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   : n145.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 07:53:08 CST 2018
1.98/2.22	% done 929 iterations in 2.021s
1.98/2.22	% SZS status Theorem for 'stdin'
1.98/2.22	% SZS output start Refutation
1.98/2.22	tff(zf_stmt_33, axiom,
1.98/2.22	  (app_encode_app(int,int,
1.98/2.22	                  app_encode_app(int,app_encode_fun(int,int),plus_plus(int),
1.98/2.22	                                 app_encode_app(nat,int,
1.98/2.22	                                                app_encode_app(int,
1.98/2.22	                                                               app_encode_fun(
1.98/2.22	                                                               nat,int),
1.98/2.22	                                                               power_power(
1.98/2.22	                                                               int),s),
1.98/2.22	                                                app_encode_app(int,nat,
1.98/2.22	                                                               number_number_of(
1.98/2.22	                                                               nat),
1.98/2.22	                                                               app_encode_app(
1.98/2.22	                                                               int,int,bit0,
1.98/2.22	                                                               app_encode_app(
1.98/2.22	                                                               int,int,bit1,
1.98/2.22	                                                               pls))))),
1.98/2.22	                  one_one(int)) =
1.98/2.22	   app_encode_app(int,int,
1.98/2.22	                  app_encode_app(int,app_encode_fun(int,int),
1.98/2.22	                                 times_times(int),
1.98/2.22	                                 app_encode_app(int,int,
1.98/2.22	                                                app_encode_app(int,
1.98/2.22	                                                               app_encode_fun(
1.98/2.22	                                                               int,int),
1.98/2.22	                                                               plus_plus(int),
1.98/2.22	                                                               app_encode_app(
1.98/2.22	                                                               int,int,
1.98/2.22	                                                               app_encode_app(
1.98/2.22	                                                               int,
1.98/2.22	                                                               app_encode_fun(
1.98/2.22	                                                               int,int),
1.98/2.22	                                                               times_times(
1.98/2.22	                                                               int),
1.98/2.22	                                                               app_encode_app(
1.98/2.22	                                                               int,int,
1.98/2.22	                                                               number_number_of(
1.98/2.22	                                                               int),
1.98/2.22	                                                               app_encode_app(
1.98/2.22	                                                               int,int,bit0,
1.98/2.22	                                                               app_encode_app(
1.98/2.22	                                                               int,int,bit0,
1.98/2.22	                                                               app_encode_app(
1.98/2.22	                                                               int,int,bit1,
1.98/2.22	                                                               pls))))),m)),
1.98/2.22	                                                one_one(int))),
1.98/2.22	                  t))).
1.98/2.22	tff('0', plain,
1.98/2.22	    app_encode_app(int, int, 
1.98/2.22	      app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.98/2.22	        app_encode_app(nat, int, 
1.98/2.22	          app_encode_app(int, app_encode_fun(nat, int), power_power(int), s), 
1.98/2.22	          app_encode_app(int, nat, number_number_of(nat), 
1.98/2.22	            app_encode_app(int, int, bit0, 
1.98/2.22	              app_encode_app(int, int, bit1, pls))))), one_one(int))
1.98/2.22	     = app_encode_app(int, int, 
1.98/2.22	         app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.98/2.22	           app_encode_app(int, int, 
1.98/2.22	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.98/2.22	               app_encode_app(int, int, 
1.98/2.22	                 app_encode_app(int, app_encode_fun(int, int), 
1.98/2.22	                   times_times(int), 
1.98/2.22	                   app_encode_app(int, int, number_number_of(int), 
1.98/2.22	                     app_encode_app(int, int, bit0, 
1.98/2.22	                       app_encode_app(int, int, bit0, 
1.98/2.22	                         app_encode_app(int, int, bit1, pls))))), m)), 
1.98/2.22	             one_one(int))), t),
1.98/2.22	    inference('cnf', [status(esa)], [zf_stmt_33])).
1.98/2.22	tff(zf_stmt_111, axiom,
1.98/2.22	  (![K:int]: (app_encode_app(int,int,number_number_of(int),K) = K))).
1.98/2.22	tff('1', plain,
1.98/2.22	    ![X165 : int]:
1.98/2.22	      app_encode_app(int, int, number_number_of(int), X165) = X165,
1.98/2.22	    inference('cnf', [status(esa)], [zf_stmt_111])).
