0.00/0.00	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : appext
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : kbo
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.20	% Computer   : n060.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 06:47:54 CST 2018
193.31/193.50	% done 7516 iterations in 193.295s
193.31/193.50	% SZS status Theorem for 'stdin'
193.31/193.50	% SZS output start Refutation
193.33/193.51	tff(zf_stmt_144, axiom,
193.33/193.51	  (app_encode_app(bool,$o,pp,
193.33/193.51	                  app_encode_app(dB,bool,
193.33/193.51	                                 app_encode_app(fun(dB,bool),
193.33/193.51	                                                app_encode_fun(dB,bool),
193.33/193.51	                                                aa(dB,bool),it),
193.33/193.51	                                 app_encode_app(dB,dB,
193.33/193.51	                                                app_encode_app(fun(dB,dB),
193.33/193.51	                                                               app_encode_fun(
193.33/193.51	                                                               dB,dB),
193.33/193.51	                                                               aa(dB,dB),
193.33/193.51	                                                               app_encode_app(
193.33/193.51	                                                               dB,fun(dB,dB),
193.33/193.51	                                                               app_encode_app(
193.33/193.51	                                                               fun(dB,
193.33/193.51	                                                                   fun(dB,dB)),
193.33/193.51	                                                               app_encode_fun(
193.33/193.51	                                                               dB,fun(dB,dB)),
193.33/193.51	                                                               aa(dB,
193.33/193.51	                                                                  fun(dB,dB)),
193.33/193.51	                                                               app),
193.33/193.51	                                                               app_encode_app(
193.33/193.51	                                                               list(dB),dB,
193.33/193.51	                                                               app_encode_app(
193.33/193.51	                                                               dB,
193.33/193.51	                                                               app_encode_fun(
193.33/193.51	                                                               list(dB),dB),
193.33/193.51	                                                               app_encode_app(
193.33/193.51	                                                               fun(dB,
193.33/193.51	                                                                   fun(dB,dB)),
193.33/193.51	                                                               app_encode_fun(
193.33/193.51	                                                               dB,
193.33/193.51	                                                               app_encode_fun(
193.33/193.51	                                                               list(dB),dB)),
193.33/193.51	                                                               foldl(dB,dB),
193.33/193.51	                                                               app),
193.33/193.51	                                                               app_encode_app(
193.33/193.51	                                                               nat,dB,
193.33/193.51	                                                               app_encode_app(
193.33/193.51	                                                               dB,
193.33/193.51	                                                               app_encode_fun(
193.33/193.51	                                                               nat,dB),
193.33/193.51	                                                               app_encode_app(
193.33/193.51	                                                               dB,
193.33/193.51	                                                               app_encode_fun(
193.33/193.51	                                                               dB,
193.33/193.51	                                                               app_encode_fun(
193.33/193.51	                                                               nat,dB)),
193.33/193.51	                                                               subst,r),s),
193.33/193.51	                                                               zero_zero(nat))),
193.33/193.51	                                                               ss))),
193.33/193.51	                                                app_encode_app(nat,dB,var,i)))))).
193.33/193.51	tff('0', plain,
193.33/193.51	    app_encode_app(bool, $o, pp, 
193.33/193.51	      app_encode_app(dB, bool, 
193.33/193.51	        app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
193.33/193.51	          aa(dB, bool), it), 
193.33/193.51	        app_encode_app(dB, dB, 
193.33/193.51	          app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), aa(dB, dB), 
193.33/193.51	            app_encode_app(dB, fun(dB, dB), 
193.33/193.51	              app_encode_app(fun(dB, fun(dB, dB)), 
193.33/193.51	                app_encode_fun(dB, fun(dB, dB)), aa(dB, fun(dB, dB)), app), 
193.33/193.51	              app_encode_app(list(dB), dB, 
193.33/193.51	                app_encode_app(dB, app_encode_fun(list(dB), dB), 
193.33/193.51	                  app_encode_app(fun(dB, fun(dB, dB)), 
193.33/193.51	                    app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
193.33/193.51	                    foldl(dB, dB), app), 
193.33/193.51	                  app_encode_app(nat, dB, 
193.33/193.51	                    app_encode_app(dB, app_encode_fun(nat, dB), 
193.33/193.51	                      app_encode_app(dB, 
193.33/193.51	                        app_encode_fun(dB, app_encode_fun(nat, dB)), subst, 
193.33/193.51	                        r), s), zero_zero(nat))), ss))), 
193.33/193.51	          app_encode_app(nat, dB, var, i)))),
193.33/193.51	    inference('cnf', [status(esa)], [zf_stmt_144])).
193.33/193.51	tff(zf_stmt_108, axiom,
193.33/193.51	  (![Ts:list(dB),Ta:dB,S:dB,R:dB]:
193.33/193.51	     ((app_encode_app(dB,dB,
193.33/193.51	                      app_encode_app(fun(dB,dB),app_encode_fun(dB,dB),
193.33/193.51	                                     aa(dB,dB),
193.33/193.51	                                     app_encode_app(dB,fun(dB,dB),
193.33/193.51	                                                    app_encode_app(fun(
193.33/193.51	                                                                   dB,
193.33/193.51	                                                                   fun(dB,dB)),
193.33/193.51	                                                                   app_encode_fun(
193.33/193.51	                                                                   dB,
193.33/193.51	                                                                   fun(dB,dB)),
193.33/193.51	                                                                   aa(
193.33/193.51	                                                                   dB,
193.33/193.51	                                                                   fun(dB,dB)),
193.33/193.51	                                                                   app),
193.33/193.51	                                                    R)),
193.33/193.51	                      S) =
193.33/193.51	       app_encode_app(list(dB),dB,
193.33/193.51	                      app_encode_app(dB,app_encode_fun(list(dB),dB),
193.33/193.51	                                     app_encode_app(fun(dB,fun(dB,dB)),
193.33/193.51	                                                    app_encode_fun(dB,
193.33/193.51	                                                                   app_encode_fun(
193.33/193.51	                                                                   list(dB),
193.33/193.51	                                                                   dB)),
193.33/193.51	                                                    foldl(dB,dB),app),
193.33/193.51	                                     Ta),
193.33/193.51	                      Ts)) <=>
193.33/193.51	      (((Ts = nil(dB)) =>
193.33/193.51	        (app_encode_app(dB,dB,
193.33/193.51	                        app_encode_app(fun(dB,dB),app_encode_fun(dB,dB),
193.33/193.51	                                       aa(dB,dB),
193.33/193.51	                                       app_encode_app(dB,fun(dB,dB),
193.33/193.51	                                                      app_encode_app(
193.33/193.51	                                                      fun(dB,fun(dB,dB)),
193.33/193.51	                                                      app_encode_fun(
193.33/193.51	                                                      dB,fun(dB,dB)),
193.33/193.51	                                                      aa(dB,fun(dB,dB)),app),
193.33/193.51	                                                      R)),
193.33/193.51	                        S) =
193.33/193.51	         Ta)) & 
193.33/193.51	       ((Ts != nil(dB)) =>
193.33/193.51	        (?[Ss:list(dB)]:
193.33/193.51	           ((Ts =
193.33/193.51	             app_encode_app(list(dB),list(dB),
193.33/193.51	                            app_encode_app(list(dB),
193.33/193.51	                                           app_encode_fun(list(dB),list(dB)),
193.33/193.51	                                           append(dB),Ss),
193.33/193.51	                            app_encode_app(list(dB),list(dB),
193.33/193.51	                                           app_encode_app(dB,
193.33/193.51	                                                          app_encode_fun(
193.33/193.51	                                                          list(dB),list(dB)),
193.33/193.51	                                                          cons(dB),S),
193.33/193.51	                                           nil(dB)))) & 
193.33/193.51	            (R =
193.33/193.51	             app_encode_app(list(dB),dB,
193.33/193.51	                            app_encode_app(dB,app_encode_fun(list(dB),dB),
193.33/193.51	                                           app_encode_app(fun(dB,fun(dB,dB)),
193.33/193.51	                                                          app_encode_fun(
193.33/193.51	                                                          dB,
193.33/193.51	                                                          app_encode_fun(
193.33/193.51	                                                          list(dB),dB)),
193.33/193.51	                                                          foldl(dB,dB),app),
193.33/193.51	                                           Ta),
193.33/193.51	                            Ss))))))))).
