2),
191.51/191.73	                     app_encode_app(list(B),list(B),
191.51/191.73	                                    app_encode_app(B,
191.51/191.73	                                                   app_encode_fun(list(B),
191.51/191.73	                                                                  list(B)),
191.51/191.73	                                                   cons(B),X2),
191.51/191.73	                                    Xs1)) =
191.51/191.73	      app_encode_app(list(B),A,
191.51/191.73	                     app_encode_app(A,app_encode_fun(list(B),A),
191.51/191.73	                                    app_encode_app(fun(A,fun(B,A)),
191.51/191.73	                                                   app_encode_fun(A,
191.51/191.73	                                                                  app_encode_fun(
191.51/191.73	                                                                  list(B),A)),
191.51/191.73	                                                   foldl(A,B),F),
191.51/191.73	                                    app_encode_app(B,A,
191.51/191.73	                                                   app_encode_app(fun(B,A),
191.51/191.73	                                                                  app_encode_fun(
191.51/191.73	                                                                  B,A),
191.51/191.73	                                                                  aa(B,A),
191.51/191.73	                                                                  app_encode_app(
191.51/191.73	                                                                  A,fun(B,A),
191.51/191.73	                                                                  app_encode_app(
191.51/191.73	                                                                  fun(
191.51/191.73	                                                                  A,fun(B,A)),
191.51/191.73	                                                                  app_encode_fun(
191.51/191.73	                                                                  A,fun(B,A)),
191.51/191.73	                                                                  aa(
191.51/191.73	                                                                  A,fun(B,A)),
191.51/191.73	                                                                  F),A2)),
191.51/191.73	                                                   X2)),
191.51/191.73	                     Xs1)))).
191.51/191.73	tff('15', plain,
191.51/191.73	    ![X210 : $tType, X211 : $tType, X212 : fun(X211, fun(X210, X211)), 
191.51/191.73	      X213 : X211, X214 : X210, X215 : list(X210)]:
191.51/191.73	      app_encode_app(list(X210), X211, 
191.51/191.73	        app_encode_app(X211, app_encode_fun(list(X210), X211), 
191.51/191.73	          app_encode_app(fun(X211, fun(X210, X211)), 
191.51/191.73	            app_encode_fun(X211, app_encode_fun(list(X210), X211)), 
191.51/191.73	            foldl(X211, X210), X212), X213), 
191.51/191.73	        app_encode_app(list(X210), list(X210), 
191.51/191.73	          app_encode_app(X210, app_encode_fun(list(X210), list(X210)), 
191.51/191.73	            cons(X210), X214), X215))
191.51/191.73	       = app_encode_app(list(X210), X211, 
191.51/191.73	           app_encode_app(X211, app_encode_fun(list(X210), X211), 
191.51/191.73	             app_encode_app(fun(X211, fun(X210, X211)), 
191.51/191.73	               app_encode_fun(X211, app_encode_fun(list(X210), X211)), 
191.51/191.73	               foldl(X211, X210), X212), 
191.51/191.73	             app_encode_app(X210, X211, 
191.51/191.73	               app_encode_app(fun(X210, X211), app_encode_fun(X210, X211), 
191.51/191.73	                 aa(X210, X211), 
191.51/191.73	                 app_encode_app(X211, fun(X210, X211), 
191.51/191.73	                   app_encode_app(fun(X211, fun(X210, X211)), 
191.51/191.73	                     app_encode_fun(X211, fun(X210, X211)), 
191.51/191.73	                     aa(X211, fun(X210, X211)), X212), X213)), X214)), X215),
191.51/191.73	    inference('cnf', [status(esa)], [zf_stmt_98])).
