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    : rpo6
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.20	% Computer   : n132.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 07:30:24 CST 2018
79.23/79.35	% done 12651 iterations in 79.144s
79.23/79.35	% SZS status Theorem for 'stdin'
79.23/79.35	% SZS output start Refutation
79.23/79.35	tff(zf_stmt_100, axiom,
79.23/79.35	  (app_encode_app(int,int,
79.23/79.35	                  app_encode_app(fun_int_int,app_encode_fun(int,int),
79.23/79.35	                                 hAPP_int_int,
79.23/79.35	                                 app_encode_app(int,fun_int_int,
79.23/79.35	                                                plus_plus_int,
79.23/79.35	                                                app_encode_app(nat,int,
79.23/79.35	                                                               app_encode_app(
79.23/79.35	                                                               fun_nat_int,
79.23/79.35	                                                               app_encode_fun(
79.23/79.35	                                                               nat,int),
79.23/79.35	                                                               hAPP_nat_int,
79.23/79.35	                                                               app_encode_app(
79.23/79.35	                                                               int,
79.23/79.35	                                                               fun_nat_int,
79.23/79.35	                                                               power_power_int,
79.23/79.35	                                                               s)),
79.23/79.35	                                                               app_encode_app(
79.23/79.35	                                                               int,nat,
79.23/79.35	                                                               number_number_of_nat,
79.23/79.35	                                                               app_encode_app(
79.23/79.35	                                                               int,int,bit0,
79.23/79.35	                                                               app_encode_app(
79.23/79.35	                                                               int,int,bit1,
79.23/79.35	                                                               pls)))))),
79.23/79.35	                  one_one_int) =
79.23/79.35	   app_encode_app(int,int,
79.23/79.35	                  app_encode_app(fun_int_int,app_encode_fun(int,int),
79.23/79.35	                                 hAPP_int_int,
79.23/79.35	                                 app_encode_app(int,fun_int_int,
79.23/79.35	                                                times_times_int,
79.23/79.35	                                                app_encode_app(int,int,
79.23/79.35	                                                               app_encode_app(
79.23/79.35	                                                               fun_int_int,
79.23/79.35	                                                               app_encode_fun(
79.23/79.35	                                                               int,int),
79.23/79.35	                                                               hAPP_int_int,
79.23/79.35	                                                               app_encode_app(
79.23/79.35	                                                               int,
79.23/79.35	                                                               fun_int_int,
79.23/79.35	                                                               plus_plus_int,
79.23/79.35	                                                               app_encode_app(
79.23/79.35	                                                               int,int,
79.23/79.35	                                                               app_encode_app(
79.23/79.35	                                                               fun_int_int,
79.23/79.35	                                                               app_encode_fun(
79.23/79.35	                                                               int,int),
79.23/79.35	                                                               hAPP_int_int,
79.23/79.35	                                                               app_encode_app(
79.23/79.35	                                                               int,
79.23/79.35	                                                               fun_int_int,
79.23/79.35	                                                               times_times_int,
79.23/79.35	                                                               app_encode_app(
79.23/79.35	                                                               int,int,
79.23/79.35	                                                               number_number_of_int,
79.23/79.35	                                                               app_encode_app(
79.23/79.35	                                                               int,int,bit0,
79.23/79.35	                                                               app_encode_app(
79.23/79.35	                                                               int,int,bit0,
79.23/79.35	                                                               app_encode_app(
79.23/79.35	                                                               int,int,bit1,
79.23/79.35	                                                               pls)))))),m))),
79.23/79.35	                                                               one_one_int))),
79.23/79.35	                  t))).
79.23/79.35	tff('0', plain,
79.23/79.35	    app_encode_app(int, int, 
79.23/79.35	      app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
79.23/79.35	        app_encode_app(int, fun_int_int, plus_plus_int, 
79.23/79.35	          app_encode_app(nat, int, 
79.23/79.35	            app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
79.23/79.35	              hAPP_nat_int, 
79.23/79.35	              app_encode_app(int, fun_nat_int, power_power_int, s)), 
79.23/79.35	            app_encode_app(int, nat, number_number_of_nat, 
79.23/79.35	              app_encode_app(int, int, bit0, 
79.23/79.35	                app_encode_app(int, int, bit1, pls)))))), one_one_int)
79.23/79.35	     = app_encode_app(int, int, 
79.23/79.35	         app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
79.23/79.35	           app_encode_app(int, fun_int_int, times_times_int, 
79.23/79.35	             app_encode_app(int, int, 
79.23/79.35	               app_encode_app(fun_int_int, app_encode_fun(int, int), 
79.23/79.35	                 hAPP_int_int, 
79.23/79.35	                 app_encode_app(int, fun_int_int, plus_plus_int, 
79.23/79.35	                   app_encode_app(int, int, 
79.23/79.35	                     app_encode_app(fun_int_int, app_encode_fun(int, int), 
79.23/79.35	                       hAPP_int_int, 
79.23/79.35	                       app_encode_app(int, fun_int_int, times_times_int, 
79.23/79.35	                         app_encode_app(int, int, number_number_of_int, 
79.23/79.35	                           app_encode_app(int, int, bit0, 
79.23/79.35	                             app_encode_app(int, int, bit0, 
79.23/79.35	                               app_encode_app(int, int, bit1, pls)))))), m))), 
79.23/79.35	               one_one_int))), t),
79.23/79.35	    inference('cnf', [status(esa)], [zf_stmt_100])).
79.23/79.35	tff(zf_stmt_269, axiom, (pls = zero_zero_int)).
79.23/79.35	tff('1', plain, pls = zero_zero_int,
79.23/79.35	    inference('cnf', [status(esa)], [zf_stmt_269])).
79.23/79.35	tff(zf_stmt_257, axiom,
79.23/79.35	  (one_one_int =
79.23/79.35	   app_encode_app(int,int,number_number_of_int,
79.23/79.35	                  app_encode_app(int,int,bit1,pls)))).
79.23/79.35	tff('2', plain,
79.23/79.35	    one_one_int
79.23/79.35	     = app_encode_app(int, int, number_number_of_int, 
79.23/79.35	         app_encode_app(int, int, bit1, pls)),
79.23/79.35	    inference('cnf', [status(esa)], [zf_stmt_257])).
79.23/79.35	tff(zf_stmt_131, axiom,
79.23/79.35	  (![K_1:int]: (app_encode_app(int,int,number_number_of_int,K_1) = K_1))).
79.23/79.35	tff('3', plain,
79.23/79.35	    ![X35 : int]: app_encode_app(int, int, number_number_of_int, X35) = X35,
79.23/79.35	    inference('cnf', [status(esa)], [zf_stmt_131])).
79.23/79.35	tff('4', plain, one_one_int = app_encode_app(int, int, bit1, zero_zero_int),
79.23/79.35	    inference('demod', [status(thm)], ['2', '1', '3'])).
79.23/79.35	tff('5', plain,
79.23/79.35	    app_encode_app(int, int, 
79.23/79.35	      app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
79.23/79.35	        app_encode_app(int, fun_int_int, plus_plus_int, 
79.23/79.35	          app_encode_app(nat, int, 
79.23/79.35	            app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
79.23/79.35	              hAPP_nat_int, 
79.23/79.35	              app_encode_app(int, fun_nat_int, power_power_int, s)), 
79.23/79.35	            app_encode_app(int, nat, number_number_of_nat, 
79.23/79.35	              app_encode_app(int, int, bit0, 
79.23/79.35	                app_encode_app(int, int, bit1, zero_zero_int)))))), 
79.23/79.35	      app_encode_app(int, int, bit1, zero_zero_int))
79.23/79.35	     = app_encode_app(int, int, 
79.23/79.35	         app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
79.23/79.35	           app_encode_app(int, fun_int_int, times_times_int, 
79.23/79.35	             app_encode_app(int, int, 
79.23/79.35	               app_encode_app(fun_int_int, app_encode_fun(int, int), 
79.23/79.35	                 hAPP_int_int, 
79.23/79.35	                 app_encode_app(int, fun_int_int, plus_plus_int, 
79.23/79.35	                   app_encode_app(int, int, 
79.23/79.35	                     app_encode_app(fun_int_int, app_encode_fun(int, int), 
79.23/79.35	                       hAPP_int_int, 
79.23/79.35	                       app_encode_app(int, fun_int_int, times_times_int, 
79.23/79.35	                         app_encode_app(int, int, bit0, 
79.23/79.35	                           app_encode_app(int, int, bit0, 
79.23/79.35	                             app_encode_app(int, int, bit1, zero_zero_int))))), 
79.23/79.35	                     m))), app_encode_app(int, int, bit1, zero_zero_int)))), 
79.23/79.35	         t),
79.23/79.35	    inference('demod', [status(thm)], ['0', '1', '4', '1', '3', '4'])).
79.23/79.35	tff(zf_stmt_231, axiom,
79.23/79.35	  (![Z:int,W:int]:
79.23/79.35	     (app_encode_app(int,int,
79.23/79.35	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
79.23/79.35	                                    hAPP_int_int,
79.23/79.35	                                    app_encode_app(int,fun_int_int,
79.23/79.35	                                                   plus_plus_int,Z)),
79.23/79.35	                     W) =
79.23/79.35	      app_encode_app(int,int,
79.23/79.35	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
79.23/79.35	                                    hAPP_int_int,
79.23/79.35	                                    app_encode_app(int,fun_int_int,
79.23/79.35	                                                   plus_plus_int,W)),
79.23/79.35	                     Z)))).
79.23/79.35	tff('6', plain,
79.23/79.35	    ![X269 : int, X270 : int]:
79.23/79.35	      app_encode_app(int, int, 
79.23/79.35	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
79.23/79.35	          app_encode_app(int, fun_int_int, plus_plus_int, X270)), X269)
79.23/79.35	       = app_encode_app(int, int, 
79.23/79.35	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
79.23/79.35	             hAPP_int_int, 
79.23/79.35	             app_encode_app(int, fun_int_int, plus_plus_int, X269)), X270),
79.23/79.35	    inference('cnf', [status(esa)], [zf_stmt_231])).
79.23/79.35	tff('7', plain,
79.23/79.35	    app_encode_app(int, int, 
79.23/79.35	      app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
79.23/79.35	        app_encode_app(int, fun_int_int, plus_plus_int, 
79.23/79.35	          app_encode_app(int, int, bit1, zero_zero_int))), 
79.23/79.35	      app_encode_app(nat, int, 
79.23/79.35	        app_encode_app(fun_nat_int, app_encode_fun(nat, int), hAPP_nat_int, 
79.23/79.35	          app_encode_app(int, fun_nat_int, power_power_int, s)), 
79.23/79.35	        app_encode_app(int, nat, number_number_of_nat, 
79.23/79.35	          app_encode_app(int, int, bit0, 
79.23/79.35	            app_encode_app(int, int, bit1, zero_zero_int)))))
79.23/79.35	     = app_encode_app(int, int, 
79.23/79.35	         app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
79.23/79.35	           app_encode_app(int, fun_int_int, times_times_int, 
79.23/79.35	             app_encode_app(int, int, 
79.23/79.35	               app_encode_app(fun_int_int, app_encode_fun(int, int), 
79.23/79.35	                 hAPP_int_int, 
79.23/79.35	                 app_encode_app(int, fun_int_int, plus_plus_int, 
79.23/79.35	                   app_encode_app(int, int, bit1, zero_zero_int))), 
79.23/79.35	               app_encode_app(int, int, 
79.23/79.35	                 app_encode_app(fun_int_int, app_encode_fun(int, int), 
79.23/79.35	                   hAPP_int_int, 
79.23/79.35	                   app_encode_app(int, fun_int_int, times_times_int, 
79.23/79.35	                     app_encode_app(int, int, bit0, 
79.23/79.35	                       app_encode_app(int, int, bit0, 
79.23/79.35	                         app_encode_app(int, int, bit1, zero_zero_int))))), 
79.23/79.35	                 m)))), t),
79.23/79.35	    inference('demod', [status(thm)], ['5', '6', '6'])).