1.98/2.22	tff('2', plain,
1.98/2.22	    app_encode_app(int, int, 
1.98/2.22	      app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.98/2.22	        app_encode_app(nat, int, 
1.98/2.22	          app_encode_app(int, app_encode_fun(nat, int), power_power(int), s), 
1.98/2.22	          app_encode_app(int, nat, number_number_of(nat), 
1.98/2.22	            app_encode_app(int, int, bit0, 
1.98/2.22	              app_encode_app(int, int, bit1, pls))))), one_one(int))
1.98/2.22	     = app_encode_app(int, int, 
1.98/2.22	         app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.98/2.22	           app_encode_app(int, int, 
1.98/2.22	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.98/2.22	               app_encode_app(int, int, 
1.98/2.22	                 app_encode_app(int, app_encode_fun(int, int), 
1.98/2.22	                   times_times(int), 
1.98/2.22	                   app_encode_app(int, int, bit0, 
1.98/2.22	                     app_encode_app(int, int, bit0, 
1.98/2.22	                       app_encode_app(int, int, bit1, pls)))), m)), 
1.98/2.22	             one_one(int))), t),
1.98/2.22	    inference('demod', [status(thm)], ['0', '1'])).
1.98/2.22	tff(zf_stmt_133, axiom, (monoid_mult(int))).
1.98/2.22	tff('3', plain, monoid_mult(int),
1.98/2.22	    inference('cnf', [status(esa)], [zf_stmt_133])).
1.98/2.22	tff(zf_stmt_40, axiom,
1.98/2.22	  (![B1:$tType]:
1.98/2.22	     ((monoid_mult(B1) & number(B1)) =>
1.98/2.22	      (![W:int]:
1.98/2.22	         (app_encode_app(nat,B1,
1.98/2.22	                         app_encode_app(B1,app_encode_fun(nat,B1),
1.98/2.22	                                        power_power(B1),
1.98/2.22	                                        app_encode_app(int,B1,
1.98/2.22	                                                       number_number_of(B1),W)),
1.98/2.22	                         app_encode_app(int,nat,number_number_of(nat),
1.98/2.22	                                        app_encode_app(int,int,bit0,
1.98/2.22	                                                       app_encode_app(
1.98/2.22	                                                       int,int,bit1,pls)))) =
1.98/2.22	          app_encode_app(B1,B1,
1.98/2.22	                         app_encode_app(B1,app_encode_fun(B1,B1),
1.98/2.22	                                        times_times(B1),
1.98/2.22	                                        app_encode_app(int,B1,
1.98/2.22	                                                       number_number_of(B1),W)),
1.98/2.22	                         app_encode_app(int,B1,number_number_of(B1),W))))))).
1.98/2.22	tff('4', plain,
1.98/2.22	    ![X0 : $tType, X1 : int]:
1.98/2.22	      (app_encode_app(nat, X0, 
1.98/2.22	         app_encode_app(X0, app_encode_fun(nat, X0), power_power(X0), 
1.98/2.22	           app_encode_app(int, X0, number_number_of(X0), X1)), 
1.98/2.22	         app_encode_app(int, nat, number_number_of(nat), 
1.98/2.22	           app_encode_app(int, int, bit0, 
1.98/2.22	             app_encode_app(int, int, bit1, pls))))
1.98/2.22	        = app_encode_app(X0, X0, 
1.98/2.22	            app_encode_app(X0, app_encode_fun(X0, X0), times_times(X0), 
1.98/2.22	              app_encode_app(int, X0, number_number_of(X0), X1)), 
1.98/2.22	            app_encode_app(int, X0, number_number_of(X0), X1))
1.98/2.22	       | ~ number(X0)
1.98/2.22	       | ~ monoid_mult(X0)),
1.98/2.22	    inference('cnf', [status(esa)], [zf_stmt_40])).
