0.00/0.00	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : app
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : 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
0.00/0.19	% Computer   : n106.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 07:30:54 CST 2018
20.91/21.05	% done 6705 iterations in 20.854s
20.91/21.05	% SZS status Theorem for 'stdin'
20.91/21.05	% SZS output start Refutation
20.91/21.06	tff(zf_stmt_51, axiom,
20.91/21.06	  (app_encode_app(int,int,
20.91/21.06	                  app_encode_app(int,app_encode_fun(int,int),plus_plus_int,
20.91/21.06	                                 app_encode_app(nat,int,
20.91/21.06	                                                app_encode_app(int,
20.91/21.06	                                                               app_encode_fun(
20.91/21.06	                                                               nat,int),
20.91/21.06	                                                               power_power_int,
20.91/21.06	                                                               s),
20.91/21.06	                                                app_encode_app(int,nat,
20.91/21.06	                                                               number_number_of_nat,
20.91/21.06	                                                               app_encode_app(
20.91/21.06	                                                               int,int,bit0,
20.91/21.06	                                                               app_encode_app(
20.91/21.06	                                                               int,int,bit1,
20.91/21.06	                                                               pls))))),
20.91/21.06	                  one_one_int) =
20.91/21.06	   app_encode_app(int,int,
20.91/21.06	                  app_encode_app(int,app_encode_fun(int,int),times_times_int,
20.91/21.06	                                 app_encode_app(int,int,
20.91/21.06	                                                app_encode_app(int,
20.91/21.06	                                                               app_encode_fun(
20.91/21.06	                                                               int,int),
20.91/21.06	                                                               plus_plus_int,
20.91/21.06	                                                               app_encode_app(
20.91/21.06	                                                               int,int,
20.91/21.06	                                                               app_encode_app(
20.91/21.06	                                                               int,
20.91/21.06	                                                               app_encode_fun(
20.91/21.06	                                                               int,int),
20.91/21.06	                                                               times_times_int,
20.91/21.06	                                                               app_encode_app(
20.91/21.06	                                                               int,int,
20.91/21.06	                                                               number_number_of_int,
20.91/21.06	                                                               app_encode_app(
20.91/21.06	                                                               int,int,bit0,
20.91/21.06	                                                               app_encode_app(
20.91/21.06	                                                               int,int,bit0,
20.91/21.06	                                                               app_encode_app(
20.91/21.06	                                                               int,int,bit1,
20.91/21.06	                                                               pls))))),m)),
20.91/21.06	                                                one_one_int)),
20.91/21.06	                  t))).
20.91/21.06	tff('0', plain,
20.91/21.06	    app_encode_app(int, int, 
20.91/21.06	      app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
20.91/21.06	        app_encode_app(nat, int, 
20.91/21.06	          app_encode_app(int, app_encode_fun(nat, int), power_power_int, s), 
20.91/21.06	          app_encode_app(int, nat, number_number_of_nat, 
20.91/21.06	            app_encode_app(int, int, bit0, 
20.91/21.06	              app_encode_app(int, int, bit1, pls))))), one_one_int)
20.91/21.06	     = app_encode_app(int, int, 
20.91/21.06	         app_encode_app(int, app_encode_fun(int, int), times_times_int, 
20.91/21.06	           app_encode_app(int, int, 
20.91/21.06	             app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
20.91/21.06	               app_encode_app(int, int, 
20.91/21.06	                 app_encode_app(int, app_encode_fun(int, int), 
20.91/21.06	                   times_times_int, 
20.91/21.06	                   app_encode_app(int, int, number_number_of_int, 
20.91/21.06	                     app_encode_app(int, int, bit0, 
20.91/21.06	                       app_encode_app(int, int, bit0, 
20.91/21.06	                         app_encode_app(int, int, bit1, pls))))), m)), 
20.91/21.06	             one_one_int)), t),
20.91/21.06	    inference('cnf', [status(esa)], [zf_stmt_51])).
20.91/21.06	tff(zf_stmt_206, axiom,
20.91/21.06	  (one_one_int =
20.91/21.06	   app_encode_app(int,int,number_number_of_int,
20.91/21.06	                  app_encode_app(int,int,bit1,pls)))).
20.91/21.06	tff('1', plain,
20.91/21.06	    one_one_int
20.91/21.06	     = app_encode_app(int, int, number_number_of_int, 
20.91/21.06	         app_encode_app(int, int, bit1, pls)),
20.91/21.06	    inference('cnf', [status(esa)], [zf_stmt_206])).
20.91/21.06	tff(zf_stmt_82, axiom,
20.91/21.06	  (![K_1:int]: (app_encode_app(int,int,number_number_of_int,K_1) = K_1))).
20.91/21.06	tff('2', plain,
20.91/21.06	    ![X31 : int]: app_encode_app(int, int, number_number_of_int, X31) = X31,
20.91/21.06	    inference('cnf', [status(esa)], [zf_stmt_82])).
20.91/21.06	tff('3', plain, one_one_int = app_encode_app(int, int, bit1, pls),
20.91/21.06	    inference('demod', [status(thm)], ['1', '2'])).
20.91/21.06	tff('4', plain,
20.91/21.06	    app_encode_app(int, int, 
20.91/21.06	      app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
20.91/21.06	        app_encode_app(nat, int, 
20.91/21.06	          app_encode_app(int, app_encode_fun(nat, int), power_power_int, s), 
20.91/21.06	          app_encode_app(int, nat, number_number_of_nat, 
20.91/21.06	            app_encode_app(int, int, bit0, 
20.91/21.06	              app_encode_app(int, int, bit1, pls))))), 
20.91/21.06	      app_encode_app(int, int, bit1, pls))
20.91/21.06	     = app_encode_app(int, int, 
20.91/21.06	         app_encode_app(int, app_encode_fun(int, int), times_times_int, 
20.91/21.06	           app_encode_app(int, int, 
20.91/21.06	             app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
20.91/21.06	               app_encode_app(int, int, 
20.91/21.06	                 app_encode_app(int, app_encode_fun(int, int), 
20.91/21.06	                   times_times_int, 
20.91/21.06	                   app_encode_app(int, int, bit0, 
20.91/21.06	                     app_encode_app(int, int, bit0, 
20.91/21.06	                       app_encode_app(int, int, bit1, pls)))), m)), 
20.91/21.06	             app_encode_app(int, int, bit1, pls))), t),
20.91/21.06	    inference('demod', [status(thm)], ['0', '3', '2', '3'])).
