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 $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n156.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 07:28:08 CST 2018
27.18/27.37	% done 2470 iterations in 27.170s
27.18/27.37	% SZS status Theorem for 'stdin'
27.18/27.37	% SZS output start Refutation
27.18/27.37	tff(zf_stmt_162, axiom, (![P:bool]: ((P = fTrue) | (P = fFalse)))).
27.18/27.37	tff('0', plain, ![X377 : bool]: (X377 = fTrue | X377 = fFalse),
27.18/27.37	    inference('cnf', [status(esa)], [zf_stmt_162])).
27.18/27.37	tff('1', plain, ![X0 : bool, X1 : bool]: (X1 = X0 | X0 = fTrue | X1 = fTrue),
27.18/27.37	    inference('sup+', [status(thm)], ['0', '0'])).
27.18/27.37	tff(zf_stmt_155, axiom, (app_encode_app(bool,$o,pp,fTrue))).
27.18/27.37	tff('2', plain, app_encode_app(bool, $o, pp, fTrue),
27.18/27.37	    inference('cnf', [status(esa)], [zf_stmt_155])).
27.18/27.37	tff('3', plain,
27.18/27.37	    ![X0 : bool, X1 : bool]:
27.18/27.37	      (app_encode_app(bool, $o, pp, X0) | X1 = fTrue | X1 = X0),
27.18/27.37	    inference('sup+', [status(thm)], ['1', '2'])).
27.18/27.37	tff(zf_stmt_118, axiom,
27.18/27.37	  (![A:$tType,Y1:list(A)]:
27.18/27.37	     ((Y1 != nil(A)) =>
27.18/27.37	      (~
27.18/27.37	        (![A2:A,List:list(A)]:
27.18/27.37	           (Y1 !=
27.18/27.37	            app_encode_app(list(A),list(A),
27.18/27.37	                           app_encode_app(A,app_encode_fun(list(A),list(A)),
27.18/27.37	                                          cons(A),A2),
27.18/27.37	                           List))))))).
27.18/27.37	tff('4', plain,
27.18/27.37	    ![X232 : $tType, X233 : list(X232)]:
27.18/27.37	      (X233
27.18/27.37	        = app_encode_app(list(X232), list(X232), 
27.18/27.37	            app_encode_app(X232, app_encode_fun(list(X232), list(X232)), 
27.18/27.37	              cons(X232), sk_A2(X232, X233)), sk_List(X232, X233))
27.18/27.37	       | X233 = nil(X232)),
27.18/27.37	    inference('cnf', [status(esa)], [zf_stmt_118])).
27.18/27.37	tff(zf_stmt_117, axiom,
27.18/27.37	  (![A:$tType,Xs:list(A)]:
27.18/27.37	     ((Xs != nil(A)) <=>
27.18/27.37	      (?[Y2:A,Ys1:list(A)]:
27.18/27.37	         (Xs =
27.18/27.37	          app_encode_app(list(A),list(A),
27.18/27.37	                         app_encode_app(A,app_encode_fun(list(A),list(A)),
27.18/27.37	                                        cons(A),Y2),
27.18/27.37	                         Ys1)))))).
27.18/27.37	tff('5', plain,
27.18/27.37	    ![X227 : $tType, X228 : list(X227)]:
27.18/27.37	      (X228
27.18/27.37	        = app_encode_app(list(X227), list(X227), 
27.18/27.37	            app_encode_app(X227, app_encode_fun(list(X227), list(X227)), 
27.18/27.37	              cons(X227), sk_Y2(X227, X228)), sk_Ys1(X227, X228))
27.18/27.37	       | X228 = nil(X227)),
27.18/27.37	    inference('cnf', [status(esa)], [zf_stmt_117])).
27.18/27.37	tff(zf_stmt_109, axiom,
27.18/27.37	  (![A:$tType,List3:list(A),A4:A,List2:list(A),Aa:A]:
27.18/27.37	     ((app_encode_app(list(A),list(A),
27.18/27.37	                      app_encode_app(A,app_encode_fun(list(A),list(A)),
27.18/27.37	                                     cons(A),Aa),
27.18/27.37	                      List2) =
27.18/27.37	       app_encode_app(list(A),list(A),
27.18/27.37	                      app_encode_app(A,app_encode_fun(list(A),list(A)),
27.18/27.37	                                     cons(A),A4),
27.18/27.37	                      List3)) <=>
27.18/27.37	      ((Aa = A4) & (List2 = List3))))).
27.18/27.37	tff('6', plain,
27.18/27.37	    ![X190 : $tType, X191 : X190, X192 : X190, X193 : list(X190), 
27.18/27.37	      X194 : list(X190)]:
27.18/27.37	      (X192 = X191
27.18/27.37	       | app_encode_app(list(X190), list(X190), 
27.18/27.37	           app_encode_app(X190, app_encode_fun(list(X190), list(X190)), 
27.18/27.37	             cons(X190), X192), X194)
27.18/27.37	          != app_encode_app(list(X190), list(X190), 
27.18/27.37	               app_encode_app(X190, app_encode_fun(list(X190), list(X190)), 
27.18/27.37	                 cons(X190), X191), X193)),
27.18/27.37	    inference('cnf', [status(esa)], [zf_stmt_109])).
27.18/27.37	tff('7', plain,
27.18/27.37	    ![X0 : $tType, X1 : list(X0), X2 : list(X0), X3 : X0]:
27.18/27.37	      (X1
27.18/27.37	        != app_encode_app(list(X0), list(X0), 
27.18/27.37	             app_encode_app(X0, app_encode_fun(list(X0), list(X0)), 
27.18/27.37	               cons(X0), X3), X2)
27.18/27.37	       | X1 = nil(X0)
27.18/27.37	       | sk_Y2(X0, X1) = X3),
27.18/27.37	    inference('sup-', [status(thm)], ['5', '6'])).
27.18/27.37	tff('8', plain,
27.18/27.37	    ![X0 : $tType, X2 : list(X0), X3 : X0]:
27.18/27.37	      (sk_Y2(X0, 
27.18/27.37	         app_encode_app(list(X0), list(X0), 
27.18/27.37	           app_encode_app(X0, app_encode_fun(list(X0), list(X0)), cons(X0), 
27.18/27.37	             X3), X2))
27.18/27.37	        = X3
27.18/27.37	       | app_encode_app(list(X0), list(X0), 
27.18/27.37	           app_encode_app(X0, app_encode_fun(list(X0), list(X0)), cons(X0), 
27.18/27.37	             X3), X2)
27.18/27.37	          = nil(X0)),
27.18/27.37	    inference('simplify', [status(thm)], ['7'])).
27.18/27.37	tff(zf_stmt_115, axiom,
27.18/27.37	  (![A:$tType,List1:list(A),A3:A]:
27.18/27.37	     (nil(A) !=
27.18/27.37	      app_encode_app(list(A),list(A),
27.18/27.37	                     app_encode_app(A,app_encode_fun(list(A),list(A)),
27.18/27.37	                                    cons(A),A3),
27.18/27.37	                     List1)))).
27.18/27.37	tff('9', plain,
27.18/27.37	    ![X221 : $tType, X222 : X221, X223 : list(X221)]:
27.18/27.37	      nil(X221)
27.18/27.37	       != app_encode_app(list(X221), list(X221), 
27.18/27.37	            app_encode_app(X221, app_encode_fun(list(X221), list(X221)), 
27.18/27.37	              cons(X221), X222), X223),
27.18/27.37	    inference('cnf', [status(esa)], [zf_stmt_115])).