79.23/79.35	tff(zf_stmt_300, axiom,
79.23/79.35	  (![A_103:int]:
79.23/79.35	     (app_encode_app(nat,int,
79.23/79.35	                     app_encode_app(fun_nat_int,app_encode_fun(nat,int),
79.23/79.35	                                    hAPP_nat_int,
79.23/79.35	                                    app_encode_app(int,fun_nat_int,
79.23/79.35	                                                   power_power_int,A_103)),
79.23/79.35	                     app_encode_app(int,nat,number_number_of_nat,
79.23/79.35	                                    app_encode_app(int,int,bit0,
79.23/79.35	                                                   app_encode_app(int,int,
79.23/79.35	                                                                  bit1,pls)))) =
79.23/79.35	      app_encode_app(int,int,
79.23/79.35	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
79.23/79.35	                                    hAPP_int_int,
79.23/79.35	                                    app_encode_app(int,fun_int_int,
79.23/79.35	                                                   times_times_int,A_103)),
79.23/79.35	                     A_103)))).
79.23/79.35	tff('8', plain,
79.23/79.35	    ![X375 : int]:
79.23/79.35	      app_encode_app(nat, int, 
79.23/79.35	        app_encode_app(fun_nat_int, app_encode_fun(nat, int), hAPP_nat_int, 
79.23/79.35	          app_encode_app(int, fun_nat_int, power_power_int, X375)), 
79.23/79.35	        app_encode_app(int, nat, number_number_of_nat, 
79.23/79.35	          app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls))))
79.23/79.35	       = app_encode_app(int, int, 
79.23/79.35	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
79.23/79.35	             hAPP_int_int, 
79.23/79.35	             app_encode_app(int, fun_int_int, times_times_int, X375)), X375),
79.23/79.35	    inference('cnf', [status(esa)], [zf_stmt_300])).
79.23/79.35	tff('9', plain,
79.23/79.35	    ![X375 : int]:
79.23/79.35	      app_encode_app(nat, int, 
79.23/79.35	        app_encode_app(fun_nat_int, app_encode_fun(nat, int), hAPP_nat_int, 
79.23/79.35	          app_encode_app(int, fun_nat_int, power_power_int, X375)), 
79.23/79.35	        app_encode_app(int, nat, number_number_of_nat, 
79.23/79.35	          app_encode_app(int, int, bit0, 
79.23/79.35	            app_encode_app(int, int, bit1, zero_zero_int))))
79.23/79.35	       = app_encode_app(int, int, 
79.23/79.35	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
79.23/79.35	             hAPP_int_int, 
79.23/79.35	             app_encode_app(int, fun_int_int, times_times_int, X375)), X375),
79.23/79.35	    inference('demod', [status(thm)], ['8', '1'])).
79.23/79.35	tff(zf_stmt_186, axiom,
79.23/79.35	  (![K_1:int,L:int]:
79.23/79.35	     (app_encode_app(int,int,
79.23/79.35	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
79.23/79.35	                                    hAPP_int_int,
79.23/79.35	                                    app_encode_app(int,fun_int_int,
79.23/79.35	                                                   times_times_int,
79.23/79.35	                                                   app_encode_app(int,int,
79.23/79.35	                                                                  bit0,K_1))),
79.23/79.35	                     L) =
79.23/79.35	      app_encode_app(int,int,bit0,
79.23/79.35	                     app_encode_app(int,int,
79.23/79.35	                                    app_encode_app(fun_int_int,
79.23/79.35	                                                   app_encode_fun(int,int),
79.23/79.35	                                                   hAPP_int_int,
79.23/79.35	                                                   app_encode_app(int,
79.23/79.35	                                                                  fun_int_int,
79.23/79.35	                                                                  times_times_int,
79.23/79.35	                                                                  K_1)),
79.23/79.35	                                    L))))).
79.23/79.35	tff('10', plain,
79.23/79.35	    ![X158 : int, X159 : int]:
79.23/79.35	      app_encode_app(int, int, 
79.23/79.35	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
79.23/79.35	          app_encode_app(int, fun_int_int, times_times_int, 
79.23/79.35	            app_encode_app(int, int, bit0, X158))), X159)
79.23/79.35	       = app_encode_app(int, int, bit0, 
79.23/79.35	           app_encode_app(int, int, 
79.23/79.35	             app_encode_app(fun_int_int, app_encode_fun(int, int), 
79.23/79.35	               hAPP_int_int, 
79.23/79.35	               app_encode_app(int, fun_int_int, times_times_int, X158)), 
79.23/79.35	             X159)),
79.23/79.35	    inference('cnf', [status(esa)], [zf_stmt_186])).
79.23/79.35	tff(zf_stmt_189, axiom,
79.23/79.35	  (![Z:int]:
79.23/79.35	     (app_encode_app(int,int,
79.23/79.35	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
79.23/79.35	                                    hAPP_int_int,
79.23/79.35	                                    app_encode_app(int,fun_int_int,
79.23/79.35	                                                   times_times_int,
79.23/79.35	                                                   one_one_int)),
79.23/79.35	                     Z) =
79.23/79.35	      Z))).
79.23/79.35	tff('11', plain,
79.23/79.35	    ![X164 : int]:
79.23/79.35	      app_encode_app(int, int, 
79.23/79.35	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
79.23/79.35	          app_encode_app(int, fun_int_int, times_times_int, one_one_int)), 
79.23/79.35	        X164)
79.23/79.35	       = X164,
79.23/79.35	    inference('cnf', [status(esa)], [zf_stmt_189])).
79.23/79.35	tff('12', plain,
79.23/79.35	    ![X164 : int]:
79.23/79.35	      app_encode_app(int, int, 
79.23/79.35	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
79.23/79.35	          app_encode_app(int, fun_int_int, times_times_int, 
79.23/79.35	            app_encode_app(int, int, bit1, zero_zero_int))), X164)
79.23/79.35	       = X164,
79.23/79.35	    inference('demod', [status(thm)], ['11', '4'])).
79.23/79.35	tff(zf_stmt_330, axiom,
79.23/79.35	  (![K_1:int,L:int]:
79.23/79.35	     (app_encode_app(int,int,
79.23/79.35	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
79.23/79.35	                                    hAPP_int_int,
79.23/79.35	                                    app_encode_app(int,fun_int_int,
79.23/79.35	                                                   plus_plus_int,
79.23/79.35	                                                   app_encode_app(int,int,
79.23/79.35	                                                                  bit1,K_1))),
79.23/79.35	                     app_encode_app(int,int,bit0,L)) =
79.23/79.35	      app_encode_app(int,int,bit1,
79.23/79.35	                     app_encode_app(int,int,
79.23/79.35	                                    app_encode_app(fun_int_int,
79.23/79.35	                                                   app_encode_fun(int,int),
79.23/79.35	                                                   hAPP_int_int,
79.23/79.35	                                                   app_encode_app(int,
79.23/79.35	                                                                  fun_int_int,
79.23/79.35	                                                                  plus_plus_int,
79.23/79.35	                                                                  K_1)),
79.23/79.35	                                    L))))).
79.23/79.35	tff('13', plain,
79.23/79.35	    ![X420 : int, X421 : int]:
79.23/79.35	      app_encode_app(int, int, 
79.23/79.35	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
79.23/79.35	          app_encode_app(int, fun_int_int, plus_plus_int, 
79.23/79.35	            app_encode_app(int, int, bit1, X420))), 
79.23/79.35	        app_encode_app(int, int, bit0, X421))
79.23/79.35	       = app_encode_app(int, int, bit1, 
79.23/79.35	           app_encode_app(int, int, 
79.23/79.35	             app_encode_app(fun_int_int, app_encode_fun(int, int), 
79.23/79.35	               hAPP_int_int, 
79.23/79.35	               app_encode_app(int, fun_int_int, plus_plus_int, X420)), X421)),
79.23/79.35	    inference('cnf', [status(esa)], [zf_stmt_330])).
79.23/79.35	tff(zf_stmt_2, axiom,
79.23/79.35	  (![X:app_encode_fun(Alpha,Beta),Y:app_encode_fun(Alpha,Beta)]:
79.23/79.35	     ((![Z:Alpha]:
79.23/79.35	         (app_encode_app(Alpha,Beta,X,Z) = app_encode_app(Alpha,Beta,Y,Z))) =>
79.23/79.35	      (X = Y)))).
79.23/79.35	tff('14', plain,
79.23/79.35	    ![X0 : $tType, X1 : $tType, X2 : app_encode_fun(X0, X1), 
79.23/79.35	      X3 : app_encode_fun(X0, X1)]:
79.23/79.35	      (X3 = X2
79.23/79.35	       | app_encode_app(X0, X1, X3, sk_Z(X1, X0, X2, X3))
79.23/79.35	          != app_encode_app(X0, X1, X2, sk_Z(X1, X0, X2, X3))),
79.23/79.35	    inference('cnf', [status(esa)], [zf_stmt_2])).
79.23/79.35	tff('15', plain,
79.23/79.35	    ![X0 : app_encode_fun(int, int)]:
79.23/79.35	      (app_encode_app(int, int, X0, sk_Z(int, int, number_number_of_int, X0))
79.23/79.35	        != sk_Z(int, int, number_number_of_int, X0)
79.23/79.35	       | X0 = number_number_of_int),
79.23/79.35	    inference('sup-', [status(thm)], ['3', '14'])).
79.23/79.35	tff('16', plain,
79.23/79.35	    (sk_Z(int, int, number_number_of_int, 
79.23/79.35	       app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
79.23/79.35	         app_encode_app(int, fun_int_int, times_times_int, 
79.23/79.35	           app_encode_app(int, int, bit1, zero_zero_int))))
79.23/79.35	      != sk_Z(int, int, number_number_of_int, 
79.23/79.35	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
79.23/79.35	             hAPP_int_int, 
79.23/79.35	             app_encode_app(int, fun_int_int, times_times_int, 
79.23/79.35	               app_encode_app(int, int, bit1, zero_zero_int))))
79.23/79.35	     | app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
79.23/79.35	         app_encode_app(int, fun_int_int, times_times_int, 
79.23/79.35	           app_encode_app(int, int, bit1, zero_zero_int)))
79.23/79.35	        = number_number_of_int),
79.23/79.35	    inference('sup-', [status(thm)], ['12', '15'])).
79.23/79.35	tff('17', plain,
79.23/79.35	    app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
79.23/79.35	      app_encode_app(int, fun_int_int, times_times_int, 
79.23/79.35	        app_encode_app(int, int, bit1, zero_zero_int)))
79.23/79.35	     = number_number_of_int,
79.23/79.35	    inference('simplify', [status(thm)], ['16'])).
79.23/79.35	tff(zf_stmt_277, axiom,
79.23/79.35	  (![K_1:int]:
79.23/79.35	     (app_encode_app(int,int,
79.23/79.35	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
79.23/79.35	                                    hAPP_int_int,
79.23/79.35	                                    app_encode_app(int,fun_int_int,
79.23/79.35	                                                   plus_plus_int,pls)),
79.23/79.35	                     K_1) =
79.23/79.35	      K_1))).
79.23/79.35	tff('18', plain,
79.23/79.35	    ![X349 : int]:
79.23/79.35	      app_encode_app(int, int, 
79.23/79.35	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
79.23/79.35	          app_encode_app(int, fun_int_int, plus_plus_int, pls)), X349)
79.23/79.35	       = X349,
79.23/79.35	    inference('cnf', [status(esa)], [zf_stmt_277])).
79.23/79.35	tff('19', plain,
79.23/79.35	    ![X349 : int]:
79.23/79.35	      app_encode_app(int, int, 
79.23/79.35	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
79.23/79.35	          app_encode_app(int, fun_int_int, plus_plus_int, zero_zero_int)), 
79.23/79.35	        X349)
79.23/79.35	       = X349,
79.23/79.35	    inference('demod', [status(thm)], ['18', '1'])).
79.23/79.35	tff('20', plain,
79.23/79.35	    (sk_Z(int, int, number_number_of_int, 
79.23/79.35	       app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
79.23/79.35	         app_encode_app(int, fun_int_int, plus_plus_int, zero_zero_int)))
79.23/79.35	      != sk_Z(int, int, number_number_of_int, 
79.23/79.35	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
79.23/79.35	             hAPP_int_int, 
79.23/79.35	             app_encode_app(int, fun_int_int, plus_plus_int, zero_zero_int)))
79.23/79.35	     | app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
79.23/79.35	         app_encode_app(int, fun_int_int, plus_plus_int, zero_zero_int))
79.23/79.35	        = number_number_of_int),
79.23/79.35	    inference('sup-', [status(thm)], ['19', '15'])).
