0.00/0.01	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.01	% app-encoded or not : app
0.00/0.01	% Variant    : fo
0.00/0.01	% Ordering    : kbo
0.00/0.01	% Command    : 
0.00/0.01	#!/bin/sh
0.00/0.01	
0.00/0.01	./zipperposition.native ${1:+"$1"} \
0.00/0.01	  -i tptp \
0.00/0.01	  -o tptp \
0.00/0.01	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.01	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.01	  --no-ho \
0.00/0.01	  --no-avatar \
0.00/0.01	  --no-induction \
0.00/0.01	  --no-unif-pattern \
0.00/0.01	  --ord $2 \
0.00/0.01	  --simultaneous-sup false \
0.00/0.01	  --no-max-vars \
0.00/0.01	  --no-fool
0.00/0.20	% Computer   : n153.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 07:29:23 CST 2018
20.44/20.63	% done 2170 iterations in 20.418s
20.44/20.63	% SZS status Theorem for 'stdin'
20.44/20.63	% SZS output start Refutation
20.44/20.63	tff(zf_stmt_161, axiom, (![P:bool]: ((P = fTrue) | (P = fFalse)))).
20.44/20.63	tff('0', plain, ![X373 : bool]: (X373 = fTrue | X373 = fFalse),
20.44/20.63	    inference('cnf', [status(esa)], [zf_stmt_161])).
20.44/20.63	tff('1', plain, ![X0 : bool, X1 : bool]: (X1 = X0 | X0 = fTrue | X1 = fTrue),
20.44/20.63	    inference('sup+', [status(thm)], ['0', '0'])).
20.44/20.63	tff(zf_stmt_154, axiom, (app_encode_app(bool,$o,pp,fTrue))).
20.44/20.63	tff('2', plain, app_encode_app(bool, $o, pp, fTrue),
20.44/20.63	    inference('cnf', [status(esa)], [zf_stmt_154])).
20.44/20.63	tff('3', plain,
20.44/20.63	    ![X0 : bool, X1 : bool]:
20.44/20.63	      (app_encode_app(bool, $o, pp, X0) | X1 = fTrue | X1 = X0),
20.44/20.63	    inference('sup+', [status(thm)], ['1', '2'])).
20.44/20.63	tff(zf_stmt_117, axiom,
20.44/20.63	  (![A:$tType,Y1:list(A)]:
20.44/20.63	     ((Y1 != nil(A)) =>
20.44/20.63	      (~
20.44/20.63	        (![A2:A,List:list(A)]:
20.44/20.63	           (Y1 !=
20.44/20.63	            app_encode_app(list(A),list(A),
20.44/20.63	                           app_encode_app(A,app_encode_fun(list(A),list(A)),
20.44/20.63	                                          cons(A),A2),
20.44/20.63	                           List))))))).
20.44/20.63	tff('4', plain,
20.44/20.63	    ![X228 : $tType, X229 : list(X228)]:
20.44/20.63	      (X229
20.44/20.63	        = app_encode_app(list(X228), list(X228), 
20.44/20.63	            app_encode_app(X228, app_encode_fun(list(X228), list(X228)), 
20.44/20.63	              cons(X228), sk_A2(X228, X229)), sk_List(X228, X229))
20.44/20.63	       | X229 = nil(X228)),
20.44/20.63	    inference('cnf', [status(esa)], [zf_stmt_117])).
20.44/20.63	tff(zf_stmt_116, axiom,
20.44/20.63	  (![A:$tType,Xs:list(A)]:
20.44/20.63	     ((Xs != nil(A)) <=>
20.44/20.63	      (?[Y2:A,Ys1:list(A)]:
20.44/20.63	         (Xs =
20.44/20.63	          app_encode_app(list(A),list(A),
20.44/20.63	                         app_encode_app(A,app_encode_fun(list(A),list(A)),
20.44/20.63	                                        cons(A),Y2),
20.44/20.63	                         Ys1)))))).
20.44/20.63	tff('5', plain,
20.44/20.63	    ![X223 : $tType, X224 : list(X223)]:
20.44/20.63	      (X224
20.44/20.63	        = app_encode_app(list(X223), list(X223), 
20.44/20.63	            app_encode_app(X223, app_encode_fun(list(X223), list(X223)), 
20.44/20.63	              cons(X223), sk_Y2(X223, X224)), sk_Ys1(X223, X224))
20.44/20.63	       | X224 = nil(X223)),
20.44/20.63	    inference('cnf', [status(esa)], [zf_stmt_116])).
20.44/20.63	tff(zf_stmt_108, axiom,
20.44/20.63	  (![A:$tType,List3:list(A),A4:A,List2:list(A),Aa:A]:
20.44/20.63	     ((app_encode_app(list(A),list(A),
20.44/20.63	                      app_encode_app(A,app_encode_fun(list(A),list(A)),
20.44/20.63	                                     cons(A),Aa),
20.44/20.63	                      List2) =
20.44/20.63	       app_encode_app(list(A),list(A),
20.44/20.63	                      app_encode_app(A,app_encode_fun(list(A),list(A)),
20.44/20.63	                                     cons(A),A4),
20.44/20.63	                      List3)) <=>
20.44/20.63	      ((Aa = A4) & (List2 = List3))))).
20.44/20.63	tff('6', plain,
20.44/20.63	    ![X186 : $tType, X187 : X186, X188 : X186, X189 : list(X186), 
20.44/20.63	      X190 : list(X186)]:
20.44/20.63	      (X188 = X187
20.44/20.63	       | app_encode_app(list(X186), list(X186), 
20.44/20.63	           app_encode_app(X186, app_encode_fun(list(X186), list(X186)), 
20.44/20.63	             cons(X186), X188), X190)
20.44/20.63	          != app_encode_app(list(X186), list(X186), 
20.44/20.63	               app_encode_app(X186, app_encode_fun(list(X186), list(X186)), 
20.44/20.63	                 cons(X186), X187), X189)),
20.44/20.63	    inference('cnf', [status(esa)], [zf_stmt_108])).
20.44/20.63	tff('7', plain,
20.44/20.63	    ![X0 : $tType, X1 : list(X0), X2 : list(X0), X3 : X0]:
20.44/20.63	      (X1
20.44/20.63	        != app_encode_app(list(X0), list(X0), 
20.44/20.63	             app_encode_app(X0, app_encode_fun(list(X0), list(X0)), 
20.44/20.63	               cons(X0), X3), X2)
20.44/20.63	       | X1 = nil(X0)
20.44/20.63	       | sk_Y2(X0, X1) = X3),
20.44/20.63	    inference('sup-', [status(thm)], ['5', '6'])).
20.44/20.63	tff('8', plain,
20.44/20.63	    ![X0 : $tType, X2 : list(X0), X3 : X0]:
20.44/20.63	      (sk_Y2(X0, 
20.44/20.63	         app_encode_app(list(X0), list(X0), 
20.44/20.63	           app_encode_app(X0, app_encode_fun(list(X0), list(X0)), cons(X0), 
20.44/20.63	             X3), X2))
20.44/20.63	        = X3
20.44/20.63	       | app_encode_app(list(X0), list(X0), 
20.44/20.63	           app_encode_app(X0, app_encode_fun(list(X0), list(X0)), cons(X0), 
20.44/20.63	             X3), X2)
20.44/20.63	          = nil(X0)),
20.44/20.63	    inference('simplify', [status(thm)], ['7'])).
20.44/20.63	tff(zf_stmt_114, axiom,
20.44/20.63	  (![A:$tType,List1:list(A),A3:A]:
20.44/20.63	     (nil(A) !=
20.44/20.63	      app_encode_app(list(A),list(A),
20.44/20.63	                     app_encode_app(A,app_encode_fun(list(A),list(A)),
20.44/20.63	                                    cons(A),A3),
20.44/20.63	                     List1)))).
