0.00/0.01	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.01	% app-encoded or not : app
0.00/0.01	% Variant    : fo
0.00/0.01	% Ordering    : rpo6
0.00/0.01	% Command    : 
0.00/0.01	#!/bin/sh
0.00/0.01	
0.00/0.01	./zipperposition.native ${1:+"$1"} \
0.00/0.01	  -i tptp \
0.00/0.01	  -o tptp \
0.00/0.01	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.01	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.01	  --no-ho \
0.00/0.01	  --no-avatar \
0.00/0.01	  --no-induction \
0.00/0.01	  --no-unif-pattern \
0.00/0.01	  --ord $2 \
0.00/0.01	  --simultaneous-sup false \
0.00/0.01	  --no-max-vars \
0.00/0.01	  --no-fool
0.00/0.20	% Computer   : n163.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 07:33:09 CST 2018
3.01/3.22	% done 1444 iterations in 3.013s
3.01/3.22	% SZS status Theorem for 'stdin'
3.01/3.22	% SZS output start Refutation
3.01/3.23	tff(zf_stmt_31, axiom,
3.01/3.23	  (app_encode_app(int,int,
3.01/3.23	                  app_encode_app(int,app_encode_fun(int,int),plus_plus_int,
3.01/3.23	                                 app_encode_app(nat,int,
3.01/3.23	                                                app_encode_app(int,
3.01/3.23	                                                               app_encode_fun(
3.01/3.23	                                                               nat,int),
3.01/3.23	                                                               power_power_int,
3.01/3.23	                                                               s),
3.01/3.23	                                                app_encode_app(int,nat,
3.01/3.23	                                                               number_number_of_nat,
3.01/3.23	                                                               app_encode_app(
3.01/3.23	                                                               int,int,bit0,
3.01/3.23	                                                               app_encode_app(
3.01/3.23	                                                               int,int,bit1,
3.01/3.23	                                                               pls))))),
3.01/3.23	                  one_one_int) =
3.01/3.23	   app_encode_app(int,int,
3.01/3.23	                  app_encode_app(int,app_encode_fun(int,int),times_times_int,
3.01/3.23	                                 app_encode_app(int,int,
3.01/3.23	                                                app_encode_app(int,
3.01/3.23	                                                               app_encode_fun(
3.01/3.23	                                                               int,int),
3.01/3.23	                                                               plus_plus_int,
3.01/3.23	                                                               app_encode_app(
3.01/3.23	                                                               int,int,
3.01/3.23	                                                               app_encode_app(
3.01/3.23	                                                               int,
3.01/3.23	                                                               app_encode_fun(
3.01/3.23	                                                               int,int),
3.01/3.23	                                                               times_times_int,
3.01/3.23	                                                               app_encode_app(
3.01/3.23	                                                               int,int,
3.01/3.23	                                                               number_number_of_int,
3.01/3.23	                                                               app_encode_app(
3.01/3.23	                                                               int,int,bit0,
3.01/3.23	                                                               app_encode_app(
3.01/3.23	                                                               int,int,bit0,
3.01/3.23	                                                               app_encode_app(
3.01/3.23	                                                               int,int,bit1,
3.01/3.23	                                                               pls))))),m)),
3.01/3.23	                                                one_one_int)),
3.01/3.23	                  t))).
3.01/3.23	tff('0', plain,
3.01/3.23	    app_encode_app(int, int, 
3.01/3.23	      app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
3.01/3.23	        app_encode_app(nat, int, 
3.01/3.23	          app_encode_app(int, app_encode_fun(nat, int), power_power_int, s), 
3.01/3.23	          app_encode_app(int, nat, number_number_of_nat, 
3.01/3.23	            app_encode_app(int, int, bit0, 
3.01/3.23	              app_encode_app(int, int, bit1, pls))))), one_one_int)
3.01/3.23	     = app_encode_app(int, int, 
3.01/3.23	         app_encode_app(int, app_encode_fun(int, int), times_times_int, 
3.01/3.23	           app_encode_app(int, int, 
3.01/3.23	             app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
3.01/3.23	               app_encode_app(int, int, 
3.01/3.23	                 app_encode_app(int, app_encode_fun(int, int), 
3.01/3.23	                   times_times_int, 
3.01/3.23	                   app_encode_app(int, int, number_number_of_int, 
3.01/3.23	                     app_encode_app(int, int, bit0, 
3.01/3.23	                       app_encode_app(int, int, bit0, 
3.01/3.23	                         app_encode_app(int, int, bit1, pls))))), m)), 
3.01/3.23	             one_one_int)), t),
3.01/3.23	    inference('cnf', [status(esa)], [zf_stmt_31])).
3.01/3.23	tff(zf_stmt_52, axiom,
3.01/3.23	  (![K:int]: (app_encode_app(int,int,number_number_of_int,K) = K))).
3.01/3.23	tff('1', plain,
3.01/3.23	    ![X16 : int]: app_encode_app(int, int, number_number_of_int, X16) = X16,
3.01/3.23	    inference('cnf', [status(esa)], [zf_stmt_52])).