27.18/27.37	tff('10', plain,
27.18/27.37	    ![X0 : $tType, X2 : list(X0), X3 : X0]:
27.18/27.37	      sk_Y2(X0, 
27.18/27.37	        app_encode_app(list(X0), list(X0), 
27.18/27.37	          app_encode_app(X0, app_encode_fun(list(X0), list(X0)), cons(X0), 
27.18/27.37	            X3), X2))
27.18/27.37	       = X3,
27.18/27.37	    inference('clc', [status(thm)], ['8', '9'])).
27.18/27.37	tff('11', plain,
27.18/27.37	    ![X0 : $tType, X1 : list(X0)]:
27.18/27.37	      (sk_Y2(X0, X1) = sk_A2(X0, X1) | X1 = nil(X0)),
27.18/27.37	    inference('sup+', [status(thm)], ['4', '10'])).
27.18/27.37	tff('12', plain,
27.18/27.37	    ![X0 : bool, X1 : list(bool)]:
27.18/27.37	      (X0 = sk_A2(bool, X1)
27.18/27.37	       | X0 = fTrue
27.18/27.37	       | app_encode_app(bool, $o, pp, sk_Y2(bool, X1))
27.18/27.37	       | X1 = nil(bool)),
27.18/27.37	    inference('sup+', [status(thm)], ['3', '11'])).
27.18/27.37	tff('13', plain,
27.18/27.37	    ![X0 : list(bool), X1 : bool]:
27.18/27.37	      (sk_A2(bool, X0) != fTrue
27.18/27.37	       | X0 = nil(bool)
27.18/27.37	       | app_encode_app(bool, $o, pp, sk_Y2(bool, X0))
27.18/27.37	       | X1 = fTrue),
27.18/27.37	    inference('eq_fact', [status(thm)], ['12'])).
27.18/27.37	tff(zf_stmt_163, conjecture,
27.18/27.37	  (app_encode_app(bool,$o,pp,
27.18/27.37	                  app_encode_app(dB,bool,
27.18/27.37	                                 app_encode_app(fun(dB,bool),
27.18/27.37	                                                app_encode_fun(dB,bool),
27.18/27.37	                                                aa(dB,bool),
27.18/27.37	                                                app_encode_app(dB,
27.18/27.37	                                                               fun(dB,bool),
27.18/27.37	                                                               app_encode_app(
27.18/27.37	                                                               fun(dB,
27.18/27.37	                                                                   fun(
27.18/27.37	                                                                   dB,bool)),
27.18/27.37	                                                               app_encode_fun(
27.18/27.37	                                                               dB,
27.18/27.37	                                                               fun(dB,bool)),
27.18/27.37	                                                               aa(dB,
27.18/27.37	                                                                  fun(
27.18/27.37	                                                                  dB,bool)),
27.18/27.37	                                                               beta),
27.18/27.37	                                                               app_encode_app(
27.18/27.37	                                                               list(dB),dB,
27.18/27.37	                                                               app_encode_app(
27.18/27.37	                                                               dB,
27.18/27.37	                                                               app_encode_fun(
27.18/27.37	                                                               list(dB),dB),
27.18/27.37	                                                               app_encode_app(
27.18/27.37	                                                               fun(dB,
27.18/27.37	                                                                   fun(dB,dB)),
27.18/27.37	                                                               app_encode_fun(
27.18/27.37	                                                               dB,
27.18/27.37	                                                               app_encode_fun(
27.18/27.37	                                                               list(dB),dB)),
27.18/27.37	                                                               foldl(dB,dB),
27.18/27.37	                                                               app),
27.18/27.37	                                                               app_encode_app(
27.18/27.37	                                                               dB,dB,
27.18/27.37	                                                               app_encode_app(
27.18/27.37	                                                               fun(dB,dB),
27.18/27.37	                                                               app_encode_fun(
27.18/27.37	                                                               dB,dB),
27.18/27.37	                                                               aa(dB,dB),
27.18/27.37	                                                               app_encode_app(
27.18/27.37	                                                               dB,fun(dB,dB),
27.18/27.37	                                                               app_encode_app(
27.18/27.37	                                                               fun(dB,
27.18/27.37	                                                                   fun(dB,dB)),
27.18/27.37	                                                               app_encode_fun(
27.18/27.37	                                                               dB,fun(dB,dB)),
27.18/27.37	                                                               aa(dB,
27.18/27.37	                                                                  fun(dB,dB)),
27.18/27.37	                                                               app),
27.18/27.37	                                                               app_encode_app(
27.18/27.37	                                                               dB,dB,abs,r))),
27.18/27.37	                                                               a)),as))),
27.18/27.37	                                 app_encode_app(list(dB),dB,
27.18/27.37	                                                app_encode_app(dB,
27.18/27.37	                                                               app_encode_fun(
27.18/27.37	                                                               list(dB),dB),
27.18/27.37	                                                               app_encode_app(
27.18/27.37	                                                               fun(dB,
27.18/27.37	                                                                   fun(dB,dB)),
27.18/27.37	                                                               app_encode_fun(
27.18/27.37	                                                               dB,
27.18/27.37	                                                               app_encode_fun(
27.18/27.37	                                                               list(dB),dB)),
27.18/27.37	                                                               foldl(dB,dB),
27.18/27.37	                                                               app),
27.18/27.37	                                                               app_encode_app(
27.18/27.37	                                                               nat,dB,
27.18/27.37	                                                               app_encode_app(
27.18/27.37	                                                               dB,
27.18/27.37	                                                               app_encode_fun(
27.18/27.37	                                                               nat,dB),
27.18/27.37	                                                               app_encode_app(
27.18/27.37	                                                               dB,
27.18/27.37	                                                               app_encode_fun(
27.18/27.37	                                                               dB,
27.18/27.37	                                                               app_encode_fun(
27.18/27.37	                                                               nat,dB)),
27.18/27.37	                                                               subst,r),a),
27.18/27.37	                                                               zero_zero(nat))),
27.18/27.37	                                                as))))).