1.98/2.22	tff('5', plain,
1.98/2.22	    ![X0 : int]:
1.98/2.22	      (~ $true
1.98/2.22	       | ~ number(int)
1.98/2.22	       | app_encode_app(nat, int, 
1.98/2.22	           app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
1.98/2.22	             app_encode_app(int, int, number_number_of(int), X0)), 
1.98/2.22	           app_encode_app(int, nat, number_number_of(nat), 
1.98/2.22	             app_encode_app(int, int, bit0, 
1.98/2.22	               app_encode_app(int, int, bit1, pls))))
1.98/2.22	          = app_encode_app(int, int, 
1.98/2.22	              app_encode_app(int, app_encode_fun(int, int), 
1.98/2.22	                times_times(int), 
1.98/2.22	                app_encode_app(int, int, number_number_of(int), X0)), 
1.98/2.22	              app_encode_app(int, int, number_number_of(int), X0))),
1.98/2.22	    inference('sup-', [status(thm)], ['3', '4'])).
1.98/2.22	tff(zf_stmt_139, axiom, (number(int))).
1.98/2.22	tff('6', plain, number(int), inference('cnf', [status(esa)], [zf_stmt_139])).
1.98/2.22	tff('7', plain,
1.98/2.22	    ![X0 : int]:
1.98/2.22	      (~ $true
1.98/2.22	       | ~ $true
1.98/2.22	       | app_encode_app(nat, int, 
1.98/2.22	           app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
1.98/2.22	             X0), 
1.98/2.22	           app_encode_app(int, nat, number_number_of(nat), 
1.98/2.22	             app_encode_app(int, int, bit0, 
1.98/2.22	               app_encode_app(int, int, bit1, pls))))
1.98/2.22	          = app_encode_app(int, int, 
1.98/2.22	              app_encode_app(int, app_encode_fun(int, int), 
1.98/2.22	                times_times(int), X0), X0)),
1.98/2.22	    inference('demod', [status(thm)], ['5', '6', '1', '1', '1'])).
1.98/2.22	tff('8', plain,
1.98/2.22	    ![X0 : int]:
1.98/2.22	      app_encode_app(nat, int, 
1.98/2.22	        app_encode_app(int, app_encode_fun(nat, int), power_power(int), X0), 
1.98/2.22	        app_encode_app(int, nat, number_number_of(nat), 
1.98/2.22	          app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls))))
1.98/2.22	       = app_encode_app(int, int, 
1.98/2.22	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.98/2.22	             X0), X0),
1.98/2.22	    inference('simplify', [status(thm)], ['7'])).
1.98/2.22	tff(zf_stmt_116, axiom,
1.98/2.22	  (![K:int]:
1.98/2.22	     (app_encode_app(int,int,
1.98/2.22	                     app_encode_app(int,app_encode_fun(int,int),
1.98/2.22	                                    plus_plus(int),K),
1.98/2.22	                     pls) =
1.98/2.22	      K))).
1.98/2.22	tff('9', plain,
1.98/2.22	    ![X179 : int]:
1.98/2.22	      app_encode_app(int, int, 
1.98/2.22	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X179), 
1.98/2.22	        pls)
1.98/2.22	       = X179,
1.98/2.22	    inference('cnf', [status(esa)], [zf_stmt_116])).
1.98/2.22	tff(zf_stmt_127, axiom,
1.98/2.22	  (![K:int]:
1.98/2.22	     (app_encode_app(int,int,bit1,K) =
1.98/2.22	      app_encode_app(int,int,
1.98/2.22	                     app_encode_app(int,app_encode_fun(int,int),
1.98/2.22	                                    plus_plus(int),
1.98/2.22	                                    app_encode_app(int,int,
1.98/2.22	                                                   app_encode_app(int,
1.98/2.22	                                                                  app_encode_fun(
1.98/2.22	                                                                  int,int),
1.98/2.22	                                                                  plus_plus(
1.98/2.22	                                                                  int),
1.98/2.22	                                                                  one_one(
1.98/2.22	                                                                  int)),
1.98/2.22	                                                   K)),
1.98/2.22	                     K)))).
1.98/2.22	tff('10', plain,
1.98/2.22	    ![X202 : int]:
1.98/2.22	      app_encode_app(int, int, bit1, X202)
1.98/2.22	       = app_encode_app(int, int, 
1.98/2.22	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.98/2.22	             app_encode_app(int, int, 
1.98/2.22	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.98/2.22	                 one_one(int)), X202)), X202),
1.98/2.22	    inference('cnf', [status(esa)], [zf_stmt_127])).