3.01/3.23	tff('2', plain,
3.01/3.23	    app_encode_app(int, int, 
3.01/3.23	      app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
3.01/3.23	        app_encode_app(nat, int, 
3.01/3.23	          app_encode_app(int, app_encode_fun(nat, int), power_power_int, s), 
3.01/3.23	          app_encode_app(int, nat, number_number_of_nat, 
3.01/3.23	            app_encode_app(int, int, bit0, 
3.01/3.23	              app_encode_app(int, int, bit1, pls))))), one_one_int)
3.01/3.23	     = app_encode_app(int, int, 
3.01/3.23	         app_encode_app(int, app_encode_fun(int, int), times_times_int, 
3.01/3.23	           app_encode_app(int, int, 
3.01/3.23	             app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
3.01/3.23	               app_encode_app(int, int, 
3.01/3.23	                 app_encode_app(int, app_encode_fun(int, int), 
3.01/3.23	                   times_times_int, 
3.01/3.23	                   app_encode_app(int, int, bit0, 
3.01/3.23	                     app_encode_app(int, int, bit0, 
3.01/3.23	                       app_encode_app(int, int, bit1, pls)))), m)), 
3.01/3.23	             one_one_int)), t),
3.01/3.23	    inference('demod', [status(thm)], ['0', '1'])).
3.01/3.23	tff(zf_stmt_132, axiom,
3.01/3.23	  (![Z:int,W:int]:
3.01/3.23	     (app_encode_app(int,int,
3.01/3.23	                     app_encode_app(int,app_encode_fun(int,int),
3.01/3.23	                                    plus_plus_int,Z),
3.01/3.23	                     W) =
3.01/3.23	      app_encode_app(int,int,
3.01/3.23	                     app_encode_app(int,app_encode_fun(int,int),
3.01/3.23	                                    plus_plus_int,W),
3.01/3.23	                     Z)))).
3.01/3.23	tff('3', plain,
3.01/3.23	    ![X201 : int, X202 : int]:
3.01/3.23	      app_encode_app(int, int, 
3.01/3.23	        app_encode_app(int, app_encode_fun(int, int), plus_plus_int, X202), 
3.01/3.23	        X201)
3.01/3.23	       = app_encode_app(int, int, 
3.01/3.23	           app_encode_app(int, app_encode_fun(int, int), plus_plus_int, X201), 
3.01/3.23	           X202),
3.01/3.23	    inference('cnf', [status(esa)], [zf_stmt_132])).
3.01/3.23	tff('4', plain,
3.01/3.23	    app_encode_app(int, int, 
3.01/3.23	      app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
3.01/3.23	        one_one_int), 
3.01/3.23	      app_encode_app(nat, int, 
3.01/3.23	        app_encode_app(int, app_encode_fun(nat, int), power_power_int, s), 
3.01/3.23	        app_encode_app(int, nat, number_number_of_nat, 
3.01/3.23	          app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls)))))
3.01/3.23	     = app_encode_app(int, int, 
3.01/3.23	         app_encode_app(int, app_encode_fun(int, int), times_times_int, 
3.01/3.23	           app_encode_app(int, int, 
3.01/3.23	             app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
3.01/3.23	               one_one_int), 
3.01/3.23	             app_encode_app(int, int, 
3.01/3.23	               app_encode_app(int, app_encode_fun(int, int), 
3.01/3.23	                 times_times_int, 
3.01/3.23	                 app_encode_app(int, int, bit0, 
3.01/3.23	                   app_encode_app(int, int, bit0, 
3.01/3.23	                     app_encode_app(int, int, bit1, pls)))), m))), t),
3.01/3.23	    inference('demod', [status(thm)], ['2', '3', '3'])).
3.01/3.23	tff(zf_stmt_91, axiom,
3.01/3.23	  (![X_4:int]:
3.01/3.23	     (app_encode_app(int,$o,
3.01/3.23	                     app_encode_app(int,app_encode_fun(int,$o),
3.01/3.23	                                    ord_less_eq_int,
3.01/3.23	                                    app_encode_app(int,int,
3.01/3.23	                                                   number_number_of_int,X_4)),
3.01/3.23	                     one_one_int) <=>
3.01/3.23	      app_encode_app(int,$o,
3.01/3.23	                     app_encode_app(int,app_encode_fun(int,$o),
3.01/3.23	                                    ord_less_eq_int,X_4),
3.01/3.23	                     app_encode_app(int,int,bit1,pls))))).
3.01/3.23	tff('5', plain,
3.01/3.23	    ![X107 : int]:
3.01/3.23	      (app_encode_app(int, $o, 
3.01/3.23	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq_int, 
3.01/3.23	           app_encode_app(int, int, number_number_of_int, X107)), 
3.01/3.23	         one_one_int)
3.01/3.23	       | ~ app_encode_app(int, $o, 
3.01/3.23	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq_int, 
3.01/3.23	               X107), app_encode_app(int, int, bit1, pls))),
3.01/3.23	    inference('cnf', [status(esa)], [zf_stmt_91])).
3.01/3.23	tff('6', plain,
3.01/3.23	    ![X107 : int]:
3.01/3.23	      (app_encode_app(int, $o, 
3.01/3.23	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq_int, X107), 
3.01/3.23	         one_one_int)
3.01/3.23	       | ~ app_encode_app(int, $o, 
3.01/3.23	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq_int, 
3.01/3.23	               X107), app_encode_app(int, int, bit1, pls))),
3.01/3.23	    inference('demod', [status(thm)], ['5', '1'])).