20.91/21.06	tff(zf_stmt_180, axiom,
20.91/21.06	  (![Z:int,W:int]:
20.91/21.06	     (app_encode_app(int,int,
20.91/21.06	                     app_encode_app(int,app_encode_fun(int,int),
20.91/21.06	                                    plus_plus_int,Z),
20.91/21.06	                     W) =
20.91/21.06	      app_encode_app(int,int,
20.91/21.06	                     app_encode_app(int,app_encode_fun(int,int),
20.91/21.06	                                    plus_plus_int,W),
20.91/21.06	                     Z)))).
20.91/21.06	tff('5', plain,
20.91/21.06	    ![X261 : int, X262 : int]:
20.91/21.06	      app_encode_app(int, int, 
20.91/21.06	        app_encode_app(int, app_encode_fun(int, int), plus_plus_int, X262), 
20.91/21.06	        X261)
20.91/21.06	       = app_encode_app(int, int, 
20.91/21.06	           app_encode_app(int, app_encode_fun(int, int), plus_plus_int, X261), 
20.91/21.06	           X262),
20.91/21.06	    inference('cnf', [status(esa)], [zf_stmt_180])).
20.91/21.06	tff('6', plain,
20.91/21.06	    app_encode_app(int, int, 
20.91/21.06	      app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
20.91/21.06	        app_encode_app(int, int, bit1, pls)), 
20.91/21.06	      app_encode_app(nat, int, 
20.91/21.06	        app_encode_app(int, app_encode_fun(nat, int), power_power_int, s), 
20.91/21.06	        app_encode_app(int, nat, number_number_of_nat, 
20.91/21.06	          app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls)))))
20.91/21.06	     = app_encode_app(int, int, 
20.91/21.06	         app_encode_app(int, app_encode_fun(int, int), times_times_int, 
20.91/21.06	           app_encode_app(int, int, 
20.91/21.06	             app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
20.91/21.06	               app_encode_app(int, int, bit1, pls)), 
20.91/21.06	             app_encode_app(int, int, 
20.91/21.06	               app_encode_app(int, app_encode_fun(int, int), 
20.91/21.06	                 times_times_int, 
20.91/21.06	                 app_encode_app(int, int, bit0, 
20.91/21.06	                   app_encode_app(int, int, bit0, 
20.91/21.06	                     app_encode_app(int, int, bit1, pls)))), m))), t),
20.91/21.06	    inference('demod', [status(thm)], ['4', '5', '5'])).
20.91/21.06	tff(zf_stmt_249, axiom,
20.91/21.06	  (![A_50:int]:
20.91/21.06	     (app_encode_app(nat,int,
20.91/21.06	                     app_encode_app(int,app_encode_fun(nat,int),
20.91/21.06	                                    power_power_int,A_50),
20.91/21.06	                     app_encode_app(int,nat,number_number_of_nat,
20.91/21.06	                                    app_encode_app(int,int,bit0,
20.91/21.06	                                                   app_encode_app(int,int,
20.91/21.06	                                                                  bit1,pls)))) =
20.91/21.06	      app_encode_app(int,int,
20.91/21.06	                     app_encode_app(int,app_encode_fun(int,int),
20.91/21.06	                                    times_times_int,A_50),
20.91/21.06	                     A_50)))).
20.91/21.06	tff('7', plain,
20.91/21.06	    ![X367 : int]:
20.91/21.06	      app_encode_app(nat, int, 
20.91/21.06	        app_encode_app(int, app_encode_fun(nat, int), power_power_int, X367), 
20.91/21.06	        app_encode_app(int, nat, number_number_of_nat, 
20.91/21.06	          app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls))))
20.91/21.06	       = app_encode_app(int, int, 
20.91/21.06	           app_encode_app(int, app_encode_fun(int, int), times_times_int, 
20.91/21.06	             X367), X367),
20.91/21.06	    inference('cnf', [status(esa)], [zf_stmt_249])).
20.91/21.06	tff(zf_stmt_137, axiom,
20.91/21.06	  (![K_1:int,L:int]:
20.91/21.06	     (app_encode_app(int,int,
20.91/21.06	                     app_encode_app(int,app_encode_fun(int,int),
20.91/21.06	                                    times_times_int,
20.91/21.06	                                    app_encode_app(int,int,bit0,K_1)),
20.91/21.06	                     L) =
20.91/21.06	      app_encode_app(int,int,bit0,
20.91/21.06	                     app_encode_app(int,int,
20.91/21.06	                                    app_encode_app(int,
20.91/21.06	                                                   app_encode_fun(int,int),
20.91/21.06	                                                   times_times_int,K_1),
20.91/21.06	                                    L))))).
20.91/21.06	tff('8', plain,
20.91/21.06	    ![X154 : int, X155 : int]:
20.91/21.06	      app_encode_app(int, int, 
20.91/21.06	        app_encode_app(int, app_encode_fun(int, int), times_times_int, 
20.91/21.06	          app_encode_app(int, int, bit0, X154)), X155)
20.91/21.06	       = app_encode_app(int, int, bit0, 
20.91/21.06	           app_encode_app(int, int, 
20.91/21.06	             app_encode_app(int, app_encode_fun(int, int), times_times_int, 
20.91/21.06	               X154), X155)),
20.91/21.06	    inference('cnf', [status(esa)], [zf_stmt_137])).
20.91/21.06	tff(zf_stmt_140, axiom,
20.91/21.06	  (![Z:int]:
20.91/21.06	     (app_encode_app(int,int,
20.91/21.06	                     app_encode_app(int,app_encode_fun(int,int),
20.91/21.06	                                    times_times_int,one_one_int),
20.91/21.06	                     Z) =
20.91/21.06	      Z))).
20.91/21.06	tff('9', plain,
20.91/21.06	    ![X160 : int]:
20.91/21.06	      app_encode_app(int, int, 
20.91/21.06	        app_encode_app(int, app_encode_fun(int, int), times_times_int, 
20.91/21.06	          one_one_int), X160)
20.91/21.06	       = X160,
20.91/21.06	    inference('cnf', [status(esa)], [zf_stmt_140])).