79.23/79.35	tff('21', plain,
79.23/79.35	    app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
79.23/79.35	      app_encode_app(int, fun_int_int, plus_plus_int, zero_zero_int))
79.23/79.35	     = number_number_of_int,
79.23/79.35	    inference('simplify', [status(thm)], ['20'])).
79.23/79.35	tff('22', plain,
79.23/79.35	    app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
79.23/79.35	      app_encode_app(int, fun_int_int, plus_plus_int, zero_zero_int))
79.23/79.35	     = app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
79.23/79.35	         app_encode_app(int, fun_int_int, times_times_int, 
79.23/79.35	           app_encode_app(int, int, bit1, zero_zero_int))),
79.23/79.35	    inference('sup+', [status(thm)], ['17', '21'])).
79.23/79.35	tff('23', plain,
79.23/79.35	    app_encode_app(int, int, 
79.23/79.35	      app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
79.23/79.35	        app_encode_app(int, fun_int_int, plus_plus_int, 
79.23/79.35	          app_encode_app(int, int, bit1, zero_zero_int))), 
79.23/79.35	      app_encode_app(int, int, 
79.23/79.35	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
79.23/79.35	          app_encode_app(int, fun_int_int, times_times_int, s)), s))
79.23/79.35	     = app_encode_app(int, int, 
79.23/79.35	         app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
79.23/79.35	           app_encode_app(int, fun_int_int, times_times_int, 
79.23/79.35	             app_encode_app(int, int, bit1, 
79.23/79.35	               app_encode_app(int, int, bit0, m)))), t),
79.23/79.35	    inference('demod', [status(thm)],
79.23/79.35	              ['7', '9', '10', '10', '12', '13', '22', '12'])).
79.23/79.35	tff(zf_stmt_522, axiom,
79.23/79.35	  (![B:int,A:int]:
79.23/79.35	     (app_encode_app(bool,$o,hBOOL,
79.23/79.35	                     app_encode_app(int,bool,
79.23/79.35	                                    app_encode_app(fun_int_bool,
79.23/79.35	                                                   app_encode_fun(int,bool),
79.23/79.35	                                                   hAPP_int_bool,
79.23/79.35	                                                   app_encode_app(int,
79.23/79.35	                                                                  fun_int_bool,
79.23/79.35	                                                                  app_encode_app(
79.23/79.35	                                                                  fun_int_fun_int_bool,
79.23/79.35	                                                                  app_encode_fun(
79.23/79.35	                                                                  int,
79.23/79.35	                                                                  fun_int_bool),
79.23/79.35	                                                                  hAPP_i1948725293t_bool,
79.23/79.35	                                                                  ord_less_int),
79.23/79.35	                                                                  zero_zero_int)),
79.23/79.35	                                    A)) =>
79.23/79.35	      (app_encode_app(bool,$o,hBOOL,
79.23/79.35	                      app_encode_app(int,bool,
79.23/79.35	                                     app_encode_app(fun_int_bool,
79.23/79.35	                                                    app_encode_fun(int,bool),
79.23/79.35	                                                    hAPP_int_bool,
79.23/79.35	                                                    app_encode_app(int,
79.23/79.35	                                                                   fun_int_bool,
79.23/79.35	                                                                   app_encode_app(
79.23/79.35	                                                                   fun_int_fun_int_bool,
79.23/79.35	                                                                   app_encode_fun(
79.23/79.35	                                                                   int,
79.23/79.35	                                                                   fun_int_bool),
79.23/79.35	                                                                   hAPP_i1948725293t_bool,
79.23/79.35	                                                                   ord_less_int),
79.23/79.35	                                                                   zero_zero_int)),
79.23/79.35	                                     app_encode_app(int,int,
79.23/79.35	                                                    app_encode_app(fun_int_int,
79.23/79.35	                                                                   app_encode_fun(
79.23/79.35	                                                                   int,int),
79.23/79.35	                                                                   hAPP_int_int,
79.23/79.35	                                                                   app_encode_app(
79.23/79.35	                                                                   int,
79.23/79.35	                                                                   fun_int_int,
79.23/79.35	                                                                   times_times_int,
79.23/79.35	                                                                   A)),
79.23/79.35	                                                    B))) =>
79.23/79.35	       app_encode_app(bool,$o,hBOOL,
79.23/79.35	                      app_encode_app(int,bool,
79.23/79.35	                                     app_encode_app(fun_int_bool,
79.23/79.35	                                                    app_encode_fun(int,bool),
79.23/79.35	                                                    hAPP_int_bool,
79.23/79.35	                                                    app_encode_app(int,
79.23/79.35	                                                                   fun_int_bool,
79.23/79.35	                                                                   app_encode_app(
79.23/79.35	                                                                   fun_int_fun_int_bool,
79.23/79.35	                                                                   app_encode_fun(
79.23/79.35	                                                                   int,
79.23/79.35	                                                                   fun_int_bool),
79.23/79.35	                                                                   hAPP_i1948725293t_bool,
79.23/79.35	                                                                   ord_less_int),
79.23/79.35	                                                                   zero_zero_int)),
79.23/79.35	                                     B)))))).
79.23/79.35	tff('24', plain,
79.23/79.35	    ![X837 : int, X838 : int]:
79.23/79.35	      (app_encode_app(bool, $o, hBOOL, 
79.23/79.35	         app_encode_app(int, bool, 
79.23/79.35	           app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.35	             hAPP_int_bool, 
79.23/79.35	             app_encode_app(int, fun_int_bool, 
79.23/79.35	               app_encode_app(fun_int_fun_int_bool, 
79.23/79.35	                 app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
79.23/79.35	                 ord_less_int), zero_zero_int)), X837))
79.23/79.35	       | ~ app_encode_app(bool, $o, hBOOL, 
79.23/79.35	             app_encode_app(int, bool, 
79.23/79.35	               app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.35	                 hAPP_int_bool, 
79.23/79.35	                 app_encode_app(int, fun_int_bool, 
79.23/79.35	                   app_encode_app(fun_int_fun_int_bool, 
79.23/79.35	                     app_encode_fun(int, fun_int_bool), 
79.23/79.35	                     hAPP_i1948725293t_bool, ord_less_int), zero_zero_int)), 
79.23/79.35	               X838))
79.23/79.35	       | ~ app_encode_app(bool, $o, hBOOL, 
79.23/79.35	             app_encode_app(int, bool, 
79.23/79.35	               app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.35	                 hAPP_int_bool, 
79.23/79.35	                 app_encode_app(int, fun_int_bool, 
79.23/79.35	                   app_encode_app(fun_int_fun_int_bool, 
79.23/79.35	                     app_encode_fun(int, fun_int_bool), 
79.23/79.35	                     hAPP_i1948725293t_bool, ord_less_int), zero_zero_int)), 
79.23/79.35	               app_encode_app(int, int, 
79.23/79.35	                 app_encode_app(fun_int_int, app_encode_fun(int, int), 
79.23/79.35	                   hAPP_int_int, 
79.23/79.35	                   app_encode_app(int, fun_int_int, times_times_int, X838)), 
79.23/79.35	                 X837)))),
79.23/79.35	    inference('cnf', [status(esa)], [zf_stmt_522])).
79.23/79.35	tff('25', plain,
79.23/79.35	    (~ app_encode_app(bool, $o, hBOOL, 
79.23/79.35	         app_encode_app(int, bool, 
79.23/79.35	           app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.35	             hAPP_int_bool, 
79.23/79.35	             app_encode_app(int, fun_int_bool, 
79.23/79.35	               app_encode_app(fun_int_fun_int_bool, 
79.23/79.35	                 app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
79.23/79.35	                 ord_less_int), zero_zero_int)), 
79.23/79.35	           app_encode_app(int, int, 
79.23/79.35	             app_encode_app(fun_int_int, app_encode_fun(int, int), 
79.23/79.35	               hAPP_int_int, 
79.23/79.35	               app_encode_app(int, fun_int_int, plus_plus_int, 
79.23/79.35	                 app_encode_app(int, int, bit1, zero_zero_int))), 
79.23/79.35	             app_encode_app(int, int, 
79.23/79.35	               app_encode_app(fun_int_int, app_encode_fun(int, int), 
79.23/79.35	                 hAPP_int_int, 
79.23/79.35	                 app_encode_app(int, fun_int_int, times_times_int, s)), s))))
79.23/79.36	     | ~ app_encode_app(bool, $o, hBOOL, 
79.23/79.36	           app_encode_app(int, bool, 
79.23/79.36	             app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.36	               hAPP_int_bool, 
79.23/79.36	               app_encode_app(int, fun_int_bool, 
79.23/79.36	                 app_encode_app(fun_int_fun_int_bool, 
79.23/79.36	                   app_encode_fun(int, fun_int_bool), 
79.23/79.36	                   hAPP_i1948725293t_bool, ord_less_int), zero_zero_int)), 
79.23/79.36	             app_encode_app(int, int, bit1, 
79.23/79.36	               app_encode_app(int, int, bit0, m))))
79.23/79.36	     | app_encode_app(bool, $o, hBOOL, 
79.23/79.36	         app_encode_app(int, bool, 
79.23/79.36	           app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.36	             hAPP_int_bool, 
79.23/79.36	             app_encode_app(int, fun_int_bool, 
79.23/79.36	               app_encode_app(fun_int_fun_int_bool, 
79.23/79.36	                 app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
79.23/79.36	                 ord_less_int), zero_zero_int)), t))),
79.23/79.36	    inference('sup-', [status(thm)], ['23', '24'])).
79.23/79.36	tff(zf_stmt_659, axiom,
79.23/79.36	  (![N_17:nat]:
79.23/79.36	     (app_encode_app(nat,int,
79.23/79.36	                     app_encode_app(fun_nat_int,app_encode_fun(nat,int),
79.23/79.36	                                    hAPP_nat_int,
79.23/79.36	                                    app_encode_app(int,fun_nat_int,
79.23/79.36	                                                   power_power_int,
79.23/79.36	                                                   one_one_int)),
79.23/79.36	                     N_17) =
79.23/79.36	      one_one_int))).
79.23/79.36	tff('26', plain,
79.23/79.36	    ![X1121 : nat]:
79.23/79.36	      app_encode_app(nat, int, 
79.23/79.36	        app_encode_app(fun_nat_int, app_encode_fun(nat, int), hAPP_nat_int, 
79.23/79.36	          app_encode_app(int, fun_nat_int, power_power_int, one_one_int)), 
79.23/79.36	        X1121)
79.23/79.36	       = one_one_int,
79.23/79.36	    inference('cnf', [status(esa)], [zf_stmt_659])).
79.23/79.36	tff('27', plain,
79.23/79.36	    ![X1121 : nat]:
79.23/79.36	      app_encode_app(nat, int, 
79.23/79.36	        app_encode_app(fun_nat_int, app_encode_fun(nat, int), hAPP_nat_int, 
79.23/79.36	          app_encode_app(int, fun_nat_int, power_power_int, 
79.23/79.36	            app_encode_app(int, int, bit1, zero_zero_int))), X1121)
79.23/79.36	       = app_encode_app(int, int, bit1, zero_zero_int),
79.23/79.36	    inference('demod', [status(thm)], ['26', '4', '4'])).