191.51/191.73	tff('16', plain,
191.51/191.73	    ![X0 : list(dB), X1 : dB, X2 : dB]:
191.51/191.73	      (app_encode_app(fun(dB, bool), $o, 
191.51/191.73	         app_encode_app(dB, app_encode_fun(fun(dB, bool), $o), member(dB), 
191.51/191.73	           app_encode_app(list(dB), dB, 
191.51/191.73	             app_encode_app(dB, app_encode_fun(list(dB), dB), 
191.51/191.73	               app_encode_app(fun(dB, fun(dB, dB)), 
191.51/191.73	                 app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
191.51/191.73	                 foldl(dB, dB), app), app_encode_app(dB, dB, abs, X2)), 
191.51/191.73	             app_encode_app(list(dB), list(dB), 
191.51/191.73	               app_encode_app(dB, app_encode_fun(list(dB), list(dB)), 
191.51/191.73	                 cons(dB), X1), X0))), it)
191.51/191.73	       | ~ app_encode_app(bool, $o, pp, 
191.51/191.73	             app_encode_app(dB, bool, 
191.51/191.73	               app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
191.51/191.73	                 aa(dB, bool), it), X1))
191.51/191.73	       | ~ app_encode_app(bool, $o, pp, 
191.51/191.73	             app_encode_app(dB, bool, 
191.51/191.73	               app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
191.51/191.73	                 aa(dB, bool), it), 
191.51/191.73	               app_encode_app(list(dB), dB, 
191.51/191.73	                 app_encode_app(dB, app_encode_fun(list(dB), dB), 
191.51/191.73	                   app_encode_app(fun(dB, fun(dB, dB)), 
191.51/191.73	                     app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
191.51/191.73	                     foldl(dB, dB), app), 
191.51/191.73	                   app_encode_app(nat, dB, 
191.51/191.73	                     app_encode_app(dB, app_encode_fun(nat, dB), 
191.51/191.73	                       app_encode_app(dB, 
191.51/191.73	                         app_encode_fun(dB, app_encode_fun(nat, dB)), subst, 
191.51/191.73	                         X2), X1), zero_zero(nat))), X0)))),
191.51/191.73	    inference('demod', [status(thm)], ['14', '15'])).
191.51/191.73	tff('17', plain,
191.51/191.73	    (~ $true
191.51/191.73	     | ~ app_encode_app(bool, $o, pp, 
191.51/191.73	           app_encode_app(dB, bool, 
191.51/191.73	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
191.51/191.73	               aa(dB, bool), it), s))
191.51/191.73	     | app_encode_app(fun(dB, bool), $o, 
191.51/191.73	         app_encode_app(dB, app_encode_fun(fun(dB, bool), $o), member(dB), 
191.51/191.73	           app_encode_app(list(dB), dB, 
191.51/191.73	             app_encode_app(dB, app_encode_fun(list(dB), dB), 
191.51/191.73	               app_encode_app(fun(dB, fun(dB, dB)), 
191.51/191.73	                 app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
191.51/191.73	                 foldl(dB, dB), app), app_encode_app(dB, dB, abs, r)), 
191.51/191.73	             app_encode_app(list(dB), list(dB), 
191.51/191.73	               app_encode_app(dB, app_encode_fun(list(dB), list(dB)), 
191.51/191.73	                 cons(dB), s), 
191.51/191.73	               app_encode_app(list(dB), list(dB), rotate1(dB), 
191.51/191.73	                 app_encode_app(list(dB), list(dB), 
191.51/191.73	                   app_encode_app(dB, app_encode_fun(list(dB), list(dB)), 
191.51/191.73	                     cons(dB), app_encode_app(nat, dB, var, i)), ss))))), it)),
191.51/191.73	    inference('sup-', [status(thm)], ['10', '16'])).
191.51/191.73	tff(zf_stmt_144, axiom,
191.51/191.73	  (app_encode_app(bool,$o,pp,
191.51/191.73	                  app_encode_app(dB,bool,
191.51/191.73	                                 app_encode_app(fun(dB,bool),
191.51/191.73	                                                app_encode_fun(dB,bool),
191.51/191.73	                                                aa(dB,bool),it),
191.51/191.73	                                 s)))).
191.51/191.73	tff('18', plain,
191.51/191.73	    app_encode_app(bool, $o, pp, 
191.51/191.73	      app_encode_app(dB, bool, 
191.51/191.73	        app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
191.51/191.73	          aa(dB, bool), it), s)),
191.51/191.73	    inference('cnf', [status(esa)], [zf_stmt_144])).