3.01/3.23	tff(zf_stmt_51, axiom,
3.01/3.23	  (![W:int]:
3.01/3.23	     app_encode_app(int,$o,
3.01/3.23	                    app_encode_app(int,app_encode_fun(int,$o),
3.01/3.23	                                   ord_less_eq_int,W),
3.01/3.23	                    W))).
3.01/3.23	tff('7', plain,
3.01/3.23	    ![X15 : int]:
3.01/3.23	      app_encode_app(int, $o, 
3.01/3.23	        app_encode_app(int, app_encode_fun(int, $o), ord_less_eq_int, X15), 
3.01/3.23	        X15),
3.01/3.23	    inference('cnf', [status(esa)], [zf_stmt_51])).
3.01/3.23	tff('8', plain,
3.01/3.23	    ![X106 : int]:
3.01/3.23	      (app_encode_app(int, $o, 
3.01/3.23	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq_int, X106), 
3.01/3.23	         app_encode_app(int, int, bit1, pls))
3.01/3.23	       | ~ app_encode_app(int, $o, 
3.01/3.23	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq_int, 
3.01/3.23	               app_encode_app(int, int, number_number_of_int, X106)), 
3.01/3.23	             one_one_int)),
3.01/3.23	    inference('cnf', [status(esa)], [zf_stmt_91])).
3.01/3.23	tff('9', plain,
3.01/3.23	    ![X106 : int]:
3.01/3.23	      (app_encode_app(int, $o, 
3.01/3.23	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq_int, X106), 
3.01/3.23	         app_encode_app(int, int, bit1, pls))
3.01/3.23	       | ~ app_encode_app(int, $o, 
3.01/3.23	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq_int, 
3.01/3.23	               X106), one_one_int)),
3.01/3.23	    inference('demod', [status(thm)], ['8', '1'])).
3.01/3.23	tff('10', plain,
3.01/3.23	    (~ $true
3.01/3.23	     | app_encode_app(int, $o, 
3.01/3.23	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq_int, 
3.01/3.23	           one_one_int), app_encode_app(int, int, bit1, pls))),
3.01/3.23	    inference('sup-', [status(thm)], ['7', '9'])).
3.01/3.23	tff('11', plain,
3.01/3.23	    app_encode_app(int, $o, 
3.01/3.23	      app_encode_app(int, app_encode_fun(int, $o), ord_less_eq_int, 
3.01/3.23	        one_one_int), app_encode_app(int, int, bit1, pls)),
3.01/3.23	    inference('simplify', [status(thm)], ['10'])).
3.01/3.23	tff(zf_stmt_60, axiom,
3.01/3.23	  (![Z:int,W:int]:
3.01/3.23	     (app_encode_app(int,$o,
3.01/3.23	                     app_encode_app(int,app_encode_fun(int,$o),
3.01/3.23	                                    ord_less_eq_int,Z),
3.01/3.23	                     W) =>
3.01/3.23	      (app_encode_app(int,$o,
3.01/3.23	                      app_encode_app(int,app_encode_fun(int,$o),
3.01/3.23	                                     ord_less_eq_int,W),
3.01/3.23	                      Z) =>
3.01/3.23	       (Z = W))))).
3.01/3.23	tff('12', plain,
3.01/3.23	    ![X35 : int, X36 : int]:
3.01/3.23	      (~ app_encode_app(int, $o, 
3.01/3.23	           app_encode_app(int, app_encode_fun(int, $o), ord_less_eq_int, X35), 
3.01/3.23	           X36)
3.01/3.23	       | X36 = X35
3.01/3.23	       | ~ app_encode_app(int, $o, 
3.01/3.23	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq_int, 
3.01/3.23	               X36), X35)),
3.01/3.23	    inference('cnf', [status(esa)], [zf_stmt_60])).
3.01/3.23	tff('13', plain,
3.01/3.23	    (~ $true
3.01/3.23	     | ~ app_encode_app(int, $o, 
3.01/3.23	           app_encode_app(int, app_encode_fun(int, $o), ord_less_eq_int, 
3.01/3.23	             app_encode_app(int, int, bit1, pls)), one_one_int)
3.01/3.23	     | app_encode_app(int, int, bit1, pls) = one_one_int),
3.01/3.23	    inference('sup-', [status(thm)], ['11', '12'])).
3.01/3.23	tff('14', plain,
3.01/3.23	    (app_encode_app(int, int, bit1, pls) = one_one_int
3.01/3.23	     | ~ app_encode_app(int, $o, 
3.01/3.23	           app_encode_app(int, app_encode_fun(int, $o), ord_less_eq_int, 
3.01/3.23	             app_encode_app(int, int, bit1, pls)), one_one_int)),
3.01/3.23	    inference('simplify', [status(thm)], ['13'])).