79.23/79.36	tff(zf_stmt_107, axiom,
79.23/79.36	  (![X:int,Y_1:int]:
79.23/79.36	     (app_encode_app(bool,$o,hBOOL,
79.23/79.36	                     app_encode_app(int,bool,
79.23/79.36	                                    app_encode_app(fun_int_bool,
79.23/79.36	                                                   app_encode_fun(int,bool),
79.23/79.36	                                                   hAPP_int_bool,
79.23/79.36	                                                   app_encode_app(int,
79.23/79.36	                                                                  fun_int_bool,
79.23/79.36	                                                                  app_encode_app(
79.23/79.36	                                                                  fun_int_fun_int_bool,
79.23/79.36	                                                                  app_encode_fun(
79.23/79.36	                                                                  int,
79.23/79.36	                                                                  fun_int_bool),
79.23/79.36	                                                                  hAPP_i1948725293t_bool,
79.23/79.36	                                                                  ord_less_int),
79.23/79.36	                                                                  zero_zero_int)),
79.23/79.36	                                    app_encode_app(int,int,
79.23/79.36	                                                   app_encode_app(fun_int_int,
79.23/79.36	                                                                  app_encode_fun(
79.23/79.36	                                                                  int,int),
79.23/79.36	                                                                  hAPP_int_int,
79.23/79.36	                                                                  app_encode_app(
79.23/79.36	                                                                  int,
79.23/79.36	                                                                  fun_int_int,
79.23/79.36	                                                                  plus_plus_int,
79.23/79.36	                                                                  app_encode_app(
79.23/79.36	                                                                  nat,int,
79.23/79.36	                                                                  app_encode_app(
79.23/79.36	                                                                  fun_nat_int,
79.23/79.36	                                                                  app_encode_fun(
79.23/79.36	                                                                  nat,int),
79.23/79.36	                                                                  hAPP_nat_int,
79.23/79.36	                                                                  app_encode_app(
79.23/79.36	                                                                  int,
79.23/79.36	                                                                  fun_nat_int,
79.23/79.36	                                                                  power_power_int,
79.23/79.36	                                                                  X)),
79.23/79.36	                                                                  app_encode_app(
79.23/79.36	                                                                  int,nat,
79.23/79.36	                                                                  number_number_of_nat,
79.23/79.36	                                                                  app_encode_app(
79.23/79.36	                                                                  int,int,
79.23/79.36	                                                                  bit0,
79.23/79.36	                                                                  app_encode_app(
79.23/79.36	                                                                  int,int,
79.23/79.36	                                                                  bit1,pls)))))),
79.23/79.36	                                                   app_encode_app(nat,int,
79.23/79.36	                                                                  app_encode_app(
79.23/79.36	                                                                  fun_nat_int,
79.23/79.36	                                                                  app_encode_fun(
79.23/79.36	                                                                  nat,int),
79.23/79.36	                                                                  hAPP_nat_int,
79.23/79.36	                                                                  app_encode_app(
79.23/79.36	                                                                  int,
79.23/79.36	                                                                  fun_nat_int,
79.23/79.36	                                                                  power_power_int,
79.23/79.36	                                                                  Y_1)),
79.23/79.36	                                                                  app_encode_app(
79.23/79.36	                                                                  int,nat,
79.23/79.36	                                                                  number_number_of_nat,
79.23/79.36	                                                                  app_encode_app(
79.23/79.36	                                                                  int,int,
79.23/79.36	                                                                  bit0,
79.23/79.36	                                                                  app_encode_app(
79.23/79.36	                                                                  int,int,
79.23/79.36	                                                                  bit1,pls))))))) <=>
79.23/79.36	      ((X != zero_zero_int) | (Y_1 != zero_zero_int))))).
79.23/79.36	tff('28', plain,
79.23/79.36	    ![X12 : int, X13 : int]:
79.23/79.36	      (app_encode_app(bool, $o, hBOOL, 
79.23/79.36	         app_encode_app(int, bool, 
79.23/79.36	           app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.36	             hAPP_int_bool, 
79.23/79.36	             app_encode_app(int, fun_int_bool, 
79.23/79.36	               app_encode_app(fun_int_fun_int_bool, 
79.23/79.36	                 app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
79.23/79.36	                 ord_less_int), zero_zero_int)), 
79.23/79.36	           app_encode_app(int, int, 
79.23/79.36	             app_encode_app(fun_int_int, app_encode_fun(int, int), 
79.23/79.36	               hAPP_int_int, 
79.23/79.36	               app_encode_app(int, fun_int_int, plus_plus_int, 
79.23/79.36	                 app_encode_app(nat, int, 
79.23/79.36	                   app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
79.23/79.36	                     hAPP_nat_int, 
79.23/79.36	                     app_encode_app(int, fun_nat_int, power_power_int, X12)), 
79.23/79.36	                   app_encode_app(int, nat, number_number_of_nat, 
79.23/79.36	                     app_encode_app(int, int, bit0, 
79.23/79.36	                       app_encode_app(int, int, bit1, pls)))))), 
79.23/79.36	             app_encode_app(nat, int, 
79.23/79.36	               app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
79.23/79.36	                 hAPP_nat_int, 
79.23/79.36	                 app_encode_app(int, fun_nat_int, power_power_int, X13)), 
79.23/79.36	               app_encode_app(int, nat, number_number_of_nat, 
79.23/79.36	                 app_encode_app(int, int, bit0, 
79.23/79.36	                   app_encode_app(int, int, bit1, pls)))))))
79.23/79.36	       | X12 = zero_zero_int),
79.23/79.36	    inference('cnf', [status(esa)], [zf_stmt_107])).
79.23/79.36	tff('29', plain,
79.23/79.36	    ![X12 : int, X13 : int]:
79.23/79.36	      (app_encode_app(bool, $o, hBOOL, 
79.23/79.36	         app_encode_app(int, bool, 
79.23/79.36	           app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.36	             hAPP_int_bool, 
79.23/79.36	             app_encode_app(int, fun_int_bool, 
79.23/79.36	               app_encode_app(fun_int_fun_int_bool, 
79.23/79.36	                 app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
79.23/79.36	                 ord_less_int), zero_zero_int)), 
79.23/79.36	           app_encode_app(int, int, 
79.23/79.36	             app_encode_app(fun_int_int, app_encode_fun(int, int), 
79.23/79.36	               hAPP_int_int, 
79.23/79.36	               app_encode_app(int, fun_int_int, plus_plus_int, 
79.23/79.36	                 app_encode_app(nat, int, 
79.23/79.36	                   app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
79.23/79.36	                     hAPP_nat_int, 
79.23/79.36	                     app_encode_app(int, fun_nat_int, power_power_int, X12)), 
79.23/79.36	                   app_encode_app(int, nat, number_number_of_nat, 
79.23/79.36	                     app_encode_app(int, int, bit0, 
79.23/79.36	                       app_encode_app(int, int, bit1, zero_zero_int)))))), 
79.23/79.36	             app_encode_app(nat, int, 
79.23/79.36	               app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
79.23/79.36	                 hAPP_nat_int, 
79.23/79.36	                 app_encode_app(int, fun_nat_int, power_power_int, X13)), 
79.23/79.36	               app_encode_app(int, nat, number_number_of_nat, 
79.23/79.36	                 app_encode_app(int, int, bit0, 
79.23/79.36	                   app_encode_app(int, int, bit1, zero_zero_int)))))))
79.23/79.36	       | X12 = zero_zero_int),
79.23/79.36	    inference('demod', [status(thm)], ['28', '1', '1'])).
79.23/79.36	tff('30', plain,
79.23/79.36	    ![X0 : int]:
79.23/79.36	      (app_encode_app(bool, $o, hBOOL, 
79.23/79.36	         app_encode_app(int, bool, 
79.23/79.36	           app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.36	             hAPP_int_bool, 
79.23/79.36	             app_encode_app(int, fun_int_bool, 
79.23/79.36	               app_encode_app(fun_int_fun_int_bool, 
79.23/79.36	                 app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
79.23/79.36	                 ord_less_int), zero_zero_int)), 
79.23/79.36	           app_encode_app(int, int, 
79.23/79.36	             app_encode_app(fun_int_int, app_encode_fun(int, int), 
79.23/79.36	               hAPP_int_int, 
79.23/79.36	               app_encode_app(int, fun_int_int, plus_plus_int, 
79.23/79.36	                 app_encode_app(int, int, bit1, zero_zero_int))), 
79.23/79.36	             app_encode_app(nat, int, 
79.23/79.36	               app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
79.23/79.36	                 hAPP_nat_int, 
79.23/79.36	                 app_encode_app(int, fun_nat_int, power_power_int, X0)), 
79.23/79.36	               app_encode_app(int, nat, number_number_of_nat, 
79.23/79.36	                 app_encode_app(int, int, bit0, 
79.23/79.36	                   app_encode_app(int, int, bit1, zero_zero_int)))))))
79.23/79.36	       | app_encode_app(int, int, bit1, zero_zero_int) = zero_zero_int),
79.23/79.36	    inference('sup+', [status(thm)], ['27', '29'])).
79.23/79.36	tff(zf_stmt_262, axiom,
79.23/79.36	  (![K_1:int]: (app_encode_app(int,int,bit1,K_1) != pls))).
79.23/79.36	tff('31', plain, ![X326 : int]: app_encode_app(int, int, bit1, X326) != pls,
79.23/79.36	    inference('cnf', [status(esa)], [zf_stmt_262])).
79.23/79.36	tff('32', plain,
79.23/79.36	    ![X326 : int]: app_encode_app(int, int, bit1, X326) != zero_zero_int,
79.23/79.36	    inference('demod', [status(thm)], ['31', '1'])).
79.23/79.36	tff('33', plain,
79.23/79.36	    ![X0 : int]:
79.23/79.36	      app_encode_app(bool, $o, hBOOL, 
79.23/79.36	        app_encode_app(int, bool, 
79.23/79.36	          app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.36	            hAPP_int_bool, 
79.23/79.36	            app_encode_app(int, fun_int_bool, 
79.23/79.36	              app_encode_app(fun_int_fun_int_bool, 
79.23/79.36	                app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
79.23/79.36	                ord_less_int), zero_zero_int)), 
79.23/79.36	          app_encode_app(int, int, 
79.23/79.36	            app_encode_app(fun_int_int, app_encode_fun(int, int), 
79.23/79.36	              hAPP_int_int, 
79.23/79.36	              app_encode_app(int, fun_int_int, plus_plus_int, 
79.23/79.36	                app_encode_app(int, int, bit1, zero_zero_int))), 
79.23/79.36	            app_encode_app(nat, int, 
79.23/79.36	              app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
79.23/79.36	                hAPP_nat_int, 
79.23/79.36	                app_encode_app(int, fun_nat_int, power_power_int, X0)), 
79.23/79.36	              app_encode_app(int, nat, number_number_of_nat, 
79.23/79.36	                app_encode_app(int, int, bit0, 
79.23/79.36	                  app_encode_app(int, int, bit1, zero_zero_int))))))),
79.23/79.36	    inference('simplify_reflect-', [status(thm)], ['30', '32'])).
79.23/79.36	tff('34', plain,
79.23/79.36	    ![X0 : int]:
79.23/79.36	      app_encode_app(bool, $o, hBOOL, 
79.23/79.36	        app_encode_app(int, bool, 
79.23/79.36	          app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.36	            hAPP_int_bool, 
79.23/79.36	            app_encode_app(int, fun_int_bool, 
79.23/79.36	              app_encode_app(fun_int_fun_int_bool, 
79.23/79.36	                app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
79.23/79.36	                ord_less_int), zero_zero_int)), 
79.23/79.36	          app_encode_app(int, int, 
79.23/79.36	            app_encode_app(fun_int_int, app_encode_fun(int, int), 
79.23/79.36	              hAPP_int_int, 
79.23/79.36	              app_encode_app(int, fun_int_int, plus_plus_int, 
79.23/79.36	                app_encode_app(int, int, bit1, zero_zero_int))), 
79.23/79.36	            app_encode_app(int, int, 
79.23/79.36	              app_encode_app(fun_int_int, app_encode_fun(int, int), 
79.23/79.36	                hAPP_int_int, 
79.23/79.36	                app_encode_app(int, fun_int_int, times_times_int, X0)), X0)))),
79.23/79.36	    inference('demod', [status(thm)], ['33', '9'])).