20.91/21.06	tff('10', plain,
20.91/21.06	    ![X160 : int]:
20.91/21.06	      app_encode_app(int, int, 
20.91/21.06	        app_encode_app(int, app_encode_fun(int, int), times_times_int, 
20.91/21.06	          app_encode_app(int, int, bit1, pls)), X160)
20.91/21.06	       = X160,
20.91/21.06	    inference('demod', [status(thm)], ['9', '3'])).
20.91/21.06	tff(zf_stmt_279, axiom,
20.91/21.06	  (![K_1:int,L:int]:
20.91/21.06	     (app_encode_app(int,int,
20.91/21.06	                     app_encode_app(int,app_encode_fun(int,int),
20.91/21.06	                                    plus_plus_int,
20.91/21.06	                                    app_encode_app(int,int,bit1,K_1)),
20.91/21.06	                     app_encode_app(int,int,bit0,L)) =
20.91/21.06	      app_encode_app(int,int,bit1,
20.91/21.06	                     app_encode_app(int,int,
20.91/21.06	                                    app_encode_app(int,
20.91/21.06	                                                   app_encode_fun(int,int),
20.91/21.06	                                                   plus_plus_int,K_1),
20.91/21.06	                                    L))))).
20.91/21.06	tff('11', plain,
20.91/21.06	    ![X412 : int, X413 : int]:
20.91/21.06	      app_encode_app(int, int, 
20.91/21.06	        app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
20.91/21.06	          app_encode_app(int, int, bit1, X412)), 
20.91/21.06	        app_encode_app(int, int, bit0, X413))
20.91/21.06	       = app_encode_app(int, int, bit1, 
20.91/21.06	           app_encode_app(int, int, 
20.91/21.06	             app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
20.91/21.06	               X412), X413)),
20.91/21.06	    inference('cnf', [status(esa)], [zf_stmt_279])).
20.91/21.06	tff(zf_stmt_226, axiom,
20.91/21.06	  (![K_1:int]:
20.91/21.06	     (app_encode_app(int,int,
20.91/21.06	                     app_encode_app(int,app_encode_fun(int,int),
20.91/21.06	                                    plus_plus_int,pls),
20.91/21.06	                     K_1) =
20.91/21.06	      K_1))).
20.91/21.06	tff('12', plain,
20.91/21.06	    ![X341 : int]:
20.91/21.06	      app_encode_app(int, int, 
20.91/21.06	        app_encode_app(int, app_encode_fun(int, int), plus_plus_int, pls), 
20.91/21.06	        X341)
20.91/21.06	       = X341,
20.91/21.06	    inference('cnf', [status(esa)], [zf_stmt_226])).
20.91/21.06	tff('13', plain,
20.91/21.06	    app_encode_app(int, int, 
20.91/21.06	      app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
20.91/21.06	        app_encode_app(int, int, bit1, pls)), 
20.91/21.06	      app_encode_app(int, int, 
20.91/21.06	        app_encode_app(int, app_encode_fun(int, int), times_times_int, s), s))
20.91/21.06	     = app_encode_app(int, int, 
20.91/21.06	         app_encode_app(int, app_encode_fun(int, int), times_times_int, 
20.91/21.06	           app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m))), 
20.91/21.06	         t),
20.91/21.06	    inference('demod', [status(thm)], ['6', '7', '8', '8', '10', '11', '12'])).
20.91/21.06	tff(zf_stmt_468, axiom,
20.91/21.06	  (![B:int,A:int]:
20.91/21.06	     (app_encode_app(int,$o,
20.91/21.06	                     app_encode_app(int,app_encode_fun(int,$o),ord_less_int,
20.91/21.06	                                    zero_zero_int),
20.91/21.06	                     A) =>
20.91/21.06	      (app_encode_app(int,$o,
20.91/21.06	                      app_encode_app(int,app_encode_fun(int,$o),ord_less_int,
20.91/21.06	                                     zero_zero_int),
20.91/21.06	                      app_encode_app(int,int,
20.91/21.06	                                     app_encode_app(int,
20.91/21.06	                                                    app_encode_fun(int,int),
20.91/21.06	                                                    times_times_int,A),
20.91/21.06	                                     B)) =>
20.91/21.06	       app_encode_app(int,$o,
20.91/21.06	                      app_encode_app(int,app_encode_fun(int,$o),ord_less_int,
20.91/21.06	                                     zero_zero_int),
20.91/21.06	                      B))))).
20.91/21.06	tff('14', plain,
20.91/21.06	    ![X826 : int, X827 : int]:
20.91/21.06	      (app_encode_app(int, $o, 
20.91/21.06	         app_encode_app(int, app_encode_fun(int, $o), ord_less_int, 
20.91/21.06	           zero_zero_int), X826)
20.91/21.06	       | ~ app_encode_app(int, $o, 
20.91/21.06	             app_encode_app(int, app_encode_fun(int, $o), ord_less_int, 
20.91/21.06	               zero_zero_int), X827)
20.91/21.06	       | ~ app_encode_app(int, $o, 
20.91/21.06	             app_encode_app(int, app_encode_fun(int, $o), ord_less_int, 
20.91/21.06	               zero_zero_int), 
20.91/21.06	             app_encode_app(int, int, 
20.91/21.06	               app_encode_app(int, app_encode_fun(int, int), 
20.91/21.06	                 times_times_int, X827), X826))),
20.91/21.06	    inference('cnf', [status(esa)], [zf_stmt_468])).
20.91/21.06	tff(zf_stmt_218, axiom, (pls = zero_zero_int)).
20.91/21.06	tff('15', plain, pls = zero_zero_int,
20.91/21.06	    inference('cnf', [status(esa)], [zf_stmt_218])).