3.01/3.23	tff('15', plain,
3.01/3.23	    (~ $true
3.01/3.23	     | ~ app_encode_app(int, $o, 
3.01/3.23	           app_encode_app(int, app_encode_fun(int, $o), ord_less_eq_int, 
3.01/3.23	             app_encode_app(int, int, bit1, pls)), 
3.01/3.23	           app_encode_app(int, int, bit1, pls))
3.01/3.23	     | app_encode_app(int, int, bit1, pls) = one_one_int),
3.01/3.23	    inference('sup-', [status(thm)], ['6', '14'])).
3.01/3.23	tff('16', plain,
3.01/3.23	    (~ $true | ~ $true | app_encode_app(int, int, bit1, pls) = one_one_int),
3.01/3.23	    inference('demod', [status(thm)], ['15', '7'])).
3.01/3.23	tff('17', plain, app_encode_app(int, int, bit1, pls) = one_one_int,
3.01/3.23	    inference('simplify', [status(thm)], ['16'])).
3.01/3.23	tff(zf_stmt_95, axiom,
3.01/3.23	  (![K:int,L:int]:
3.01/3.23	     (app_encode_app(int,int,
3.01/3.23	                     app_encode_app(int,app_encode_fun(int,int),
3.01/3.23	                                    times_times_int,
3.01/3.23	                                    app_encode_app(int,int,bit0,K)),
3.01/3.23	                     L) =
3.01/3.23	      app_encode_app(int,int,bit0,
3.01/3.23	                     app_encode_app(int,int,
3.01/3.23	                                    app_encode_app(int,
3.01/3.23	                                                   app_encode_fun(int,int),
3.01/3.23	                                                   times_times_int,K),
3.01/3.23	                                    L))))).
3.01/3.23	tff('18', plain,
3.01/3.23	    ![X111 : int, X112 : int]:
3.01/3.23	      app_encode_app(int, int, 
3.01/3.23	        app_encode_app(int, app_encode_fun(int, int), times_times_int, 
3.01/3.23	          app_encode_app(int, int, bit0, X111)), X112)
3.01/3.23	       = app_encode_app(int, int, bit0, 
3.01/3.23	           app_encode_app(int, int, 
3.01/3.23	             app_encode_app(int, app_encode_fun(int, int), times_times_int, 
3.01/3.23	               X111), X112)),
3.01/3.23	    inference('cnf', [status(esa)], [zf_stmt_95])).
3.01/3.23	tff(zf_stmt_98, axiom,
3.01/3.23	  (![Z:int]:
3.01/3.23	     (app_encode_app(int,int,
3.01/3.23	                     app_encode_app(int,app_encode_fun(int,int),
3.01/3.23	                                    times_times_int,one_one_int),
3.01/3.23	                     Z) =
3.01/3.23	      Z))).
3.01/3.23	tff('19', plain,
3.01/3.23	    ![X117 : int]:
3.01/3.23	      app_encode_app(int, int, 
3.01/3.23	        app_encode_app(int, app_encode_fun(int, int), times_times_int, 
3.01/3.23	          one_one_int), X117)
3.01/3.23	       = X117,
3.01/3.23	    inference('cnf', [status(esa)], [zf_stmt_98])).
3.01/3.23	tff('20', plain,
3.01/3.23	    ![X117 : int]:
3.01/3.23	      app_encode_app(int, int, 
3.01/3.23	        app_encode_app(int, app_encode_fun(int, int), times_times_int, 
3.01/3.23	          app_encode_app(int, int, bit1, pls)), X117)
3.01/3.23	       = X117,
3.01/3.23	    inference('demod', [status(thm)], ['19', '17'])).
3.01/3.23	tff('21', plain,
3.01/3.23	    app_encode_app(int, int, 
3.01/3.23	      app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
3.01/3.23	        app_encode_app(int, int, bit1, pls)), 
3.01/3.23	      app_encode_app(nat, int, 
3.01/3.23	        app_encode_app(int, app_encode_fun(nat, int), power_power_int, s), 
3.01/3.23	        app_encode_app(int, nat, number_number_of_nat, 
3.01/3.23	          app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls)))))
3.01/3.23	     = app_encode_app(int, int, 
3.01/3.23	         app_encode_app(int, app_encode_fun(int, int), times_times_int, 
3.01/3.23	           app_encode_app(int, int, 
3.01/3.23	             app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
3.01/3.23	               app_encode_app(int, int, bit1, pls)), 
3.01/3.23	             app_encode_app(int, int, bit0, 
3.01/3.23	               app_encode_app(int, int, bit0, m)))), t),
3.01/3.23	    inference('demod', [status(thm)], ['4', '17', '17', '18', '18', '20'])).
3.01/3.23	tff(zf_stmt_41, axiom,
3.01/3.23	  (app_encode_app(nat,int,
3.01/3.23	                  app_encode_app(int,app_encode_fun(nat,int),power_power_int,
3.01/3.23	                                 one_one_int),
3.01/3.23	                  app_encode_app(int,nat,number_number_of_nat,
3.01/3.23	                                 app_encode_app(int,int,bit0,
3.01/3.23	                                                app_encode_app(int,int,bit1,
3.01/3.23	                                                               pls)))) =
3.01/3.23	   one_one_int)).