193.33/193.51	tff('1', plain,
193.33/193.51	    ![X257 : list(dB), X258 : dB, X260 : dB, X261 : dB, X262 : list(dB)]:
193.33/193.51	      (app_encode_app(dB, dB, 
193.33/193.51	         app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), aa(dB, dB), 
193.33/193.51	           app_encode_app(dB, fun(dB, dB), 
193.33/193.51	             app_encode_app(fun(dB, fun(dB, dB)), 
193.33/193.51	               app_encode_fun(dB, fun(dB, dB)), aa(dB, fun(dB, dB)), app), 
193.33/193.51	             X261)), X260)
193.33/193.51	        = app_encode_app(list(dB), dB, 
193.33/193.51	            app_encode_app(dB, app_encode_fun(list(dB), dB), 
193.33/193.51	              app_encode_app(fun(dB, fun(dB, dB)), 
193.33/193.51	                app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
193.33/193.51	                foldl(dB, dB), app), X258), X257)
193.33/193.51	       | X261
193.33/193.51	          != app_encode_app(list(dB), dB, 
193.33/193.51	               app_encode_app(dB, app_encode_fun(list(dB), dB), 
193.33/193.51	                 app_encode_app(fun(dB, fun(dB, dB)), 
193.33/193.51	                   app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
193.33/193.51	                   foldl(dB, dB), app), X258), X262)
193.33/193.51	       | X257
193.33/193.51	          != app_encode_app(list(dB), list(dB), 
193.33/193.51	               app_encode_app(list(dB), app_encode_fun(list(dB), list(dB)), 
193.33/193.51	                 append(dB), X262), 
193.33/193.51	               app_encode_app(list(dB), list(dB), 
193.33/193.51	                 app_encode_app(dB, app_encode_fun(list(dB), list(dB)), 
193.33/193.51	                   cons(dB), X260), nil(dB)))
193.33/193.51	       | X257 = nil(dB)),
193.33/193.51	    inference('cnf', [status(esa)], [zf_stmt_108])).
193.33/193.51	tff('2', plain,
193.33/193.51	    ![X258 : dB, X260 : dB, X262 : list(dB)]:
193.33/193.51	      (app_encode_app(list(dB), list(dB), 
193.33/193.51	         app_encode_app(list(dB), app_encode_fun(list(dB), list(dB)), 
193.33/193.51	           append(dB), X262), 
193.33/193.51	         app_encode_app(list(dB), list(dB), 
193.33/193.51	           app_encode_app(dB, app_encode_fun(list(dB), list(dB)), cons(dB), 
193.33/193.51	             X260), nil(dB)))
193.33/193.51	        = nil(dB)
193.33/193.51	       | app_encode_app(dB, dB, 
193.33/193.51	           app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), aa(dB, dB), 
193.33/193.51	             app_encode_app(dB, fun(dB, dB), 
193.33/193.51	               app_encode_app(fun(dB, fun(dB, dB)), 
193.33/193.51	                 app_encode_fun(dB, fun(dB, dB)), aa(dB, fun(dB, dB)), app), 
193.33/193.51	               app_encode_app(list(dB), dB, 
193.33/193.51	                 app_encode_app(dB, app_encode_fun(list(dB), dB), 
193.33/193.51	                   app_encode_app(fun(dB, fun(dB, dB)), 
193.33/193.51	                     app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
193.33/193.51	                     foldl(dB, dB), app), X258), X262))), X260)
193.33/193.51	          = app_encode_app(list(dB), dB, 
193.33/193.51	              app_encode_app(dB, app_encode_fun(list(dB), dB), 
193.33/193.51	                app_encode_app(fun(dB, fun(dB, dB)), 
193.33/193.51	                  app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
193.33/193.51	                  foldl(dB, dB), app), X258), 
193.33/193.51	              app_encode_app(list(dB), list(dB), 
193.33/193.51	                app_encode_app(list(dB), app_encode_fun(list(dB), list(dB)), 
193.33/193.51	                  append(dB), X262), 
193.33/193.51	                app_encode_app(list(dB), list(dB), 
193.33/193.51	                  app_encode_app(dB, app_encode_fun(list(dB), list(dB)), 
193.33/193.51	                    cons(dB), X260), nil(dB))))),
193.33/193.51	    inference('simplify', [status(thm)], ['1'])).
193.33/193.51	tff(zf_stmt_139, axiom,
193.33/193.51	  (![A:$tType,B:$tType,Xs:list(B),X:B]:
193.33/193.51	     ((app_encode_app(list(A),list(A),rotate1(A),nil(A)) = nil(A)) & 
193.33/193.51	      (app_encode_app(list(B),list(B),rotate1(B),
193.33/193.51	                      app_encode_app(list(B),list(B),
193.33/193.51	                                     app_encode_app(B,
193.33/193.51	                                                    app_encode_fun(list(B),
193.33/193.51	                                                                   list(B)),
193.33/193.51	                                                    cons(B),X),
193.33/193.51	                                     Xs)) =
193.33/193.51	       app_encode_app(list(B),list(B),
193.33/193.51	                      app_encode_app(list(B),app_encode_fun(list(B),list(B)),
193.33/193.51	                                     append(B),Xs),
193.33/193.51	                      app_encode_app(list(B),list(B),
193.33/193.51	                                     app_encode_app(B,
193.33/193.51	                                                    app_encode_fun(list(B),
193.33/193.51	                                                                   list(B)),
193.33/193.51	                                                    cons(B),X),
193.33/193.51	                                     nil(B))))))).
193.33/193.51	tff('3', plain,
193.33/193.51	    ![X401 : $tType, X402 : list(X401), X403 : X401]:
193.33/193.51	      app_encode_app(list(X401), list(X401), rotate1(X401), 
193.33/193.51	        app_encode_app(list(X401), list(X401), 
193.33/193.51	          app_encode_app(X401, app_encode_fun(list(X401), list(X401)), 
193.33/193.51	            cons(X401), X403), X402))
193.33/193.51	       = app_encode_app(list(X401), list(X401), 
193.33/193.51	           app_encode_app(list(X401), 
193.33/193.51	             app_encode_fun(list(X401), list(X401)), append(X401), X402), 
193.33/193.51	           app_encode_app(list(X401), list(X401), 
193.33/193.51	             app_encode_app(X401, app_encode_fun(list(X401), list(X401)), 
193.33/193.51	               cons(X401), X403), nil(X401))),
193.33/193.51	    inference('cnf', [status(esa)], [zf_stmt_139])).
193.33/193.51	tff('4', plain,
193.33/193.51	    ![X258 : dB, X260 : dB, X262 : list(dB)]:
193.33/193.51	      (app_encode_app(list(dB), list(dB), rotate1(dB), 
193.33/193.51	         app_encode_app(list(dB), list(dB), 
193.33/193.51	           app_encode_app(dB, app_encode_fun(list(dB), list(dB)), cons(dB), 
193.33/193.51	             X260), X262))
193.33/193.51	        = nil(dB)
193.33/193.51	       | app_encode_app(dB, dB, 
193.33/193.51	           app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), aa(dB, dB), 
193.33/193.51	             app_encode_app(dB, fun(dB, dB), 
193.33/193.51	               app_encode_app(fun(dB, fun(dB, dB)), 
193.33/193.51	                 app_encode_fun(dB, fun(dB, dB)), aa(dB, fun(dB, dB)), app), 
193.33/193.51	               app_encode_app(list(dB), dB, 
193.33/193.51	                 app_encode_app(dB, app_encode_fun(list(dB), dB), 
193.33/193.51	                   app_encode_app(fun(dB, fun(dB, dB)), 
193.33/193.51	                     app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
193.33/193.51	                     foldl(dB, dB), app), X258), X262))), X260)
193.33/193.51	          = app_encode_app(list(dB), dB, 
193.33/193.51	              app_encode_app(dB, app_encode_fun(list(dB), dB), 
193.33/193.51	                app_encode_app(fun(dB, fun(dB, dB)), 
193.33/193.51	                  app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
193.33/193.51	                  foldl(dB, dB), app), X258), 
193.33/193.51	              app_encode_app(list(dB), list(dB), rotate1(dB), 
193.33/193.51	                app_encode_app(list(dB), list(dB), 
193.33/193.51	                  app_encode_app(dB, app_encode_fun(list(dB), list(dB)), 
193.33/193.51	                    cons(dB), X260), X262)))),
193.33/193.51	    inference('demod', [status(thm)], ['2', '3', '3'])).