20.44/20.63	tff('9', plain,
20.44/20.63	    ![X217 : $tType, X218 : X217, X219 : list(X217)]:
20.44/20.63	      nil(X217)
20.44/20.63	       != app_encode_app(list(X217), list(X217), 
20.44/20.63	            app_encode_app(X217, app_encode_fun(list(X217), list(X217)), 
20.44/20.63	              cons(X217), X218), X219),
20.44/20.63	    inference('cnf', [status(esa)], [zf_stmt_114])).
20.44/20.63	tff('10', plain,
20.44/20.63	    ![X0 : $tType, X2 : list(X0), X3 : X0]:
20.44/20.63	      sk_Y2(X0, 
20.44/20.63	        app_encode_app(list(X0), list(X0), 
20.44/20.63	          app_encode_app(X0, app_encode_fun(list(X0), list(X0)), cons(X0), 
20.44/20.63	            X3), X2))
20.44/20.63	       = X3,
20.44/20.63	    inference('clc', [status(thm)], ['8', '9'])).
20.44/20.63	tff('11', plain,
20.44/20.63	    ![X0 : $tType, X1 : list(X0)]:
20.44/20.63	      (sk_Y2(X0, X1) = sk_A2(X0, X1) | X1 = nil(X0)),
20.44/20.63	    inference('sup+', [status(thm)], ['4', '10'])).
20.44/20.63	tff('12', plain,
20.44/20.63	    ![X0 : bool, X1 : list(bool)]:
20.44/20.63	      (X0 = sk_A2(bool, X1)
20.44/20.63	       | X0 = fTrue
20.44/20.63	       | app_encode_app(bool, $o, pp, sk_Y2(bool, X1))
20.44/20.63	       | X1 = nil(bool)),
20.44/20.63	    inference('sup+', [status(thm)], ['3', '11'])).
20.44/20.63	tff('13', plain,
20.44/20.63	    ![X0 : list(bool), X1 : bool]:
20.44/20.63	      (sk_A2(bool, X0) != fTrue
20.44/20.63	       | X0 = nil(bool)
20.44/20.63	       | app_encode_app(bool, $o, pp, sk_Y2(bool, X0))
20.44/20.63	       | X1 = fTrue),
20.44/20.63	    inference('eq_fact', [status(thm)], ['12'])).
20.44/20.63	tff(zf_stmt_162, conjecture,
20.44/20.63	  (app_encode_app(bool,$o,pp,
20.44/20.63	                  app_encode_app(dB,bool,
20.44/20.63	                                 app_encode_app(fun(dB,bool),
20.44/20.63	                                                app_encode_fun(dB,bool),
20.44/20.63	                                                aa(dB,bool),
20.44/20.63	                                                app_encode_app(dB,
20.44/20.63	                                                               fun(dB,bool),
20.44/20.63	                                                               app_encode_app(
20.44/20.63	                                                               fun(dB,
20.44/20.63	                                                                   fun(
20.44/20.63	                                                                   dB,bool)),
20.44/20.63	                                                               app_encode_fun(
20.44/20.63	                                                               dB,
20.44/20.63	                                                               fun(dB,bool)),
20.44/20.63	                                                               aa(dB,
20.44/20.63	                                                                  fun(
20.44/20.63	                                                                  dB,bool)),
20.44/20.63	                                                               beta),
20.44/20.63	                                                               app_encode_app(
20.44/20.63	                                                               list(dB),dB,
20.44/20.63	                                                               app_encode_app(
20.44/20.63	                                                               dB,
20.44/20.63	                                                               app_encode_fun(
20.44/20.63	                                                               list(dB),dB),
20.44/20.63	                                                               app_encode_app(
20.44/20.63	                                                               fun(dB,
20.44/20.63	                                                                   fun(dB,dB)),
20.44/20.63	                                                               app_encode_fun(
20.44/20.63	                                                               dB,
20.44/20.63	                                                               app_encode_fun(
20.44/20.63	                                                               list(dB),dB)),
20.44/20.63	                                                               foldl(dB,dB),
20.44/20.63	                                                               app),
20.44/20.63	                                                               app_encode_app(
20.44/20.63	                                                               dB,dB,
20.44/20.63	                                                               app_encode_app(
20.44/20.63	                                                               fun(dB,dB),
20.44/20.63	                                                               app_encode_fun(
20.44/20.63	                                                               dB,dB),
20.44/20.63	                                                               aa(dB,dB),
20.44/20.63	                                                               app_encode_app(
20.44/20.63	                                                               dB,fun(dB,dB),
20.44/20.63	                                                               app_encode_app(
20.44/20.63	                                                               fun(dB,
20.44/20.63	                                                                   fun(dB,dB)),
20.44/20.63	                                                               app_encode_fun(
20.44/20.63	                                                               dB,fun(dB,dB)),
20.44/20.63	                                                               aa(dB,
20.44/20.63	                                                                  fun(dB,dB)),
20.44/20.63	                                                               app),
20.44/20.63	                                                               app_encode_app(
20.44/20.63	                                                               dB,dB,abs,r))),
20.44/20.63	                                                               a)),as))),
20.44/20.63	                                 app_encode_app(list(dB),dB,
20.44/20.63	                                                app_encode_app(dB,
20.44/20.63	                                                               app_encode_fun(
20.44/20.63	                                                               list(dB),dB),
20.44/20.63	                                                               app_encode_app(
20.44/20.63	                                                               fun(dB,
20.44/20.63	                                                                   fun(dB,dB)),
20.44/20.63	                                                               app_encode_fun(
20.44/20.63	                                                               dB,
20.44/20.63	                                                               app_encode_fun(
20.44/20.63	                                                               list(dB),dB)),
20.44/20.63	                                                               foldl(dB,dB),
20.44/20.63	                                                               app),
20.44/20.63	                                                               app_encode_app(
20.44/20.63	                                                               nat,dB,
20.44/20.63	                                                               app_encode_app(
20.44/20.63	                                                               dB,
20.44/20.63	                                                               app_encode_fun(
20.44/20.63	                                                               nat,dB),
20.44/20.63	                                                               app_encode_app(
20.44/20.63	                                                               dB,
20.44/20.63	                                                               app_encode_fun(
20.44/20.63	                                                               dB,
20.44/20.63	                                                               app_encode_fun(
20.44/20.63	                                                               nat,dB)),
20.44/20.63	                                                               subst,r),a),
20.44/20.63	                                                               zero_zero(nat))),
20.44/20.63	                                                as))))).