20.91/21.06	tff('16', plain,
20.91/21.06	    ![X826 : int, X827 : int]:
20.91/21.06	      (app_encode_app(int, $o, 
20.91/21.06	         app_encode_app(int, app_encode_fun(int, $o), ord_less_int, pls), 
20.91/21.06	         X826)
20.91/21.06	       | ~ app_encode_app(int, $o, 
20.91/21.06	             app_encode_app(int, app_encode_fun(int, $o), ord_less_int, pls), 
20.91/21.06	             X827)
20.91/21.06	       | ~ app_encode_app(int, $o, 
20.91/21.06	             app_encode_app(int, app_encode_fun(int, $o), ord_less_int, pls), 
20.91/21.06	             app_encode_app(int, int, 
20.91/21.06	               app_encode_app(int, app_encode_fun(int, int), 
20.91/21.06	                 times_times_int, X827), X826))),
20.91/21.06	    inference('demod', [status(thm)], ['14', '15', '15', '15'])).
20.91/21.06	tff('17', plain,
20.91/21.06	    (~ app_encode_app(int, $o, 
20.91/21.06	         app_encode_app(int, app_encode_fun(int, $o), ord_less_int, pls), 
20.91/21.06	         app_encode_app(int, int, 
20.91/21.06	           app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
20.91/21.06	             app_encode_app(int, int, bit1, pls)), 
20.91/21.06	           app_encode_app(int, int, 
20.91/21.06	             app_encode_app(int, app_encode_fun(int, int), times_times_int, 
20.91/21.06	               s), s)))
20.91/21.06	     | ~ app_encode_app(int, $o, 
20.91/21.06	           app_encode_app(int, app_encode_fun(int, $o), ord_less_int, pls), 
20.91/21.06	           app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m)))
20.91/21.06	     | app_encode_app(int, $o, 
20.91/21.06	         app_encode_app(int, app_encode_fun(int, $o), ord_less_int, pls), t)),
20.91/21.06	    inference('sup-', [status(thm)], ['13', '16'])).
20.91/21.06	tff(zf_stmt_410, axiom,
20.91/21.06	  (![A_37:int]:
20.91/21.06	     (app_encode_app(int,int,
20.91/21.06	                     app_encode_app(int,app_encode_fun(int,int),
20.91/21.06	                                    times_times_int,A_37),
20.91/21.06	                     zero_zero_int) =
20.91/21.06	      zero_zero_int))).
20.91/21.06	tff('18', plain,
20.91/21.06	    ![X683 : int]:
20.91/21.06	      app_encode_app(int, int, 
20.91/21.06	        app_encode_app(int, app_encode_fun(int, int), times_times_int, X683), 
20.91/21.06	        zero_zero_int)
20.91/21.06	       = zero_zero_int,
20.91/21.06	    inference('cnf', [status(esa)], [zf_stmt_410])).
20.91/21.06	tff('19', plain,
20.91/21.06	    ![X683 : int]:
20.91/21.06	      app_encode_app(int, int, 
20.91/21.06	        app_encode_app(int, app_encode_fun(int, int), times_times_int, X683), 
20.91/21.06	        pls)
20.91/21.06	       = pls,
20.91/21.06	    inference('demod', [status(thm)], ['18', '15', '15'])).
20.91/21.06	tff(zf_stmt_114, axiom,
20.91/21.06	  (![X_24:int,Y_16:int]:
20.91/21.06	     app_encode_app(int,$o,
20.91/21.06	                    app_encode_app(int,app_encode_fun(int,$o),
20.91/21.06	                                   ord_less_eq_int,zero_zero_int),
20.91/21.06	                    app_encode_app(int,int,
20.91/21.06	                                   app_encode_app(int,
20.91/21.06	                                                  app_encode_fun(int,int),
20.91/21.06	                                                  plus_plus_int,
20.91/21.06	                                                  app_encode_app(int,int,
20.91/21.06	                                                                 app_encode_app(
20.91/21.06	                                                                 int,
20.91/21.06	                                                                 app_encode_fun(
20.91/21.06	                                                                 int,int),
20.91/21.06	                                                                 times_times_int,
20.91/21.06	                                                                 X_24),X_24)),
20.91/21.06	                                   app_encode_app(int,int,
20.91/21.06	                                                  app_encode_app(int,
20.91/21.06	                                                                 app_encode_fun(
20.91/21.06	                                                                 int,int),
20.91/21.06	                                                                 times_times_int,
20.91/21.06	                                                                 Y_16),
20.91/21.06	                                                  Y_16))))).
20.91/21.06	tff('20', plain,
20.91/21.06	    ![X108 : int, X109 : int]:
20.91/21.06	      app_encode_app(int, $o, 
20.91/21.06	        app_encode_app(int, app_encode_fun(int, $o), ord_less_eq_int, 
20.91/21.06	          zero_zero_int), 
20.91/21.06	        app_encode_app(int, int, 
20.91/21.06	          app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
20.91/21.06	            app_encode_app(int, int, 
20.91/21.06	              app_encode_app(int, app_encode_fun(int, int), times_times_int, 
20.91/21.06	                X108), X108)), 
20.91/21.06	          app_encode_app(int, int, 
20.91/21.06	            app_encode_app(int, app_encode_fun(int, int), times_times_int, 
20.91/21.06	              X109), X109))),
20.91/21.06	    inference('cnf', [status(esa)], [zf_stmt_114])).
20.91/21.06	tff('21', plain,
20.91/21.06	    ![X108 : int, X109 : int]:
20.91/21.06	      app_encode_app(int, $o, 
20.91/21.06	        app_encode_app(int, app_encode_fun(int, $o), ord_less_eq_int, pls), 
20.91/21.06	        app_encode_app(int, int, 
20.91/21.06	          app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
20.91/21.06	            app_encode_app(int, int, 
20.91/21.06	              app_encode_app(int, app_encode_fun(int, int), times_times_int, 
20.91/21.06	                X108), X108)), 
20.91/21.06	          app_encode_app(int, int, 
20.91/21.06	            app_encode_app(int, app_encode_fun(int, int), times_times_int, 
20.91/21.06	              X109), X109))),
20.91/21.06	    inference('demod', [status(thm)], ['20', '15'])).
20.91/21.06	tff('22', plain,
20.91/21.06	    ![X0 : int]:
20.91/21.06	      app_encode_app(int, $o, 
20.91/21.06	        app_encode_app(int, app_encode_fun(int, $o), ord_less_eq_int, pls), 
20.91/21.06	        app_encode_app(int, int, 
20.91/21.06	          app_encode_app(int, app_encode_fun(int, int), plus_plus_int, pls), 
20.91/21.06	          app_encode_app(int, int, 
20.91/21.06	            app_encode_app(int, app_encode_fun(int, int), times_times_int, 
20.91/21.06	              X0), X0))),
20.91/21.06	    inference('sup+', [status(thm)], ['19', '21'])).