193.33/193.51	tff(zf_stmt_113, axiom,
193.33/193.51	  (![A:$tType,Ys1:list(A),Xs1:list(A)]:
193.33/193.51	     ((nil(A) =
193.33/193.51	       app_encode_app(list(A),list(A),
193.33/193.51	                      app_encode_app(list(A),app_encode_fun(list(A),list(A)),
193.33/193.51	                                     append(A),Xs1),
193.33/193.51	                      Ys1)) <=>
193.33/193.51	      ((Xs1 = nil(A)) & (Ys1 = nil(A)))))).
193.33/193.51	tff('5', plain,
193.33/193.51	    ![X281 : $tType, X282 : list(X281), X283 : list(X281)]:
193.33/193.51	      (X283 = nil(X281)
193.33/193.51	       | nil(X281)
193.33/193.51	          != app_encode_app(list(X281), list(X281), 
193.33/193.51	               app_encode_app(list(X281), 
193.33/193.51	                 app_encode_fun(list(X281), list(X281)), append(X281), X282), 
193.33/193.51	               X283)),
193.33/193.51	    inference('cnf', [status(esa)], [zf_stmt_113])).
193.33/193.51	tff('6', plain,
193.33/193.51	    ![X0 : $tType, X1 : list(X0), X2 : X0]:
193.33/193.51	      (nil(X0)
193.33/193.51	        != app_encode_app(list(X0), list(X0), rotate1(X0), 
193.33/193.51	             app_encode_app(list(X0), list(X0), 
193.33/193.51	               app_encode_app(X0, app_encode_fun(list(X0), list(X0)), 
193.33/193.51	                 cons(X0), X2), X1))
193.33/193.51	       | app_encode_app(list(X0), list(X0), 
193.33/193.51	           app_encode_app(X0, app_encode_fun(list(X0), list(X0)), cons(X0), 
193.33/193.51	             X2), nil(X0))
193.33/193.51	          = nil(X0)),
193.33/193.51	    inference('sup-', [status(thm)], ['3', '5'])).
193.33/193.51	tff(zf_stmt_97, axiom,
193.33/193.51	  (![A:$tType,Xs:list(A),X:A]:
193.33/193.51	     (app_encode_app(list(A),list(A),
193.33/193.51	                     app_encode_app(A,app_encode_fun(list(A),list(A)),
193.33/193.51	                                    cons(A),X),
193.33/193.51	                     Xs) !=
193.33/193.51	      Xs))).
193.33/193.51	tff('7', plain,
193.33/193.51	    ![X208 : $tType, X209 : list(X208), X210 : X208]:
193.33/193.51	      app_encode_app(list(X208), list(X208), 
193.33/193.51	        app_encode_app(X208, app_encode_fun(list(X208), list(X208)), 
193.33/193.51	          cons(X208), X210), X209)
193.33/193.51	       != X209,
193.33/193.51	    inference('cnf', [status(esa)], [zf_stmt_97])).
193.33/193.51	tff('8', plain,
193.33/193.51	    ![X0 : $tType, X1 : list(X0), X2 : X0]:
193.33/193.51	      nil(X0)
193.33/193.51	       != app_encode_app(list(X0), list(X0), rotate1(X0), 
193.33/193.51	            app_encode_app(list(X0), list(X0), 
193.33/193.51	              app_encode_app(X0, app_encode_fun(list(X0), list(X0)), 
193.33/193.51	                cons(X0), X2), X1)),
193.33/193.51	    inference('simplify_reflect-', [status(thm)], ['6', '7'])).
193.33/193.51	tff('9', plain,
193.33/193.51	    ![X258 : dB, X260 : dB, X262 : list(dB)]:
193.33/193.51	      app_encode_app(dB, dB, 
193.33/193.51	        app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), aa(dB, dB), 
193.33/193.51	          app_encode_app(dB, fun(dB, dB), 
193.33/193.51	            app_encode_app(fun(dB, fun(dB, dB)), 
193.33/193.51	              app_encode_fun(dB, fun(dB, dB)), aa(dB, fun(dB, dB)), app), 
193.33/193.51	            app_encode_app(list(dB), dB, 
193.33/193.51	              app_encode_app(dB, app_encode_fun(list(dB), dB), 
193.33/193.51	                app_encode_app(fun(dB, fun(dB, dB)), 
193.33/193.51	                  app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
193.33/193.51	                  foldl(dB, dB), app), X258), X262))), X260)
193.33/193.51	       = app_encode_app(list(dB), dB, 
193.33/193.51	           app_encode_app(dB, app_encode_fun(list(dB), dB), 
193.33/193.51	             app_encode_app(fun(dB, fun(dB, dB)), 
193.33/193.51	               app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
193.33/193.51	               foldl(dB, dB), app), X258), 
193.33/193.51	           app_encode_app(list(dB), list(dB), rotate1(dB), 
193.33/193.51	             app_encode_app(list(dB), list(dB), 
193.33/193.51	               app_encode_app(dB, app_encode_fun(list(dB), list(dB)), 
193.33/193.51	                 cons(dB), X260), X262))),
193.33/193.51	    inference('clc', [status(thm)], ['4', '8'])).
193.33/193.51	tff('10', plain,
193.33/193.51	    app_encode_app(bool, $o, pp, 
193.33/193.51	      app_encode_app(dB, bool, 
193.33/193.51	        app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
193.33/193.51	          aa(dB, bool), it), 
193.33/193.51	        app_encode_app(list(dB), dB, 
193.33/193.51	          app_encode_app(dB, app_encode_fun(list(dB), dB), 
193.33/193.51	            app_encode_app(fun(dB, fun(dB, dB)), 
193.33/193.51	              app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
193.33/193.51	              foldl(dB, dB), app), 
193.33/193.51	            app_encode_app(nat, dB, 
193.33/193.51	              app_encode_app(dB, app_encode_fun(nat, dB), 
193.33/193.51	                app_encode_app(dB, 
193.33/193.51	                  app_encode_fun(dB, app_encode_fun(nat, dB)), subst, r), s), 
193.33/193.51	              zero_zero(nat))), 
193.33/193.51	          app_encode_app(list(dB), list(dB), rotate1(dB), 
193.33/193.51	            app_encode_app(list(dB), list(dB), 
193.33/193.51	              app_encode_app(dB, app_encode_fun(list(dB), list(dB)), 
193.33/193.51	                cons(dB), app_encode_app(nat, dB, var, i)), ss))))),
193.33/193.51	    inference('demod', [status(thm)], ['0', '9'])).