27.18/27.37	tff(zf_stmt_0, negated_conjecture,
27.18/27.37	  (~
27.18/27.37	    app_encode_app(bool,$o,pp,
27.18/27.37	                   app_encode_app(dB,bool,
27.18/27.37	                                  app_encode_app(fun(dB,bool),
27.18/27.37	                                                 app_encode_fun(dB,bool),
27.18/27.37	                                                 aa(dB,bool),
27.18/27.37	                                                 app_encode_app(dB,
27.18/27.37	                                                                fun(dB,bool),
27.18/27.37	                                                                app_encode_app(
27.18/27.37	                                                                fun(dB,
27.18/27.37	                                                                    fun(
27.18/27.37	                                                                    dB,bool)),
27.18/27.37	                                                                app_encode_fun(
27.18/27.37	                                                                dB,
27.18/27.37	                                                                fun(dB,bool)),
27.18/27.37	                                                                aa(dB,
27.18/27.38	                                                                   fun(
27.18/27.38	                                                                   dB,bool)),
27.18/27.38	                                                                beta),
27.18/27.38	                                                                app_encode_app(
27.18/27.38	                                                                list(dB),dB,
27.18/27.38	                                                                app_encode_app(
27.18/27.38	                                                                dB,
27.18/27.38	                                                                app_encode_fun(
27.18/27.38	                                                                list(dB),dB),
27.18/27.38	                                                                app_encode_app(
27.18/27.38	                                                                fun(dB,
27.18/27.38	                                                                    fun(
27.18/27.38	                                                                    dB,dB)),
27.18/27.38	                                                                app_encode_fun(
27.18/27.38	                                                                dB,
27.18/27.38	                                                                app_encode_fun(
27.18/27.38	                                                                list(dB),dB)),
27.18/27.38	                                                                foldl(dB,dB),
27.18/27.38	                                                                app),
27.18/27.38	                                                                app_encode_app(
27.18/27.38	                                                                dB,dB,
27.18/27.38	                                                                app_encode_app(
27.18/27.38	                                                                fun(dB,dB),
27.18/27.38	                                                                app_encode_fun(
27.18/27.38	                                                                dB,dB),
27.18/27.38	                                                                aa(dB,dB),
27.18/27.38	                                                                app_encode_app(
27.18/27.38	                                                                dB,
27.18/27.38	                                                                fun(dB,dB),
27.18/27.38	                                                                app_encode_app(
27.18/27.38	                                                                fun(dB,
27.18/27.38	                                                                    fun(
27.18/27.38	                                                                    dB,dB)),
27.18/27.38	                                                                app_encode_fun(
27.18/27.38	                                                                dB,fun(dB,dB)),
27.18/27.38	                                                                aa(dB,
27.18/27.38	                                                                   fun(dB,dB)),
27.18/27.38	                                                                app),
27.18/27.38	                                                                app_encode_app(
27.18/27.38	                                                                dB,dB,abs,r))),
27.18/27.38	                                                                a)),as))),
27.18/27.38	                                  app_encode_app(list(dB),dB,
27.18/27.38	                                                 app_encode_app(dB,
27.18/27.38	                                                                app_encode_fun(
27.18/27.38	                                                                list(dB),dB),
27.18/27.38	                                                                app_encode_app(
27.18/27.38	                                                                fun(dB,
27.18/27.38	                                                                    fun(
27.18/27.38	                                                                    dB,dB)),
27.18/27.38	                                                                app_encode_fun(
27.18/27.38	                                                                dB,
27.18/27.38	                                                                app_encode_fun(
27.18/27.38	                                                                list(dB),dB)),
27.18/27.38	                                                                foldl(dB,dB),
27.18/27.38	                                                                app),
27.18/27.38	                                                                app_encode_app(
27.18/27.38	                                                                nat,dB,
27.18/27.38	                                                                app_encode_app(
27.18/27.38	                                                                dB,
27.18/27.38	                                                                app_encode_fun(
27.18/27.38	                                                                nat,dB),
27.18/27.38	                                                                app_encode_app(
27.18/27.38	                                                                dB,
27.18/27.38	                                                                app_encode_fun(
27.18/27.38	                                                                dB,
27.18/27.38	                                                                app_encode_fun(
27.18/27.38	                                                                nat,dB)),
27.18/27.38	                                                                subst,r),a),
27.18/27.38	                                                                zero_zero(
27.18/27.38	                                                                nat))),
27.18/27.38	                                                 as))))).
27.18/27.38	tff('14', plain,
27.18/27.38	    ~ app_encode_app(bool, $o, pp, 
27.18/27.38	        app_encode_app(dB, bool, 
27.18/27.38	          app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
27.18/27.38	            aa(dB, bool), 
27.18/27.38	            app_encode_app(dB, fun(dB, bool), 
27.18/27.38	              app_encode_app(fun(dB, fun(dB, bool)), 
27.18/27.38	                app_encode_fun(dB, fun(dB, bool)), aa(dB, fun(dB, bool)), 
27.18/27.38	                beta), 
27.18/27.38	              app_encode_app(list(dB), dB, 
27.18/27.38	                app_encode_app(dB, app_encode_fun(list(dB), dB), 
27.18/27.38	                  app_encode_app(fun(dB, fun(dB, dB)), 
27.18/27.38	                    app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
27.18/27.38	                    foldl(dB, dB), app), 
27.18/27.38	                  app_encode_app(dB, dB, 
27.18/27.38	                    app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), 
27.18/27.38	                      aa(dB, dB), 
27.18/27.38	                      app_encode_app(dB, fun(dB, dB), 
27.18/27.38	                        app_encode_app(fun(dB, fun(dB, dB)), 
27.18/27.38	                          app_encode_fun(dB, fun(dB, dB)), 
27.18/27.38	                          aa(dB, fun(dB, dB)), app), 
27.18/27.38	                        app_encode_app(dB, dB, abs, r))), a)), as))), 
27.18/27.38	          app_encode_app(list(dB), dB, 
27.18/27.38	            app_encode_app(dB, app_encode_fun(list(dB), dB), 
27.18/27.38	              app_encode_app(fun(dB, fun(dB, dB)), 
27.18/27.38	                app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
27.18/27.38	                foldl(dB, dB), app), 
27.18/27.38	              app_encode_app(nat, dB, 
27.18/27.38	                app_encode_app(dB, app_encode_fun(nat, dB), 
27.18/27.38	                  app_encode_app(dB, 
27.18/27.38	                    app_encode_fun(dB, app_encode_fun(nat, dB)), subst, r), 
27.18/27.38	                  a), zero_zero(nat))), as))),
27.18/27.38	    inference('cnf', [status(esa)], [zf_stmt_0])).
27.18/27.38	tff(zf_stmt_157, axiom,
27.18/27.38	  (![A:$tType,C:$tType,B:$tType,R:A,Q:B,P:fun(A,fun(B,C))]:
27.18/27.38	     (app_encode_app(A,C,
27.18/27.38	                     app_encode_app(fun(A,C),app_encode_fun(A,C),aa(A,C),
27.18/27.38	                                    app_encode_app(B,fun(A,C),
27.18/27.38	                                                   app_encode_app(fun(
27.18/27.38	                                                                  A,fun(B,C)),
27.18/27.38	                                                                  app_encode_fun(
27.18/27.38	                                                                  B,fun(A,C)),
27.18/27.38	                                                                  combc(
27.18/27.38	                                                                  A,B,C),P),
27.18/27.38	                                                   Q)),
27.18/27.38	                     R) =
27.18/27.38	      app_encode_app(B,C,
27.18/27.38	                     app_encode_app(fun(B,C),app_encode_fun(B,C),aa(B,C),
27.18/27.38	                                    app_encode_app(A,fun(B,C),
27.18/27.38	                                                   app_encode_app(fun(
27.18/27.38	                                                                  A,fun(B,C)),
27.18/27.38	                                                                  app_encode_fun(
27.18/27.38	                                                                  A,fun(B,C)),
27.18/27.38	                                                                  aa(
27.18/27.38	                                                                  A,fun(B,C)),
27.18/27.38	                                                                  P),
27.18/27.38	                                                   R)),
27.18/27.38	                     Q)))).
27.18/27.38	tff('15', plain,
27.18/27.38	    ![X365 : $tType, X366 : $tType, X367 : $tType, 
27.18/27.38	      X368 : fun(X367, fun(X365, X366)), X369 : X367, X370 : X365]:
27.18/27.38	      app_encode_app(X367, X366, 
27.18/27.38	        app_encode_app(fun(X367, X366), app_encode_fun(X367, X366), 
27.18/27.38	          aa(X367, X366), 
27.18/27.38	          app_encode_app(X365, fun(X367, X366), 
27.18/27.38	            app_encode_app(fun(X367, fun(X365, X366)), 
27.18/27.38	              app_encode_fun(X365, fun(X367, X366)), 
27.18/27.38	              combc(X367, X365, X366), X368), X370)), X369)
27.18/27.38	       = app_encode_app(X365, X366, 
27.18/27.38	           app_encode_app(fun(X365, X366), app_encode_fun(X365, X366), 
27.18/27.38	             aa(X365, X366), 
27.18/27.38	             app_encode_app(X367, fun(X365, X366), 
27.18/27.38	               app_encode_app(fun(X367, fun(X365, X366)), 
27.18/27.38	                 app_encode_fun(X367, fun(X365, X366)), 
27.18/27.38	                 aa(X367, fun(X365, X366)), X368), X369)), X370),
27.18/27.38	    inference('cnf', [status(esa)], [zf_stmt_157])).