79.23/79.36	tff(zf_stmt_133, axiom,
79.23/79.36	  (![Z:int,W:int]:
79.23/79.36	     (app_encode_app(bool,$o,hBOOL,
79.23/79.36	                     app_encode_app(int,bool,
79.23/79.36	                                    app_encode_app(fun_int_bool,
79.23/79.36	                                                   app_encode_fun(int,bool),
79.23/79.36	                                                   hAPP_int_bool,
79.23/79.36	                                                   app_encode_app(int,
79.23/79.36	                                                                  fun_int_bool,
79.23/79.36	                                                                  app_encode_app(
79.23/79.36	                                                                  fun_int_fun_int_bool,
79.23/79.36	                                                                  app_encode_fun(
79.23/79.36	                                                                  int,
79.23/79.36	                                                                  fun_int_bool),
79.23/79.36	                                                                  hAPP_i1948725293t_bool,
79.23/79.36	                                                                  ord_less_eq_int),
79.23/79.36	                                                                  Z)),
79.23/79.36	                                    W)) | 
79.23/79.36	      app_encode_app(bool,$o,hBOOL,
79.23/79.36	                     app_encode_app(int,bool,
79.23/79.36	                                    app_encode_app(fun_int_bool,
79.23/79.36	                                                   app_encode_fun(int,bool),
79.23/79.36	                                                   hAPP_int_bool,
79.23/79.36	                                                   app_encode_app(int,
79.23/79.36	                                                                  fun_int_bool,
79.23/79.36	                                                                  app_encode_app(
79.23/79.36	                                                                  fun_int_fun_int_bool,
79.23/79.36	                                                                  app_encode_fun(
79.23/79.36	                                                                  int,
79.23/79.36	                                                                  fun_int_bool),
79.23/79.36	                                                                  hAPP_i1948725293t_bool,
79.23/79.36	                                                                  ord_less_eq_int),
79.23/79.36	                                                                  W)),
79.23/79.36	                                    Z))))).
79.23/79.36	tff('35', plain,
79.23/79.36	    ![X38 : int, X39 : int]:
79.23/79.36	      (app_encode_app(bool, $o, hBOOL, 
79.23/79.36	         app_encode_app(int, bool, 
79.23/79.36	           app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.36	             hAPP_int_bool, 
79.23/79.36	             app_encode_app(int, fun_int_bool, 
79.23/79.36	               app_encode_app(fun_int_fun_int_bool, 
79.23/79.36	                 app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
79.23/79.36	                 ord_less_eq_int), X38)), X39))
79.23/79.36	       | app_encode_app(bool, $o, hBOOL, 
79.23/79.36	           app_encode_app(int, bool, 
79.23/79.36	             app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.36	               hAPP_int_bool, 
79.23/79.36	               app_encode_app(int, fun_int_bool, 
79.23/79.36	                 app_encode_app(fun_int_fun_int_bool, 
79.23/79.36	                   app_encode_fun(int, fun_int_bool), 
79.23/79.36	                   hAPP_i1948725293t_bool, ord_less_eq_int), X39)), X38))),
79.23/79.36	    inference('cnf', [status(esa)], [zf_stmt_133])).
79.23/79.36	tff(zf_stmt_128, axiom,
79.23/79.36	  (app_encode_app(bool,$o,hBOOL,
79.23/79.36	                  app_encode_app(int,bool,
79.23/79.36	                                 app_encode_app(fun_int_bool,
79.23/79.36	                                                app_encode_fun(int,bool),
79.23/79.36	                                                hAPP_int_bool,zprime),
79.23/79.36	                                 app_encode_app(int,int,
79.23/79.36	                                                app_encode_app(fun_int_int,
79.23/79.36	                                                               app_encode_fun(
79.23/79.36	                                                               int,int),
79.23/79.36	                                                               hAPP_int_int,
79.23/79.36	                                                               app_encode_app(
79.23/79.36	                                                               int,
79.23/79.36	                                                               fun_int_int,
79.23/79.36	                                                               plus_plus_int,
79.23/79.36	                                                               app_encode_app(
79.23/79.36	                                                               int,int,
79.23/79.36	                                                               app_encode_app(
79.23/79.36	                                                               fun_int_int,
79.23/79.36	                                                               app_encode_fun(
79.23/79.36	                                                               int,int),
79.23/79.36	                                                               hAPP_int_int,
79.23/79.36	                                                               app_encode_app(
79.23/79.36	                                                               int,
79.23/79.36	                                                               fun_int_int,
79.23/79.36	                                                               times_times_int,
79.23/79.36	                                                               app_encode_app(
79.23/79.36	                                                               int,int,
79.23/79.36	                                                               number_number_of_int,
79.23/79.36	                                                               app_encode_app(
79.23/79.36	                                                               int,int,bit0,
79.23/79.36	                                                               app_encode_app(
79.23/79.36	                                                               int,int,bit0,
79.23/79.36	                                                               app_encode_app(
79.23/79.36	                                                               int,int,bit1,
79.23/79.36	                                                               pls)))))),m))),
79.23/79.36	                                                one_one_int))))).
79.23/79.36	tff('36', plain,
79.23/79.36	    app_encode_app(bool, $o, hBOOL, 
79.23/79.36	      app_encode_app(int, bool, 
79.23/79.36	        app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.36	          hAPP_int_bool, zprime), 
79.23/79.36	        app_encode_app(int, int, 
79.23/79.36	          app_encode_app(fun_int_int, app_encode_fun(int, int), 
79.23/79.36	            hAPP_int_int, 
79.23/79.36	            app_encode_app(int, fun_int_int, plus_plus_int, 
79.23/79.36	              app_encode_app(int, int, 
79.23/79.36	                app_encode_app(fun_int_int, app_encode_fun(int, int), 
79.23/79.36	                  hAPP_int_int, 
79.23/79.36	                  app_encode_app(int, fun_int_int, times_times_int, 
79.23/79.36	                    app_encode_app(int, int, number_number_of_int, 
79.23/79.36	                      app_encode_app(int, int, bit0, 
79.23/79.36	                        app_encode_app(int, int, bit0, 
79.23/79.36	                          app_encode_app(int, int, bit1, pls)))))), m))), 
79.23/79.36	          one_one_int))),
79.23/79.36	    inference('cnf', [status(esa)], [zf_stmt_128])).
79.23/79.36	tff('37', plain,
79.23/79.36	    app_encode_app(bool, $o, hBOOL, 
79.23/79.36	      app_encode_app(int, bool, 
79.23/79.36	        app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.36	          hAPP_int_bool, zprime), 
79.23/79.36	        app_encode_app(int, int, 
79.23/79.36	          app_encode_app(fun_int_int, app_encode_fun(int, int), 
79.23/79.36	            hAPP_int_int, 
79.23/79.36	            app_encode_app(int, fun_int_int, plus_plus_int, 
79.23/79.36	              app_encode_app(int, int, bit1, zero_zero_int))), 
79.23/79.36	          app_encode_app(int, int, 
79.23/79.36	            app_encode_app(fun_int_int, app_encode_fun(int, int), 
79.23/79.36	              hAPP_int_int, 
79.23/79.36	              app_encode_app(int, fun_int_int, times_times_int, 
79.23/79.36	                app_encode_app(int, int, bit0, 
79.23/79.36	                  app_encode_app(int, int, bit0, 
79.23/79.36	                    app_encode_app(int, int, bit1, zero_zero_int))))), m)))),
79.23/79.36	    inference('demod', [status(thm)], ['36', '1', '3', '4', '6'])).
79.23/79.36	tff('38', plain,
79.23/79.36	    app_encode_app(bool, $o, hBOOL, 
79.23/79.36	      app_encode_app(int, bool, 
79.23/79.36	        app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.36	          hAPP_int_bool, zprime), 
79.23/79.36	        app_encode_app(int, int, 
79.23/79.36	          app_encode_app(fun_int_int, app_encode_fun(int, int), 
79.23/79.36	            hAPP_int_int, 
79.23/79.36	            app_encode_app(int, fun_int_int, plus_plus_int, 
79.23/79.36	              app_encode_app(int, int, bit1, zero_zero_int))), 
79.23/79.36	          app_encode_app(int, int, bit0, app_encode_app(int, int, bit0, m))))),
79.23/79.36	    inference('demod', [status(thm)], ['37', '10', '10', '12'])).
79.23/79.36	tff(zf_stmt_333, axiom,
79.23/79.36	  (![K_1:int]:
79.23/79.36	     (app_encode_app(int,int,bit1,K_1) =
79.23/79.36	      app_encode_app(int,int,
79.23/79.36	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
79.23/79.36	                                    hAPP_int_int,
79.23/79.36	                                    app_encode_app(int,fun_int_int,
79.23/79.36	                                                   plus_plus_int,
79.23/79.36	                                                   app_encode_app(int,int,
79.23/79.36	                                                                  app_encode_app(
79.23/79.36	                                                                  fun_int_int,
79.23/79.36	                                                                  app_encode_fun(
79.23/79.36	                                                                  int,int),
79.23/79.36	                                                                  hAPP_int_int,
79.23/79.36	                                                                  app_encode_app(
79.23/79.36	                                                                  int,
79.23/79.36	                                                                  fun_int_int,
79.23/79.36	                                                                  plus_plus_int,
79.23/79.36	                                                                  one_one_int)),
79.23/79.36	                                                                  K_1))),
79.23/79.36	                     K_1)))).
79.23/79.36	tff('39', plain,
79.23/79.36	    ![X424 : int]:
79.23/79.36	      app_encode_app(int, int, bit1, X424)
79.23/79.36	       = app_encode_app(int, int, 
79.23/79.36	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
79.23/79.36	             hAPP_int_int, 
79.23/79.36	             app_encode_app(int, fun_int_int, plus_plus_int, 
79.23/79.36	               app_encode_app(int, int, 
79.23/79.36	                 app_encode_app(fun_int_int, app_encode_fun(int, int), 
79.23/79.36	                   hAPP_int_int, 
79.23/79.36	                   app_encode_app(int, fun_int_int, plus_plus_int, 
79.23/79.36	                     one_one_int)), X424))), X424),
79.23/79.36	    inference('cnf', [status(esa)], [zf_stmt_333])).
79.23/79.36	tff('40', plain,
79.23/79.36	    ![X424 : int]:
79.23/79.36	      app_encode_app(int, int, bit1, X424)
79.23/79.36	       = app_encode_app(int, int, 
79.23/79.36	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
79.23/79.36	             hAPP_int_int, 
79.23/79.36	             app_encode_app(int, fun_int_int, plus_plus_int, X424)), 
79.23/79.36	           app_encode_app(int, int, 
79.23/79.36	             app_encode_app(fun_int_int, app_encode_fun(int, int), 
79.23/79.36	               hAPP_int_int, 
79.23/79.36	               app_encode_app(int, fun_int_int, plus_plus_int, 
79.23/79.36	                 app_encode_app(int, int, bit1, zero_zero_int))), X424)),
79.23/79.36	    inference('demod', [status(thm)], ['39', '4', '6'])).
79.23/79.36	tff(zf_stmt_230, axiom,
79.23/79.36	  (![X_1:int,Y:int,Z:int]:
79.23/79.36	     (app_encode_app(int,int,
79.23/79.36	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
79.23/79.36	                                    hAPP_int_int,
79.23/79.36	                                    app_encode_app(int,fun_int_int,
79.23/79.36	                                                   plus_plus_int,X_1)),
79.23/79.36	                     app_encode_app(int,int,
79.23/79.36	                                    app_encode_app(fun_int_int,
79.23/79.36	                                                   app_encode_fun(int,int),
79.23/79.36	                                                   hAPP_int_int,
79.23/79.36	                                                   app_encode_app(int,
79.23/79.36	                                                                  fun_int_int,
79.23/79.36	                                                                  plus_plus_int,
79.23/79.36	                                                                  Y)),
79.23/79.36	                                    Z)) =
79.23/79.36	      app_encode_app(int,int,
79.23/79.36	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
79.23/79.36	                                    hAPP_int_int,
79.23/79.36	                                    app_encode_app(int,fun_int_int,
79.23/79.36	                                                   plus_plus_int,Y)),
79.23/79.36	                     app_encode_app(int,int,
79.23/79.36	                                    app_encode_app(fun_int_int,
79.23/79.36	                                                   app_encode_fun(int,int),
79.23/79.36	                                                   hAPP_int_int,
79.23/79.36	                                                   app_encode_app(int,
79.23/79.36	                                                                  fun_int_int,
79.23/79.36	                                                                  plus_plus_int,
79.23/79.36	                                                                  X_1)),
79.23/79.36	                                    Z))))).
79.23/79.36	tff('41', plain,
79.23/79.36	    ![X266 : int, X267 : int, X268 : int]:
79.23/79.36	      app_encode_app(int, int, 
79.23/79.36	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
79.23/79.36	          app_encode_app(int, fun_int_int, plus_plus_int, X267)), 
79.23/79.36	        app_encode_app(int, int, 
79.23/79.36	          app_encode_app(fun_int_int, app_encode_fun(int, int), 
79.23/79.36	            hAPP_int_int, 
79.23/79.36	            app_encode_app(int, fun_int_int, plus_plus_int, X266)), X268))
79.23/79.36	       = app_encode_app(int, int, 
79.23/79.36	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
79.23/79.36	             hAPP_int_int, 
79.23/79.36	             app_encode_app(int, fun_int_int, plus_plus_int, X266)), 
79.23/79.36	           app_encode_app(int, int, 
79.23/79.36	             app_encode_app(fun_int_int, app_encode_fun(int, int), 
79.23/79.36	               hAPP_int_int, 
79.23/79.36	               app_encode_app(int, fun_int_int, plus_plus_int, X267)), X268)),
79.23/79.36	    inference('cnf', [status(esa)], [zf_stmt_230])).