20.44/20.63	tff(zf_stmt_0, negated_conjecture,
20.44/20.63	  (~
20.44/20.63	    app_encode_app(bool,$o,pp,
20.44/20.63	                   app_encode_app(dB,bool,
20.44/20.63	                                  app_encode_app(fun(dB,bool),
20.44/20.63	                                                 app_encode_fun(dB,bool),
20.44/20.63	                                                 aa(dB,bool),
20.44/20.63	                                                 app_encode_app(dB,
20.44/20.63	                                                                fun(dB,bool),
20.44/20.63	                                                                app_encode_app(
20.44/20.63	                                                                fun(dB,
20.44/20.63	                                                                    fun(
20.44/20.63	                                                                    dB,bool)),
20.44/20.63	                                                                app_encode_fun(
20.44/20.63	                                                                dB,
20.44/20.63	                                                                fun(dB,bool)),
20.44/20.63	                                                                aa(dB,
20.44/20.63	                                                                   fun(
20.44/20.63	                                                                   dB,bool)),
20.44/20.63	                                                                beta),
20.44/20.63	                                                                app_encode_app(
20.44/20.63	                                                                list(dB),dB,
20.44/20.63	                                                                app_encode_app(
20.44/20.63	                                                                dB,
20.44/20.63	                                                                app_encode_fun(
20.44/20.63	                                                                list(dB),dB),
20.44/20.63	                                                                app_encode_app(
20.44/20.63	                                                                fun(dB,
20.44/20.63	                                                                    fun(
20.44/20.63	                                                                    dB,dB)),
20.44/20.63	                                                                app_encode_fun(
20.44/20.63	                                                                dB,
20.44/20.63	                                                                app_encode_fun(
20.44/20.63	                                                                list(dB),dB)),
20.44/20.63	                                                                foldl(dB,dB),
20.44/20.63	                                                                app),
20.44/20.63	                                                                app_encode_app(
20.44/20.63	                                                                dB,dB,
20.44/20.63	                                                                app_encode_app(
20.44/20.63	                                                                fun(dB,dB),
20.44/20.63	                                                                app_encode_fun(
20.44/20.63	                                                                dB,dB),
20.44/20.63	                                                                aa(dB,dB),
20.44/20.63	                                                                app_encode_app(
20.44/20.63	                                                                dB,
20.44/20.63	                                                                fun(dB,dB),
20.44/20.63	                                                                app_encode_app(
20.44/20.63	                                                                fun(dB,
20.44/20.63	                                                                    fun(
20.44/20.63	                                                                    dB,dB)),
20.44/20.63	                                                                app_encode_fun(
20.44/20.63	                                                                dB,fun(dB,dB)),
20.44/20.63	                                                                aa(dB,
20.44/20.63	                                                                   fun(dB,dB)),
20.44/20.63	                                                                app),
20.44/20.63	                                                                app_encode_app(
20.44/20.63	                                                                dB,dB,abs,r))),
20.44/20.63	                                                                a)),as))),
20.44/20.63	                                  app_encode_app(list(dB),dB,
20.44/20.63	                                                 app_encode_app(dB,
20.44/20.63	                                                                app_encode_fun(
20.44/20.63	                                                                list(dB),dB),
20.44/20.63	                                                                app_encode_app(
20.44/20.63	                                                                fun(dB,
20.44/20.63	                                                                    fun(
20.44/20.63	                                                                    dB,dB)),
20.44/20.63	                                                                app_encode_fun(
20.44/20.63	                                                                dB,
20.44/20.63	                                                                app_encode_fun(
20.44/20.63	                                                                list(dB),dB)),
20.44/20.63	                                                                foldl(dB,dB),
20.44/20.63	                                                                app),
20.44/20.63	                                                                app_encode_app(
20.44/20.63	                                                                nat,dB,
20.44/20.63	                                                                app_encode_app(
20.44/20.63	                                                                dB,
20.44/20.63	                                                                app_encode_fun(
20.44/20.63	                                                                nat,dB),
20.44/20.63	                                                                app_encode_app(
20.44/20.63	                                                                dB,
20.44/20.63	                                                                app_encode_fun(
20.44/20.63	                                                                dB,
20.44/20.63	                                                                app_encode_fun(
20.44/20.63	                                                                nat,dB)),
20.44/20.63	                                                                subst,r),a),
20.44/20.63	                                                                zero_zero(
20.44/20.63	                                                                nat))),
20.44/20.63	                                                 as))))).
20.44/20.63	tff('14', plain,
20.44/20.63	    ~ app_encode_app(bool, $o, pp, 
20.44/20.63	        app_encode_app(dB, bool, 
20.44/20.63	          app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
20.44/20.63	            aa(dB, bool), 
20.44/20.63	            app_encode_app(dB, fun(dB, bool), 
20.44/20.63	              app_encode_app(fun(dB, fun(dB, bool)), 
20.44/20.63	                app_encode_fun(dB, fun(dB, bool)), aa(dB, fun(dB, bool)), 
20.44/20.63	                beta), 
20.44/20.63	              app_encode_app(list(dB), dB, 
20.44/20.63	                app_encode_app(dB, app_encode_fun(list(dB), dB), 
20.44/20.63	                  app_encode_app(fun(dB, fun(dB, dB)), 
20.44/20.63	                    app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
20.44/20.63	                    foldl(dB, dB), app), 
20.44/20.63	                  app_encode_app(dB, dB, 
20.44/20.63	                    app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), 
20.44/20.63	                      aa(dB, dB), 
20.44/20.63	                      app_encode_app(dB, fun(dB, dB), 
20.44/20.63	                        app_encode_app(fun(dB, fun(dB, dB)), 
20.44/20.63	                          app_encode_fun(dB, fun(dB, dB)), 
20.44/20.63	                          aa(dB, fun(dB, dB)), app), 
20.44/20.63	                        app_encode_app(dB, dB, abs, r))), a)), as))), 
20.44/20.63	          app_encode_app(list(dB), dB, 
20.44/20.63	            app_encode_app(dB, app_encode_fun(list(dB), dB), 
20.44/20.63	              app_encode_app(fun(dB, fun(dB, dB)), 
20.44/20.63	                app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
20.44/20.63	                foldl(dB, dB), app), 
20.44/20.63	              app_encode_app(nat, dB, 
20.44/20.63	                app_encode_app(dB, app_encode_fun(nat, dB), 
20.44/20.63	                  app_encode_app(dB, 
20.44/20.63	                    app_encode_fun(dB, app_encode_fun(nat, dB)), subst, r), 
20.44/20.63	                  a), zero_zero(nat))), as))),
20.44/20.63	    inference('cnf', [status(esa)], [zf_stmt_0])).
20.44/20.63	tff(zf_stmt_156, axiom,
20.44/20.63	  (![A:$tType,C:$tType,B:$tType,R:A,Q:B,P:fun(A,fun(B,C))]:
20.44/20.63	     (app_encode_app(A,C,
20.44/20.63	                     app_encode_app(fun(A,C),app_encode_fun(A,C),aa(A,C),
20.44/20.63	                                    app_encode_app(B,fun(A,C),
20.44/20.63	                                                   app_encode_app(fun(
20.44/20.63	                                                                  A,fun(B,C)),
20.44/20.63	                                                                  app_encode_fun(
20.44/20.63	                                                                  B,fun(A,C)),
20.44/20.63	                                                                  combc(
20.44/20.63	                                                                  A,B,C),P),
20.44/20.63	                                                   Q)),
20.44/20.63	                     R) =
20.44/20.63	      app_encode_app(B,C,
20.44/20.63	                     app_encode_app(fun(B,C),app_encode_fun(B,C),aa(B,C),
20.44/20.63	                                    app_encode_app(A,fun(B,C),
20.44/20.63	                                                   app_encode_app(fun(
20.44/20.63	                                                                  A,fun(B,C)),
20.44/20.63	                                                                  app_encode_fun(
20.44/20.63	                                                                  A,fun(B,C)),
20.44/20.63	                                                                  aa(
20.44/20.63	                                                                  A,fun(B,C)),
20.44/20.63	                                                                  P),
20.44/20.63	                                                   R)),
20.44/20.63	                     Q)))).