27.18/27.38	tff('16', plain,
27.18/27.38	    ~ app_encode_app(bool, $o, pp, 
27.18/27.38	        app_encode_app(dB, bool, 
27.18/27.38	          app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
27.18/27.38	            aa(dB, bool), 
27.18/27.38	            app_encode_app(dB, fun(dB, bool), 
27.18/27.38	              app_encode_app(fun(dB, fun(dB, bool)), 
27.18/27.38	                app_encode_fun(dB, fun(dB, bool)), combc(dB, dB, bool), beta), 
27.18/27.38	              app_encode_app(list(dB), dB, 
27.18/27.38	                app_encode_app(dB, app_encode_fun(list(dB), dB), 
27.18/27.38	                  app_encode_app(fun(dB, fun(dB, dB)), 
27.18/27.38	                    app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
27.18/27.38	                    foldl(dB, dB), app), 
27.18/27.38	                  app_encode_app(nat, dB, 
27.18/27.38	                    app_encode_app(dB, app_encode_fun(nat, dB), 
27.18/27.38	                      app_encode_app(dB, 
27.18/27.38	                        app_encode_fun(dB, app_encode_fun(nat, dB)), subst, 
27.18/27.38	                        r), a), zero_zero(nat))), as))), 
27.18/27.38	          app_encode_app(list(dB), dB, 
27.18/27.38	            app_encode_app(dB, app_encode_fun(list(dB), dB), 
27.18/27.38	              app_encode_app(fun(dB, fun(dB, dB)), 
27.18/27.38	                app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
27.18/27.38	                foldl(dB, dB), app), 
27.18/27.38	              app_encode_app(dB, dB, 
27.18/27.38	                app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), 
27.18/27.38	                  aa(dB, dB), 
27.18/27.38	                  app_encode_app(dB, fun(dB, dB), 
27.18/27.38	                    app_encode_app(fun(dB, fun(dB, dB)), 
27.18/27.38	                      app_encode_fun(dB, fun(dB, dB)), combc(dB, dB, dB), 
27.18/27.38	                      app), a)), app_encode_app(dB, dB, abs, r))), as))),
27.18/27.38	    inference('demod', [status(thm)], ['14', '15', '15'])).
27.18/27.38	tff('17', plain,
27.18/27.38	    ![X0 : list(bool)]:
27.18/27.38	      (~ app_encode_app(bool, $o, pp, fTrue)
27.18/27.38	       | app_encode_app(bool, $o, pp, sk_Y2(bool, X0))
27.18/27.38	       | X0 = nil(bool)
27.18/27.38	       | sk_A2(bool, X0) != fTrue),
27.18/27.38	    inference('sup-', [status(thm)], ['13', '16'])).
27.18/27.38	tff('18', plain,
27.18/27.38	    ![X0 : list(bool)]:
27.18/27.38	      (~ $true
27.18/27.38	       | app_encode_app(bool, $o, pp, sk_Y2(bool, X0))
27.18/27.38	       | X0 = nil(bool)
27.18/27.38	       | sk_A2(bool, X0) != fTrue),
27.18/27.38	    inference('demod', [status(thm)], ['17', '2'])).
27.18/27.38	tff('19', plain,
27.18/27.38	    ![X0 : list(bool)]:
27.18/27.38	      (sk_A2(bool, X0) != fTrue
27.18/27.38	       | X0 = nil(bool)
27.18/27.38	       | app_encode_app(bool, $o, pp, sk_Y2(bool, X0))),
27.18/27.38	    inference('simplify', [status(thm)], ['18'])).
27.18/27.38	tff(zf_stmt_154, axiom, (~app_encode_app(bool,$o,pp,fFalse))).
27.18/27.38	tff('20', plain, ~ app_encode_app(bool, $o, pp, fFalse),
27.18/27.38	    inference('cnf', [status(esa)], [zf_stmt_154])).
27.18/27.38	tff('21', plain,
27.18/27.38	    ![X0 : bool]: (~ app_encode_app(bool, $o, pp, X0) | X0 = fTrue),
27.18/27.38	    inference('sup-', [status(thm)], ['0', '20'])).
27.18/27.38	tff('22', plain,
27.18/27.38	    ![X0 : list(bool)]:
27.18/27.38	      (~ $true
27.18/27.38	       | X0 = nil(bool)
27.18/27.38	       | sk_A2(bool, X0) != fTrue
27.18/27.38	       | sk_Y2(bool, X0) = fTrue),
27.18/27.38	    inference('sup-', [status(thm)], ['19', '21'])).
27.18/27.38	tff('23', plain,
27.18/27.38	    ![X0 : list(bool)]:
27.18/27.38	      (sk_Y2(bool, X0) = fTrue | sk_A2(bool, X0) != fTrue | X0 = nil(bool)),
27.18/27.38	    inference('simplify', [status(thm)], ['22'])).
27.18/27.38	tff('24', plain,
27.18/27.38	    ![X0 : bool, X1 : bool]: (X1 = X0 | X0 = fFalse | X1 = fFalse),
27.18/27.38	    inference('sup+', [status(thm)], ['0', '0'])).
27.18/27.38	tff('25', plain,
27.18/27.38	    ![X0 : bool, X1 : bool]:
27.18/27.38	      (~ app_encode_app(bool, $o, pp, X0) | X1 = fFalse | X1 = X0),
27.18/27.38	    inference('sup-', [status(thm)], ['24', '20'])).
27.18/27.38	tff('26', plain,
27.18/27.38	    ![X0 : list(bool), X1 : bool]:
27.18/27.38	      (~ $true
27.18/27.38	       | X0 = nil(bool)
27.18/27.38	       | sk_A2(bool, X0) != fTrue
27.18/27.38	       | X1 = sk_Y2(bool, X0)
27.18/27.38	       | X1 = fFalse),
27.18/27.38	    inference('sup-', [status(thm)], ['19', '25'])).
27.18/27.38	tff('27', plain,
27.18/27.38	    ![X0 : list(bool), X1 : bool]:
27.18/27.38	      (X1 = fFalse
27.18/27.38	       | X1 = sk_Y2(bool, X0)
27.18/27.38	       | sk_A2(bool, X0) != fTrue
27.18/27.38	       | X0 = nil(bool)),
27.18/27.38	    inference('simplify', [status(thm)], ['26'])).
27.18/27.38	tff('28', plain,
27.18/27.38	    ![X0 : bool, X1 : list(bool)]:
27.18/27.38	      (fFalse != sk_Y2(bool, X1)
27.18/27.38	       | X1 = nil(bool)
27.18/27.38	       | sk_A2(bool, X1) != fTrue
27.18/27.38	       | X0 = sk_Y2(bool, X1)),
27.18/27.38	    inference('eq_fact', [status(thm)], ['27'])).
27.18/27.38	tff('29', plain,
27.18/27.38	    ![X0 : list(bool), X1 : bool]:
27.18/27.38	      (fFalse != fTrue
27.18/27.38	       | X0 = nil(bool)
27.18/27.38	       | sk_A2(bool, X0) != fTrue
27.18/27.38	       | X1 = sk_Y2(bool, X0)
27.18/27.38	       | sk_A2(bool, X0) != fTrue
27.18/27.38	       | X0 = nil(bool)),
27.18/27.38	    inference('sup-', [status(thm)], ['23', '28'])).
27.18/27.38	tff('30', plain,
27.18/27.38	    ![X0 : list(bool), X1 : bool]:
27.18/27.38	      (X1 = sk_Y2(bool, X0)
27.18/27.38	       | sk_A2(bool, X0) != fTrue
27.18/27.38	       | X0 = nil(bool)
27.18/27.38	       | fFalse != fTrue),
27.18/27.38	    inference('simplify', [status(thm)], ['29'])).