79.23/79.36	tff('42', plain,
79.23/79.36	    ![X0 : int]:
79.23/79.36	      app_encode_app(int, int, bit1, X0)
79.23/79.36	       = app_encode_app(int, int, 
79.23/79.36	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
79.23/79.36	             hAPP_int_int, 
79.23/79.36	             app_encode_app(int, fun_int_int, plus_plus_int, 
79.23/79.36	               app_encode_app(int, int, bit1, zero_zero_int))), 
79.23/79.36	           app_encode_app(int, int, 
79.23/79.36	             app_encode_app(fun_int_int, app_encode_fun(int, int), 
79.23/79.36	               hAPP_int_int, 
79.23/79.36	               app_encode_app(int, fun_int_int, plus_plus_int, X0)), X0)),
79.23/79.36	    inference('sup+', [status(thm)], ['40', '41'])).
79.23/79.36	tff(zf_stmt_279, axiom,
79.23/79.36	  (![K_1:int]:
79.23/79.36	     (app_encode_app(int,int,bit0,K_1) =
79.23/79.36	      app_encode_app(int,int,
79.23/79.36	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
79.23/79.36	                                    hAPP_int_int,
79.23/79.36	                                    app_encode_app(int,fun_int_int,
79.23/79.36	                                                   plus_plus_int,K_1)),
79.23/79.36	                     K_1)))).
79.23/79.36	tff('43', plain,
79.23/79.36	    ![X352 : int]:
79.23/79.36	      app_encode_app(int, int, bit0, X352)
79.23/79.36	       = app_encode_app(int, int, 
79.23/79.36	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
79.23/79.36	             hAPP_int_int, 
79.23/79.36	             app_encode_app(int, fun_int_int, plus_plus_int, X352)), X352),
79.23/79.36	    inference('cnf', [status(esa)], [zf_stmt_279])).
79.23/79.36	tff('44', plain,
79.23/79.36	    ![X0 : int]:
79.23/79.36	      app_encode_app(int, int, bit1, X0)
79.23/79.36	       = app_encode_app(int, int, 
79.23/79.36	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
79.23/79.36	             hAPP_int_int, 
79.23/79.36	             app_encode_app(int, fun_int_int, plus_plus_int, 
79.23/79.36	               app_encode_app(int, int, bit1, zero_zero_int))), 
79.23/79.36	           app_encode_app(int, int, bit0, X0)),
79.23/79.36	    inference('demod', [status(thm)], ['42', '43'])).
79.23/79.36	tff('45', plain,
79.23/79.36	    app_encode_app(bool, $o, hBOOL, 
79.23/79.36	      app_encode_app(int, bool, 
79.23/79.36	        app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.36	          hAPP_int_bool, zprime), 
79.23/79.36	        app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m)))),
79.23/79.36	    inference('demod', [status(thm)], ['38', '44'])).
79.23/79.36	tff(zf_stmt_540, axiom,
79.23/79.36	  (![P_2:int]:
79.23/79.36	     (app_encode_app(bool,$o,hBOOL,
79.23/79.36	                     app_encode_app(int,bool,
79.23/79.36	                                    app_encode_app(fun_int_bool,
79.23/79.36	                                                   app_encode_fun(int,bool),
79.23/79.36	                                                   hAPP_int_bool,zprime),
79.23/79.36	                                    P_2)) <=>
79.23/79.36	      (app_encode_app(bool,$o,hBOOL,
79.23/79.36	                      app_encode_app(int,bool,
79.23/79.36	                                     app_encode_app(fun_int_bool,
79.23/79.36	                                                    app_encode_fun(int,bool),
79.23/79.36	                                                    hAPP_int_bool,
79.23/79.36	                                                    app_encode_app(int,
79.23/79.36	                                                                   fun_int_bool,
79.23/79.36	                                                                   app_encode_app(
79.23/79.36	                                                                   fun_int_fun_int_bool,
79.23/79.36	                                                                   app_encode_fun(
79.23/79.36	                                                                   int,
79.23/79.36	                                                                   fun_int_bool),
79.23/79.36	                                                                   hAPP_i1948725293t_bool,
79.23/79.36	                                                                   ord_less_int),
79.23/79.36	                                                                   one_one_int)),
79.23/79.36	                                     P_2)) & 
79.23/79.36	       (![M_2:int]:
79.23/79.36	          ((app_encode_app(bool,$o,hBOOL,
79.23/79.36	                           app_encode_app(int,bool,
79.23/79.36	                                          app_encode_app(fun_int_bool,
79.23/79.36	                                                         app_encode_fun(
79.23/79.36	                                                         int,bool),
79.23/79.36	                                                         hAPP_int_bool,
79.23/79.36	                                                         app_encode_app(
79.23/79.36	                                                         int,fun_int_bool,
79.23/79.36	                                                         app_encode_app(
79.23/79.36	                                                         fun_int_fun_int_bool,
79.23/79.36	                                                         app_encode_fun(
79.23/79.36	                                                         int,fun_int_bool),
79.23/79.36	                                                         hAPP_i1948725293t_bool,
79.23/79.36	                                                         ord_less_eq_int),
79.23/79.36	                                                         zero_zero_int)),
79.23/79.36	                                          M_2)) & 
79.23/79.36	            app_encode_app(bool,$o,hBOOL,
79.23/79.36	                           app_encode_app(int,bool,
79.23/79.36	                                          app_encode_app(fun_int_bool,
79.23/79.36	                                                         app_encode_fun(
79.23/79.36	                                                         int,bool),
79.23/79.36	                                                         hAPP_int_bool,
79.23/79.36	                                                         app_encode_app(
79.23/79.36	                                                         int,fun_int_bool,
79.23/79.36	                                                         app_encode_app(
79.23/79.36	                                                         fun_int_fun_int_bool,
79.23/79.36	                                                         app_encode_fun(
79.23/79.36	                                                         int,fun_int_bool),
79.23/79.36	                                                         hAPP_i1948725293t_bool,
79.23/79.36	                                                         dvd_dvd_int),M_2)),
79.23/79.36	                                          P_2))) =>
79.23/79.36	           ((M_2 = one_one_int) | (M_2 = P_2)))))))).
79.23/79.36	tff('46', plain,
79.23/79.36	    ![X883 : int]:
79.23/79.36	      (app_encode_app(bool, $o, hBOOL, 
79.23/79.36	         app_encode_app(int, bool, 
79.23/79.36	           app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.36	             hAPP_int_bool, 
79.23/79.36	             app_encode_app(int, fun_int_bool, 
79.23/79.36	               app_encode_app(fun_int_fun_int_bool, 
79.23/79.36	                 app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
79.23/79.36	                 ord_less_int), one_one_int)), X883))
79.23/79.36	       | ~ app_encode_app(bool, $o, hBOOL, 
79.23/79.36	             app_encode_app(int, bool, 
79.23/79.36	               app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.36	                 hAPP_int_bool, zprime), X883))),
79.23/79.36	    inference('cnf', [status(esa)], [zf_stmt_540])).
79.23/79.36	tff('47', plain,
79.23/79.36	    ![X883 : int]:
79.23/79.36	      (app_encode_app(bool, $o, hBOOL, 
79.23/79.36	         app_encode_app(int, bool, 
79.23/79.36	           app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.36	             hAPP_int_bool, 
79.23/79.36	             app_encode_app(int, fun_int_bool, 
79.23/79.36	               app_encode_app(fun_int_fun_int_bool, 
79.23/79.36	                 app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
79.23/79.36	                 ord_less_int), 
79.23/79.36	               app_encode_app(int, int, bit1, zero_zero_int))), X883))
79.23/79.36	       | ~ app_encode_app(bool, $o, hBOOL, 
79.23/79.36	             app_encode_app(int, bool, 
79.23/79.36	               app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.36	                 hAPP_int_bool, zprime), X883))),
79.23/79.36	    inference('demod', [status(thm)], ['46', '4'])).
79.23/79.36	tff('48', plain,
79.23/79.36	    (~ $true
79.23/79.36	     | app_encode_app(bool, $o, hBOOL, 
79.23/79.36	         app_encode_app(int, bool, 
79.23/79.36	           app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.36	             hAPP_int_bool, 
79.23/79.36	             app_encode_app(int, fun_int_bool, 
79.23/79.36	               app_encode_app(fun_int_fun_int_bool, 
79.23/79.36	                 app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
79.23/79.36	                 ord_less_int), 
79.23/79.36	               app_encode_app(int, int, bit1, zero_zero_int))), 
79.23/79.36	           app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m))))),
79.23/79.36	    inference('sup-', [status(thm)], ['45', '47'])).
79.23/79.36	tff('49', plain,
79.23/79.36	    app_encode_app(bool, $o, hBOOL, 
79.23/79.36	      app_encode_app(int, bool, 
79.23/79.36	        app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.36	          hAPP_int_bool, 
79.23/79.36	          app_encode_app(int, fun_int_bool, 
79.23/79.36	            app_encode_app(fun_int_fun_int_bool, 
79.23/79.36	              app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
79.23/79.36	              ord_less_int), app_encode_app(int, int, bit1, zero_zero_int))), 
79.23/79.36	        app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m)))),
79.23/79.36	    inference('simplify', [status(thm)], ['48'])).
79.23/79.36	tff(zf_stmt_270, axiom,
79.23/79.36	  (![K1:int,K2:int]:
79.23/79.36	     (app_encode_app(bool,$o,hBOOL,
79.23/79.36	                     app_encode_app(int,bool,
79.23/79.36	                                    app_encode_app(fun_int_bool,
79.23/79.36	                                                   app_encode_fun(int,bool),
79.23/79.36	                                                   hAPP_int_bool,
79.23/79.36	                                                   app_encode_app(int,
79.23/79.36	                                                                  fun_int_bool,
79.23/79.36	                                                                  app_encode_app(
79.23/79.36	                                                                  fun_int_fun_int_bool,
79.23/79.36	                                                                  app_encode_fun(
79.23/79.36	                                                                  int,
79.23/79.36	                                                                  fun_int_bool),
79.23/79.36	                                                                  hAPP_i1948725293t_bool,
79.23/79.36	                                                                  ord_less_int),
79.23/79.36	                                                                  app_encode_app(
79.23/79.36	                                                                  int,int,
79.23/79.36	                                                                  bit1,K1))),
79.23/79.36	                                    app_encode_app(int,int,bit1,K2))) <=>
79.23/79.36	      app_encode_app(bool,$o,hBOOL,
79.23/79.36	                     app_encode_app(int,bool,
79.23/79.36	                                    app_encode_app(fun_int_bool,
79.23/79.36	                                                   app_encode_fun(int,bool),
79.23/79.36	                                                   hAPP_int_bool,
79.23/79.36	                                                   app_encode_app(int,
79.23/79.36	                                                                  fun_int_bool,
79.23/79.36	                                                                  app_encode_app(
79.23/79.36	                                                                  fun_int_fun_int_bool,
79.23/79.36	                                                                  app_encode_fun(
79.23/79.36	                                                                  int,
79.23/79.36	                                                                  fun_int_bool),
79.23/79.36	                                                                  hAPP_i1948725293t_bool,
79.23/79.36	                                                                  ord_less_int),
79.23/79.36	                                                                  K1)),
79.23/79.36	                                    K2))))).