3.01/3.23	tff('22', plain,
3.01/3.23	    app_encode_app(nat, int, 
3.01/3.23	      app_encode_app(int, app_encode_fun(nat, int), power_power_int, 
3.01/3.23	        one_one_int), 
3.01/3.23	      app_encode_app(int, nat, number_number_of_nat, 
3.01/3.23	        app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls))))
3.01/3.23	     = one_one_int,
3.01/3.23	    inference('cnf', [status(esa)], [zf_stmt_41])).
3.01/3.23	tff(zf_stmt_35, axiom,
3.01/3.23	  (![X:int,Y:int]:
3.01/3.23	     (~
3.01/3.23	       app_encode_app(int,$o,
3.01/3.23	                      app_encode_app(int,app_encode_fun(int,$o),ord_less_int,
3.01/3.23	                                     app_encode_app(int,int,
3.01/3.23	                                                    app_encode_app(int,
3.01/3.23	                                                                   app_encode_fun(
3.01/3.23	                                                                   int,int),
3.01/3.23	                                                                   plus_plus_int,
3.01/3.23	                                                                   app_encode_app(
3.01/3.23	                                                                   nat,int,
3.01/3.23	                                                                   app_encode_app(
3.01/3.23	                                                                   int,
3.01/3.23	                                                                   app_encode_fun(
3.01/3.23	                                                                   nat,int),
3.01/3.23	                                                                   power_power_int,
3.01/3.23	                                                                   X),
3.01/3.23	                                                                   app_encode_app(
3.01/3.23	                                                                   int,nat,
3.01/3.23	                                                                   number_number_of_nat,
3.01/3.23	                                                                   app_encode_app(
3.01/3.23	                                                                   int,int,
3.01/3.23	                                                                   bit0,
3.01/3.23	                                                                   app_encode_app(
3.01/3.23	                                                                   int,int,
3.01/3.23	                                                                   bit1,pls))))),
3.01/3.23	                                                    app_encode_app(nat,int,
3.01/3.23	                                                                   app_encode_app(
3.01/3.23	                                                                   int,
3.01/3.23	                                                                   app_encode_fun(
3.01/3.23	                                                                   nat,int),
3.01/3.23	                                                                   power_power_int,
3.01/3.23	                                                                   Y),
3.01/3.23	                                                                   app_encode_app(
3.01/3.23	                                                                   int,nat,
3.01/3.23	                                                                   number_number_of_nat,
3.01/3.23	                                                                   app_encode_app(
3.01/3.23	                                                                   int,int,
3.01/3.23	                                                                   bit0,
3.01/3.23	                                                                   app_encode_app(
3.01/3.23	                                                                   int,int,
3.01/3.23	                                                                   bit1,pls)))))),
3.01/3.23	                      zero_zero_int)))).
3.01/3.23	tff('23', plain,
3.01/3.23	    ![X0 : int, X1 : int]:
3.01/3.23	      ~ app_encode_app(int, $o, 
3.01/3.23	          app_encode_app(int, app_encode_fun(int, $o), ord_less_int, 
3.01/3.23	            app_encode_app(int, int, 
3.01/3.23	              app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
3.01/3.23	                app_encode_app(nat, int, 
3.01/3.23	                  app_encode_app(int, app_encode_fun(nat, int), 
3.01/3.23	                    power_power_int, X0), 
3.01/3.23	                  app_encode_app(int, nat, number_number_of_nat, 
3.01/3.23	                    app_encode_app(int, int, bit0, 
3.01/3.23	                      app_encode_app(int, int, bit1, pls))))), 
3.01/3.23	              app_encode_app(nat, int, 
3.01/3.23	                app_encode_app(int, app_encode_fun(nat, int), 
3.01/3.23	                  power_power_int, X1), 
3.01/3.23	                app_encode_app(int, nat, number_number_of_nat, 
3.01/3.23	                  app_encode_app(int, int, bit0, 
3.01/3.23	                    app_encode_app(int, int, bit1, pls)))))), zero_zero_int),
3.01/3.23	    inference('cnf', [status(esa)], [zf_stmt_35])).
3.01/3.23	tff(zf_stmt_133, axiom,
3.01/3.23	  (zero_zero_int = app_encode_app(int,int,number_number_of_int,pls))).
3.01/3.23	tff('24', plain,
3.01/3.23	    zero_zero_int = app_encode_app(int, int, number_number_of_int, pls),
3.01/3.23	    inference('cnf', [status(esa)], [zf_stmt_133])).
3.01/3.23	tff('25', plain, zero_zero_int = pls,
3.01/3.23	    inference('demod', [status(thm)], ['24', '1'])).