27.18/27.38	tff('31', plain,
27.18/27.38	    ![X0 : bool, X1 : list(bool)]:
27.18/27.38	      (app_encode_app(bool, $o, pp, X0)
27.18/27.38	       | fFalse != fTrue
27.18/27.38	       | X1 = nil(bool)
27.18/27.38	       | sk_A2(bool, X1) != fTrue
27.18/27.38	       | X1 = nil(bool)
27.18/27.38	       | sk_A2(bool, X1) != fTrue),
27.18/27.38	    inference('sup+', [status(thm)], ['30', '19'])).
27.18/27.38	tff('32', plain,
27.18/27.38	    ![X0 : bool, X1 : list(bool)]:
27.18/27.38	      (sk_A2(bool, X1) != fTrue
27.18/27.38	       | X1 = nil(bool)
27.18/27.38	       | fFalse != fTrue
27.18/27.38	       | app_encode_app(bool, $o, pp, X0)),
27.18/27.38	    inference('simplify', [status(thm)], ['31'])).
27.18/27.38	tff('33', plain, ![X0 : bool]: (fFalse != fTrue | X0 = fTrue),
27.18/27.38	    inference('eq_fact', [status(thm)], ['0'])).
27.18/27.38	tff('34', plain,
27.18/27.38	    ![X0 : bool, X1 : list(bool)]:
27.18/27.38	      (app_encode_app(bool, $o, pp, X0) | fFalse != fTrue | X1 = nil(bool)),
27.18/27.38	    inference('clc', [status(thm)], ['32', '33'])).
27.18/27.38	tff('35', plain,
27.18/27.38	    ![X0 : list(bool)]: (~ $true | X0 = nil(bool) | fFalse != fTrue),
27.18/27.38	    inference('sup-', [status(thm)], ['34', '16'])).
27.18/27.38	tff('36', plain, ![X0 : list(bool)]: (fFalse != fTrue | X0 = nil(bool)),
27.18/27.38	    inference('simplify', [status(thm)], ['35'])).
27.18/27.38	tff(zf_stmt_120, axiom,
27.18/27.38	  (![A:$tType,X2:A]:
27.18/27.38	     (app_encode_app(list(A),list(A),
27.18/27.38	                     app_encode_app(A,app_encode_fun(list(A),list(A)),
27.18/27.38	                                    insert(A),X2),
27.18/27.38	                     nil(A)) =
27.18/27.38	      app_encode_app(list(A),list(A),
27.18/27.38	                     app_encode_app(A,app_encode_fun(list(A),list(A)),
27.18/27.38	                                    cons(A),X2),
27.18/27.38	                     nil(A))))).
27.18/27.38	tff('37', plain,
27.18/27.38	    ![X246 : $tType, X247 : X246]:
27.18/27.38	      app_encode_app(list(X246), list(X246), 
27.18/27.38	        app_encode_app(X246, app_encode_fun(list(X246), list(X246)), 
27.18/27.38	          insert(X246), X247), nil(X246))
27.18/27.38	       = app_encode_app(list(X246), list(X246), 
27.18/27.38	           app_encode_app(X246, app_encode_fun(list(X246), list(X246)), 
27.18/27.38	             cons(X246), X247), nil(X246)),
27.18/27.38	    inference('cnf', [status(esa)], [zf_stmt_120])).
27.18/27.38	tff('38', plain,
27.18/27.38	    ![X0 : bool]:
27.18/27.38	      (nil(bool)
27.18/27.38	        = app_encode_app(list(bool), list(bool), 
27.18/27.38	            app_encode_app(bool, app_encode_fun(list(bool), list(bool)), 
27.18/27.38	              cons(bool), X0), nil(bool))
27.18/27.38	       | fFalse != fTrue),
27.18/27.38	    inference('sup+', [status(thm)], ['36', '37'])).
27.18/27.38	tff(zf_stmt_113, axiom,
27.18/27.38	  (![A:$tType,Xs1:list(A),X2:A]:
27.18/27.38	     (app_encode_app(list(A),list(A),
27.18/27.38	                     app_encode_app(A,app_encode_fun(list(A),list(A)),
27.18/27.38	                                    cons(A),X2),
27.18/27.38	                     Xs1) !=
27.18/27.38	      Xs1))).
27.18/27.38	tff('39', plain,
27.18/27.38	    ![X215 : $tType, X216 : list(X215), X217 : X215]:
27.18/27.38	      app_encode_app(list(X215), list(X215), 
27.18/27.38	        app_encode_app(X215, app_encode_fun(list(X215), list(X215)), 
27.18/27.38	          cons(X215), X217), X216)
27.18/27.38	       != X216,
27.18/27.38	    inference('cnf', [status(esa)], [zf_stmt_113])).
27.18/27.38	tff('40', plain, fFalse != fTrue,
27.18/27.38	    inference('simplify_reflect-', [status(thm)], ['38', '39'])).
27.18/27.38	tff(zf_stmt_64, axiom,
27.18/27.38	  (![Ss1:list(dB),S:dB,Ra:dB]:
27.18/27.38	     (app_encode_app(bool,$o,pp,
27.18/27.38	                     app_encode_app(dB,bool,
27.18/27.38	                                    app_encode_app(fun(dB,bool),
27.18/27.38	                                                   app_encode_fun(dB,bool),
27.18/27.38	                                                   aa(dB,bool),
27.18/27.38	                                                   app_encode_app(dB,
27.18/27.38	                                                                  fun(
27.18/27.38	                                                                  dB,bool),
27.18/27.38	                                                                  app_encode_app(
27.18/27.38	                                                                  fun(
27.18/27.38	                                                                  dB,
27.18/27.38	                                                                  fun(
27.18/27.38	                                                                  dB,bool)),
27.18/27.38	                                                                  app_encode_fun(
27.18/27.38	                                                                  dB,
27.18/27.38	                                                                  fun(
27.18/27.38	                                                                  dB,bool)),
27.18/27.38	                                                                  aa(
27.18/27.38	                                                                  dB,
27.18/27.38	                                                                  fun(
27.18/27.38	                                                                  dB,bool)),
27.18/27.38	                                                                  beta),Ra)),
27.18/27.38	                                    S)) =>
27.18/27.38	      app_encode_app(bool,$o,pp,
27.18/27.38	                     app_encode_app(dB,bool,
27.18/27.38	                                    app_encode_app(fun(dB,bool),
27.18/27.38	                                                   app_encode_fun(dB,bool),
27.18/27.38	                                                   aa(dB,bool),
27.18/27.38	                                                   app_encode_app(dB,
27.18/27.38	                                                                  fun(
27.18/27.38	                                                                  dB,bool),
27.18/27.38	                                                                  app_encode_app(
27.18/27.38	                                                                  fun(
27.18/27.38	                                                                  dB,
27.18/27.38	                                                                  fun(
27.18/27.38	                                                                  dB,bool)),
27.18/27.38	                                                                  app_encode_fun(
27.18/27.38	                                                                  dB,
27.18/27.38	                                                                  fun(
27.18/27.38	                                                                  dB,bool)),
27.18/27.38	                                                                  aa(
27.18/27.38	                                                                  dB,
27.18/27.38	                                                                  fun(
27.18/27.38	                                                                  dB,bool)),
27.18/27.38	                                                                  beta),
27.18/27.38	                                                                  app_encode_app(
27.18/27.38	                                                                  list(dB),
27.18/27.38	                                                                  dB,
27.18/27.38	                                                                  app_encode_app(
27.18/27.38	                                                                  dB,
27.18/27.38	                                                                  app_encode_fun(
27.18/27.38	                                                                  list(dB),dB),
27.18/27.38	                                                                  app_encode_app(
27.18/27.38	                                                                  fun(
27.18/27.38	                                                                  dB,
27.18/27.38	                                                                  fun(dB,dB)),
27.18/27.38	                                                                  app_encode_fun(
27.18/27.38	                                                                  dB,
27.18/27.38	                                                                  app_encode_fun(
27.18/27.38	                                                                  list(dB),dB)),
27.18/27.38	                                                                  foldl(
27.18/27.38	                                                                  dB,dB),app),
27.18/27.38	                                                                  Ra),Ss1))),
27.18/27.38	                                    app_encode_app(list(dB),dB,
27.18/27.38	                                                   app_encode_app(dB,
27.18/27.38	                                                                  app_encode_fun(
27.18/27.38	                                                                  list(dB),dB),
27.18/27.38	                                                                  app_encode_app(
27.18/27.38	                                                                  fun(
27.18/27.38	                                                                  dB,
27.18/27.38	                                                                  fun(dB,dB)),
27.18/27.38	                                                                  app_encode_fun(
27.18/27.38	                                                                  dB,
27.18/27.38	                                                                  app_encode_fun(
27.18/27.38	                                                                  list(dB),dB)),
27.18/27.38	                                                                  foldl(
27.18/27.38	                                                                  dB,dB),app),
27.18/27.38	                                                                  S),
27.18/27.38	                                                   Ss1)))))).