79.23/79.36	tff('50', plain,
79.23/79.36	    ![X336 : int, X337 : int]:
79.23/79.36	      (app_encode_app(bool, $o, hBOOL, 
79.23/79.36	         app_encode_app(int, bool, 
79.23/79.36	           app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.36	             hAPP_int_bool, 
79.23/79.36	             app_encode_app(int, fun_int_bool, 
79.23/79.36	               app_encode_app(fun_int_fun_int_bool, 
79.23/79.36	                 app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
79.23/79.36	                 ord_less_int), X336)), X337))
79.23/79.36	       | ~ app_encode_app(bool, $o, hBOOL, 
79.23/79.36	             app_encode_app(int, bool, 
79.23/79.36	               app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.36	                 hAPP_int_bool, 
79.23/79.36	                 app_encode_app(int, fun_int_bool, 
79.23/79.36	                   app_encode_app(fun_int_fun_int_bool, 
79.23/79.36	                     app_encode_fun(int, fun_int_bool), 
79.23/79.36	                     hAPP_i1948725293t_bool, ord_less_int), 
79.23/79.36	                   app_encode_app(int, int, bit1, X336))), 
79.23/79.36	               app_encode_app(int, int, bit1, X337)))),
79.23/79.36	    inference('cnf', [status(esa)], [zf_stmt_270])).
79.23/79.36	tff('51', plain,
79.23/79.36	    (~ $true
79.23/79.36	     | app_encode_app(bool, $o, hBOOL, 
79.23/79.36	         app_encode_app(int, bool, 
79.23/79.36	           app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.36	             hAPP_int_bool, 
79.23/79.36	             app_encode_app(int, fun_int_bool, 
79.23/79.36	               app_encode_app(fun_int_fun_int_bool, 
79.23/79.36	                 app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
79.23/79.36	                 ord_less_int), zero_zero_int)), 
79.23/79.36	           app_encode_app(int, int, bit0, m)))),
79.23/79.36	    inference('sup-', [status(thm)], ['49', '50'])).
79.23/79.36	tff('52', plain,
79.23/79.36	    app_encode_app(bool, $o, hBOOL, 
79.23/79.36	      app_encode_app(int, bool, 
79.23/79.36	        app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.36	          hAPP_int_bool, 
79.23/79.36	          app_encode_app(int, fun_int_bool, 
79.23/79.36	            app_encode_app(fun_int_fun_int_bool, 
79.23/79.36	              app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
79.23/79.36	              ord_less_int), zero_zero_int)), 
79.23/79.36	        app_encode_app(int, int, bit0, m))),
79.23/79.36	    inference('simplify', [status(thm)], ['51'])).
79.23/79.36	tff(zf_stmt_171, axiom,
79.23/79.36	  (![V_4:int,W_1:int]:
79.23/79.36	     (app_encode_app(bool,$o,hBOOL,
79.23/79.36	                     app_encode_app(int,bool,
79.23/79.36	                                    app_encode_app(fun_int_bool,
79.23/79.36	                                                   app_encode_fun(int,bool),
79.23/79.36	                                                   hAPP_int_bool,
79.23/79.36	                                                   app_encode_app(int,
79.23/79.36	                                                                  fun_int_bool,
79.23/79.36	                                                                  app_encode_app(
79.23/79.36	                                                                  fun_int_fun_int_bool,
79.23/79.36	                                                                  app_encode_fun(
79.23/79.36	                                                                  int,
79.23/79.36	                                                                  fun_int_bool),
79.23/79.36	                                                                  hAPP_i1948725293t_bool,
79.23/79.36	                                                                  ord_less_eq_int),
79.23/79.36	                                                                  app_encode_app(
79.23/79.36	                                                                  int,int,
79.23/79.36	                                                                  number_number_of_int,
79.23/79.36	                                                                  V_4))),
79.23/79.36	                                    app_encode_app(int,int,
79.23/79.36	                                                   number_number_of_int,W_1))) <=>
79.23/79.36	      (~
79.23/79.36	        app_encode_app(bool,$o,hBOOL,
79.23/79.36	                       app_encode_app(int,bool,
79.23/79.36	                                      app_encode_app(fun_int_bool,
79.23/79.36	                                                     app_encode_fun(int,bool),
79.23/79.36	                                                     hAPP_int_bool,
79.23/79.36	                                                     app_encode_app(int,
79.23/79.36	                                                                    fun_int_bool,
79.23/79.36	                                                                    app_encode_app(
79.23/79.36	                                                                    fun_int_fun_int_bool,
79.23/79.36	                                                                    app_encode_fun(
79.23/79.36	                                                                    int,
79.23/79.36	                                                                    fun_int_bool),
79.23/79.36	                                                                    hAPP_i1948725293t_bool,
79.23/79.36	                                                                    ord_less_int),
79.23/79.36	                                                                    app_encode_app(
79.23/79.36	                                                                    int,int,
79.23/79.36	                                                                    number_number_of_int,
79.23/79.36	                                                                    W_1))),
79.23/79.36	                                      app_encode_app(int,int,
79.23/79.36	                                                     number_number_of_int,V_4))))))).
79.23/79.36	tff('53', plain,
79.23/79.36	    ![X130 : int, X131 : int]:
79.23/79.36	      (~ app_encode_app(bool, $o, hBOOL, 
79.23/79.36	           app_encode_app(int, bool, 
79.23/79.36	             app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.36	               hAPP_int_bool, 
79.23/79.36	               app_encode_app(int, fun_int_bool, 
79.23/79.36	                 app_encode_app(fun_int_fun_int_bool, 
79.23/79.36	                   app_encode_fun(int, fun_int_bool), 
79.23/79.36	                   hAPP_i1948725293t_bool, ord_less_int), 
79.23/79.36	                 app_encode_app(int, int, number_number_of_int, X130))), 
79.23/79.36	             app_encode_app(int, int, number_number_of_int, X131)))
79.23/79.36	       | ~ app_encode_app(bool, $o, hBOOL, 
79.23/79.36	             app_encode_app(int, bool, 
79.23/79.36	               app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.36	                 hAPP_int_bool, 
79.23/79.36	                 app_encode_app(int, fun_int_bool, 
79.23/79.36	                   app_encode_app(fun_int_fun_int_bool, 
79.23/79.36	                     app_encode_fun(int, fun_int_bool), 
79.23/79.36	                     hAPP_i1948725293t_bool, ord_less_eq_int), 
79.23/79.36	                   app_encode_app(int, int, number_number_of_int, X131))), 
79.23/79.36	               app_encode_app(int, int, number_number_of_int, X130)))),
79.23/79.36	    inference('cnf', [status(esa)], [zf_stmt_171])).
79.23/79.36	tff('54', plain,
79.23/79.36	    ![X130 : int, X131 : int]:
79.23/79.36	      (~ app_encode_app(bool, $o, hBOOL, 
79.23/79.36	           app_encode_app(int, bool, 
79.23/79.36	             app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.36	               hAPP_int_bool, 
79.23/79.36	               app_encode_app(int, fun_int_bool, 
79.23/79.36	                 app_encode_app(fun_int_fun_int_bool, 
79.23/79.36	                   app_encode_fun(int, fun_int_bool), 
79.23/79.36	                   hAPP_i1948725293t_bool, ord_less_int), X130)), X131))
79.23/79.36	       | ~ app_encode_app(bool, $o, hBOOL, 
79.23/79.36	             app_encode_app(int, bool, 
79.23/79.36	               app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.36	                 hAPP_int_bool, 
79.23/79.36	                 app_encode_app(int, fun_int_bool, 
79.23/79.36	                   app_encode_app(fun_int_fun_int_bool, 
79.23/79.36	                     app_encode_fun(int, fun_int_bool), 
79.23/79.36	                     hAPP_i1948725293t_bool, ord_less_eq_int), X131)), X130))),
79.23/79.36	    inference('demod', [status(thm)], ['53', '3', '3', '3', '3'])).
79.23/79.36	tff('55', plain,
79.23/79.36	    (~ $true
79.23/79.36	     | ~ app_encode_app(bool, $o, hBOOL, 
79.23/79.36	           app_encode_app(int, bool, 
79.23/79.36	             app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.36	               hAPP_int_bool, 
79.23/79.36	               app_encode_app(int, fun_int_bool, 
79.23/79.36	                 app_encode_app(fun_int_fun_int_bool, 
79.23/79.36	                   app_encode_fun(int, fun_int_bool), 
79.23/79.36	                   hAPP_i1948725293t_bool, ord_less_eq_int), 
79.23/79.36	                 app_encode_app(int, int, bit0, m))), zero_zero_int))),
79.23/79.36	    inference('sup-', [status(thm)], ['52', '54'])).
79.23/79.36	tff('56', plain,
79.23/79.36	    ~ app_encode_app(bool, $o, hBOOL, 
79.23/79.36	        app_encode_app(int, bool, 
79.23/79.36	          app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.36	            hAPP_int_bool, 
79.23/79.36	            app_encode_app(int, fun_int_bool, 
79.23/79.36	              app_encode_app(fun_int_fun_int_bool, 
79.23/79.36	                app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
79.23/79.36	                ord_less_eq_int), app_encode_app(int, int, bit0, m))), 
79.23/79.36	          zero_zero_int)),
79.23/79.36	    inference('simplify', [status(thm)], ['55'])).
79.23/79.36	tff('57', plain,
79.23/79.36	    (~ $true
79.23/79.36	     | app_encode_app(bool, $o, hBOOL, 
79.23/79.36	         app_encode_app(int, bool, 
79.23/79.36	           app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.36	             hAPP_int_bool, 
79.23/79.36	             app_encode_app(int, fun_int_bool, 
79.23/79.36	               app_encode_app(fun_int_fun_int_bool, 
79.23/79.36	                 app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
79.23/79.36	                 ord_less_eq_int), zero_zero_int)), 
79.23/79.36	           app_encode_app(int, int, bit0, m)))),
79.23/79.36	    inference('sup-', [status(thm)], ['35', '56'])).
79.23/79.36	tff('58', plain,
79.23/79.36	    app_encode_app(bool, $o, hBOOL, 
79.23/79.36	      app_encode_app(int, bool, 
79.23/79.36	        app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.36	          hAPP_int_bool, 
79.23/79.36	          app_encode_app(int, fun_int_bool, 
79.23/79.36	            app_encode_app(fun_int_fun_int_bool, 
79.23/79.36	              app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
79.23/79.36	              ord_less_eq_int), zero_zero_int)), 
79.23/79.36	        app_encode_app(int, int, bit0, m))),
79.23/79.36	    inference('simplify', [status(thm)], ['57'])).
79.23/79.36	tff(zf_stmt_194, axiom,
79.23/79.36	  (![K:int]:
79.23/79.36	     (app_encode_app(bool,$o,hBOOL,
79.23/79.36	                     app_encode_app(int,bool,
79.23/79.36	                                    app_encode_app(fun_int_bool,
79.23/79.36	                                                   app_encode_fun(int,bool),
79.23/79.36	                                                   hAPP_int_bool,
79.23/79.36	                                                   app_encode_app(int,
79.23/79.36	                                                                  fun_int_bool,
79.23/79.36	                                                                  app_encode_app(
79.23/79.36	                                                                  fun_int_fun_int_bool,
79.23/79.36	                                                                  app_encode_fun(
79.23/79.36	                                                                  int,
79.23/79.36	                                                                  fun_int_bool),
79.23/79.36	                                                                  hAPP_i1948725293t_bool,
79.23/79.36	                                                                  ord_less_int),
79.23/79.36	                                                                  pls)),
79.23/79.36	                                    app_encode_app(int,int,bit1,K))) <=>
79.23/79.36	      app_encode_app(bool,$o,hBOOL,
79.23/79.36	                     app_encode_app(int,bool,
79.23/79.36	                                    app_encode_app(fun_int_bool,
79.23/79.36	                                                   app_encode_fun(int,bool),
79.23/79.36	                                                   hAPP_int_bool,
79.23/79.36	                                                   app_encode_app(int,
79.23/79.36	                                                                  fun_int_bool,
79.23/79.36	                                                                  app_encode_app(
79.23/79.36	                                                                  fun_int_fun_int_bool,
79.23/79.36	                                                                  app_encode_fun(
79.23/79.36	                                                                  int,
79.23/79.36	                                                                  fun_int_bool),
79.23/79.36	                                                                  hAPP_i1948725293t_bool,
79.23/79.36	                                                                  ord_less_eq_int),
79.23/79.36	                                                                  pls)),
79.23/79.36	                                    K))))).