20.91/21.06	tff('23', plain,
20.91/21.06	    ![X0 : int]:
20.91/21.06	      app_encode_app(int, $o, 
20.91/21.06	        app_encode_app(int, app_encode_fun(int, $o), ord_less_eq_int, pls), 
20.91/21.06	        app_encode_app(int, int, 
20.91/21.06	          app_encode_app(int, app_encode_fun(int, int), times_times_int, X0), 
20.91/21.06	          X0)),
20.91/21.06	    inference('demod', [status(thm)], ['22', '12'])).
20.91/21.06	tff(zf_stmt_156, axiom,
20.91/21.06	  (![W_1:int,Z_1:int]:
20.91/21.06	     (app_encode_app(int,$o,
20.91/21.06	                     app_encode_app(int,app_encode_fun(int,$o),ord_less_int,
20.91/21.06	                                    W_1),
20.91/21.06	                     app_encode_app(int,int,
20.91/21.06	                                    app_encode_app(int,
20.91/21.06	                                                   app_encode_fun(int,int),
20.91/21.06	                                                   plus_plus_int,Z_1),
20.91/21.06	                                    one_one_int)) <=>
20.91/21.06	      app_encode_app(int,$o,
20.91/21.06	                     app_encode_app(int,app_encode_fun(int,$o),
20.91/21.06	                                    ord_less_eq_int,W_1),
20.91/21.06	                     Z_1)))).
20.91/21.06	tff('24', plain,
20.91/21.06	    ![X195 : int, X197 : int]:
20.91/21.06	      (app_encode_app(int, $o, 
20.91/21.06	         app_encode_app(int, app_encode_fun(int, $o), ord_less_int, X195), 
20.91/21.06	         app_encode_app(int, int, 
20.91/21.06	           app_encode_app(int, app_encode_fun(int, int), plus_plus_int, X197), 
20.91/21.06	           one_one_int))
20.91/21.06	       | ~ app_encode_app(int, $o, 
20.91/21.06	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq_int, 
20.91/21.06	               X195), X197)),
20.91/21.06	    inference('cnf', [status(esa)], [zf_stmt_156])).
20.91/21.06	tff('25', plain,
20.91/21.06	    ![X195 : int, X197 : int]:
20.91/21.06	      (app_encode_app(int, $o, 
20.91/21.06	         app_encode_app(int, app_encode_fun(int, $o), ord_less_int, X195), 
20.91/21.06	         app_encode_app(int, int, 
20.91/21.06	           app_encode_app(int, app_encode_fun(int, int), plus_plus_int, X197), 
20.91/21.06	           app_encode_app(int, int, bit1, pls)))
20.91/21.06	       | ~ app_encode_app(int, $o, 
20.91/21.06	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq_int, 
20.91/21.06	               X195), X197)),
20.91/21.06	    inference('demod', [status(thm)], ['24', '3'])).
20.91/21.06	tff('26', plain,
20.91/21.06	    ![X0 : int]:
20.91/21.06	      (~ $true
20.91/21.06	       | app_encode_app(int, $o, 
20.91/21.06	           app_encode_app(int, app_encode_fun(int, $o), ord_less_int, pls), 
20.91/21.06	           app_encode_app(int, int, 
20.91/21.06	             app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
20.91/21.06	               app_encode_app(int, int, 
20.91/21.06	                 app_encode_app(int, app_encode_fun(int, int), 
20.91/21.06	                   times_times_int, X0), X0)), 
20.91/21.06	             app_encode_app(int, int, bit1, pls)))),
20.91/21.06	    inference('sup-', [status(thm)], ['23', '25'])).
20.91/21.06	tff('27', plain,
20.91/21.06	    ![X0 : int]:
20.91/21.06	      (~ $true
20.91/21.06	       | app_encode_app(int, $o, 
20.91/21.06	           app_encode_app(int, app_encode_fun(int, $o), ord_less_int, pls), 
20.91/21.06	           app_encode_app(int, int, 
20.91/21.06	             app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
20.91/21.06	               app_encode_app(int, int, bit1, pls)), 
20.91/21.06	             app_encode_app(int, int, 
20.91/21.06	               app_encode_app(int, app_encode_fun(int, int), 
20.91/21.06	                 times_times_int, X0), X0)))),
20.91/21.06	    inference('demod', [status(thm)], ['26', '5'])).
20.91/21.06	tff('28', plain,
20.91/21.06	    ![X0 : int]:
20.91/21.06	      app_encode_app(int, $o, 
20.91/21.06	        app_encode_app(int, app_encode_fun(int, $o), ord_less_int, pls), 
20.91/21.06	        app_encode_app(int, int, 
20.91/21.06	          app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
20.91/21.06	            app_encode_app(int, int, bit1, pls)), 
20.91/21.06	          app_encode_app(int, int, 
20.91/21.06	            app_encode_app(int, app_encode_fun(int, int), times_times_int, 
20.91/21.06	              X0), X0))),
20.91/21.06	    inference('simplify', [status(thm)], ['27'])).
20.91/21.06	tff(zf_stmt_84, axiom,
20.91/21.06	  (![Z:int,W:int]:
20.91/21.06	     (app_encode_app(int,$o,
20.91/21.06	                     app_encode_app(int,app_encode_fun(int,$o),
20.91/21.06	                                    ord_less_eq_int,Z),
20.91/21.06	                     W) | 
20.91/21.06	      app_encode_app(int,$o,
20.91/21.06	                     app_encode_app(int,app_encode_fun(int,$o),
20.91/21.06	                                    ord_less_eq_int,W),
20.91/21.06	                     Z)))).
20.91/21.06	tff('29', plain,
20.91/21.06	    ![X34 : int, X35 : int]:
20.91/21.06	      (app_encode_app(int, $o, 
20.91/21.06	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq_int, X34), 
20.91/21.06	         X35)
20.91/21.06	       | app_encode_app(int, $o, 
20.91/21.06	           app_encode_app(int, app_encode_fun(int, $o), ord_less_eq_int, X35), 
20.91/21.06	           X34)),
20.91/21.06	    inference('cnf', [status(esa)], [zf_stmt_84])).