27.18/27.38	tff('41', plain,
27.18/27.38	    ![X27 : dB, X28 : list(dB), X29 : dB]:
27.18/27.38	      (app_encode_app(bool, $o, pp, 
27.18/27.38	         app_encode_app(dB, bool, 
27.18/27.38	           app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
27.18/27.38	             aa(dB, bool), 
27.18/27.38	             app_encode_app(dB, fun(dB, bool), 
27.18/27.38	               app_encode_app(fun(dB, fun(dB, bool)), 
27.18/27.38	                 app_encode_fun(dB, fun(dB, bool)), aa(dB, fun(dB, bool)), 
27.18/27.38	                 beta), 
27.18/27.38	               app_encode_app(list(dB), dB, 
27.18/27.38	                 app_encode_app(dB, app_encode_fun(list(dB), dB), 
27.18/27.38	                   app_encode_app(fun(dB, fun(dB, dB)), 
27.18/27.38	                     app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
27.18/27.38	                     foldl(dB, dB), app), X27), X28))), 
27.18/27.38	           app_encode_app(list(dB), dB, 
27.18/27.38	             app_encode_app(dB, app_encode_fun(list(dB), dB), 
27.18/27.38	               app_encode_app(fun(dB, fun(dB, dB)), 
27.18/27.38	                 app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
27.18/27.38	                 foldl(dB, dB), app), X29), X28)))
27.18/27.38	       | ~ app_encode_app(bool, $o, pp, 
27.18/27.38	             app_encode_app(dB, bool, 
27.18/27.38	               app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
27.18/27.38	                 aa(dB, bool), 
27.18/27.38	                 app_encode_app(dB, fun(dB, bool), 
27.18/27.38	                   app_encode_app(fun(dB, fun(dB, bool)), 
27.18/27.38	                     app_encode_fun(dB, fun(dB, bool)), 
27.18/27.38	                     aa(dB, fun(dB, bool)), beta), X27)), X29))),
27.18/27.38	    inference('cnf', [status(esa)], [zf_stmt_64])).
27.18/27.38	tff('42', plain,
27.18/27.38	    ![X0 : list(dB), X1 : dB, X2 : dB, X3 : bool]:
27.18/27.38	      (app_encode_app(bool, $o, pp, fFalse)
27.18/27.38	       | X3 = fFalse
27.18/27.38	       | X3
27.18/27.38	          = app_encode_app(dB, bool, 
27.18/27.38	              app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
27.18/27.38	                aa(dB, bool), 
27.18/27.38	                app_encode_app(dB, fun(dB, bool), 
27.18/27.38	                  app_encode_app(fun(dB, fun(dB, bool)), 
27.18/27.38	                    app_encode_fun(dB, fun(dB, bool)), 
27.18/27.38	                    aa(dB, fun(dB, bool)), beta), 
27.18/27.38	                  app_encode_app(list(dB), dB, 
27.18/27.38	                    app_encode_app(dB, app_encode_fun(list(dB), dB), 
27.18/27.38	                      app_encode_app(fun(dB, fun(dB, dB)), 
27.18/27.38	                        app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
27.18/27.38	                        foldl(dB, dB), app), X2), X0))), 
27.18/27.38	              app_encode_app(list(dB), dB, 
27.18/27.38	                app_encode_app(dB, app_encode_fun(list(dB), dB), 
27.18/27.38	                  app_encode_app(fun(dB, fun(dB, dB)), 
27.18/27.38	                    app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
27.18/27.38	                    foldl(dB, dB), app), X1), X0))
27.18/27.38	       | ~ app_encode_app(bool, $o, pp, 
27.18/27.38	             app_encode_app(dB, bool, 
27.18/27.38	               app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
27.18/27.38	                 aa(dB, bool), 
27.18/27.38	                 app_encode_app(dB, fun(dB, bool), 
27.18/27.38	                   app_encode_app(fun(dB, fun(dB, bool)), 
27.18/27.38	                     app_encode_fun(dB, fun(dB, bool)), 
27.18/27.38	                     aa(dB, fun(dB, bool)), beta), X2)), X1))),
27.18/27.38	    inference('sup+', [status(thm)], ['24', '41'])).
27.18/27.38	tff('43', plain,
27.18/27.38	    ![X0 : list(dB), X1 : dB, X2 : dB, X3 : bool]:
27.18/27.38	      (app_encode_app(bool, $o, pp, fFalse)
27.18/27.38	       | X3 = fFalse
27.18/27.38	       | X3
27.18/27.38	          = app_encode_app(dB, bool, 
27.18/27.38	              app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
27.18/27.38	                aa(dB, bool), 
27.18/27.38	                app_encode_app(dB, fun(dB, bool), 
27.18/27.38	                  app_encode_app(fun(dB, fun(dB, bool)), 
27.18/27.38	                    app_encode_fun(dB, fun(dB, bool)), combc(dB, dB, bool), 
27.18/27.38	                    beta), 
27.18/27.38	                  app_encode_app(list(dB), dB, 
27.18/27.38	                    app_encode_app(dB, app_encode_fun(list(dB), dB), 
27.18/27.38	                      app_encode_app(fun(dB, fun(dB, dB)), 
27.18/27.38	                        app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
27.18/27.38	                        foldl(dB, dB), app), X1), X0))), 
27.18/27.38	              app_encode_app(list(dB), dB, 
27.18/27.38	                app_encode_app(dB, app_encode_fun(list(dB), dB), 
27.18/27.38	                  app_encode_app(fun(dB, fun(dB, dB)), 
27.18/27.38	                    app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
27.18/27.38	                    foldl(dB, dB), app), X2), X0))
27.18/27.38	       | ~ app_encode_app(bool, $o, pp, 
27.18/27.38	             app_encode_app(dB, bool, 
27.18/27.38	               app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
27.18/27.38	                 aa(dB, bool), 
27.18/27.38	                 app_encode_app(dB, fun(dB, bool), 
27.18/27.38	                   app_encode_app(fun(dB, fun(dB, bool)), 
27.18/27.38	                     app_encode_fun(dB, fun(dB, bool)), combc(dB, dB, bool), 
27.18/27.38	                     beta), X1)), X2))),
27.18/27.38	    inference('demod', [status(thm)], ['42', '15', '15'])).