193.33/193.51	tff(zf_stmt_43, axiom,
193.33/193.51	  (![Ss2:list(dB),S:dB,R:dB]:
193.33/193.51	     (app_encode_app(bool,$o,pp,
193.33/193.51	                     app_encode_app(dB,bool,
193.33/193.51	                                    app_encode_app(fun(dB,bool),
193.33/193.51	                                                   app_encode_fun(dB,bool),
193.33/193.51	                                                   aa(dB,bool),it),
193.33/193.51	                                    app_encode_app(list(dB),dB,
193.33/193.51	                                                   app_encode_app(dB,
193.33/193.51	                                                                  app_encode_fun(
193.33/193.51	                                                                  list(dB),dB),
193.33/193.51	                                                                  app_encode_app(
193.33/193.51	                                                                  fun(
193.33/193.51	                                                                  dB,
193.33/193.51	                                                                  fun(dB,dB)),
193.33/193.51	                                                                  app_encode_fun(
193.33/193.51	                                                                  dB,
193.33/193.51	                                                                  app_encode_fun(
193.33/193.51	                                                                  list(dB),dB)),
193.33/193.51	                                                                  foldl(
193.33/193.51	                                                                  dB,dB),app),
193.33/193.51	                                                                  app_encode_app(
193.33/193.51	                                                                  nat,dB,
193.33/193.51	                                                                  app_encode_app(
193.33/193.51	                                                                  dB,
193.33/193.51	                                                                  app_encode_fun(
193.33/193.51	                                                                  nat,dB),
193.33/193.51	                                                                  app_encode_app(
193.33/193.51	                                                                  dB,
193.33/193.51	                                                                  app_encode_fun(
193.33/193.51	                                                                  dB,
193.33/193.51	                                                                  app_encode_fun(
193.33/193.51	                                                                  nat,dB)),
193.33/193.51	                                                                  subst,R),S),
193.33/193.51	                                                                  zero_zero(
193.33/193.51	                                                                  nat))),
193.33/193.51	                                                   Ss2))) =>
193.33/193.51	      (app_encode_app(bool,$o,pp,
193.33/193.51	                      app_encode_app(dB,bool,
193.33/193.51	                                     app_encode_app(fun(dB,bool),
193.33/193.51	                                                    app_encode_fun(dB,bool),
193.33/193.51	                                                    aa(dB,bool),it),
193.33/193.51	                                     S)) =>
193.33/193.51	       app_encode_app(bool,$o,pp,
193.33/193.51	                      app_encode_app(dB,bool,
193.33/193.51	                                     app_encode_app(fun(dB,bool),
193.33/193.51	                                                    app_encode_fun(dB,bool),
193.33/193.51	                                                    aa(dB,bool),it),
193.33/193.51	                                     app_encode_app(list(dB),dB,
193.33/193.51	                                                    app_encode_app(dB,
193.33/193.51	                                                                   app_encode_fun(
193.33/193.51	                                                                   list(dB),
193.33/193.51	                                                                   dB),
193.33/193.51	                                                                   app_encode_app(
193.33/193.51	                                                                   fun(
193.33/193.51	                                                                   dB,
193.33/193.51	                                                                   fun(dB,dB)),
193.33/193.51	                                                                   app_encode_fun(
193.33/193.51	                                                                   dB,
193.33/193.51	                                                                   app_encode_fun(
193.33/193.51	                                                                   list(dB),
193.33/193.51	                                                                   dB)),
193.33/193.51	                                                                   foldl(
193.33/193.51	                                                                   dB,dB),app),
193.33/193.51	                                                                   app_encode_app(
193.33/193.51	                                                                   dB,dB,
193.33/193.51	                                                                   app_encode_app(
193.33/193.51	                                                                   fun(dB,dB),
193.33/193.51	                                                                   app_encode_fun(
193.33/193.51	                                                                   dB,dB),
193.33/193.51	                                                                   aa(dB,dB),
193.33/193.51	                                                                   app_encode_app(
193.33/193.51	                                                                   dB,
193.33/193.51	                                                                   fun(dB,dB),
193.33/193.51	                                                                   app_encode_app(
193.33/193.51	                                                                   fun(
193.33/193.51	                                                                   dB,
193.33/193.51	                                                                   fun(dB,dB)),
193.33/193.51	                                                                   app_encode_fun(
193.33/193.51	                                                                   dB,
193.33/193.51	                                                                   fun(dB,dB)),
193.33/193.51	                                                                   aa(
193.33/193.51	                                                                   dB,
193.33/193.51	                                                                   fun(dB,dB)),
193.33/193.51	                                                                   app),
193.33/193.51	                                                                   app_encode_app(
193.33/193.51	                                                                   dB,dB,abs,
193.33/193.51	                                                                   R))),S)),
193.33/193.51	                                                    Ss2))))))).
193.33/193.51	tff('11', plain,
193.33/193.51	    ![X8 : dB, X9 : dB, X10 : list(dB)]:
193.33/193.51	      (~ app_encode_app(bool, $o, pp, 
193.33/193.51	           app_encode_app(dB, bool, 
193.33/193.51	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
193.33/193.51	               aa(dB, bool), it), X8))
193.33/193.51	       | ~ app_encode_app(bool, $o, pp, 
193.33/193.51	             app_encode_app(dB, bool, 
193.33/193.51	               app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
193.33/193.51	                 aa(dB, bool), it), 
193.33/193.51	               app_encode_app(list(dB), dB, 
193.33/193.51	                 app_encode_app(dB, app_encode_fun(list(dB), dB), 
193.33/193.51	                   app_encode_app(fun(dB, fun(dB, dB)), 
193.33/193.51	                     app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
193.33/193.51	                     foldl(dB, dB), app), 
193.33/193.51	                   app_encode_app(nat, dB, 
193.33/193.51	                     app_encode_app(dB, app_encode_fun(nat, dB), 
193.33/193.51	                       app_encode_app(dB, 
193.33/193.51	                         app_encode_fun(dB, app_encode_fun(nat, dB)), subst, 
193.33/193.51	                         X9), X8), zero_zero(nat))), X10)))
193.33/193.51	       | app_encode_app(bool, $o, pp, 
193.33/193.51	           app_encode_app(dB, bool, 
193.33/193.51	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
193.33/193.51	               aa(dB, bool), it), 
193.33/193.51	             app_encode_app(list(dB), dB, 
193.33/193.51	               app_encode_app(dB, app_encode_fun(list(dB), dB), 
193.33/193.51	                 app_encode_app(fun(dB, fun(dB, dB)), 
193.33/193.51	                   app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
193.33/193.51	                   foldl(dB, dB), app), 
193.33/193.51	                 app_encode_app(dB, dB, 
193.33/193.51	                   app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), 
193.33/193.51	                     aa(dB, dB), 
193.33/193.51	                     app_encode_app(dB, fun(dB, dB), 
193.33/193.51	                       app_encode_app(fun(dB, fun(dB, dB)), 
193.33/193.51	                         app_encode_fun(dB, fun(dB, dB)), 
193.33/193.51	                         aa(dB, fun(dB, dB)), app), 
193.33/193.51	                       app_encode_app(dB, dB, abs, X9))), X8)), X10)))),
193.33/193.51	    inference('cnf', [status(esa)], [zf_stmt_43])).
193.33/193.51	tff(zf_stmt_116, axiom,
193.33/193.51	  (![A:$tType,A1:fun(A,bool),X2:A]:
193.33/193.51	     (app_encode_app(fun(A,bool),$o,
193.33/193.51	                     app_encode_app(A,app_encode_fun(fun(A,bool),$o),
193.33/193.51	                                    member(A),X2),
193.33/193.51	                     A1) <=>
193.33/193.51	      app_encode_app(bool,$o,pp,
193.33/193.51	                     app_encode_app(A,bool,
193.33/193.51	                                    app_encode_app(fun(A,bool),
193.33/193.51	                                                   app_encode_fun(A,bool),
193.33/193.51	                                                   aa(A,bool),A1),
193.33/193.51	                                    X2))))).
193.33/193.51	tff('12', plain,
193.33/193.51	    ![X293 : $tType, X294 : fun(X293, bool), X296 : X293]:
193.33/193.51	      (app_encode_app(fun(X293, bool), $o, 
193.33/193.51	         app_encode_app(X293, app_encode_fun(fun(X293, bool), $o), 
193.33/193.51	           member(X293), X296), X294)
193.33/193.51	       | ~ app_encode_app(bool, $o, pp, 
193.33/193.51	             app_encode_app(X293, bool, 
193.33/193.51	               app_encode_app(fun(X293, bool), app_encode_fun(X293, bool), 
193.33/193.51	                 aa(X293, bool), X294), X296))),
193.33/193.51	    inference('cnf', [status(esa)], [zf_stmt_116])).
193.33/193.51	tff('13', plain,
193.33/193.51	    ![X0 : list(dB), X1 : dB, X2 : dB]:
193.33/193.51	      (~ $true
193.33/193.51	       | ~ app_encode_app(bool, $o, pp, 
193.33/193.51	             app_encode_app(dB, bool, 
193.33/193.51	               app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
193.33/193.51	                 aa(dB, bool), it), 
193.33/193.51	               app_encode_app(list(dB), dB, 
193.33/193.51	                 app_encode_app(dB, app_encode_fun(list(dB), dB), 
193.33/193.51	                   app_encode_app(fun(dB, fun(dB, dB)), 
193.33/193.51	                     app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
193.33/193.51	                     foldl(dB, dB), app), 
193.33/193.51	                   app_encode_app(nat, dB, 
193.33/193.51	                     app_encode_app(dB, app_encode_fun(nat, dB), 
193.33/193.51	                       app_encode_app(dB, 
193.33/193.51	                         app_encode_fun(dB, app_encode_fun(nat, dB)), subst, 
193.33/193.51	                         X2), X1), zero_zero(nat))), X0)))
193.33/193.51	       | ~ app_encode_app(bool, $o, pp, 
193.33/193.51	             app_encode_app(dB, bool, 
193.33/193.51	               app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
193.33/193.51	                 aa(dB, bool), it), X1))
193.33/193.51	       | app_encode_app(fun(dB, bool), $o, 
193.33/193.51	           app_encode_app(dB, app_encode_fun(fun(dB, bool), $o), member(dB), 
193.33/193.51	             app_encode_app(list(dB), dB, 
193.33/193.51	               app_encode_app(dB, app_encode_fun(list(dB), dB), 
193.33/193.51	                 app_encode_app(fun(dB, fun(dB, dB)), 
193.33/193.51	                   app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
193.33/193.51	                   foldl(dB, dB), app), 
193.33/193.51	                 app_encode_app(dB, dB, 
193.33/193.51	                   app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), 
193.33/193.51	                     aa(dB, dB), 
193.33/193.51	                     app_encode_app(dB, fun(dB, dB), 
193.33/193.51	                       app_encode_app(fun(dB, fun(dB, dB)), 
193.33/193.51	                         app_encode_fun(dB, fun(dB, dB)), 
193.33/193.51	                         aa(dB, fun(dB, dB)), app), 
193.33/193.51	                       app_encode_app(dB, dB, abs, X2))), X1)), X0)), it)),
193.33/193.51	    inference('sup-', [status(thm)], ['11', '12'])).