79.23/79.36	tff('59', plain,
79.23/79.36	    ![X176 : int]:
79.23/79.36	      (app_encode_app(bool, $o, hBOOL, 
79.23/79.36	         app_encode_app(int, bool, 
79.23/79.36	           app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.36	             hAPP_int_bool, 
79.23/79.36	             app_encode_app(int, fun_int_bool, 
79.23/79.36	               app_encode_app(fun_int_fun_int_bool, 
79.23/79.36	                 app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
79.23/79.36	                 ord_less_int), pls)), app_encode_app(int, int, bit1, X176)))
79.23/79.36	       | ~ app_encode_app(bool, $o, hBOOL, 
79.23/79.36	             app_encode_app(int, bool, 
79.23/79.36	               app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.36	                 hAPP_int_bool, 
79.23/79.36	                 app_encode_app(int, fun_int_bool, 
79.23/79.36	                   app_encode_app(fun_int_fun_int_bool, 
79.23/79.36	                     app_encode_fun(int, fun_int_bool), 
79.23/79.36	                     hAPP_i1948725293t_bool, ord_less_eq_int), pls)), X176))),
79.23/79.36	    inference('cnf', [status(esa)], [zf_stmt_194])).
79.23/79.36	tff('60', plain,
79.23/79.36	    ![X176 : int]:
79.23/79.36	      (app_encode_app(bool, $o, hBOOL, 
79.23/79.36	         app_encode_app(int, bool, 
79.23/79.36	           app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.36	             hAPP_int_bool, 
79.23/79.36	             app_encode_app(int, fun_int_bool, 
79.23/79.36	               app_encode_app(fun_int_fun_int_bool, 
79.23/79.36	                 app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
79.23/79.36	                 ord_less_int), zero_zero_int)), 
79.23/79.36	           app_encode_app(int, int, bit1, X176)))
79.23/79.36	       | ~ app_encode_app(bool, $o, hBOOL, 
79.23/79.36	             app_encode_app(int, bool, 
79.23/79.36	               app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.36	                 hAPP_int_bool, 
79.23/79.36	                 app_encode_app(int, fun_int_bool, 
79.23/79.36	                   app_encode_app(fun_int_fun_int_bool, 
79.23/79.36	                     app_encode_fun(int, fun_int_bool), 
79.23/79.36	                     hAPP_i1948725293t_bool, ord_less_eq_int), zero_zero_int)), 
79.23/79.36	               X176))),
79.23/79.36	    inference('demod', [status(thm)], ['59', '1', '1'])).
79.23/79.36	tff('61', plain,
79.23/79.36	    (~ $true
79.23/79.36	     | app_encode_app(bool, $o, hBOOL, 
79.23/79.36	         app_encode_app(int, bool, 
79.23/79.36	           app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.36	             hAPP_int_bool, 
79.23/79.36	             app_encode_app(int, fun_int_bool, 
79.23/79.36	               app_encode_app(fun_int_fun_int_bool, 
79.23/79.36	                 app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
79.23/79.36	                 ord_less_int), zero_zero_int)), 
79.23/79.36	           app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m))))),
79.23/79.36	    inference('sup-', [status(thm)], ['58', '60'])).
79.23/79.36	tff('62', plain,
79.23/79.36	    app_encode_app(bool, $o, hBOOL, 
79.23/79.36	      app_encode_app(int, bool, 
79.23/79.36	        app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.36	          hAPP_int_bool, 
79.23/79.36	          app_encode_app(int, fun_int_bool, 
79.23/79.36	            app_encode_app(fun_int_fun_int_bool, 
79.23/79.36	              app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
79.23/79.36	              ord_less_int), zero_zero_int)), 
79.23/79.36	        app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m)))),
79.23/79.36	    inference('simplify', [status(thm)], ['61'])).
79.23/79.36	tff('63', plain,
79.23/79.36	    (~ $true
79.23/79.36	     | ~ $true
79.23/79.36	     | app_encode_app(bool, $o, hBOOL, 
79.23/79.36	         app_encode_app(int, bool, 
79.23/79.36	           app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.36	             hAPP_int_bool, 
79.23/79.36	             app_encode_app(int, fun_int_bool, 
79.23/79.36	               app_encode_app(fun_int_fun_int_bool, 
79.23/79.36	                 app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
79.23/79.36	                 ord_less_int), zero_zero_int)), t))),
79.23/79.36	    inference('demod', [status(thm)], ['25', '34', '62'])).
79.23/79.36	tff('64', plain,
79.23/79.36	    app_encode_app(bool, $o, hBOOL, 
79.23/79.36	      app_encode_app(int, bool, 
79.23/79.36	        app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.36	          hAPP_int_bool, 
79.23/79.36	          app_encode_app(int, fun_int_bool, 
79.23/79.36	            app_encode_app(fun_int_fun_int_bool, 
79.23/79.36	              app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
79.23/79.36	              ord_less_int), zero_zero_int)), t)),
79.23/79.36	    inference('simplify', [status(thm)], ['63'])).
79.23/79.36	tff(zf_stmt_147, axiom,
79.23/79.36	  (![Z_1:int,W_1:int]:
79.23/79.36	     (app_encode_app(bool,$o,hBOOL,
79.23/79.36	                     app_encode_app(int,bool,
79.23/79.36	                                    app_encode_app(fun_int_bool,
79.23/79.36	                                                   app_encode_fun(int,bool),
79.23/79.36	                                                   hAPP_int_bool,
79.23/79.36	                                                   app_encode_app(int,
79.23/79.36	                                                                  fun_int_bool,
79.23/79.36	                                                                  app_encode_app(
79.23/79.36	                                                                  fun_int_fun_int_bool,
79.23/79.36	                                                                  app_encode_fun(
79.23/79.36	                                                                  int,
79.23/79.36	                                                                  fun_int_bool),
79.23/79.36	                                                                  hAPP_i1948725293t_bool,
79.23/79.36	                                                                  ord_less_int),
79.23/79.36	                                                                  Z_1)),
79.23/79.36	                                    W_1)) <=>
79.23/79.36	      (app_encode_app(bool,$o,hBOOL,
79.23/79.36	                      app_encode_app(int,bool,
79.23/79.36	                                     app_encode_app(fun_int_bool,
79.23/79.36	                                                    app_encode_fun(int,bool),
79.23/79.36	                                                    hAPP_int_bool,
79.23/79.36	                                                    app_encode_app(int,
79.23/79.36	                                                                   fun_int_bool,
79.23/79.36	                                                                   app_encode_app(
79.23/79.36	                                                                   fun_int_fun_int_bool,
79.23/79.36	                                                                   app_encode_fun(
79.23/79.36	                                                                   int,
79.23/79.36	                                                                   fun_int_bool),
79.23/79.36	                                                                   hAPP_i1948725293t_bool,
79.23/79.36	                                                                   ord_less_eq_int),
79.23/79.36	                                                                   Z_1)),
79.23/79.36	                                     W_1)) & 
79.23/79.36	       (Z_1 != W_1))))).
79.23/79.36	tff('65', plain,
79.23/79.36	    ![X74 : int, X75 : int]:
79.23/79.36	      (app_encode_app(bool, $o, hBOOL, 
79.23/79.36	         app_encode_app(int, bool, 
79.23/79.36	           app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.36	             hAPP_int_bool, 
79.23/79.36	             app_encode_app(int, fun_int_bool, 
79.23/79.36	               app_encode_app(fun_int_fun_int_bool, 
79.23/79.36	                 app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
79.23/79.36	                 ord_less_eq_int), X74)), X75))
79.23/79.36	       | ~ app_encode_app(bool, $o, hBOOL, 
79.23/79.36	             app_encode_app(int, bool, 
79.23/79.36	               app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.36	                 hAPP_int_bool, 
79.23/79.36	                 app_encode_app(int, fun_int_bool, 
79.23/79.36	                   app_encode_app(fun_int_fun_int_bool, 
79.23/79.36	                     app_encode_fun(int, fun_int_bool), 
79.23/79.36	                     hAPP_i1948725293t_bool, ord_less_int), X74)), X75))),
79.23/79.36	    inference('cnf', [status(esa)], [zf_stmt_147])).
79.23/79.36	tff(zf_stmt_97, axiom,
79.23/79.36	  (app_encode_app(bool,$o,hBOOL,
79.23/79.36	                  app_encode_app(int,bool,
79.23/79.36	                                 app_encode_app(fun_int_bool,
79.23/79.36	                                                app_encode_fun(int,bool),
79.23/79.36	                                                hAPP_int_bool,
79.23/79.36	                                                app_encode_app(int,
79.23/79.36	                                                               fun_int_bool,
79.23/79.36	                                                               app_encode_app(
79.23/79.36	                                                               fun_int_fun_int_bool,
79.23/79.36	                                                               app_encode_fun(
79.23/79.36	                                                               int,
79.23/79.36	                                                               fun_int_bool),
79.23/79.36	                                                               hAPP_i1948725293t_bool,
79.23/79.36	                                                               ord_less_int),
79.23/79.36	                                                               t)),
79.23/79.36	                                 zero_zero_int)))).
79.23/79.36	tff('66', plain,
79.23/79.36	    app_encode_app(bool, $o, hBOOL, 
79.23/79.36	      app_encode_app(int, bool, 
79.23/79.36	        app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.36	          hAPP_int_bool, 
79.23/79.36	          app_encode_app(int, fun_int_bool, 
79.23/79.36	            app_encode_app(fun_int_fun_int_bool, 
79.23/79.36	              app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
79.23/79.36	              ord_less_int), t)), zero_zero_int)),
79.23/79.36	    inference('cnf', [status(esa)], [zf_stmt_97])).
79.23/79.36	tff('67', plain,
79.23/79.36	    (~ $true
79.23/79.36	     | ~ app_encode_app(bool, $o, hBOOL, 
79.23/79.36	           app_encode_app(int, bool, 
79.23/79.36	             app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.36	               hAPP_int_bool, 
79.23/79.36	               app_encode_app(int, fun_int_bool, 
79.23/79.36	                 app_encode_app(fun_int_fun_int_bool, 
79.23/79.36	                   app_encode_fun(int, fun_int_bool), 
79.23/79.36	                   hAPP_i1948725293t_bool, ord_less_eq_int), zero_zero_int)), 
79.23/79.36	             t))),
79.23/79.36	    inference('sup-', [status(thm)], ['66', '54'])).
79.23/79.36	tff('68', plain,
79.23/79.36	    ~ app_encode_app(bool, $o, hBOOL, 
79.23/79.36	        app_encode_app(int, bool, 
79.23/79.36	          app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.36	            hAPP_int_bool, 
79.23/79.36	            app_encode_app(int, fun_int_bool, 
79.23/79.36	              app_encode_app(fun_int_fun_int_bool, 
79.23/79.36	                app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
79.23/79.36	                ord_less_eq_int), zero_zero_int)), t)),
79.23/79.36	    inference('simplify', [status(thm)], ['67'])).
79.23/79.36	tff('69', plain,
79.23/79.36	    (~ $true
79.23/79.36	     | ~ app_encode_app(bool, $o, hBOOL, 
79.23/79.36	           app_encode_app(int, bool, 
79.23/79.36	             app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.36	               hAPP_int_bool, 
79.23/79.36	               app_encode_app(int, fun_int_bool, 
79.23/79.36	                 app_encode_app(fun_int_fun_int_bool, 
79.23/79.36	                   app_encode_fun(int, fun_int_bool), 
79.23/79.36	                   hAPP_i1948725293t_bool, ord_less_int), zero_zero_int)), t))),
79.23/79.36	    inference('sup-', [status(thm)], ['65', '68'])).
79.23/79.36	tff('70', plain,
79.23/79.36	    ~ app_encode_app(bool, $o, hBOOL, 
79.23/79.36	        app_encode_app(int, bool, 
79.23/79.36	          app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
79.23/79.36	            hAPP_int_bool, 
79.23/79.36	            app_encode_app(int, fun_int_bool, 
79.23/79.36	              app_encode_app(fun_int_fun_int_bool, 
79.23/79.36	                app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
79.23/79.36	                ord_less_int), zero_zero_int)), t)),
79.23/79.36	    inference('simplify', [status(thm)], ['69'])).
79.23/79.36	tff('71', plain, ~ $true, inference('sup-', [status(thm)], ['64', '70'])).
79.23/79.36	tff('72', plain, $false, inference('simplify', [status(thm)], ['71'])).
79.23/79.36	
79.23/79.36	% SZS output end Refutation
79.23/79.36	EOF