20.91/21.06	tff(zf_stmt_79, axiom,
20.91/21.06	  (app_encode_app(int,$o,zprime,
20.91/21.06	                  app_encode_app(int,int,
20.91/21.06	                                 app_encode_app(int,app_encode_fun(int,int),
20.91/21.06	                                                plus_plus_int,
20.91/21.06	                                                app_encode_app(int,int,
20.91/21.06	                                                               app_encode_app(
20.91/21.06	                                                               int,
20.91/21.06	                                                               app_encode_fun(
20.91/21.06	                                                               int,int),
20.91/21.06	                                                               times_times_int,
20.91/21.06	                                                               app_encode_app(
20.91/21.06	                                                               int,int,
20.91/21.06	                                                               number_number_of_int,
20.91/21.06	                                                               app_encode_app(
20.91/21.06	                                                               int,int,bit0,
20.91/21.06	                                                               app_encode_app(
20.91/21.06	                                                               int,int,bit0,
20.91/21.06	                                                               app_encode_app(
20.91/21.06	                                                               int,int,bit1,
20.91/21.06	                                                               pls))))),m)),
20.91/21.06	                                 one_one_int)))).
20.91/21.06	tff('30', plain,
20.91/21.06	    app_encode_app(int, $o, zprime, 
20.91/21.06	      app_encode_app(int, int, 
20.91/21.06	        app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
20.91/21.06	          app_encode_app(int, int, 
20.91/21.06	            app_encode_app(int, app_encode_fun(int, int), times_times_int, 
20.91/21.06	              app_encode_app(int, int, number_number_of_int, 
20.91/21.06	                app_encode_app(int, int, bit0, 
20.91/21.06	                  app_encode_app(int, int, bit0, 
20.91/21.06	                    app_encode_app(int, int, bit1, pls))))), m)), 
20.91/21.06	        one_one_int)),
20.91/21.06	    inference('cnf', [status(esa)], [zf_stmt_79])).
20.91/21.06	tff('31', plain,
20.91/21.06	    app_encode_app(int, $o, zprime, 
20.91/21.06	      app_encode_app(int, int, 
20.91/21.06	        app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
20.91/21.06	          app_encode_app(int, int, bit1, pls)), 
20.91/21.06	        app_encode_app(int, int, 
20.91/21.06	          app_encode_app(int, app_encode_fun(int, int), times_times_int, 
20.91/21.06	            app_encode_app(int, int, bit0, 
20.91/21.06	              app_encode_app(int, int, bit0, 
20.91/21.06	                app_encode_app(int, int, bit1, pls)))), m))),
20.91/21.06	    inference('demod', [status(thm)], ['30', '2', '3', '5'])).
20.91/21.06	tff('32', plain,
20.91/21.06	    app_encode_app(int, $o, zprime, 
20.91/21.06	      app_encode_app(int, int, 
20.91/21.06	        app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
20.91/21.06	          app_encode_app(int, int, bit1, pls)), 
20.91/21.06	        app_encode_app(int, int, bit0, app_encode_app(int, int, bit0, m)))),
20.91/21.06	    inference('demod', [status(thm)], ['31', '8', '8', '10'])).
20.91/21.06	tff('33', plain,
20.91/21.06	    app_encode_app(int, $o, zprime, 
20.91/21.06	      app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m))),
20.91/21.06	    inference('demod', [status(thm)], ['32', '11', '12'])).
20.91/21.06	tff(zf_stmt_489, axiom,
20.91/21.06	  (![P_1:int]:
20.91/21.06	     (app_encode_app(int,$o,zprime,P_1) <=>
20.91/21.06	      (app_encode_app(int,$o,
20.91/21.06	                      app_encode_app(int,app_encode_fun(int,$o),ord_less_int,
20.91/21.06	                                     one_one_int),
20.91/21.06	                      P_1) & 
20.91/21.06	       (![M_8:int]:
20.91/21.06	          ((app_encode_app(int,$o,
20.91/21.06	                           app_encode_app(int,app_encode_fun(int,$o),
20.91/21.06	                                          ord_less_eq_int,zero_zero_int),
20.91/21.06	                           M_8) & 
20.91/21.06	            app_encode_app(int,$o,
20.91/21.06	                           app_encode_app(int,app_encode_fun(int,$o),
20.91/21.06	                                          dvd_dvd_int,M_8),
20.91/21.06	                           P_1)) =>
20.91/21.06	           ((M_8 = one_one_int) | (M_8 = P_1)))))))).
20.91/21.06	tff('34', plain,
20.91/21.06	    ![X875 : int]:
20.91/21.06	      (app_encode_app(int, $o, 
20.91/21.06	         app_encode_app(int, app_encode_fun(int, $o), ord_less_int, 
20.91/21.06	           one_one_int), X875)
20.91/21.06	       | ~ app_encode_app(int, $o, zprime, X875)),
20.91/21.06	    inference('cnf', [status(esa)], [zf_stmt_489])).
20.91/21.06	tff('35', plain,
20.91/21.06	    ![X875 : int]:
20.91/21.06	      (app_encode_app(int, $o, 
20.91/21.06	         app_encode_app(int, app_encode_fun(int, $o), ord_less_int, 
20.91/21.06	           app_encode_app(int, int, bit1, pls)), X875)
20.91/21.06	       | ~ app_encode_app(int, $o, zprime, X875)),
20.91/21.06	    inference('demod', [status(thm)], ['34', '3'])).
20.91/21.06	tff('36', plain,
20.91/21.06	    (~ $true
20.91/21.06	     | app_encode_app(int, $o, 
20.91/21.06	         app_encode_app(int, app_encode_fun(int, $o), ord_less_int, 
20.91/21.06	           app_encode_app(int, int, bit1, pls)), 
20.91/21.06	         app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m)))),
20.91/21.06	    inference('sup-', [status(thm)], ['33', '35'])).
20.91/21.06	tff('37', plain,
20.91/21.06	    app_encode_app(int, $o, 
20.91/21.06	      app_encode_app(int, app_encode_fun(int, $o), ord_less_int, 
20.91/21.06	        app_encode_app(int, int, bit1, pls)), 
20.91/21.06	      app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m))),
20.91/21.06	    inference('simplify', [status(thm)], ['36'])).