3.01/3.23	tff('26', plain,
3.01/3.23	    ![X0 : int, X1 : int]:
3.01/3.23	      ~ app_encode_app(int, $o, 
3.01/3.23	          app_encode_app(int, app_encode_fun(int, $o), ord_less_int, 
3.01/3.23	            app_encode_app(int, int, 
3.01/3.23	              app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
3.01/3.23	                app_encode_app(nat, int, 
3.01/3.23	                  app_encode_app(int, app_encode_fun(nat, int), 
3.01/3.23	                    power_power_int, X0), 
3.01/3.23	                  app_encode_app(int, nat, number_number_of_nat, 
3.01/3.23	                    app_encode_app(int, int, bit0, 
3.01/3.23	                      app_encode_app(int, int, bit1, pls))))), 
3.01/3.23	              app_encode_app(nat, int, 
3.01/3.23	                app_encode_app(int, app_encode_fun(nat, int), 
3.01/3.23	                  power_power_int, X1), 
3.01/3.23	                app_encode_app(int, nat, number_number_of_nat, 
3.01/3.23	                  app_encode_app(int, int, bit0, 
3.01/3.23	                    app_encode_app(int, int, bit1, pls)))))), pls),
3.01/3.23	    inference('demod', [status(thm)], ['23', '25'])).
3.01/3.23	tff('27', plain,
3.01/3.23	    ![X0 : int]:
3.01/3.23	      ~ app_encode_app(int, $o, 
3.01/3.23	          app_encode_app(int, app_encode_fun(int, $o), ord_less_int, 
3.01/3.23	            app_encode_app(int, int, 
3.01/3.23	              app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
3.01/3.23	                one_one_int), 
3.01/3.23	              app_encode_app(nat, int, 
3.01/3.23	                app_encode_app(int, app_encode_fun(nat, int), 
3.01/3.23	                  power_power_int, X0), 
3.01/3.23	                app_encode_app(int, nat, number_number_of_nat, 
3.01/3.23	                  app_encode_app(int, int, bit0, 
3.01/3.23	                    app_encode_app(int, int, bit1, pls)))))), pls),
3.01/3.23	    inference('sup-', [status(thm)], ['22', '26'])).
3.01/3.23	tff(zf_stmt_45, axiom,
3.01/3.23	  (![W_7:int]:
3.01/3.23	     (app_encode_app(int,int,
3.01/3.23	                     app_encode_app(int,app_encode_fun(int,int),
3.01/3.23	                                    plus_plus_int,one_one_int),
3.01/3.23	                     app_encode_app(int,int,number_number_of_int,W_7)) =
3.01/3.23	      app_encode_app(int,int,number_number_of_int,
3.01/3.23	                     app_encode_app(int,int,
3.01/3.23	                                    app_encode_app(int,
3.01/3.23	                                                   app_encode_fun(int,int),
3.01/3.23	                                                   plus_plus_int,
3.01/3.23	                                                   app_encode_app(int,int,
3.01/3.23	                                                                  bit1,pls)),
3.01/3.23	                                    W_7))))).
3.01/3.23	tff('28', plain,
3.01/3.23	    ![X13 : int]:
3.01/3.23	      app_encode_app(int, int, 
3.01/3.23	        app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
3.01/3.23	          one_one_int), app_encode_app(int, int, number_number_of_int, X13))
3.01/3.23	       = app_encode_app(int, int, number_number_of_int, 
3.01/3.23	           app_encode_app(int, int, 
3.01/3.23	             app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
3.01/3.23	               app_encode_app(int, int, bit1, pls)), X13)),
3.01/3.23	    inference('cnf', [status(esa)], [zf_stmt_45])).
3.01/3.23	tff('29', plain,
3.01/3.23	    ![X13 : int]:
3.01/3.23	      app_encode_app(int, int, 
3.01/3.23	        app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
3.01/3.23	          one_one_int), X13)
3.01/3.23	       = app_encode_app(int, int, 
3.01/3.23	           app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
3.01/3.23	             app_encode_app(int, int, bit1, pls)), X13),
3.01/3.23	    inference('demod', [status(thm)], ['28', '1', '1'])).
3.01/3.23	tff('30', plain,
3.01/3.23	    ![X0 : int]:
3.01/3.23	      ~ app_encode_app(int, $o, 
3.01/3.23	          app_encode_app(int, app_encode_fun(int, $o), ord_less_int, 
3.01/3.23	            app_encode_app(int, int, 
3.01/3.23	              app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
3.01/3.23	                app_encode_app(int, int, bit1, pls)), 
3.01/3.23	              app_encode_app(nat, int, 
3.01/3.23	                app_encode_app(int, app_encode_fun(nat, int), 
3.01/3.23	                  power_power_int, X0), 
3.01/3.23	                app_encode_app(int, nat, number_number_of_nat, 
3.01/3.23	                  app_encode_app(int, int, bit0, 
3.01/3.23	                    app_encode_app(int, int, bit1, pls)))))), pls),
3.01/3.23	    inference('demod', [status(thm)], ['27', '29'])).
3.01/3.23	tff('31', plain,
3.01/3.23	    ~ app_encode_app(int, $o, 
3.01/3.23	        app_encode_app(int, app_encode_fun(int, $o), ord_less_int, 
3.01/3.23	          app_encode_app(int, int, 
3.01/3.23	            app_encode_app(int, app_encode_fun(int, int), times_times_int, 
3.01/3.23	              app_encode_app(int, int, 
3.01/3.23	                app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
3.01/3.23	                  app_encode_app(int, int, bit1, pls)), 
3.01/3.23	                app_encode_app(int, int, bit0, 
3.01/3.23	                  app_encode_app(int, int, bit0, m)))), t)), pls),
3.01/3.23	    inference('sup-', [status(thm)], ['21', '30'])).