193.33/193.51	tff('14', plain,
193.33/193.51	    ![X0 : list(dB), X1 : dB, X2 : dB]:
193.33/193.51	      (app_encode_app(fun(dB, bool), $o, 
193.33/193.51	         app_encode_app(dB, app_encode_fun(fun(dB, bool), $o), member(dB), 
193.33/193.51	           app_encode_app(list(dB), dB, 
193.33/193.51	             app_encode_app(dB, app_encode_fun(list(dB), dB), 
193.33/193.51	               app_encode_app(fun(dB, fun(dB, dB)), 
193.33/193.51	                 app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
193.33/193.51	                 foldl(dB, dB), app), 
193.33/193.51	               app_encode_app(dB, dB, 
193.33/193.51	                 app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), 
193.33/193.51	                   aa(dB, dB), 
193.33/193.51	                   app_encode_app(dB, fun(dB, dB), 
193.33/193.51	                     app_encode_app(fun(dB, fun(dB, dB)), 
193.33/193.51	                       app_encode_fun(dB, fun(dB, dB)), aa(dB, fun(dB, dB)), 
193.33/193.51	                       app), app_encode_app(dB, dB, abs, X2))), X1)), X0)), 
193.33/193.51	         it)
193.33/193.51	       | ~ app_encode_app(bool, $o, pp, 
193.33/193.51	             app_encode_app(dB, bool, 
193.33/193.51	               app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
193.33/193.51	                 aa(dB, bool), it), X1))
193.33/193.51	       | ~ app_encode_app(bool, $o, pp, 
193.33/193.51	             app_encode_app(dB, bool, 
193.33/193.51	               app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
193.33/193.51	                 aa(dB, bool), it), 
193.33/193.51	               app_encode_app(list(dB), dB, 
193.33/193.51	                 app_encode_app(dB, app_encode_fun(list(dB), dB), 
193.33/193.51	                   app_encode_app(fun(dB, fun(dB, dB)), 
193.33/193.51	                     app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
193.33/193.51	                     foldl(dB, dB), app), 
193.33/193.51	                   app_encode_app(nat, dB, 
193.33/193.51	                     app_encode_app(dB, app_encode_fun(nat, dB), 
193.33/193.51	                       app_encode_app(dB, 
193.33/193.51	                         app_encode_fun(dB, app_encode_fun(nat, dB)), subst, 
193.33/193.51	                         X2), X1), zero_zero(nat))), X0)))),
193.33/193.51	    inference('simplify', [status(thm)], ['13'])).
193.33/193.51	tff(zf_stmt_99, axiom,
193.33/193.51	  (![A:$tType,B:$tType,Xs1:list(B),X2:B,A2:A,F:fun(A,fun(B,A))]:
193.33/193.51	     (app_encode_app(list(B),A,
193.33/193.51	                     app_encode_app(A,app_encode_fun(list(B),A),
193.33/193.51	                                    app_encode_app(fun(A,fun(B,A)),
193.33/193.51	                                                   app_encode_fun(A,
193.33/193.51	                                                                  app_encode_fun(
193.33/193.51	                                                                  list(B),A)),
193.33/193.51	                                                   foldl(A,B),F),
193.33/193.51	                                    A2),
193.33/193.51	                     app_encode_app(list(B),list(B),
193.33/193.51	                                    app_encode_app(B,
193.33/193.51	                                                   app_encode_fun(list(B),
193.33/193.51	                                                                  list(B)),
193.33/193.51	                                                   cons(B),X2),
193.33/193.51	                                    Xs1)) =
193.33/193.51	      app_encode_app(list(B),A,
193.33/193.51	                     app_encode_app(A,app_encode_fun(list(B),A),
193.33/193.51	                                    app_encode_app(fun(A,fun(B,A)),
193.33/193.51	                                                   app_encode_fun(A,
193.33/193.51	                                                                  app_encode_fun(
193.33/193.51	                                                                  list(B),A)),
193.33/193.51	                                                   foldl(A,B),F),
193.33/193.51	                                    app_encode_app(B,A,
193.33/193.51	                                                   app_encode_app(fun(B,A),
193.33/193.51	                                                                  app_encode_fun(
193.33/193.51	                                                                  B,A),
193.33/193.51	                                                                  aa(B,A),
193.33/193.51	                                                                  app_encode_app(
193.33/193.51	                                                                  A,fun(B,A),
193.33/193.51	                                                                  app_encode_app(
193.33/193.51	                                                                  fun(
193.33/193.51	                                                                  A,fun(B,A)),
193.33/193.51	                                                                  app_encode_fun(
193.33/193.51	                                                                  A,fun(B,A)),
193.33/193.51	                                                                  aa(
193.33/193.51	                                                                  A,fun(B,A)),
193.33/193.51	                                                                  F),A2)),
193.33/193.51	                                                   X2)),
193.33/193.51	                     Xs1)))).
193.33/193.51	tff('15', plain,
193.33/193.51	    ![X214 : $tType, X215 : $tType, X216 : fun(X215, fun(X214, X215)), 
193.33/193.51	      X217 : X215, X218 : X214, X219 : list(X214)]:
193.33/193.51	      app_encode_app(list(X214), X215, 
193.33/193.51	        app_encode_app(X215, app_encode_fun(list(X214), X215), 
193.33/193.51	          app_encode_app(fun(X215, fun(X214, X215)), 
193.33/193.51	            app_encode_fun(X215, app_encode_fun(list(X214), X215)), 
193.33/193.51	            foldl(X215, X214), X216), X217), 
193.33/193.51	        app_encode_app(list(X214), list(X214), 
193.33/193.51	          app_encode_app(X214, app_encode_fun(list(X214), list(X214)), 
193.33/193.51	            cons(X214), X218), X219))
193.33/193.51	       = app_encode_app(list(X214), X215, 
193.33/193.51	           app_encode_app(X215, app_encode_fun(list(X214), X215), 
193.33/193.51	             app_encode_app(fun(X215, fun(X214, X215)), 
193.33/193.51	               app_encode_fun(X215, app_encode_fun(list(X214), X215)), 
193.33/193.51	               foldl(X215, X214), X216), 
193.33/193.51	             app_encode_app(X214, X215, 
193.33/193.51	               app_encode_app(fun(X214, X215), app_encode_fun(X214, X215), 
193.33/193.51	                 aa(X214, X215), 
193.33/193.51	                 app_encode_app(X215, fun(X214, X215), 
193.33/193.51	                   app_encode_app(fun(X215, fun(X214, X215)), 
193.33/193.51	                     app_encode_fun(X215, fun(X214, X215)), 
193.33/193.51	                     aa(X215, fun(X214, X215)), X216), X217)), X218)), X219),
193.33/193.51	    inference('cnf', [status(esa)], [zf_stmt_99])).