191.51/191.73	tff(zf_stmt_111, axiom,
191.51/191.73	  (![A:$tType,Ys3:list(A),Xs:list(A),X:A]:
191.51/191.73	     (app_encode_app(list(A),list(A),
191.51/191.73	                     app_encode_app(list(A),app_encode_fun(list(A),list(A)),
191.51/191.73	                                    append(A),
191.51/191.73	                                    app_encode_app(list(A),list(A),
191.51/191.73	                                                   app_encode_app(A,
191.51/191.73	                                                                  app_encode_fun(
191.51/191.73	                                                                  list(A),
191.51/191.73	                                                                  list(A)),
191.51/191.73	                                                                  cons(A),X),
191.51/191.73	                                                   Xs)),
191.51/191.73	                     Ys3) =
191.51/191.73	      app_encode_app(list(A),list(A),
191.51/191.73	                     app_encode_app(A,app_encode_fun(list(A),list(A)),
191.51/191.73	                                    cons(A),X),
191.51/191.73	                     app_encode_app(list(A),list(A),
191.51/191.73	                                    app_encode_app(list(A),
191.51/191.73	                                                   app_encode_fun(list(A),
191.51/191.73	                                                                  list(A)),
191.51/191.73	                                                   append(A),Xs),
191.51/191.73	                                    Ys3))))).
191.51/191.73	tff('19', plain,
191.51/191.73	    ![X273 : $tType, X274 : X273, X275 : list(X273), X276 : list(X273)]:
191.51/191.73	      app_encode_app(list(X273), list(X273), 
191.51/191.73	        app_encode_app(list(X273), app_encode_fun(list(X273), list(X273)), 
191.51/191.73	          append(X273), 
191.51/191.73	          app_encode_app(list(X273), list(X273), 
191.51/191.73	            app_encode_app(X273, app_encode_fun(list(X273), list(X273)), 
191.51/191.73	              cons(X273), X274), X275)), X276)
191.51/191.73	       = app_encode_app(list(X273), list(X273), 
191.51/191.73	           app_encode_app(X273, app_encode_fun(list(X273), list(X273)), 
191.51/191.73	             cons(X273), X274), 
191.51/191.73	           app_encode_app(list(X273), list(X273), 
191.51/191.73	             app_encode_app(list(X273), 
191.51/191.73	               app_encode_fun(list(X273), list(X273)), append(X273), X275), 
191.51/191.73	             X276)),
191.51/191.73	    inference('cnf', [status(esa)], [zf_stmt_111])).
191.51/191.73	tff('20', plain,
191.51/191.73	    ![X0 : $tType, X1 : list(X0), X2 : X0, X3 : X0]:
191.51/191.73	      app_encode_app(list(X0), list(X0), rotate1(X0), 
191.51/191.73	        app_encode_app(list(X0), list(X0), 
191.51/191.73	          app_encode_app(X0, app_encode_fun(list(X0), list(X0)), cons(X0), 
191.51/191.73	            X3), 
191.51/191.73	          app_encode_app(list(X0), list(X0), 
191.51/191.73	            app_encode_app(X0, app_encode_fun(list(X0), list(X0)), cons(X0), 
191.51/191.73	              X2), X1)))
191.51/191.73	       = app_encode_app(list(X0), list(X0), 
191.51/191.73	           app_encode_app(X0, app_encode_fun(list(X0), list(X0)), cons(X0), 
191.51/191.73	             X2), 
191.51/191.73	           app_encode_app(list(X0), list(X0), 
191.51/191.73	             app_encode_app(list(X0), app_encode_fun(list(X0), list(X0)), 
191.51/191.73	               append(X0), X1), 
191.51/191.73	             app_encode_app(list(X0), list(X0), 
191.51/191.73	               app_encode_app(X0, app_encode_fun(list(X0), list(X0)), 
191.51/191.73	                 cons(X0), X3), nil(X0)))),
191.51/191.73	    inference('sup+', [status(thm)], ['3', '19'])).