3.01/3.23	tff(zf_stmt_30, axiom,
3.01/3.23	  (app_encode_app(int,$o,
3.01/3.23	                  app_encode_app(int,app_encode_fun(int,$o),ord_less_int,
3.01/3.23	                                 app_encode_app(int,int,
3.01/3.23	                                                app_encode_app(int,
3.01/3.23	                                                               app_encode_fun(
3.01/3.23	                                                               int,int),
3.01/3.23	                                                               times_times_int,
3.01/3.23	                                                               app_encode_app(
3.01/3.23	                                                               int,int,
3.01/3.23	                                                               app_encode_app(
3.01/3.23	                                                               int,
3.01/3.23	                                                               app_encode_fun(
3.01/3.23	                                                               int,int),
3.01/3.23	                                                               plus_plus_int,
3.01/3.23	                                                               app_encode_app(
3.01/3.23	                                                               int,int,
3.01/3.23	                                                               app_encode_app(
3.01/3.23	                                                               int,
3.01/3.23	                                                               app_encode_fun(
3.01/3.23	                                                               int,int),
3.01/3.23	                                                               times_times_int,
3.01/3.23	                                                               app_encode_app(
3.01/3.23	                                                               int,int,
3.01/3.23	                                                               number_number_of_int,
3.01/3.23	                                                               app_encode_app(
3.01/3.23	                                                               int,int,bit0,
3.01/3.23	                                                               app_encode_app(
3.01/3.23	                                                               int,int,bit0,
3.01/3.23	                                                               app_encode_app(
3.01/3.23	                                                               int,int,bit1,
3.01/3.23	                                                               pls))))),m)),
3.01/3.23	                                                               one_one_int)),
3.01/3.23	                                                t)),
3.01/3.23	                  app_encode_app(int,int,
3.01/3.23	                                 app_encode_app(int,app_encode_fun(int,int),
3.01/3.23	                                                times_times_int,
3.01/3.23	                                                app_encode_app(int,int,
3.01/3.23	                                                               app_encode_app(
3.01/3.23	                                                               int,
3.01/3.23	                                                               app_encode_fun(
3.01/3.23	                                                               int,int),
3.01/3.23	                                                               plus_plus_int,
3.01/3.23	                                                               app_encode_app(
3.01/3.23	                                                               int,int,
3.01/3.23	                                                               app_encode_app(
3.01/3.23	                                                               int,
3.01/3.23	                                                               app_encode_fun(
3.01/3.23	                                                               int,int),
3.01/3.23	                                                               times_times_int,
3.01/3.23	                                                               app_encode_app(
3.01/3.23	                                                               int,int,
3.01/3.23	                                                               number_number_of_int,
3.01/3.23	                                                               app_encode_app(
3.01/3.23	                                                               int,int,bit0,
3.01/3.23	                                                               app_encode_app(
3.01/3.23	                                                               int,int,bit0,
3.01/3.23	                                                               app_encode_app(
3.01/3.23	                                                               int,int,bit1,
3.01/3.23	                                                               pls))))),m)),
3.01/3.23	                                                               one_one_int)),
3.01/3.23	                                 zero_zero_int)))).
3.01/3.23	tff('32', plain,
3.01/3.23	    app_encode_app(int, $o, 
3.01/3.23	      app_encode_app(int, app_encode_fun(int, $o), ord_less_int, 
3.01/3.23	        app_encode_app(int, int, 
3.01/3.23	          app_encode_app(int, app_encode_fun(int, int), times_times_int, 
3.01/3.23	            app_encode_app(int, int, 
3.01/3.23	              app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
3.01/3.23	                app_encode_app(int, int, 
3.01/3.23	                  app_encode_app(int, app_encode_fun(int, int), 
3.01/3.23	                    times_times_int, 
3.01/3.23	                    app_encode_app(int, int, number_number_of_int, 
3.01/3.23	                      app_encode_app(int, int, bit0, 
3.01/3.23	                        app_encode_app(int, int, bit0, 
3.01/3.23	                          app_encode_app(int, int, bit1, pls))))), m)), 
3.01/3.23	              one_one_int)), t)), 
3.01/3.23	      app_encode_app(int, int, 
3.01/3.23	        app_encode_app(int, app_encode_fun(int, int), times_times_int, 
3.01/3.23	          app_encode_app(int, int, 
3.01/3.23	            app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
3.01/3.23	              app_encode_app(int, int, 
3.01/3.23	                app_encode_app(int, app_encode_fun(int, int), 
3.01/3.23	                  times_times_int, 
3.01/3.23	                  app_encode_app(int, int, number_number_of_int, 
3.01/3.23	                    app_encode_app(int, int, bit0, 
3.01/3.23	                      app_encode_app(int, int, bit0, 
3.01/3.23	                        app_encode_app(int, int, bit1, pls))))), m)), 
3.01/3.23	            one_one_int)), zero_zero_int)),
3.01/3.23	    inference('cnf', [status(esa)], [zf_stmt_30])).