20.91/21.06	tff(zf_stmt_219, axiom,
20.91/21.06	  (![K1:int,K2:int]:
20.91/21.06	     (app_encode_app(int,$o,
20.91/21.06	                     app_encode_app(int,app_encode_fun(int,$o),ord_less_int,
20.91/21.06	                                    app_encode_app(int,int,bit1,K1)),
20.91/21.06	                     app_encode_app(int,int,bit1,K2)) <=>
20.91/21.06	      app_encode_app(int,$o,
20.91/21.06	                     app_encode_app(int,app_encode_fun(int,$o),ord_less_int,
20.91/21.06	                                    K1),
20.91/21.06	                     K2)))).
20.91/21.06	tff('38', plain,
20.91/21.06	    ![X328 : int, X329 : int]:
20.91/21.06	      (app_encode_app(int, $o, 
20.91/21.06	         app_encode_app(int, app_encode_fun(int, $o), ord_less_int, X328), 
20.91/21.06	         X329)
20.91/21.06	       | ~ app_encode_app(int, $o, 
20.91/21.06	             app_encode_app(int, app_encode_fun(int, $o), ord_less_int, 
20.91/21.06	               app_encode_app(int, int, bit1, X328)), 
20.91/21.06	             app_encode_app(int, int, bit1, X329))),
20.91/21.06	    inference('cnf', [status(esa)], [zf_stmt_219])).
20.91/21.06	tff('39', plain,
20.91/21.06	    (~ $true
20.91/21.06	     | app_encode_app(int, $o, 
20.91/21.06	         app_encode_app(int, app_encode_fun(int, $o), ord_less_int, pls), 
20.91/21.06	         app_encode_app(int, int, bit0, m))),
20.91/21.06	    inference('sup-', [status(thm)], ['37', '38'])).
20.91/21.06	tff('40', plain,
20.91/21.06	    app_encode_app(int, $o, 
20.91/21.06	      app_encode_app(int, app_encode_fun(int, $o), ord_less_int, pls), 
20.91/21.06	      app_encode_app(int, int, bit0, m)),
20.91/21.06	    inference('simplify', [status(thm)], ['39'])).
20.91/21.06	tff(zf_stmt_122, axiom,
20.91/21.06	  (![V_7:int,W_1:int]:
20.91/21.06	     (app_encode_app(int,$o,
20.91/21.06	                     app_encode_app(int,app_encode_fun(int,$o),
20.91/21.06	                                    ord_less_eq_int,
20.91/21.06	                                    app_encode_app(int,int,
20.91/21.06	                                                   number_number_of_int,V_7)),
20.91/21.06	                     app_encode_app(int,int,number_number_of_int,W_1)) <=>
20.91/21.06	      (~
20.91/21.06	        app_encode_app(int,$o,
20.91/21.06	                       app_encode_app(int,app_encode_fun(int,$o),
20.91/21.06	                                      ord_less_int,
20.91/21.06	                                      app_encode_app(int,int,
20.91/21.06	                                                     number_number_of_int,W_1)),
20.91/21.06	                       app_encode_app(int,int,number_number_of_int,V_7)))))).
20.91/21.06	tff('41', plain,
20.91/21.06	    ![X126 : int, X127 : int]:
20.91/21.06	      (~ app_encode_app(int, $o, 
20.91/21.06	           app_encode_app(int, app_encode_fun(int, $o), ord_less_int, 
20.91/21.06	             app_encode_app(int, int, number_number_of_int, X126)), 
20.91/21.06	           app_encode_app(int, int, number_number_of_int, X127))
20.91/21.06	       | ~ app_encode_app(int, $o, 
20.91/21.06	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq_int, 
20.91/21.06	               app_encode_app(int, int, number_number_of_int, X127)), 
20.91/21.06	             app_encode_app(int, int, number_number_of_int, X126))),
20.91/21.06	    inference('cnf', [status(esa)], [zf_stmt_122])).
20.91/21.06	tff('42', plain,
20.91/21.06	    ![X126 : int, X127 : int]:
20.91/21.06	      (~ app_encode_app(int, $o, 
20.91/21.06	           app_encode_app(int, app_encode_fun(int, $o), ord_less_int, X126), 
20.91/21.06	           X127)
20.91/21.06	       | ~ app_encode_app(int, $o, 
20.91/21.06	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq_int, 
20.91/21.06	               X127), X126)),
20.91/21.06	    inference('demod', [status(thm)], ['41', '2', '2', '2', '2'])).
20.91/21.06	tff('43', plain,
20.91/21.06	    (~ $true
20.91/21.06	     | ~ app_encode_app(int, $o, 
20.91/21.06	           app_encode_app(int, app_encode_fun(int, $o), ord_less_eq_int, 
20.91/21.06	             app_encode_app(int, int, bit0, m)), pls)),
20.91/21.06	    inference('sup-', [status(thm)], ['40', '42'])).
20.91/21.06	tff('44', plain,
20.91/21.06	    ~ app_encode_app(int, $o, 
20.91/21.06	        app_encode_app(int, app_encode_fun(int, $o), ord_less_eq_int, 
20.91/21.06	          app_encode_app(int, int, bit0, m)), pls),
20.91/21.06	    inference('simplify', [status(thm)], ['43'])).
20.91/21.06	tff('45', plain,
20.91/21.06	    (~ $true
20.91/21.06	     | app_encode_app(int, $o, 
20.91/21.06	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq_int, pls), 
20.91/21.06	         app_encode_app(int, int, bit0, m))),
20.91/21.06	    inference('sup-', [status(thm)], ['29', '44'])).
20.91/21.06	tff('46', plain,
20.91/21.06	    app_encode_app(int, $o, 
20.91/21.06	      app_encode_app(int, app_encode_fun(int, $o), ord_less_eq_int, pls), 
20.91/21.06	      app_encode_app(int, int, bit0, m)),
20.91/21.06	    inference('simplify', [status(thm)], ['45'])).