20.44/20.63	tff('15', plain,
20.44/20.63	    ![X361 : $tType, X362 : $tType, X363 : $tType, 
20.44/20.63	      X364 : fun(X363, fun(X361, X362)), X365 : X363, X366 : X361]:
20.44/20.63	      app_encode_app(X363, X362, 
20.44/20.63	        app_encode_app(fun(X363, X362), app_encode_fun(X363, X362), 
20.44/20.63	          aa(X363, X362), 
20.44/20.63	          app_encode_app(X361, fun(X363, X362), 
20.44/20.63	            app_encode_app(fun(X363, fun(X361, X362)), 
20.44/20.63	              app_encode_fun(X361, fun(X363, X362)), 
20.44/20.63	              combc(X363, X361, X362), X364), X366)), X365)
20.44/20.63	       = app_encode_app(X361, X362, 
20.44/20.63	           app_encode_app(fun(X361, X362), app_encode_fun(X361, X362), 
20.44/20.63	             aa(X361, X362), 
20.44/20.63	             app_encode_app(X363, fun(X361, X362), 
20.44/20.63	               app_encode_app(fun(X363, fun(X361, X362)), 
20.44/20.63	                 app_encode_fun(X363, fun(X361, X362)), 
20.44/20.63	                 aa(X363, fun(X361, X362)), X364), X365)), X366),
20.44/20.63	    inference('cnf', [status(esa)], [zf_stmt_156])).
20.44/20.63	tff('16', plain,
20.44/20.63	    ~ app_encode_app(bool, $o, pp, 
20.44/20.63	        app_encode_app(dB, bool, 
20.44/20.63	          app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
20.44/20.63	            aa(dB, bool), 
20.44/20.63	            app_encode_app(dB, fun(dB, bool), 
20.44/20.63	              app_encode_app(fun(dB, fun(dB, bool)), 
20.44/20.63	                app_encode_fun(dB, fun(dB, bool)), combc(dB, dB, bool), beta), 
20.44/20.63	              app_encode_app(list(dB), dB, 
20.44/20.63	                app_encode_app(dB, app_encode_fun(list(dB), dB), 
20.44/20.63	                  app_encode_app(fun(dB, fun(dB, dB)), 
20.44/20.63	                    app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
20.44/20.63	                    foldl(dB, dB), app), 
20.44/20.63	                  app_encode_app(nat, dB, 
20.44/20.63	                    app_encode_app(dB, app_encode_fun(nat, dB), 
20.44/20.63	                      app_encode_app(dB, 
20.44/20.63	                        app_encode_fun(dB, app_encode_fun(nat, dB)), subst, 
20.44/20.63	                        r), a), zero_zero(nat))), as))), 
20.44/20.63	          app_encode_app(list(dB), dB, 
20.44/20.63	            app_encode_app(dB, app_encode_fun(list(dB), dB), 
20.44/20.63	              app_encode_app(fun(dB, fun(dB, dB)), 
20.44/20.63	                app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
20.44/20.63	                foldl(dB, dB), app), 
20.44/20.63	              app_encode_app(dB, dB, 
20.44/20.63	                app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), 
20.44/20.63	                  aa(dB, dB), 
20.44/20.63	                  app_encode_app(dB, fun(dB, dB), 
20.44/20.63	                    app_encode_app(fun(dB, fun(dB, dB)), 
20.44/20.63	                      app_encode_fun(dB, fun(dB, dB)), combc(dB, dB, dB), 
20.44/20.63	                      app), a)), app_encode_app(dB, dB, abs, r))), as))),
20.44/20.63	    inference('demod', [status(thm)], ['14', '15', '15'])).
20.44/20.63	tff('17', plain,
20.44/20.63	    ![X0 : list(bool)]:
20.44/20.63	      (~ app_encode_app(bool, $o, pp, fTrue)
20.44/20.63	       | app_encode_app(bool, $o, pp, sk_Y2(bool, X0))
20.44/20.63	       | X0 = nil(bool)
20.44/20.63	       | sk_A2(bool, X0) != fTrue),
20.44/20.63	    inference('sup-', [status(thm)], ['13', '16'])).
20.44/20.63	tff('18', plain,
20.44/20.63	    ![X0 : list(bool)]:
20.44/20.63	      (~ $true
20.44/20.63	       | app_encode_app(bool, $o, pp, sk_Y2(bool, X0))
20.44/20.63	       | X0 = nil(bool)
20.44/20.63	       | sk_A2(bool, X0) != fTrue),
20.44/20.63	    inference('demod', [status(thm)], ['17', '2'])).
20.44/20.63	tff('19', plain,
20.44/20.63	    ![X0 : list(bool)]:
20.44/20.63	      (sk_A2(bool, X0) != fTrue
20.44/20.63	       | X0 = nil(bool)
20.44/20.63	       | app_encode_app(bool, $o, pp, sk_Y2(bool, X0))),
20.44/20.63	    inference('simplify', [status(thm)], ['18'])).
20.44/20.63	tff(zf_stmt_153, axiom, (~app_encode_app(bool,$o,pp,fFalse))).
20.44/20.63	tff('20', plain, ~ app_encode_app(bool, $o, pp, fFalse),
20.44/20.63	    inference('cnf', [status(esa)], [zf_stmt_153])).
20.44/20.63	tff('21', plain,
20.44/20.63	    ![X0 : bool]: (~ app_encode_app(bool, $o, pp, X0) | X0 = fTrue),
20.44/20.63	    inference('sup-', [status(thm)], ['0', '20'])).
20.44/20.63	tff('22', plain,
20.44/20.63	    ![X0 : list(bool)]:
20.44/20.63	      (~ $true
20.44/20.63	       | X0 = nil(bool)
20.44/20.63	       | sk_A2(bool, X0) != fTrue
20.44/20.63	       | sk_Y2(bool, X0) = fTrue),
20.44/20.63	    inference('sup-', [status(thm)], ['19', '21'])).
20.44/20.63	tff('23', plain,
20.44/20.63	    ![X0 : list(bool)]:
20.44/20.63	      (sk_Y2(bool, X0) = fTrue | sk_A2(bool, X0) != fTrue | X0 = nil(bool)),
20.44/20.63	    inference('simplify', [status(thm)], ['22'])).
20.44/20.63	tff('24', plain,
20.44/20.63	    ![X0 : bool, X1 : bool]: (X1 = X0 | X0 = fFalse | X1 = fFalse),
20.44/20.63	    inference('sup+', [status(thm)], ['0', '0'])).
20.44/20.63	tff('25', plain,
20.44/20.63	    ![X0 : bool, X1 : bool]:
20.44/20.63	      (~ app_encode_app(bool, $o, pp, X0) | X1 = fFalse | X1 = X0),
20.44/20.63	    inference('sup-', [status(thm)], ['24', '20'])).
20.44/20.63	tff('26', plain,
20.44/20.63	    ![X0 : list(bool), X1 : bool]:
20.44/20.63	      (~ $true
20.44/20.63	       | X0 = nil(bool)
20.44/20.63	       | sk_A2(bool, X0) != fTrue
20.44/20.63	       | X1 = sk_Y2(bool, X0)
20.44/20.63	       | X1 = fFalse),
20.44/20.63	    inference('sup-', [status(thm)], ['19', '25'])).
20.44/20.63	tff('27', plain,
20.44/20.63	    ![X0 : list(bool), X1 : bool]:
20.44/20.63	      (X1 = fFalse
20.44/20.63	       | X1 = sk_Y2(bool, X0)
20.44/20.63	       | sk_A2(bool, X0) != fTrue
20.44/20.63	       | X0 = nil(bool)),
20.44/20.63	    inference('simplify', [status(thm)], ['26'])).
20.44/20.63	tff('28', plain,
20.44/20.63	    ![X0 : bool, X1 : list(bool)]:
20.44/20.63	      (fFalse != sk_Y2(bool, X1)
20.44/20.63	       | X1 = nil(bool)
20.44/20.63	       | sk_A2(bool, X1) != fTrue
20.44/20.63	       | X0 = sk_Y2(bool, X1)),
20.44/20.63	    inference('eq_fact', [status(thm)], ['27'])).