191.51/191.73	tff('21', plain,
191.51/191.73	    ![X0 : $tType, X1 : list(X0), X2 : X0, X3 : X0]:
191.51/191.73	      app_encode_app(list(X0), list(X0), rotate1(X0), 
191.51/191.73	        app_encode_app(list(X0), list(X0), 
191.51/191.73	          app_encode_app(X0, app_encode_fun(list(X0), list(X0)), cons(X0), 
191.51/191.73	            X3), 
191.51/191.73	          app_encode_app(list(X0), list(X0), 
191.51/191.73	            app_encode_app(X0, app_encode_fun(list(X0), list(X0)), cons(X0), 
191.51/191.73	              X2), X1)))
191.51/191.73	       = app_encode_app(list(X0), list(X0), 
191.51/191.73	           app_encode_app(X0, app_encode_fun(list(X0), list(X0)), cons(X0), 
191.51/191.73	             X2), 
191.51/191.73	           app_encode_app(list(X0), list(X0), rotate1(X0), 
191.51/191.73	             app_encode_app(list(X0), list(X0), 
191.51/191.73	               app_encode_app(X0, app_encode_fun(list(X0), list(X0)), 
191.51/191.73	                 cons(X0), X3), X1))),
191.51/191.73	    inference('demod', [status(thm)], ['20', '3'])).
191.51/191.73	tff('22', plain,
191.51/191.73	    (~ $true
191.51/191.73	     | ~ $true
191.51/191.73	     | app_encode_app(fun(dB, bool), $o, 
191.51/191.73	         app_encode_app(dB, app_encode_fun(fun(dB, bool), $o), member(dB), 
191.51/191.73	           app_encode_app(list(dB), dB, 
191.51/191.73	             app_encode_app(dB, app_encode_fun(list(dB), dB), 
191.51/191.73	               app_encode_app(fun(dB, fun(dB, dB)), 
191.51/191.73	                 app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
191.51/191.73	                 foldl(dB, dB), app), app_encode_app(dB, dB, abs, r)), 
191.51/191.73	             app_encode_app(list(dB), list(dB), rotate1(dB), 
191.51/191.73	               app_encode_app(list(dB), list(dB), 
191.51/191.73	                 app_encode_app(dB, app_encode_fun(list(dB), list(dB)), 
191.51/191.73	                   cons(dB), app_encode_app(nat, dB, var, i)), 
191.51/191.73	                 app_encode_app(list(dB), list(dB), 
191.51/191.73	                   app_encode_app(dB, app_encode_fun(list(dB), list(dB)), 
191.51/191.73	                     cons(dB), s), ss))))), it)),
191.51/191.73	    inference('demod', [status(thm)], ['17', '18', '21'])).
191.51/191.73	tff('23', plain,
191.51/191.73	    app_encode_app(fun(dB, bool), $o, 
191.51/191.73	      app_encode_app(dB, app_encode_fun(fun(dB, bool), $o), member(dB), 
191.51/191.73	        app_encode_app(list(dB), dB, 
191.51/191.73	          app_encode_app(dB, app_encode_fun(list(dB), dB), 
191.51/191.73	            app_encode_app(fun(dB, fun(dB, dB)), 
191.51/191.73	              app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
191.51/191.73	              foldl(dB, dB), app), app_encode_app(dB, dB, abs, r)), 
191.51/191.73	          app_encode_app(list(dB), list(dB), rotate1(dB), 
191.51/191.73	            app_encode_app(list(dB), list(dB), 
191.51/191.73	              app_encode_app(dB, app_encode_fun(list(dB), list(dB)), 
191.51/191.73	                cons(dB), app_encode_app(nat, dB, var, i)), 
191.51/191.73	              app_encode_app(list(dB), list(dB), 
191.51/191.73	                app_encode_app(dB, app_encode_fun(list(dB), list(dB)), 
191.51/191.73	                  cons(dB), s), ss))))), it),
191.51/191.73	    inference('simplify', [status(thm)], ['22'])).
191.51/191.73	tff('24', plain,
191.51/191.73	    ![X289 : $tType, X290 : fun(X289, bool), X291 : X289]:
191.51/191.73	      (app_encode_app(bool, $o, pp, 
191.51/191.73	         app_encode_app(X289, bool, 
191.51/191.73	           app_encode_app(fun(X289, bool), app_encode_fun(X289, bool), 
191.51/191.73	             aa(X289, bool), X290), X291))
191.51/191.73	       | ~ app_encode_app(fun(X289, bool), $o, 
191.51/191.73	             app_encode_app(X289, app_encode_fun(fun(X289, bool), $o), 
191.51/191.73	               member(X289), X291), X290)),
191.51/191.73	    inference('cnf', [status(esa)], [zf_stmt_115])).