20.91/21.06	tff(zf_stmt_145, axiom,
20.91/21.06	  (![K:int]:
20.91/21.06	     (app_encode_app(int,$o,
20.91/21.06	                     app_encode_app(int,app_encode_fun(int,$o),ord_less_int,
20.91/21.06	                                    pls),
20.91/21.06	                     app_encode_app(int,int,bit1,K)) <=>
20.91/21.06	      app_encode_app(int,$o,
20.91/21.06	                     app_encode_app(int,app_encode_fun(int,$o),
20.91/21.06	                                    ord_less_eq_int,pls),
20.91/21.06	                     K)))).
20.91/21.06	tff('47', plain,
20.91/21.06	    ![X172 : int]:
20.91/21.06	      (app_encode_app(int, $o, 
20.91/21.06	         app_encode_app(int, app_encode_fun(int, $o), ord_less_int, pls), 
20.91/21.06	         app_encode_app(int, int, bit1, X172))
20.91/21.06	       | ~ app_encode_app(int, $o, 
20.91/21.06	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq_int, 
20.91/21.06	               pls), X172)),
20.91/21.06	    inference('cnf', [status(esa)], [zf_stmt_145])).
20.91/21.06	tff('48', plain,
20.91/21.06	    (~ $true
20.91/21.06	     | app_encode_app(int, $o, 
20.91/21.06	         app_encode_app(int, app_encode_fun(int, $o), ord_less_int, pls), 
20.91/21.06	         app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m)))),
20.91/21.06	    inference('sup-', [status(thm)], ['46', '47'])).
20.91/21.06	tff('49', plain,
20.91/21.06	    app_encode_app(int, $o, 
20.91/21.06	      app_encode_app(int, app_encode_fun(int, $o), ord_less_int, pls), 
20.91/21.06	      app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m))),
20.91/21.06	    inference('simplify', [status(thm)], ['48'])).
20.91/21.06	tff('50', plain,
20.91/21.06	    (~ $true
20.91/21.06	     | ~ $true
20.91/21.06	     | app_encode_app(int, $o, 
20.91/21.06	         app_encode_app(int, app_encode_fun(int, $o), ord_less_int, pls), t)),
20.91/21.06	    inference('demod', [status(thm)], ['17', '28', '49'])).
20.91/21.06	tff('51', plain,
20.91/21.06	    app_encode_app(int, $o, 
20.91/21.06	      app_encode_app(int, app_encode_fun(int, $o), ord_less_int, pls), t),
20.91/21.06	    inference('simplify', [status(thm)], ['50'])).
20.91/21.06	tff(zf_stmt_98, axiom,
20.91/21.06	  (![Z_1:int,W_1:int]:
20.91/21.06	     (app_encode_app(int,$o,
20.91/21.06	                     app_encode_app(int,app_encode_fun(int,$o),ord_less_int,
20.91/21.06	                                    Z_1),
20.91/21.06	                     W_1) <=>
20.91/21.06	      (app_encode_app(int,$o,
20.91/21.06	                      app_encode_app(int,app_encode_fun(int,$o),
20.91/21.06	                                     ord_less_eq_int,Z_1),
20.91/21.06	                      W_1) & 
20.91/21.06	       (Z_1 != W_1))))).
20.91/21.06	tff('52', plain,
20.91/21.06	    ![X70 : int, X71 : int]:
20.91/21.06	      (app_encode_app(int, $o, 
20.91/21.06	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq_int, X70), 
20.91/21.06	         X71)
20.91/21.06	       | ~ app_encode_app(int, $o, 
20.91/21.06	             app_encode_app(int, app_encode_fun(int, $o), ord_less_int, X70), 
20.91/21.06	             X71)),
20.91/21.06	    inference('cnf', [status(esa)], [zf_stmt_98])).
20.91/21.06	tff(zf_stmt_48, axiom,
20.91/21.06	  (app_encode_app(int,$o,
20.91/21.06	                  app_encode_app(int,app_encode_fun(int,$o),ord_less_int,t),
20.91/21.06	                  zero_zero_int))).
20.91/21.06	tff('53', plain,
20.91/21.06	    app_encode_app(int, $o, 
20.91/21.06	      app_encode_app(int, app_encode_fun(int, $o), ord_less_int, t), 
20.91/21.06	      zero_zero_int),
20.91/21.06	    inference('cnf', [status(esa)], [zf_stmt_48])).
20.91/21.06	tff('54', plain,
20.91/21.06	    app_encode_app(int, $o, 
20.91/21.06	      app_encode_app(int, app_encode_fun(int, $o), ord_less_int, t), pls),
20.91/21.06	    inference('demod', [status(thm)], ['53', '15'])).
20.91/21.06	tff('55', plain,
20.91/21.06	    (~ $true
20.91/21.06	     | ~ app_encode_app(int, $o, 
20.91/21.06	           app_encode_app(int, app_encode_fun(int, $o), ord_less_eq_int, pls), 
20.91/21.06	           t)),
20.91/21.06	    inference('sup-', [status(thm)], ['54', '42'])).
20.91/21.06	tff('56', plain,
20.91/21.06	    ~ app_encode_app(int, $o, 
20.91/21.06	        app_encode_app(int, app_encode_fun(int, $o), ord_less_eq_int, pls), 
20.91/21.06	        t),
20.91/21.06	    inference('simplify', [status(thm)], ['55'])).
20.91/21.06	tff('57', plain,
20.91/21.06	    (~ $true
20.91/21.06	     | ~ app_encode_app(int, $o, 
20.91/21.06	           app_encode_app(int, app_encode_fun(int, $o), ord_less_int, pls), 
20.91/21.06	           t)),
20.91/21.06	    inference('sup-', [status(thm)], ['52', '56'])).
20.91/21.06	tff('58', plain,
20.91/21.06	    ~ app_encode_app(int, $o, 
20.91/21.06	        app_encode_app(int, app_encode_fun(int, $o), ord_less_int, pls), t),
20.91/21.06	    inference('simplify', [status(thm)], ['57'])).
20.91/21.06	tff('59', plain, ~ $true, inference('sup-', [status(thm)], ['51', '58'])).
20.91/21.06	tff('60', plain, $false, inference('simplify', [status(thm)], ['59'])).
20.91/21.06	
20.91/21.06	% SZS output end Refutation
20.91/21.06	EOF