20.44/20.63	tff('29', plain,
20.44/20.63	    ![X0 : list(bool), X1 : bool]:
20.44/20.63	      (fFalse != fTrue
20.44/20.63	       | X0 = nil(bool)
20.44/20.63	       | sk_A2(bool, X0) != fTrue
20.44/20.63	       | X1 = sk_Y2(bool, X0)
20.44/20.63	       | sk_A2(bool, X0) != fTrue
20.44/20.63	       | X0 = nil(bool)),
20.44/20.63	    inference('sup-', [status(thm)], ['23', '28'])).
20.44/20.63	tff('30', plain,
20.44/20.63	    ![X0 : list(bool), X1 : bool]:
20.44/20.63	      (X1 = sk_Y2(bool, X0)
20.44/20.63	       | sk_A2(bool, X0) != fTrue
20.44/20.63	       | X0 = nil(bool)
20.44/20.63	       | fFalse != fTrue),
20.44/20.63	    inference('simplify', [status(thm)], ['29'])).
20.44/20.63	tff('31', plain,
20.44/20.63	    ![X0 : bool, X1 : list(bool)]:
20.44/20.63	      (app_encode_app(bool, $o, pp, X0)
20.44/20.63	       | fFalse != fTrue
20.44/20.63	       | X1 = nil(bool)
20.44/20.63	       | sk_A2(bool, X1) != fTrue
20.44/20.63	       | X1 = nil(bool)
20.44/20.63	       | sk_A2(bool, X1) != fTrue),
20.44/20.63	    inference('sup+', [status(thm)], ['30', '19'])).
20.44/20.63	tff('32', plain,
20.44/20.63	    ![X0 : bool, X1 : list(bool)]:
20.44/20.63	      (sk_A2(bool, X1) != fTrue
20.44/20.63	       | X1 = nil(bool)
20.44/20.63	       | fFalse != fTrue
20.44/20.63	       | app_encode_app(bool, $o, pp, X0)),
20.44/20.63	    inference('simplify', [status(thm)], ['31'])).
20.44/20.63	tff('33', plain, ![X0 : bool]: (fFalse != fTrue | X0 = fTrue),
20.44/20.63	    inference('eq_fact', [status(thm)], ['0'])).
20.44/20.63	tff('34', plain,
20.44/20.63	    ![X0 : bool, X1 : list(bool)]:
20.44/20.63	      (app_encode_app(bool, $o, pp, X0) | fFalse != fTrue | X1 = nil(bool)),
20.44/20.63	    inference('clc', [status(thm)], ['32', '33'])).
20.44/20.63	tff('35', plain,
20.44/20.63	    ![X0 : list(bool)]: (~ $true | X0 = nil(bool) | fFalse != fTrue),
20.44/20.63	    inference('sup-', [status(thm)], ['34', '16'])).
20.44/20.63	tff('36', plain, ![X0 : list(bool)]: (fFalse != fTrue | X0 = nil(bool)),
20.44/20.63	    inference('simplify', [status(thm)], ['35'])).
20.44/20.63	tff(zf_stmt_119, axiom,
20.44/20.63	  (![A:$tType,X2:A]:
20.44/20.63	     (app_encode_app(list(A),list(A),
20.44/20.63	                     app_encode_app(A,app_encode_fun(list(A),list(A)),
20.44/20.63	                                    insert(A),X2),
20.44/20.63	                     nil(A)) =
20.44/20.63	      app_encode_app(list(A),list(A),
20.44/20.63	                     app_encode_app(A,app_encode_fun(list(A),list(A)),
20.44/20.63	                                    cons(A),X2),
20.44/20.63	                     nil(A))))).
20.44/20.63	tff('37', plain,
20.44/20.63	    ![X242 : $tType, X243 : X242]:
20.44/20.63	      app_encode_app(list(X242), list(X242), 
20.44/20.63	        app_encode_app(X242, app_encode_fun(list(X242), list(X242)), 
20.44/20.63	          insert(X242), X243), nil(X242))
20.44/20.63	       = app_encode_app(list(X242), list(X242), 
20.44/20.63	           app_encode_app(X242, app_encode_fun(list(X242), list(X242)), 
20.44/20.63	             cons(X242), X243), nil(X242)),
20.44/20.63	    inference('cnf', [status(esa)], [zf_stmt_119])).
20.44/20.63	tff('38', plain,
20.44/20.63	    ![X0 : bool]:
20.44/20.63	      (nil(bool)
20.44/20.63	        = app_encode_app(list(bool), list(bool), 
20.44/20.63	            app_encode_app(bool, app_encode_fun(list(bool), list(bool)), 
20.44/20.63	              cons(bool), X0), nil(bool))
20.44/20.63	       | fFalse != fTrue),
20.44/20.63	    inference('sup+', [status(thm)], ['36', '37'])).
20.44/20.63	tff(zf_stmt_112, axiom,
20.44/20.63	  (![A:$tType,Xs1:list(A),X2:A]:
20.44/20.63	     (app_encode_app(list(A),list(A),
20.44/20.63	                     app_encode_app(A,app_encode_fun(list(A),list(A)),
20.44/20.63	                                    cons(A),X2),
20.44/20.63	                     Xs1) !=
20.44/20.63	      Xs1))).
20.44/20.63	tff('39', plain,
20.44/20.63	    ![X211 : $tType, X212 : list(X211), X213 : X211]:
20.44/20.63	      app_encode_app(list(X211), list(X211), 
20.44/20.63	        app_encode_app(X211, app_encode_fun(list(X211), list(X211)), 
20.44/20.63	          cons(X211), X213), X212)
20.44/20.63	       != X212,
20.44/20.63	    inference('cnf', [status(esa)], [zf_stmt_112])).
20.44/20.63	tff('40', plain, fFalse != fTrue,
20.44/20.63	    inference('simplify_reflect-', [status(thm)], ['38', '39'])).