3.01/3.23	tff(zf_stmt_53, axiom,
3.01/3.23	  (![Z:int,W:int]:
3.01/3.23	     (app_encode_app(int,int,
3.01/3.23	                     app_encode_app(int,app_encode_fun(int,int),
3.01/3.23	                                    times_times_int,Z),
3.01/3.23	                     W) =
3.01/3.23	      app_encode_app(int,int,
3.01/3.23	                     app_encode_app(int,app_encode_fun(int,int),
3.01/3.23	                                    times_times_int,W),
3.01/3.23	                     Z)))).
3.01/3.23	tff('33', plain,
3.01/3.23	    ![X17 : int, X18 : int]:
3.01/3.23	      app_encode_app(int, int, 
3.01/3.23	        app_encode_app(int, app_encode_fun(int, int), times_times_int, X18), 
3.01/3.23	        X17)
3.01/3.23	       = app_encode_app(int, int, 
3.01/3.23	           app_encode_app(int, app_encode_fun(int, int), times_times_int, 
3.01/3.23	             X17), X18),
3.01/3.23	    inference('cnf', [status(esa)], [zf_stmt_53])).
3.01/3.23	tff(zf_stmt_94, axiom,
3.01/3.23	  (![W:int]:
3.01/3.23	     (app_encode_app(int,int,
3.01/3.23	                     app_encode_app(int,app_encode_fun(int,int),
3.01/3.23	                                    times_times_int,pls),
3.01/3.23	                     W) =
3.01/3.23	      pls))).
3.01/3.23	tff('34', plain,
3.01/3.23	    ![X110 : int]:
3.01/3.23	      app_encode_app(int, int, 
3.01/3.23	        app_encode_app(int, app_encode_fun(int, int), times_times_int, pls), 
3.01/3.23	        X110)
3.01/3.23	       = pls,
3.01/3.23	    inference('cnf', [status(esa)], [zf_stmt_94])).
3.01/3.23	tff('35', plain,
3.01/3.23	    ![X0 : int]:
3.01/3.23	      app_encode_app(int, int, 
3.01/3.23	        app_encode_app(int, app_encode_fun(int, int), times_times_int, X0), 
3.01/3.23	        pls)
3.01/3.23	       = pls,
3.01/3.23	    inference('sup+', [status(thm)], ['33', '34'])).
3.01/3.23	tff('36', plain,
3.01/3.23	    app_encode_app(int, $o, 
3.01/3.23	      app_encode_app(int, app_encode_fun(int, $o), ord_less_int, 
3.01/3.23	        app_encode_app(int, int, 
3.01/3.23	          app_encode_app(int, app_encode_fun(int, int), times_times_int, 
3.01/3.23	            app_encode_app(int, int, 
3.01/3.23	              app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
3.01/3.23	                app_encode_app(int, int, 
3.01/3.23	                  app_encode_app(int, app_encode_fun(int, int), 
3.01/3.23	                    times_times_int, 
3.01/3.23	                    app_encode_app(int, int, bit0, 
3.01/3.23	                      app_encode_app(int, int, bit0, 
3.01/3.23	                        app_encode_app(int, int, bit1, pls)))), m)), 
3.01/3.23	              one_one_int)), t)), pls),
3.01/3.23	    inference('demod', [status(thm)], ['32', '1', '1', '25', '35'])).
3.01/3.23	tff('37', plain,
3.01/3.23	    app_encode_app(int, $o, 
3.01/3.23	      app_encode_app(int, app_encode_fun(int, $o), ord_less_int, 
3.01/3.23	        app_encode_app(int, int, 
3.01/3.23	          app_encode_app(int, app_encode_fun(int, int), times_times_int, 
3.01/3.23	            app_encode_app(int, int, 
3.01/3.23	              app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
3.01/3.23	                one_one_int), 
3.01/3.23	              app_encode_app(int, int, 
3.01/3.23	                app_encode_app(int, app_encode_fun(int, int), 
3.01/3.23	                  times_times_int, 
3.01/3.23	                  app_encode_app(int, int, bit0, 
3.01/3.23	                    app_encode_app(int, int, bit0, 
3.01/3.23	                      app_encode_app(int, int, bit1, pls)))), m))), t)), pls),
3.01/3.23	    inference('demod', [status(thm)], ['36', '3'])).
3.01/3.23	tff('38', plain,
3.01/3.23	    app_encode_app(int, $o, 
3.01/3.23	      app_encode_app(int, app_encode_fun(int, $o), ord_less_int, 
3.01/3.23	        app_encode_app(int, int, 
3.01/3.23	          app_encode_app(int, app_encode_fun(int, int), times_times_int, 
3.01/3.23	            app_encode_app(int, int, 
3.01/3.23	              app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
3.01/3.23	                app_encode_app(int, int, bit1, pls)), 
3.01/3.23	              app_encode_app(int, int, bit0, 
3.01/3.23	                app_encode_app(int, int, bit0, m)))), t)), pls),
3.01/3.23	    inference('demod', [status(thm)], ['37', '17', '18', '18', '20'])).
3.01/3.23	tff('39', plain, ~ $true, inference('demod', [status(thm)], ['31', '38'])).
3.01/3.23	tff('40', plain, $false, inference('simplify', [status(thm)], ['39'])).
3.01/3.23	
3.01/3.23	% SZS output end Refutation
3.01/3.23	EOF