191.51/191.73	tff(zf_stmt_146, conjecture,
191.51/191.73	  (app_encode_app(bool,$o,pp,
191.51/191.73	                  app_encode_app(dB,bool,
191.51/191.73	                                 app_encode_app(fun(dB,bool),
191.51/191.73	                                                app_encode_fun(dB,bool),
191.51/191.73	                                                aa(dB,bool),it),
191.51/191.73	                                 app_encode_app(dB,dB,
191.51/191.73	                                                app_encode_app(fun(dB,dB),
191.51/191.73	                                                               app_encode_fun(
191.51/191.73	                                                               dB,dB),
191.51/191.73	                                                               aa(dB,dB),
191.51/191.73	                                                               app_encode_app(
191.51/191.73	                                                               dB,fun(dB,dB),
191.51/191.73	                                                               app_encode_app(
191.51/191.73	                                                               fun(dB,
191.51/191.73	                                                                   fun(dB,dB)),
191.51/191.73	                                                               app_encode_fun(
191.51/191.73	                                                               dB,fun(dB,dB)),
191.51/191.73	                                                               aa(dB,
191.51/191.73	                                                                  fun(dB,dB)),
191.51/191.73	                                                               app),
191.51/191.73	                                                               app_encode_app(
191.51/191.73	                                                               list(dB),dB,
191.51/191.73	                                                               app_encode_app(
191.51/191.73	                                                               dB,
191.51/191.73	                                                               app_encode_fun(
191.51/191.73	                                                               list(dB),dB),
191.51/191.73	                                                               app_encode_app(
191.51/191.73	                                                               fun(dB,
191.51/191.73	                                                                   fun(dB,dB)),
191.51/191.73	                                                               app_encode_fun(
191.51/191.73	                                                               dB,
191.51/191.73	                                                               app_encode_fun(
191.51/191.73	                                                               list(dB),dB)),
191.51/191.73	                                                               foldl(dB,dB),
191.51/191.73	                                                               app),
191.51/191.73	                                                               app_encode_app(
191.51/191.73	                                                               dB,dB,
191.51/191.73	                                                               app_encode_app(
191.51/191.73	                                                               fun(dB,dB),
191.51/191.73	                                                               app_encode_fun(
191.51/191.73	                                                               dB,dB),
191.51/191.73	                                                               aa(dB,dB),
191.51/191.73	                                                               app_encode_app(
191.51/191.73	                                                               dB,fun(dB,dB),
191.51/191.73	                                                               app_encode_app(
191.51/191.73	                                                               fun(dB,
191.51/191.73	                                                                   fun(dB,dB)),
191.51/191.73	                                                               app_encode_fun(
191.51/191.73	                                                               dB,fun(dB,dB)),
191.51/191.73	                                                               aa(dB,
191.51/191.73	                                                                  fun(dB,dB)),
191.51/191.73	                                                               app),
191.51/191.73	                                                               app_encode_app(
191.51/191.73	                                                               dB,dB,abs,r))),
191.51/191.73	                                                               s)),ss))),
191.51/191.73	                                                app_encode_app(nat,dB,var,i)))))).