20.44/20.63	tff(zf_stmt_63, axiom,
20.44/20.63	  (![Ss1:list(dB),S:dB,Ra:dB]:
20.44/20.63	     (app_encode_app(bool,$o,pp,
20.44/20.63	                     app_encode_app(dB,bool,
20.44/20.63	                                    app_encode_app(fun(dB,bool),
20.44/20.63	                                                   app_encode_fun(dB,bool),
20.44/20.63	                                                   aa(dB,bool),
20.44/20.63	                                                   app_encode_app(dB,
20.44/20.63	                                                                  fun(
20.44/20.63	                                                                  dB,bool),
20.44/20.63	                                                                  app_encode_app(
20.44/20.63	                                                                  fun(
20.44/20.63	                                                                  dB,
20.44/20.63	                                                                  fun(
20.44/20.63	                                                                  dB,bool)),
20.44/20.63	                                                                  app_encode_fun(
20.44/20.63	                                                                  dB,
20.44/20.63	                                                                  fun(
20.44/20.63	                                                                  dB,bool)),
20.44/20.63	                                                                  aa(
20.44/20.63	                                                                  dB,
20.44/20.63	                                                                  fun(
20.44/20.63	                                                                  dB,bool)),
20.44/20.63	                                                                  beta),Ra)),
20.44/20.63	                                    S)) =>
20.44/20.63	      app_encode_app(bool,$o,pp,
20.44/20.63	                     app_encode_app(dB,bool,
20.44/20.63	                                    app_encode_app(fun(dB,bool),
20.44/20.63	                                                   app_encode_fun(dB,bool),
20.44/20.63	                                                   aa(dB,bool),
20.44/20.63	                                                   app_encode_app(dB,
20.44/20.63	                                                                  fun(
20.44/20.63	                                                                  dB,bool),
20.44/20.63	                                                                  app_encode_app(
20.44/20.63	                                                                  fun(
20.44/20.63	                                                                  dB,
20.44/20.63	                                                                  fun(
20.44/20.63	                                                                  dB,bool)),
20.44/20.63	                                                                  app_encode_fun(
20.44/20.63	                                                                  dB,
20.44/20.63	                                                                  fun(
20.44/20.63	                                                                  dB,bool)),
20.44/20.63	                                                                  aa(
20.44/20.63	                                                                  dB,
20.44/20.63	                                                                  fun(
20.44/20.63	                                                                  dB,bool)),
20.44/20.63	                                                                  beta),
20.44/20.63	                                                                  app_encode_app(
20.44/20.63	                                                                  list(dB),
20.44/20.63	                                                                  dB,
20.44/20.63	                                                                  app_encode_app(
20.44/20.63	                                                                  dB,
20.44/20.63	                                                                  app_encode_fun(
20.44/20.63	                                                                  list(dB),dB),
20.44/20.63	                                                                  app_encode_app(
20.44/20.63	                                                                  fun(
20.44/20.63	                                                                  dB,
20.44/20.63	                                                                  fun(dB,dB)),
20.44/20.63	                                                                  app_encode_fun(
20.44/20.63	                                                                  dB,
20.44/20.63	                                                                  app_encode_fun(
20.44/20.63	                                                                  list(dB),dB)),
20.44/20.63	                                                                  foldl(
20.44/20.63	                                                                  dB,dB),app),
20.44/20.63	                                                                  Ra),Ss1))),
20.44/20.63	                                    app_encode_app(list(dB),dB,
20.44/20.63	                                                   app_encode_app(dB,
20.44/20.63	                                                                  app_encode_fun(
20.44/20.63	                                                                  list(dB),dB),
20.44/20.63	                                                                  app_encode_app(
20.44/20.63	                                                                  fun(
20.44/20.63	                                                                  dB,
20.44/20.63	                                                                  fun(dB,dB)),
20.44/20.63	                                                                  app_encode_fun(
20.44/20.63	                                                                  dB,
20.44/20.63	                                                                  app_encode_fun(
20.44/20.63	                                                                  list(dB),dB)),
20.44/20.63	                                                                  foldl(
20.44/20.63	                                                                  dB,dB),app),
20.44/20.63	                                                                  S),
20.44/20.63	                                                   Ss1)))))).
20.44/20.63	tff('41', plain,
20.44/20.63	    ![X23 : dB, X24 : list(dB), X25 : dB]:
20.44/20.63	      (app_encode_app(bool, $o, pp, 
20.44/20.63	         app_encode_app(dB, bool, 
20.44/20.63	           app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
20.44/20.63	             aa(dB, bool), 
20.44/20.63	             app_encode_app(dB, fun(dB, bool), 
20.44/20.63	               app_encode_app(fun(dB, fun(dB, bool)), 
20.44/20.63	                 app_encode_fun(dB, fun(dB, bool)), aa(dB, fun(dB, bool)), 
20.44/20.63	                 beta), 
20.44/20.63	               app_encode_app(list(dB), dB, 
20.44/20.63	                 app_encode_app(dB, app_encode_fun(list(dB), dB), 
20.44/20.63	                   app_encode_app(fun(dB, fun(dB, dB)), 
20.44/20.63	                     app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
20.44/20.63	                     foldl(dB, dB), app), X23), X24))), 
20.44/20.63	           app_encode_app(list(dB), dB, 
20.44/20.63	             app_encode_app(dB, app_encode_fun(list(dB), dB), 
20.44/20.63	               app_encode_app(fun(dB, fun(dB, dB)), 
20.44/20.63	                 app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
20.44/20.63	                 foldl(dB, dB), app), X25), X24)))
20.44/20.63	       | ~ app_encode_app(bool, $o, pp, 
20.44/20.63	             app_encode_app(dB, bool, 
20.44/20.63	               app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
20.44/20.63	                 aa(dB, bool), 
20.44/20.63	                 app_encode_app(dB, fun(dB, bool), 
20.44/20.63	                   app_encode_app(fun(dB, fun(dB, bool)), 
20.44/20.63	                     app_encode_fun(dB, fun(dB, bool)), 
20.44/20.63	                     aa(dB, fun(dB, bool)), beta), X23)), X25))),
20.44/20.63	    inference('cnf', [status(esa)], [zf_stmt_63])).
20.44/20.63	tff('42', plain,
20.44/20.63	    ![X0 : list(dB), X1 : dB, X2 : dB, X3 : bool]:
20.44/20.63	      (app_encode_app(bool, $o, pp, fFalse)
20.44/20.63	       | X3 = fFalse
20.44/20.63	       | X3
20.44/20.63	          = app_encode_app(dB, bool, 
20.44/20.63	              app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
20.44/20.63	                aa(dB, bool), 
20.44/20.63	                app_encode_app(dB, fun(dB, bool), 
20.44/20.63	                  app_encode_app(fun(dB, fun(dB, bool)), 
20.44/20.63	                    app_encode_fun(dB, fun(dB, bool)), 
20.44/20.63	                    aa(dB, fun(dB, bool)), beta), 
20.44/20.63	                  app_encode_app(list(dB), dB, 
20.44/20.63	                    app_encode_app(dB, app_encode_fun(list(dB), dB), 
20.44/20.63	                      app_encode_app(fun(dB, fun(dB, dB)), 
20.44/20.63	                        app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
20.44/20.63	                        foldl(dB, dB), app), X2), X0))), 
20.44/20.63	              app_encode_app(list(dB), dB, 
20.44/20.63	                app_encode_app(dB, app_encode_fun(list(dB), dB), 
20.44/20.63	                  app_encode_app(fun(dB, fun(dB, dB)), 
20.44/20.63	                    app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
20.44/20.63	                    foldl(dB, dB), app), X1), X0))
20.44/20.63	       | ~ app_encode_app(bool, $o, pp, 
20.44/20.63	             app_encode_app(dB, bool, 
20.44/20.63	               app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
20.44/20.63	                 aa(dB, bool), 
20.44/20.63	                 app_encode_app(dB, fun(dB, bool), 
20.44/20.63	                   app_encode_app(fun(dB, fun(dB, bool)), 
20.44/20.63	                     app_encode_fun(dB, fun(dB, bool)), 
20.44/20.63	                     aa(dB, fun(dB, bool)), beta), X2)), X1))),
20.44/20.63	    inference('sup+', [status(thm)], ['24', '41'])).
20.44/20.63	tff('43', plain,
20.44/20.63	    ![X0 : list(dB), X1 : dB, X2 : dB, X3 : bool]:
20.44/20.63	      (app_encode_app(bool, $o, pp, fFalse)
20.44/20.63	       | X3 = fFalse
20.44/20.63	       | X3
20.44/20.63	          = app_encode_app(dB, bool, 
20.44/20.63	              app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
20.44/20.63	                aa(dB, bool), 
20.44/20.63	                app_encode_app(dB, fun(dB, bool), 
20.44/20.63	                  app_encode_app(fun(dB, fun(dB, bool)), 
20.44/20.63	                    app_encode_fun(dB, fun(dB, bool)), combc(dB, dB, bool), 
20.44/20.63	                    beta), 
20.44/20.63	                  app_encode_app(list(dB), dB, 
20.44/20.63	                    app_encode_app(dB, app_encode_fun(list(dB), dB), 
20.44/20.63	                      app_encode_app(fun(dB, fun(dB, dB)), 
20.44/20.63	                        app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
20.44/20.63	                        foldl(dB, dB), app), X1), X0))), 
20.44/20.63	              app_encode_app(list(dB), dB, 
20.44/20.63	                app_encode_app(dB, app_encode_fun(list(dB), dB), 
20.44/20.63	                  app_encode_app(fun(dB, fun(dB, dB)), 
20.44/20.63	                    app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
20.44/20.63	                    foldl(dB, dB), app), X2), X0))
20.44/20.63	       | ~ app_encode_app(bool, $o, pp, 
20.44/20.63	             app_encode_app(dB, bool, 
20.44/20.63	               app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
20.44/20.63	                 aa(dB, bool), 
20.44/20.63	                 app_encode_app(dB, fun(dB, bool), 
20.44/20.63	                   app_encode_app(fun(dB, fun(dB, bool)), 
20.44/20.63	                     app_encode_fun(dB, fun(dB, bool)), combc(dB, dB, bool), 
20.44/20.63	                     beta), X1)), X2))),
20.44/20.63	    inference('demod', [status(thm)], ['42', '15', '15'])).