193.33/193.51	tff('16', plain,
193.33/193.51	    ![X0 : list(dB), X1 : dB, X2 : dB]:
193.33/193.51	      (app_encode_app(fun(dB, bool), $o, 
193.33/193.51	         app_encode_app(dB, app_encode_fun(fun(dB, bool), $o), member(dB), 
193.33/193.51	           app_encode_app(list(dB), dB, 
193.33/193.51	             app_encode_app(dB, app_encode_fun(list(dB), dB), 
193.33/193.51	               app_encode_app(fun(dB, fun(dB, dB)), 
193.33/193.51	                 app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
193.33/193.51	                 foldl(dB, dB), app), app_encode_app(dB, dB, abs, X2)), 
193.33/193.51	             app_encode_app(list(dB), list(dB), 
193.33/193.51	               app_encode_app(dB, app_encode_fun(list(dB), list(dB)), 
193.33/193.51	                 cons(dB), X1), X0))), it)
193.33/193.51	       | ~ app_encode_app(bool, $o, pp, 
193.33/193.51	             app_encode_app(dB, bool, 
193.33/193.51	               app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
193.33/193.51	                 aa(dB, bool), it), X1))
193.33/193.51	       | ~ app_encode_app(bool, $o, pp, 
193.33/193.51	             app_encode_app(dB, bool, 
193.33/193.51	               app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
193.33/193.51	                 aa(dB, bool), it), 
193.33/193.51	               app_encode_app(list(dB), dB, 
193.33/193.51	                 app_encode_app(dB, app_encode_fun(list(dB), dB), 
193.33/193.51	                   app_encode_app(fun(dB, fun(dB, dB)), 
193.33/193.51	                     app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
193.33/193.51	                     foldl(dB, dB), app), 
193.33/193.51	                   app_encode_app(nat, dB, 
193.33/193.51	                     app_encode_app(dB, app_encode_fun(nat, dB), 
193.33/193.51	                       app_encode_app(dB, 
193.33/193.51	                         app_encode_fun(dB, app_encode_fun(nat, dB)), subst, 
193.33/193.51	                         X2), X1), zero_zero(nat))), X0)))),
193.33/193.51	    inference('demod', [status(thm)], ['14', '15'])).
193.33/193.51	tff('17', plain,
193.33/193.51	    (~ $true
193.33/193.51	     | ~ app_encode_app(bool, $o, pp, 
193.33/193.51	           app_encode_app(dB, bool, 
193.33/193.51	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
193.33/193.51	               aa(dB, bool), it), s))
193.33/193.51	     | app_encode_app(fun(dB, bool), $o, 
193.33/193.51	         app_encode_app(dB, app_encode_fun(fun(dB, bool), $o), member(dB), 
193.33/193.51	           app_encode_app(list(dB), dB, 
193.33/193.51	             app_encode_app(dB, app_encode_fun(list(dB), dB), 
193.33/193.51	               app_encode_app(fun(dB, fun(dB, dB)), 
193.33/193.51	                 app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
193.33/193.51	                 foldl(dB, dB), app), app_encode_app(dB, dB, abs, r)), 
193.33/193.51	             app_encode_app(list(dB), list(dB), 
193.33/193.51	               app_encode_app(dB, app_encode_fun(list(dB), list(dB)), 
193.33/193.51	                 cons(dB), s), 
193.33/193.51	               app_encode_app(list(dB), list(dB), rotate1(dB), 
193.33/193.51	                 app_encode_app(list(dB), list(dB), 
193.33/193.51	                   app_encode_app(dB, app_encode_fun(list(dB), list(dB)), 
193.33/193.51	                     cons(dB), app_encode_app(nat, dB, var, i)), ss))))), it)),
193.33/193.51	    inference('sup-', [status(thm)], ['10', '16'])).
193.33/193.51	tff(zf_stmt_145, axiom,
193.33/193.51	  (app_encode_app(bool,$o,pp,
193.33/193.51	                  app_encode_app(dB,bool,
193.33/193.51	                                 app_encode_app(fun(dB,bool),
193.33/193.51	                                                app_encode_fun(dB,bool),
193.33/193.51	                                                aa(dB,bool),it),
193.33/193.51	                                 s)))).
193.33/193.51	tff('18', plain,
193.33/193.51	    app_encode_app(bool, $o, pp, 
193.33/193.51	      app_encode_app(dB, bool, 
193.33/193.51	        app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
193.33/193.51	          aa(dB, bool), it), s)),
193.33/193.51	    inference('cnf', [status(esa)], [zf_stmt_145])).
193.33/193.51	tff(zf_stmt_112, axiom,
193.33/193.51	  (![A:$tType,Ys3:list(A),Xs:list(A),X:A]:
193.33/193.51	     (app_encode_app(list(A),list(A),
193.33/193.51	                     app_encode_app(list(A),app_encode_fun(list(A),list(A)),
193.33/193.51	                                    append(A),
193.33/193.51	                                    app_encode_app(list(A),list(A),
193.33/193.51	                                                   app_encode_app(A,
193.33/193.51	                                                                  app_encode_fun(
193.33/193.51	                                                                  list(A),
193.33/193.51	                                                                  list(A)),
193.33/193.51	                                                                  cons(A),X),
193.33/193.51	                                                   Xs)),
193.33/193.51	                     Ys3) =
193.33/193.51	      app_encode_app(list(A),list(A),
193.33/193.51	                     app_encode_app(A,app_encode_fun(list(A),list(A)),
193.33/193.51	                                    cons(A),X),
193.33/193.51	                     app_encode_app(list(A),list(A),
193.33/193.51	                                    app_encode_app(list(A),
193.33/193.51	                                                   app_encode_fun(list(A),
193.33/193.51	                                                                  list(A)),
193.33/193.51	                                                   append(A),Xs),
193.33/193.51	                                    Ys3))))).
193.33/193.51	tff('19', plain,
193.33/193.51	    ![X277 : $tType, X278 : X277, X279 : list(X277), X280 : list(X277)]:
193.33/193.51	      app_encode_app(list(X277), list(X277), 
193.33/193.51	        app_encode_app(list(X277), app_encode_fun(list(X277), list(X277)), 
193.33/193.51	          append(X277), 
193.33/193.51	          app_encode_app(list(X277), list(X277), 
193.33/193.51	            app_encode_app(X277, app_encode_fun(list(X277), list(X277)), 
193.33/193.51	              cons(X277), X278), X279)), X280)
193.33/193.51	       = app_encode_app(list(X277), list(X277), 
193.33/193.51	           app_encode_app(X277, app_encode_fun(list(X277), list(X277)), 
193.33/193.51	             cons(X277), X278), 
193.33/193.51	           app_encode_app(list(X277), list(X277), 
193.33/193.51	             app_encode_app(list(X277), 
193.33/193.51	               app_encode_fun(list(X277), list(X277)), append(X277), X279), 
193.33/193.51	             X280)),
193.33/193.51	    inference('cnf', [status(esa)], [zf_stmt_112])).
193.33/193.51	tff('20', plain,
193.33/193.51	    ![X0 : $tType, X1 : list(X0), X2 : X0, X3 : X0]:
193.33/193.51	      app_encode_app(list(X0), list(X0), rotate1(X0), 
193.33/193.51	        app_encode_app(list(X0), list(X0), 
193.33/193.51	          app_encode_app(X0, app_encode_fun(list(X0), list(X0)), cons(X0), 
193.33/193.51	            X3), 
193.33/193.51	          app_encode_app(list(X0), list(X0), 
193.33/193.51	            app_encode_app(X0, app_encode_fun(list(X0), list(X0)), cons(X0), 
193.33/193.51	              X2), X1)))
193.33/193.51	       = app_encode_app(list(X0), list(X0), 
193.33/193.51	           app_encode_app(X0, app_encode_fun(list(X0), list(X0)), cons(X0), 
193.33/193.51	             X2), 
193.33/193.51	           app_encode_app(list(X0), list(X0), 
193.33/193.51	             app_encode_app(list(X0), app_encode_fun(list(X0), list(X0)), 
193.33/193.51	               append(X0), X1), 
193.33/193.51	             app_encode_app(list(X0), list(X0), 
193.33/193.51	               app_encode_app(X0, app_encode_fun(list(X0), list(X0)), 
193.33/193.51	                 cons(X0), X3), nil(X0)))),
193.33/193.51	    inference('sup+', [status(thm)], ['3', '19'])).