27.18/27.38	tff('44', plain,
27.18/27.38	    ![X0 : list(dB), X1 : dB, X2 : dB, X3 : bool]:
27.18/27.38	      (~ app_encode_app(bool, $o, pp, 
27.18/27.38	           app_encode_app(dB, bool, 
27.18/27.38	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
27.18/27.38	               aa(dB, bool), 
27.18/27.38	               app_encode_app(dB, fun(dB, bool), 
27.18/27.38	                 app_encode_app(fun(dB, fun(dB, bool)), 
27.18/27.38	                   app_encode_fun(dB, fun(dB, bool)), combc(dB, dB, bool), 
27.18/27.38	                   beta), X1)), X2))
27.18/27.38	       | X3
27.18/27.38	          = app_encode_app(dB, bool, 
27.18/27.38	              app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
27.18/27.38	                aa(dB, bool), 
27.18/27.38	                app_encode_app(dB, fun(dB, bool), 
27.18/27.38	                  app_encode_app(fun(dB, fun(dB, bool)), 
27.18/27.38	                    app_encode_fun(dB, fun(dB, bool)), combc(dB, dB, bool), 
27.18/27.38	                    beta), 
27.18/27.38	                  app_encode_app(list(dB), dB, 
27.18/27.38	                    app_encode_app(dB, app_encode_fun(list(dB), dB), 
27.18/27.38	                      app_encode_app(fun(dB, fun(dB, dB)), 
27.18/27.38	                        app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
27.18/27.38	                        foldl(dB, dB), app), X1), X0))), 
27.18/27.38	              app_encode_app(list(dB), dB, 
27.18/27.38	                app_encode_app(dB, app_encode_fun(list(dB), dB), 
27.18/27.38	                  app_encode_app(fun(dB, fun(dB, dB)), 
27.18/27.38	                    app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
27.18/27.38	                    foldl(dB, dB), app), X2), X0))
27.18/27.38	       | X3 = fFalse),
27.18/27.38	    inference('clc', [status(thm)], ['43', '20'])).
27.18/27.38	tff('45', plain,
27.18/27.38	    ![X0 : bool]:
27.18/27.38	      (~ app_encode_app(bool, $o, pp, X0)
27.18/27.38	       | X0 = fFalse
27.18/27.38	       | ~ app_encode_app(bool, $o, pp, 
27.18/27.38	             app_encode_app(dB, bool, 
27.18/27.38	               app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
27.18/27.38	                 aa(dB, bool), 
27.18/27.38	                 app_encode_app(dB, fun(dB, bool), 
27.18/27.38	                   app_encode_app(fun(dB, fun(dB, bool)), 
27.18/27.38	                     app_encode_fun(dB, fun(dB, bool)), combc(dB, dB, bool), 
27.18/27.38	                     beta), 
27.18/27.38	                   app_encode_app(nat, dB, 
27.18/27.38	                     app_encode_app(dB, app_encode_fun(nat, dB), 
27.18/27.38	                       app_encode_app(dB, 
27.18/27.38	                         app_encode_fun(dB, app_encode_fun(nat, dB)), subst, 
27.18/27.38	                         r), a), zero_zero(nat)))), 
27.18/27.38	               app_encode_app(dB, dB, 
27.18/27.38	                 app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), 
27.18/27.38	                   aa(dB, dB), 
27.18/27.38	                   app_encode_app(dB, fun(dB, dB), 
27.18/27.38	                     app_encode_app(fun(dB, fun(dB, dB)), 
27.18/27.38	                       app_encode_fun(dB, fun(dB, dB)), combc(dB, dB, dB), 
27.18/27.38	                       app), a)), app_encode_app(dB, dB, abs, r))))),
27.18/27.38	    inference('sup-', [status(thm)], ['44', '16'])).
27.18/27.38	tff(zf_stmt_57, axiom,
27.18/27.38	  (![T:dB,S2:dB]:
27.18/27.38	     app_encode_app(bool,$o,pp,
27.18/27.38	                    app_encode_app(dB,bool,
27.18/27.38	                                   app_encode_app(fun(dB,bool),
27.18/27.38	                                                  app_encode_fun(dB,bool),
27.18/27.38	                                                  aa(dB,bool),
27.18/27.38	                                                  app_encode_app(dB,
27.18/27.38	                                                                 fun(dB,bool),
27.18/27.38	                                                                 app_encode_app(
27.18/27.38	                                                                 fun(
27.18/27.38	                                                                 dB,
27.18/27.38	                                                                 fun(dB,bool)),
27.18/27.38	                                                                 app_encode_fun(
27.18/27.38	                                                                 dB,
27.18/27.38	                                                                 fun(dB,bool)),
27.18/27.38	                                                                 aa(dB,
27.18/27.38	                                                                    fun(
27.18/27.38	                                                                    dB,bool)),
27.18/27.38	                                                                 beta),
27.18/27.38	                                                                 app_encode_app(
27.18/27.38	                                                                 dB,dB,
27.18/27.38	                                                                 app_encode_app(
27.18/27.38	                                                                 fun(dB,dB),
27.18/27.38	                                                                 app_encode_fun(
27.18/27.38	                                                                 dB,dB),
27.18/27.38	                                                                 aa(dB,dB),
27.18/27.38	                                                                 app_encode_app(
27.18/27.38	                                                                 dB,
27.18/27.38	                                                                 fun(dB,dB),
27.18/27.38	                                                                 app_encode_app(
27.18/27.38	                                                                 fun(
27.18/27.38	                                                                 dB,
27.18/27.38	                                                                 fun(dB,dB)),
27.18/27.38	                                                                 app_encode_fun(
27.18/27.38	                                                                 dB,
27.18/27.38	                                                                 fun(dB,dB)),
27.18/27.38	                                                                 aa(dB,
27.18/27.38	                                                                    fun(
27.18/27.38	                                                                    dB,dB)),
27.18/27.38	                                                                 app),
27.18/27.38	                                                                 app_encode_app(
27.18/27.38	                                                                 dB,dB,abs,S2))),
27.18/27.38	                                                                 T))),
27.18/27.38	                                   app_encode_app(nat,dB,
27.18/27.38	                                                  app_encode_app(dB,
27.18/27.38	                                                                 app_encode_fun(
27.18/27.38	                                                                 nat,dB),
27.18/27.38	                                                                 app_encode_app(
27.18/27.38	                                                                 dB,
27.18/27.38	                                                                 app_encode_fun(
27.18/27.38	                                                                 dB,
27.18/27.38	                                                                 app_encode_fun(
27.18/27.38	                                                                 nat,dB)),
27.18/27.38	                                                                 subst,S2),T),
27.18/27.38	                                                  zero_zero(nat)))))).
27.18/27.38	tff('46', plain,
27.18/27.38	    ![X4 : dB, X5 : dB]:
27.18/27.38	      app_encode_app(bool, $o, pp, 
27.18/27.38	        app_encode_app(dB, bool, 
27.18/27.38	          app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
27.18/27.38	            aa(dB, bool), 
27.18/27.38	            app_encode_app(dB, fun(dB, bool), 
27.18/27.38	              app_encode_app(fun(dB, fun(dB, bool)), 
27.18/27.38	                app_encode_fun(dB, fun(dB, bool)), aa(dB, fun(dB, bool)), 
27.18/27.38	                beta), 
27.18/27.38	              app_encode_app(dB, dB, 
27.18/27.38	                app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), 
27.18/27.38	                  aa(dB, dB), 
27.18/27.38	                  app_encode_app(dB, fun(dB, dB), 
27.18/27.38	                    app_encode_app(fun(dB, fun(dB, dB)), 
27.18/27.38	                      app_encode_fun(dB, fun(dB, dB)), aa(dB, fun(dB, dB)), 
27.18/27.38	                      app), app_encode_app(dB, dB, abs, X4))), X5))), 
27.18/27.38	          app_encode_app(nat, dB, 
27.18/27.38	            app_encode_app(dB, app_encode_fun(nat, dB), 
27.18/27.38	              app_encode_app(dB, 
27.18/27.38	                app_encode_fun(dB, app_encode_fun(nat, dB)), subst, X4), X5), 
27.18/27.38	            zero_zero(nat)))),
27.18/27.38	    inference('cnf', [status(esa)], [zf_stmt_57])).