20.44/20.63	tff('44', plain,
20.44/20.63	    ![X0 : list(dB), X1 : dB, X2 : dB, X3 : bool]:
20.44/20.63	      (~ app_encode_app(bool, $o, pp, 
20.44/20.63	           app_encode_app(dB, bool, 
20.44/20.63	             app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
20.44/20.63	               aa(dB, bool), 
20.44/20.63	               app_encode_app(dB, fun(dB, bool), 
20.44/20.63	                 app_encode_app(fun(dB, fun(dB, bool)), 
20.44/20.63	                   app_encode_fun(dB, fun(dB, bool)), combc(dB, dB, bool), 
20.44/20.63	                   beta), X1)), X2))
20.44/20.63	       | X3
20.44/20.63	          = app_encode_app(dB, bool, 
20.44/20.63	              app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
20.44/20.63	                aa(dB, bool), 
20.44/20.63	                app_encode_app(dB, fun(dB, bool), 
20.44/20.63	                  app_encode_app(fun(dB, fun(dB, bool)), 
20.44/20.63	                    app_encode_fun(dB, fun(dB, bool)), combc(dB, dB, bool), 
20.44/20.63	                    beta), 
20.44/20.63	                  app_encode_app(list(dB), dB, 
20.44/20.63	                    app_encode_app(dB, app_encode_fun(list(dB), dB), 
20.44/20.63	                      app_encode_app(fun(dB, fun(dB, dB)), 
20.44/20.63	                        app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
20.44/20.63	                        foldl(dB, dB), app), X1), X0))), 
20.44/20.63	              app_encode_app(list(dB), dB, 
20.44/20.63	                app_encode_app(dB, app_encode_fun(list(dB), dB), 
20.44/20.63	                  app_encode_app(fun(dB, fun(dB, dB)), 
20.44/20.63	                    app_encode_fun(dB, app_encode_fun(list(dB), dB)), 
20.44/20.63	                    foldl(dB, dB), app), X2), X0))
20.44/20.63	       | X3 = fFalse),
20.44/20.63	    inference('clc', [status(thm)], ['43', '20'])).
20.44/20.63	tff('45', plain,
20.44/20.63	    ![X0 : bool]:
20.44/20.63	      (~ app_encode_app(bool, $o, pp, X0)
20.44/20.63	       | X0 = fFalse
20.44/20.63	       | ~ app_encode_app(bool, $o, pp, 
20.44/20.63	             app_encode_app(dB, bool, 
20.44/20.63	               app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
20.44/20.63	                 aa(dB, bool), 
20.44/20.63	                 app_encode_app(dB, fun(dB, bool), 
20.44/20.63	                   app_encode_app(fun(dB, fun(dB, bool)), 
20.44/20.63	                     app_encode_fun(dB, fun(dB, bool)), combc(dB, dB, bool), 
20.44/20.63	                     beta), 
20.44/20.63	                   app_encode_app(nat, dB, 
20.44/20.63	                     app_encode_app(dB, app_encode_fun(nat, dB), 
20.44/20.63	                       app_encode_app(dB, 
20.44/20.63	                         app_encode_fun(dB, app_encode_fun(nat, dB)), subst, 
20.44/20.63	                         r), a), zero_zero(nat)))), 
20.44/20.63	               app_encode_app(dB, dB, 
20.44/20.63	                 app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), 
20.44/20.63	                   aa(dB, dB), 
20.44/20.63	                   app_encode_app(dB, fun(dB, dB), 
20.44/20.63	                     app_encode_app(fun(dB, fun(dB, dB)), 
20.44/20.63	                       app_encode_fun(dB, fun(dB, dB)), combc(dB, dB, dB), 
20.44/20.63	                       app), a)), app_encode_app(dB, dB, abs, r))))),
20.44/20.63	    inference('sup-', [status(thm)], ['44', '16'])).
20.44/20.63	tff(zf_stmt_56, axiom,
20.44/20.63	  (![T:dB,S2:dB]:
20.44/20.63	     app_encode_app(bool,$o,pp,
20.44/20.63	                    app_encode_app(dB,bool,
20.44/20.63	                                   app_encode_app(fun(dB,bool),
20.44/20.63	                                                  app_encode_fun(dB,bool),
20.44/20.63	                                                  aa(dB,bool),
20.44/20.63	                                                  app_encode_app(dB,
20.44/20.63	                                                                 fun(dB,bool),
20.44/20.63	                                                                 app_encode_app(
20.44/20.63	                                                                 fun(
20.44/20.63	                                                                 dB,
20.44/20.63	                                                                 fun(dB,bool)),
20.44/20.63	                                                                 app_encode_fun(
20.44/20.63	                                                                 dB,
20.44/20.63	                                                                 fun(dB,bool)),
20.44/20.63	                                                                 aa(dB,
20.44/20.63	                                                                    fun(
20.44/20.63	                                                                    dB,bool)),
20.44/20.63	                                                                 beta),
20.44/20.63	                                                                 app_encode_app(
20.44/20.63	                                                                 dB,dB,
20.44/20.63	                                                                 app_encode_app(
20.44/20.63	                                                                 fun(dB,dB),
20.44/20.63	                                                                 app_encode_fun(
20.44/20.63	                                                                 dB,dB),
20.44/20.63	                                                                 aa(dB,dB),
20.44/20.63	                                                                 app_encode_app(
20.44/20.63	                                                                 dB,
20.44/20.63	                                                                 fun(dB,dB),
20.44/20.63	                                                                 app_encode_app(
20.44/20.63	                                                                 fun(
20.44/20.63	                                                                 dB,
20.44/20.63	                                                                 fun(dB,dB)),
20.44/20.63	                                                                 app_encode_fun(
20.44/20.63	                                                                 dB,
20.44/20.63	                                                                 fun(dB,dB)),
20.44/20.63	                                                                 aa(dB,
20.44/20.63	                                                                    fun(
20.44/20.63	                                                                    dB,dB)),
20.44/20.63	                                                                 app),
20.44/20.63	                                                                 app_encode_app(
20.44/20.63	                                                                 dB,dB,abs,S2))),
20.44/20.63	                                                                 T))),
20.44/20.63	                                   app_encode_app(nat,dB,
20.44/20.63	                                                  app_encode_app(dB,
20.44/20.63	                                                                 app_encode_fun(
20.44/20.63	                                                                 nat,dB),
20.44/20.63	                                                                 app_encode_app(
20.44/20.63	                                                                 dB,
20.44/20.63	                                                                 app_encode_fun(
20.44/20.63	                                                                 dB,
20.44/20.63	                                                                 app_encode_fun(
20.44/20.63	                                                                 nat,dB)),
20.44/20.63	                                                                 subst,S2),T),
20.44/20.63	                                                  zero_zero(nat)))))).