193.33/193.51	tff('21', plain,
193.33/193.51	    ![X0 : $tType, X1 : list(X0), X2 : X0, X3 : X0]:
193.33/193.51	      app_encode_app(list(X0), list(X0), rotate1(X0), 
193.33/193.51	        app_encode_app(list(X0), list(X0), 
193.33/193.51	          app_encode_app(X0, app_encode_fun(list(X0), list(X0)), cons(X0), 
193.33/193.51	            X3), 
193.33/193.51	          app_encode_app(list(X0), list(X0), 
193.33/193.51	            app_encode_app(X0, app_encode_fun(list(X0), list(X0)), cons(X0), 
193.33/193.51	              X2), X1)))
193.33/193.51	       = app_encode_app(list(X0), list(X0), 
193.33/193.51	           app_encode_app(X0, app_encode_fun(list(X0), list(X0)), cons(X0), 
193.33/193.51	             X2), 
193.33/193.51	           app_encode_app(list(X0), list(X0), rotate1(X0), 
193.33/193.51	             app_encode_app(list(X0), list(X0), 
193.33/193.51	               app_encode_app(X0, app_encode_fun(list(X0), list(X0)), 
193.33/193.51	                 cons(X0), X3), X1))),
193.33/193.51	    inference('demod', [status(thm)], ['20', '3'])).
193.33/193.51	tff('22', plain,
193.33/193.51	    (~ $true
193.33/193.51	     | ~ $true
193.33/193.51	     | app_encode_app(fun(dB, bool), $o, 
193.33/193.51	         app_encode_app(dB, app_encode_fun(fun(dB, bool), $o), member(dB), 
193.33/193.51	           app_encode_app(list(dB), dB, 
193.33/193.51	             app_encode_app(dB, app_encode_fun(list(dB), dB), 
193.33/193.51	               app_encode_app(fun(dB, fun(dB, dB)), 
193.33/193.51	                 app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
193.33/193.51	                 foldl(dB, dB), app), app_encode_app(dB, dB, abs, r)), 
193.33/193.51	             app_encode_app(list(dB), list(dB), rotate1(dB), 
193.33/193.51	               app_encode_app(list(dB), list(dB), 
193.33/193.51	                 app_encode_app(dB, app_encode_fun(list(dB), list(dB)), 
193.33/193.51	                   cons(dB), app_encode_app(nat, dB, var, i)), 
193.33/193.51	                 app_encode_app(list(dB), list(dB), 
193.33/193.51	                   app_encode_app(dB, app_encode_fun(list(dB), list(dB)), 
193.33/193.51	                     cons(dB), s), ss))))), it)),
193.33/193.51	    inference('demod', [status(thm)], ['17', '18', '21'])).
193.33/193.51	tff('23', plain,
193.33/193.51	    app_encode_app(fun(dB, bool), $o, 
193.33/193.51	      app_encode_app(dB, app_encode_fun(fun(dB, bool), $o), member(dB), 
193.33/193.51	        app_encode_app(list(dB), dB, 
193.33/193.51	          app_encode_app(dB, app_encode_fun(list(dB), dB), 
193.33/193.51	            app_encode_app(fun(dB, fun(dB, dB)), 
193.33/193.51	              app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
193.33/193.51	              foldl(dB, dB), app), app_encode_app(dB, dB, abs, r)), 
193.33/193.51	          app_encode_app(list(dB), list(dB), rotate1(dB), 
193.33/193.51	            app_encode_app(list(dB), list(dB), 
193.33/193.51	              app_encode_app(dB, app_encode_fun(list(dB), list(dB)), 
193.33/193.51	                cons(dB), app_encode_app(nat, dB, var, i)), 
193.33/193.51	              app_encode_app(list(dB), list(dB), 
193.33/193.51	                app_encode_app(dB, app_encode_fun(list(dB), list(dB)), 
193.33/193.51	                  cons(dB), s), ss))))), it),
193.33/193.51	    inference('simplify', [status(thm)], ['22'])).
193.33/193.51	tff('24', plain,
193.33/193.51	    ![X293 : $tType, X294 : fun(X293, bool), X295 : X293]:
193.33/193.51	      (app_encode_app(bool, $o, pp, 
193.33/193.51	         app_encode_app(X293, bool, 
193.33/193.51	           app_encode_app(fun(X293, bool), app_encode_fun(X293, bool), 
193.33/193.51	             aa(X293, bool), X294), X295))
193.33/193.51	       | ~ app_encode_app(fun(X293, bool), $o, 
193.33/193.51	             app_encode_app(X293, app_encode_fun(fun(X293, bool), $o), 
193.33/193.51	               member(X293), X295), X294)),
193.33/193.51	    inference('cnf', [status(esa)], [zf_stmt_116])).
193.33/193.51	tff(zf_stmt_147, conjecture,
193.33/193.51	  (app_encode_app(bool,$o,pp,
193.33/193.51	                  app_encode_app(dB,bool,
193.33/193.51	                                 app_encode_app(fun(dB,bool),
193.33/193.51	                                                app_encode_fun(dB,bool),
193.33/193.51	                                                aa(dB,bool),it),
193.33/193.51	                                 app_encode_app(dB,dB,
193.33/193.51	                                                app_encode_app(fun(dB,dB),
193.33/193.51	                                                               app_encode_fun(
193.33/193.51	                                                               dB,dB),
193.33/193.51	                                                               aa(dB,dB),
193.33/193.51	                                                               app_encode_app(
193.33/193.51	                                                               dB,fun(dB,dB),
193.33/193.51	                                                               app_encode_app(
193.33/193.51	                                                               fun(dB,
193.33/193.51	                                                                   fun(dB,dB)),
193.33/193.51	                                                               app_encode_fun(
193.33/193.51	                                                               dB,fun(dB,dB)),
193.33/193.51	                                                               aa(dB,
193.33/193.51	                                                                  fun(dB,dB)),
193.33/193.51	                                                               app),
193.33/193.51	                                                               app_encode_app(
193.33/193.51	                                                               list(dB),dB,
193.33/193.51	                                                               app_encode_app(
193.33/193.51	                                                               dB,
193.33/193.51	                                                               app_encode_fun(
193.33/193.51	                                                               list(dB),dB),
193.33/193.51	                                                               app_encode_app(
193.33/193.51	                                                               fun(dB,
193.33/193.51	                                                                   fun(dB,dB)),
193.33/193.51	                                                               app_encode_fun(
193.33/193.51	                                                               dB,
193.33/193.51	                                                               app_encode_fun(
193.33/193.51	                                                               list(dB),dB)),
193.33/193.51	                                                               foldl(dB,dB),
193.33/193.51	                                                               app),
193.33/193.51	                                                               app_encode_app(
193.33/193.51	                                                               dB,dB,
193.33/193.51	                                                               app_encode_app(
193.33/193.51	                                                               fun(dB,dB),
193.33/193.51	                                                               app_encode_fun(
193.33/193.51	                                                               dB,dB),
193.33/193.51	                                                               aa(dB,dB),
193.33/193.51	                                                               app_encode_app(
193.33/193.51	                                                               dB,fun(dB,dB),
193.33/193.51	                                                               app_encode_app(
193.33/193.51	                                                               fun(dB,
193.33/193.51	                                                                   fun(dB,dB)),
193.33/193.51	                                                               app_encode_fun(
193.33/193.51	                                                               dB,fun(dB,dB)),
193.33/193.51	                                                               aa(dB,
193.33/193.51	                                                                  fun(dB,dB)),
193.33/193.51	                                                               app),
193.33/193.51	                                                               app_encode_app(
193.33/193.51	                                                               dB,dB,abs,r))),
193.33/193.51	                                                               s)),ss))),
193.33/193.51	                                                app_encode_app(nat,dB,var,i)))))).