191.51/191.73	tff(zf_stmt_0, negated_conjecture,
191.51/191.73	  (~
191.51/191.73	    app_encode_app(bool,$o,pp,
191.51/191.73	                   app_encode_app(dB,bool,
191.51/191.73	                                  app_encode_app(fun(dB,bool),
191.51/191.73	                                                 app_encode_fun(dB,bool),
191.51/191.73	                                                 aa(dB,bool),it),
191.51/191.73	                                  app_encode_app(dB,dB,
191.51/191.73	                                                 app_encode_app(fun(dB,dB),
191.51/191.73	                                                                app_encode_fun(
191.51/191.73	                                                                dB,dB),
191.51/191.73	                                                                aa(dB,dB),
191.51/191.73	                                                                app_encode_app(
191.51/191.73	                                                                dB,
191.51/191.73	                                                                fun(dB,dB),
191.51/191.73	                                                                app_encode_app(
191.51/191.73	                                                                fun(dB,
191.51/191.73	                                                                    fun(
191.51/191.73	                                                                    dB,dB)),
191.51/191.73	                                                                app_encode_fun(
191.51/191.73	                                                                dB,fun(dB,dB)),
191.51/191.73	                                                                aa(dB,
191.51/191.73	                                                                   fun(dB,dB)),
191.51/191.73	                                                                app),
191.51/191.73	                                                                app_encode_app(
191.51/191.73	                                                                list(dB),dB,
191.51/191.73	                                                                app_encode_app(
191.51/191.73	                                                                dB,
191.51/191.73	                                                                app_encode_fun(
191.51/191.73	                                                                list(dB),dB),
191.51/191.73	                                                                app_encode_app(
191.51/191.73	                                                                fun(dB,
191.51/191.73	                                                                    fun(
191.51/191.73	                                                                    dB,dB)),
191.51/191.73	                                                                app_encode_fun(
191.51/191.73	                                                                dB,
191.51/191.73	                                                                app_encode_fun(
191.51/191.73	                                                                list(dB),dB)),
191.51/191.73	                                                                foldl(dB,dB),
191.51/191.73	                                                                app),
191.51/191.73	                                                                app_encode_app(
191.51/191.73	                                                                dB,dB,
191.51/191.73	                                                                app_encode_app(
191.51/191.73	                                                                fun(dB,dB),
191.51/191.73	                                                                app_encode_fun(
191.51/191.73	                                                                dB,dB),
191.51/191.73	                                                                aa(dB,dB),
191.51/191.73	                                                                app_encode_app(
191.51/191.73	                                                                dB,
191.51/191.73	                                                                fun(dB,dB),
191.51/191.73	                                                                app_encode_app(
191.51/191.73	                                                                fun(dB,
191.51/191.73	                                                                    fun(
191.51/191.73	                                                                    dB,dB)),
191.51/191.73	                                                                app_encode_fun(
191.51/191.73	                                                                dB,fun(dB,dB)),
191.51/191.73	                                                                aa(dB,
191.51/191.73	                                                                   fun(dB,dB)),
191.51/191.73	                                                                app),
191.51/191.73	                                                                app_encode_app(
191.51/191.73	                                                                dB,dB,abs,r))),
191.51/191.73	                                                                s)),ss))),
191.51/191.73	                                                 app_encode_app(nat,dB,var,i)))))).
191.51/191.73	tff('25', plain,
191.51/191.73	    ~ app_encode_app(bool, $o, pp, 
191.51/191.73	        app_encode_app(dB, bool, 
191.51/191.73	          app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
191.51/191.73	            aa(dB, bool), it), 
191.51/191.73	          app_encode_app(dB, dB, 
191.51/191.73	            app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), aa(dB, dB), 
191.51/191.73	              app_encode_app(dB, fun(dB, dB), 
191.51/191.73	                app_encode_app(fun(dB, fun(dB, dB)), 
191.51/191.73	                  app_encode_fun(dB, fun(dB, dB)), aa(dB, fun(dB, dB)), app), 
191.51/191.73	                app_encode_app(list(dB), dB, 
191.51/191.73	                  app_encode_app(dB, app_encode_fun(list(dB), dB), 
191.51/191.73	                    app_encode_app(fun(dB, fun(dB, dB)), 
191.51/191.73	                      app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
191.51/191.73	                      foldl(dB, dB), app), 
191.51/191.73	                    app_encode_app(dB, dB, 
191.51/191.73	                      app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), 
191.51/191.73	                        aa(dB, dB), 
191.51/191.73	                        app_encode_app(dB, fun(dB, dB), 
191.51/191.73	                          app_encode_app(fun(dB, fun(dB, dB)), 
191.51/191.73	                            app_encode_fun(dB, fun(dB, dB)), 
191.51/191.73	                            aa(dB, fun(dB, dB)), app), 
191.51/191.73	                          app_encode_app(dB, dB, abs, r))), s)), ss))), 
191.51/191.73	            app_encode_app(nat, dB, var, i)))),
191.51/191.73	    inference('cnf', [status(esa)], [zf_stmt_0])).