27.18/27.38	tff('47', plain,
27.18/27.38	    ![X0 : bool, X1 : dB, X2 : dB]:
27.18/27.38	      (app_encode_app(bool, $o, pp, X0)
27.18/27.38	       | X0 = fTrue
27.18/27.38	       | app_encode_app(dB, bool, 
27.18/27.38	           app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
27.18/27.38	             aa(dB, bool), 
27.18/27.38	             app_encode_app(dB, fun(dB, bool), 
27.18/27.38	               app_encode_app(fun(dB, fun(dB, bool)), 
27.18/27.38	                 app_encode_fun(dB, fun(dB, bool)), aa(dB, fun(dB, bool)), 
27.18/27.38	                 beta), 
27.18/27.38	               app_encode_app(dB, dB, 
27.18/27.38	                 app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), 
27.18/27.38	                   aa(dB, dB), 
27.18/27.38	                   app_encode_app(dB, fun(dB, dB), 
27.18/27.38	                     app_encode_app(fun(dB, fun(dB, dB)), 
27.18/27.38	                       app_encode_fun(dB, fun(dB, dB)), aa(dB, fun(dB, dB)), 
27.18/27.38	                       app), app_encode_app(dB, dB, abs, X2))), X1))), 
27.18/27.38	           app_encode_app(nat, dB, 
27.18/27.38	             app_encode_app(dB, app_encode_fun(nat, dB), 
27.18/27.38	               app_encode_app(dB, 
27.18/27.38	                 app_encode_fun(dB, app_encode_fun(nat, dB)), subst, X2), X1), 
27.18/27.38	             zero_zero(nat)))
27.18/27.38	          = fTrue),
27.18/27.38	    inference('sup+', [status(thm)], ['1', '46'])).
27.18/27.38	tff('48', plain,
27.18/27.38	    ![X0 : bool, X1 : dB, X2 : dB]:
27.18/27.38	      (app_encode_app(bool, $o, pp, X0)
27.18/27.38	       | X0 = fTrue
27.18/27.38	       | app_encode_app(dB, bool, 
27.18/27.38	           app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
27.18/27.38	             aa(dB, bool), 
27.18/27.38	             app_encode_app(dB, fun(dB, bool), 
27.18/27.38	               app_encode_app(fun(dB, fun(dB, bool)), 
27.18/27.38	                 app_encode_fun(dB, fun(dB, bool)), combc(dB, dB, bool), 
27.18/27.38	                 beta), 
27.18/27.38	               app_encode_app(nat, dB, 
27.18/27.38	                 app_encode_app(dB, app_encode_fun(nat, dB), 
27.18/27.38	                   app_encode_app(dB, 
27.18/27.38	                     app_encode_fun(dB, app_encode_fun(nat, dB)), subst, X2), 
27.18/27.38	                   X1), zero_zero(nat)))), 
27.18/27.38	           app_encode_app(dB, dB, 
27.18/27.38	             app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), aa(dB, dB), 
27.18/27.38	               app_encode_app(dB, fun(dB, dB), 
27.18/27.38	                 app_encode_app(fun(dB, fun(dB, dB)), 
27.18/27.38	                   app_encode_fun(dB, fun(dB, dB)), combc(dB, dB, dB), app), 
27.18/27.38	                 X1)), app_encode_app(dB, dB, abs, X2)))
27.18/27.38	          = fTrue),
27.18/27.38	    inference('demod', [status(thm)], ['47', '15', '15'])).
27.18/27.38	tff('49', plain,
27.18/27.38	    ![X0 : bool, X1 : dB, X2 : dB]:
27.18/27.38	      (app_encode_app(dB, bool, 
27.18/27.38	         app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
27.18/27.38	           aa(dB, bool), 
27.18/27.38	           app_encode_app(dB, fun(dB, bool), 
27.18/27.38	             app_encode_app(fun(dB, fun(dB, bool)), 
27.18/27.38	               app_encode_fun(dB, fun(dB, bool)), combc(dB, dB, bool), beta), 
27.18/27.38	             app_encode_app(nat, dB, 
27.18/27.38	               app_encode_app(dB, app_encode_fun(nat, dB), 
27.18/27.38	                 app_encode_app(dB, 
27.18/27.38	                   app_encode_fun(dB, app_encode_fun(nat, dB)), subst, X2), 
27.18/27.38	                 X1), zero_zero(nat)))), 
27.18/27.38	         app_encode_app(dB, dB, 
27.18/27.38	           app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), aa(dB, dB), 
27.18/27.38	             app_encode_app(dB, fun(dB, dB), 
27.18/27.38	               app_encode_app(fun(dB, fun(dB, dB)), 
27.18/27.38	                 app_encode_fun(dB, fun(dB, dB)), combc(dB, dB, dB), app), 
27.18/27.38	               X1)), app_encode_app(dB, dB, abs, X2)))
27.18/27.38	        = fTrue
27.18/27.38	       | X0 = fTrue),
27.18/27.38	    inference('clc', [status(thm)], ['48', '21'])).
27.18/27.38	tff('50', plain,
27.18/27.38	    ![X0 : dB, X1 : dB]:
27.18/27.38	      app_encode_app(dB, bool, 
27.18/27.38	        app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
27.18/27.38	          aa(dB, bool), 
27.18/27.38	          app_encode_app(dB, fun(dB, bool), 
27.18/27.38	            app_encode_app(fun(dB, fun(dB, bool)), 
27.18/27.38	              app_encode_fun(dB, fun(dB, bool)), combc(dB, dB, bool), beta), 
27.18/27.38	            app_encode_app(nat, dB, 
27.18/27.38	              app_encode_app(dB, app_encode_fun(nat, dB), 
27.18/27.38	                app_encode_app(dB, 
27.18/27.38	                  app_encode_fun(dB, app_encode_fun(nat, dB)), subst, X0), 
27.18/27.38	                X1), zero_zero(nat)))), 
27.18/27.38	        app_encode_app(dB, dB, 
27.18/27.38	          app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), aa(dB, dB), 
27.18/27.38	            app_encode_app(dB, fun(dB, dB), 
27.18/27.38	              app_encode_app(fun(dB, fun(dB, dB)), 
27.18/27.38	                app_encode_fun(dB, fun(dB, dB)), combc(dB, dB, dB), app), X1)), 
27.18/27.38	          app_encode_app(dB, dB, abs, X0)))
27.18/27.38	       = fTrue,
27.18/27.38	    inference('condensation', [status(thm)], ['49'])).
27.18/27.38	tff('51', plain,
27.18/27.38	    ![X0 : bool]:
27.18/27.38	      (~ app_encode_app(bool, $o, pp, X0) | X0 = fFalse | ~ $true),
27.18/27.38	    inference('demod', [status(thm)], ['45', '50', '2'])).
27.18/27.38	tff('52', plain,
27.18/27.38	    ![X0 : bool]: (X0 = fFalse | ~ app_encode_app(bool, $o, pp, X0)),
27.18/27.38	    inference('simplify', [status(thm)], ['51'])).
27.18/27.38	tff('53', plain,
27.18/27.38	    ![X0 : bool]: (app_encode_app(bool, $o, pp, X0) | X0 = fFalse),
27.18/27.38	    inference('sup+', [status(thm)], ['0', '2'])).
27.18/27.38	tff('54', plain, ![X0 : bool]: X0 = fFalse,
27.18/27.38	    inference('clc', [status(thm)], ['52', '53'])).
27.18/27.38	tff('55', plain, fFalse != fFalse,
27.18/27.38	    inference('demod', [status(thm)], ['40', '54'])).
27.18/27.38	tff('56', plain, $false, inference('simplify', [status(thm)], ['55'])).
27.18/27.38	
27.18/27.38	% SZS output end Refutation
27.18/27.38	EOF