193.33/193.51	tff(zf_stmt_0, negated_conjecture,
193.33/193.51	  (~
193.33/193.51	    app_encode_app(bool,$o,pp,
193.33/193.51	                   app_encode_app(dB,bool,
193.33/193.51	                                  app_encode_app(fun(dB,bool),
193.33/193.51	                                                 app_encode_fun(dB,bool),
193.33/193.51	                                                 aa(dB,bool),it),
193.33/193.51	                                  app_encode_app(dB,dB,
193.33/193.51	                                                 app_encode_app(fun(dB,dB),
193.33/193.51	                                                                app_encode_fun(
193.33/193.51	                                                                dB,dB),
193.33/193.51	                                                                aa(dB,dB),
193.33/193.51	                                                                app_encode_app(
193.33/193.51	                                                                dB,
193.33/193.51	                                                                fun(dB,dB),
193.33/193.51	                                                                app_encode_app(
193.33/193.51	                                                                fun(dB,
193.33/193.51	                                                                    fun(
193.33/193.51	                                                                    dB,dB)),
193.33/193.51	                                                                app_encode_fun(
193.33/193.51	                                                                dB,fun(dB,dB)),
193.33/193.51	                                                                aa(dB,
193.33/193.51	                                                                   fun(dB,dB)),
193.33/193.51	                                                                app),
193.33/193.51	                                                                app_encode_app(
193.33/193.51	                                                                list(dB),dB,
193.33/193.51	                                                                app_encode_app(
193.33/193.51	                                                                dB,
193.33/193.51	                                                                app_encode_fun(
193.33/193.51	                                                                list(dB),dB),
193.33/193.51	                                                                app_encode_app(
193.33/193.51	                                                                fun(dB,
193.33/193.51	                                                                    fun(
193.33/193.51	                                                                    dB,dB)),
193.33/193.51	                                                                app_encode_fun(
193.33/193.51	                                                                dB,
193.33/193.51	                                                                app_encode_fun(
193.33/193.51	                                                                list(dB),dB)),
193.33/193.51	                                                                foldl(dB,dB),
193.33/193.51	                                                                app),
193.33/193.51	                                                                app_encode_app(
193.33/193.51	                                                                dB,dB,
193.33/193.51	                                                                app_encode_app(
193.33/193.51	                                                                fun(dB,dB),
193.33/193.51	                                                                app_encode_fun(
193.33/193.51	                                                                dB,dB),
193.33/193.51	                                                                aa(dB,dB),
193.33/193.51	                                                                app_encode_app(
193.33/193.51	                                                                dB,
193.33/193.51	                                                                fun(dB,dB),
193.33/193.51	                                                                app_encode_app(
193.33/193.51	                                                                fun(dB,
193.33/193.51	                                                                    fun(
193.33/193.51	                                                                    dB,dB)),
193.33/193.51	                                                                app_encode_fun(
193.33/193.51	                                                                dB,fun(dB,dB)),
193.33/193.51	                                                                aa(dB,
193.33/193.51	                                                                   fun(dB,dB)),
193.33/193.51	                                                                app),
193.33/193.51	                                                                app_encode_app(
193.33/193.51	                                                                dB,dB,abs,r))),
193.33/193.51	                                                                s)),ss))),
193.33/193.51	                                                 app_encode_app(nat,dB,var,i)))))).
193.33/193.51	tff('25', plain,
193.33/193.51	    ~ app_encode_app(bool, $o, pp, 
193.33/193.51	        app_encode_app(dB, bool, 
193.33/193.51	          app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
193.33/193.51	            aa(dB, bool), it), 
193.33/193.51	          app_encode_app(dB, dB, 
193.33/193.51	            app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), aa(dB, dB), 
193.33/193.51	              app_encode_app(dB, fun(dB, dB), 
193.33/193.51	                app_encode_app(fun(dB, fun(dB, dB)), 
193.33/193.51	                  app_encode_fun(dB, fun(dB, dB)), aa(dB, fun(dB, dB)), app), 
193.33/193.51	                app_encode_app(list(dB), dB, 
193.33/193.51	                  app_encode_app(dB, app_encode_fun(list(dB), dB), 
193.33/193.51	                    app_encode_app(fun(dB, fun(dB, dB)), 
193.33/193.51	                      app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
193.33/193.51	                      foldl(dB, dB), app), 
193.33/193.51	                    app_encode_app(dB, dB, 
193.33/193.51	                      app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), 
193.33/193.51	                        aa(dB, dB), 
193.33/193.51	                        app_encode_app(dB, fun(dB, dB), 
193.33/193.51	                          app_encode_app(fun(dB, fun(dB, dB)), 
193.33/193.51	                            app_encode_fun(dB, fun(dB, dB)), 
193.33/193.51	                            aa(dB, fun(dB, dB)), app), 
193.33/193.51	                          app_encode_app(dB, dB, abs, r))), s)), ss))), 
193.33/193.51	            app_encode_app(nat, dB, var, i)))),
193.33/193.51	    inference('cnf', [status(esa)], [zf_stmt_0])).
193.33/193.51	tff('26', plain,
193.33/193.51	    ~ app_encode_app(bool, $o, pp, 
193.33/193.51	        app_encode_app(dB, bool, 
193.33/193.51	          app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
193.33/193.51	            aa(dB, bool), it), 
193.33/193.51	          app_encode_app(list(dB), dB, 
193.33/193.51	            app_encode_app(dB, app_encode_fun(list(dB), dB), 
193.33/193.51	              app_encode_app(fun(dB, fun(dB, dB)), 
193.33/193.51	                app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
193.33/193.51	                foldl(dB, dB), app), app_encode_app(dB, dB, abs, r)), 
193.33/193.51	            app_encode_app(list(dB), list(dB), rotate1(dB), 
193.33/193.51	              app_encode_app(list(dB), list(dB), 
193.33/193.51	                app_encode_app(dB, app_encode_fun(list(dB), list(dB)), 
193.33/193.51	                  cons(dB), app_encode_app(nat, dB, var, i)), 
193.33/193.51	                app_encode_app(list(dB), list(dB), 
193.33/193.51	                  app_encode_app(dB, app_encode_fun(list(dB), list(dB)), 
193.33/193.51	                    cons(dB), s), ss)))))),
193.33/193.51	    inference('demod', [status(thm)], ['25', '15', '9'])).
193.33/193.51	tff('27', plain,
193.33/193.51	    (~ $true
193.33/193.51	     | ~ app_encode_app(fun(dB, bool), $o, 
193.33/193.51	           app_encode_app(dB, app_encode_fun(fun(dB, bool), $o), member(dB), 
193.33/193.51	             app_encode_app(list(dB), dB, 
193.33/193.51	               app_encode_app(dB, app_encode_fun(list(dB), dB), 
193.33/193.51	                 app_encode_app(fun(dB, fun(dB, dB)), 
193.33/193.51	                   app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
193.33/193.51	                   foldl(dB, dB), app), app_encode_app(dB, dB, abs, r)), 
193.33/193.51	               app_encode_app(list(dB), list(dB), rotate1(dB), 
193.33/193.51	                 app_encode_app(list(dB), list(dB), 
193.33/193.51	                   app_encode_app(dB, app_encode_fun(list(dB), list(dB)), 
193.33/193.51	                     cons(dB), app_encode_app(nat, dB, var, i)), 
193.33/193.51	                   app_encode_app(list(dB), list(dB), 
193.33/193.51	                     app_encode_app(dB, app_encode_fun(list(dB), list(dB)), 
193.33/193.51	                       cons(dB), s), ss))))), it)),
193.33/193.51	    inference('sup-', [status(thm)], ['24', '26'])).
193.33/193.51	tff('28', plain,
193.33/193.51	    ~ app_encode_app(fun(dB, bool), $o, 
193.33/193.51	        app_encode_app(dB, app_encode_fun(fun(dB, bool), $o), member(dB), 
193.33/193.51	          app_encode_app(list(dB), dB, 
193.33/193.51	            app_encode_app(dB, app_encode_fun(list(dB), dB), 
193.33/193.51	              app_encode_app(fun(dB, fun(dB, dB)), 
193.33/193.51	                app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
193.33/193.51	                foldl(dB, dB), app), app_encode_app(dB, dB, abs, r)), 
193.33/193.51	            app_encode_app(list(dB), list(dB), rotate1(dB), 
193.33/193.51	              app_encode_app(list(dB), list(dB), 
193.33/193.51	                app_encode_app(dB, app_encode_fun(list(dB), list(dB)), 
193.33/193.51	                  cons(dB), app_encode_app(nat, dB, var, i)), 
193.33/193.51	                app_encode_app(list(dB), list(dB), 
193.33/193.51	                  app_encode_app(dB, app_encode_fun(list(dB), list(dB)), 
193.33/193.51	                    cons(dB), s), ss))))), it),
193.33/193.51	    inference('simplify', [status(thm)], ['27'])).
193.33/193.51	tff('29', plain, ~ $true, inference('sup-', [status(thm)], ['23', '28'])).
193.33/193.51	tff('30', plain, $false, inference('simplify', [status(thm)], ['29'])).
193.33/193.51	
193.33/193.51	% SZS output end Refutation
193.33/193.52	EOF