191.51/191.73	tff('26', plain,
191.51/191.73	    ~ app_encode_app(bool, $o, pp, 
191.51/191.73	        app_encode_app(dB, bool, 
191.51/191.73	          app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
191.51/191.73	            aa(dB, bool), it), 
191.51/191.73	          app_encode_app(list(dB), dB, 
191.51/191.73	            app_encode_app(dB, app_encode_fun(list(dB), dB), 
191.51/191.73	              app_encode_app(fun(dB, fun(dB, dB)), 
191.51/191.73	                app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
191.51/191.73	                foldl(dB, dB), app), app_encode_app(dB, dB, abs, r)), 
191.51/191.73	            app_encode_app(list(dB), list(dB), rotate1(dB), 
191.51/191.73	              app_encode_app(list(dB), list(dB), 
191.51/191.73	                app_encode_app(dB, app_encode_fun(list(dB), list(dB)), 
191.51/191.73	                  cons(dB), app_encode_app(nat, dB, var, i)), 
191.51/191.73	                app_encode_app(list(dB), list(dB), 
191.51/191.73	                  app_encode_app(dB, app_encode_fun(list(dB), list(dB)), 
191.51/191.73	                    cons(dB), s), ss)))))),
191.51/191.73	    inference('demod', [status(thm)], ['25', '15', '9'])).
191.51/191.73	tff('27', plain,
191.51/191.73	    (~ $true
191.51/191.73	     | ~ app_encode_app(fun(dB, bool), $o, 
191.51/191.73	           app_encode_app(dB, app_encode_fun(fun(dB, bool), $o), member(dB), 
191.51/191.73	             app_encode_app(list(dB), dB, 
191.51/191.73	               app_encode_app(dB, app_encode_fun(list(dB), dB), 
191.51/191.73	                 app_encode_app(fun(dB, fun(dB, dB)), 
191.51/191.73	                   app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
191.51/191.73	                   foldl(dB, dB), app), app_encode_app(dB, dB, abs, r)), 
191.51/191.73	               app_encode_app(list(dB), list(dB), rotate1(dB), 
191.51/191.73	                 app_encode_app(list(dB), list(dB), 
191.51/191.73	                   app_encode_app(dB, app_encode_fun(list(dB), list(dB)), 
191.51/191.73	                     cons(dB), app_encode_app(nat, dB, var, i)), 
191.51/191.73	                   app_encode_app(list(dB), list(dB), 
191.51/191.73	                     app_encode_app(dB, app_encode_fun(list(dB), list(dB)), 
191.51/191.73	                       cons(dB), s), ss))))), it)),
191.51/191.73	    inference('sup-', [status(thm)], ['24', '26'])).
191.51/191.73	tff('28', plain,
191.51/191.73	    ~ app_encode_app(fun(dB, bool), $o, 
191.51/191.73	        app_encode_app(dB, app_encode_fun(fun(dB, bool), $o), member(dB), 
191.51/191.73	          app_encode_app(list(dB), dB, 
191.51/191.73	            app_encode_app(dB, app_encode_fun(list(dB), dB), 
191.51/191.73	              app_encode_app(fun(dB, fun(dB, dB)), 
191.51/191.73	                app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
191.51/191.73	                foldl(dB, dB), app), app_encode_app(dB, dB, abs, r)), 
191.51/191.73	            app_encode_app(list(dB), list(dB), rotate1(dB), 
191.51/191.73	              app_encode_app(list(dB), list(dB), 
191.51/191.73	                app_encode_app(dB, app_encode_fun(list(dB), list(dB)), 
191.51/191.73	                  cons(dB), app_encode_app(nat, dB, var, i)), 
191.51/191.73	                app_encode_app(list(dB), list(dB), 
191.51/191.73	                  app_encode_app(dB, app_encode_fun(list(dB), list(dB)), 
191.51/191.73	                    cons(dB), s), ss))))), it),
191.51/191.73	    inference('simplify', [status(thm)], ['27'])).
191.51/191.73	tff('29', plain, ~ $true, inference('sup-', [status(thm)], ['23', '28'])).
191.51/191.73	tff('30', plain, $false, inference('simplify', [status(thm)], ['29'])).
191.51/191.73	
191.51/191.73	% SZS output end Refutation
191.51/191.73	EOF