20.44/20.63	tff('46', plain,
20.44/20.63	    ![X0 : dB, X1 : dB]:
20.44/20.63	      app_encode_app(bool, $o, pp, 
20.44/20.63	        app_encode_app(dB, bool, 
20.44/20.63	          app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
20.44/20.63	            aa(dB, bool), 
20.44/20.63	            app_encode_app(dB, fun(dB, bool), 
20.44/20.63	              app_encode_app(fun(dB, fun(dB, bool)), 
20.44/20.63	                app_encode_fun(dB, fun(dB, bool)), aa(dB, fun(dB, bool)), 
20.44/20.63	                beta), 
20.44/20.63	              app_encode_app(dB, dB, 
20.44/20.63	                app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), 
20.44/20.63	                  aa(dB, dB), 
20.44/20.63	                  app_encode_app(dB, fun(dB, dB), 
20.44/20.63	                    app_encode_app(fun(dB, fun(dB, dB)), 
20.44/20.63	                      app_encode_fun(dB, fun(dB, dB)), aa(dB, fun(dB, dB)), 
20.44/20.63	                      app), app_encode_app(dB, dB, abs, X0))), X1))), 
20.44/20.63	          app_encode_app(nat, dB, 
20.44/20.63	            app_encode_app(dB, app_encode_fun(nat, dB), 
20.44/20.63	              app_encode_app(dB, 
20.44/20.63	                app_encode_fun(dB, app_encode_fun(nat, dB)), subst, X0), X1), 
20.44/20.63	            zero_zero(nat)))),
20.44/20.63	    inference('cnf', [status(esa)], [zf_stmt_56])).
20.44/20.63	tff('47', plain,
20.44/20.63	    ![X0 : dB, X1 : dB]:
20.44/20.63	      (~ $true
20.44/20.63	       | app_encode_app(dB, bool, 
20.44/20.63	           app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
20.44/20.63	             aa(dB, bool), 
20.44/20.63	             app_encode_app(dB, fun(dB, bool), 
20.44/20.63	               app_encode_app(fun(dB, fun(dB, bool)), 
20.44/20.63	                 app_encode_fun(dB, fun(dB, bool)), aa(dB, fun(dB, bool)), 
20.44/20.63	                 beta), 
20.44/20.63	               app_encode_app(dB, dB, 
20.44/20.63	                 app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), 
20.44/20.63	                   aa(dB, dB), 
20.44/20.63	                   app_encode_app(dB, fun(dB, dB), 
20.44/20.63	                     app_encode_app(fun(dB, fun(dB, dB)), 
20.44/20.63	                       app_encode_fun(dB, fun(dB, dB)), aa(dB, fun(dB, dB)), 
20.44/20.63	                       app), app_encode_app(dB, dB, abs, X1))), X0))), 
20.44/20.63	           app_encode_app(nat, dB, 
20.44/20.63	             app_encode_app(dB, app_encode_fun(nat, dB), 
20.44/20.63	               app_encode_app(dB, 
20.44/20.63	                 app_encode_fun(dB, app_encode_fun(nat, dB)), subst, X1), X0), 
20.44/20.63	             zero_zero(nat)))
20.44/20.63	          = fTrue),
20.44/20.63	    inference('sup-', [status(thm)], ['46', '21'])).
20.44/20.63	tff('48', plain,
20.44/20.63	    ![X0 : dB, X1 : dB]:
20.44/20.63	      app_encode_app(dB, bool, 
20.44/20.63	        app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
20.44/20.63	          aa(dB, bool), 
20.44/20.63	          app_encode_app(dB, fun(dB, bool), 
20.44/20.63	            app_encode_app(fun(dB, fun(dB, bool)), 
20.44/20.63	              app_encode_fun(dB, fun(dB, bool)), aa(dB, fun(dB, bool)), beta), 
20.44/20.63	            app_encode_app(dB, dB, 
20.44/20.63	              app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), 
20.44/20.63	                aa(dB, dB), 
20.44/20.63	                app_encode_app(dB, fun(dB, dB), 
20.44/20.63	                  app_encode_app(fun(dB, fun(dB, dB)), 
20.44/20.63	                    app_encode_fun(dB, fun(dB, dB)), aa(dB, fun(dB, dB)), 
20.44/20.63	                    app), app_encode_app(dB, dB, abs, X1))), X0))), 
20.44/20.63	        app_encode_app(nat, dB, 
20.44/20.63	          app_encode_app(dB, app_encode_fun(nat, dB), 
20.44/20.63	            app_encode_app(dB, app_encode_fun(dB, app_encode_fun(nat, dB)), 
20.44/20.63	              subst, X1), X0), zero_zero(nat)))
20.44/20.63	       = fTrue,
20.44/20.63	    inference('simplify', [status(thm)], ['47'])).
20.44/20.63	tff('49', plain,
20.44/20.63	    ![X0 : dB, X1 : dB]:
20.44/20.63	      app_encode_app(dB, bool, 
20.44/20.63	        app_encode_app(fun(dB, bool), app_encode_fun(dB, bool), 
20.44/20.63	          aa(dB, bool), 
20.44/20.63	          app_encode_app(dB, fun(dB, bool), 
20.44/20.63	            app_encode_app(fun(dB, fun(dB, bool)), 
20.44/20.63	              app_encode_fun(dB, fun(dB, bool)), combc(dB, dB, bool), beta), 
20.44/20.63	            app_encode_app(nat, dB, 
20.44/20.63	              app_encode_app(dB, app_encode_fun(nat, dB), 
20.44/20.63	                app_encode_app(dB, 
20.44/20.63	                  app_encode_fun(dB, app_encode_fun(nat, dB)), subst, X1), 
20.44/20.63	                X0), zero_zero(nat)))), 
20.44/20.63	        app_encode_app(dB, dB, 
20.44/20.63	          app_encode_app(fun(dB, dB), app_encode_fun(dB, dB), aa(dB, dB), 
20.44/20.63	            app_encode_app(dB, fun(dB, dB), 
20.44/20.63	              app_encode_app(fun(dB, fun(dB, dB)), 
20.44/20.63	                app_encode_fun(dB, fun(dB, dB)), combc(dB, dB, dB), app), X0)), 
20.44/20.63	          app_encode_app(dB, dB, abs, X1)))
20.44/20.63	       = fTrue,
20.44/20.63	    inference('demod', [status(thm)], ['48', '15', '15'])).
20.44/20.63	tff('50', plain,
20.44/20.63	    ![X0 : bool]:
20.44/20.63	      (~ app_encode_app(bool, $o, pp, X0) | X0 = fFalse | ~ $true),
20.44/20.63	    inference('demod', [status(thm)], ['45', '49', '2'])).
20.44/20.63	tff('51', plain,
20.44/20.63	    ![X0 : bool]: (X0 = fFalse | ~ app_encode_app(bool, $o, pp, X0)),
20.44/20.63	    inference('simplify', [status(thm)], ['50'])).
20.44/20.63	tff('52', plain,
20.44/20.63	    ![X0 : bool]: (app_encode_app(bool, $o, pp, X0) | X0 = fFalse),
20.44/20.63	    inference('sup+', [status(thm)], ['0', '2'])).
20.44/20.63	tff('53', plain, ![X0 : bool]: X0 = fFalse,
20.44/20.63	    inference('clc', [status(thm)], ['51', '52'])).
20.44/20.63	tff('54', plain, fFalse != fFalse,
20.44/20.63	    inference('demod', [status(thm)], ['40', '53'])).
20.44/20.63	tff('55', plain, $false, inference('simplify', [status(thm)], ['54'])).
20.44/20.63	
20.44/20.63	% SZS output end Refutation
20.44/20.64	EOF