1.98/2.22	tff('11', plain,
1.98/2.22	    app_encode_app(int, int, bit1, pls)
1.98/2.22	     = app_encode_app(int, int, 
1.98/2.22	         app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.98/2.22	           one_one(int)), pls),
1.98/2.22	    inference('sup+', [status(thm)], ['9', '10'])).
1.98/2.22	tff('12', plain, app_encode_app(int, int, bit1, pls) = one_one(int),
1.98/2.22	    inference('demod', [status(thm)], ['11', '9'])).
1.98/2.22	tff(zf_stmt_66, axiom,
1.98/2.22	  (![L1:int,K:int]:
1.98/2.22	     (app_encode_app(int,int,
1.98/2.22	                     app_encode_app(int,app_encode_fun(int,int),
1.98/2.22	                                    times_times(int),
1.98/2.22	                                    app_encode_app(int,int,bit0,K)),
1.98/2.22	                     L1) =
1.98/2.22	      app_encode_app(int,int,bit0,
1.98/2.22	                     app_encode_app(int,int,
1.98/2.22	                                    app_encode_app(int,
1.98/2.22	                                                   app_encode_fun(int,int),
1.98/2.22	                                                   times_times(int),K),
1.98/2.22	                                    L1))))).
1.98/2.22	tff('13', plain,
1.98/2.22	    ![X47 : int, X48 : int]:
1.98/2.22	      app_encode_app(int, int, 
1.98/2.22	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.98/2.22	          app_encode_app(int, int, bit0, X47)), X48)
1.98/2.22	       = app_encode_app(int, int, bit0, 
1.98/2.22	           app_encode_app(int, int, 
1.98/2.22	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.98/2.22	               X47), X48)),
1.98/2.22	    inference('cnf', [status(esa)], [zf_stmt_66])).
1.98/2.22	tff(zf_stmt_65, axiom,
1.98/2.22	  (![W:int]:
1.98/2.22	     (app_encode_app(int,int,
1.98/2.22	                     app_encode_app(int,app_encode_fun(int,int),
1.98/2.22	                                    times_times(int),pls),
1.98/2.22	                     W) =
1.98/2.22	      pls))).
1.98/2.22	tff('14', plain,
1.98/2.22	    ![X46 : int]:
1.98/2.22	      app_encode_app(int, int, 
1.98/2.22	        app_encode_app(int, app_encode_fun(int, int), times_times(int), pls), 
1.98/2.22	        X46)
1.98/2.22	       = pls,
1.98/2.22	    inference('cnf', [status(esa)], [zf_stmt_65])).
1.98/2.22	tff(zf_stmt_45, axiom,
1.98/2.22	  (![L1:int,K:int]:
1.98/2.22	     (app_encode_app(int,int,
1.98/2.22	                     app_encode_app(int,app_encode_fun(int,int),
1.98/2.22	                                    times_times(int),
1.98/2.22	                                    app_encode_app(int,int,bit1,K)),
1.98/2.22	                     L1) =
1.98/2.22	      app_encode_app(int,int,
1.98/2.22	                     app_encode_app(int,app_encode_fun(int,int),
1.98/2.22	                                    plus_plus(int),
1.98/2.22	                                    app_encode_app(int,int,bit0,
1.98/2.22	                                                   app_encode_app(int,int,
1.98/2.22	                                                                  app_encode_app(
1.98/2.22	                                                                  int,
1.98/2.22	                                                                  app_encode_fun(
1.98/2.22	                                                                  int,int),
1.98/2.22	                                                                  times_times(
1.98/2.22	                                                                  int),K),L1))),
1.98/2.22	                     L1)))).
1.98/2.22	tff('15', plain,
1.98/2.22	    ![X8 : int, X9 : int]:
1.98/2.22	      app_encode_app(int, int, 
1.98/2.22	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.98/2.22	          app_encode_app(int, int, bit1, X8)), X9)
1.98/2.22	       = app_encode_app(int, int, 
1.98/2.22	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.98/2.22	             app_encode_app(int, int, bit0, 
1.98/2.22	               app_encode_app(int, int, 
1.98/2.22	                 app_encode_app(int, app_encode_fun(int, int), 
1.98/2.22	                   times_times(int), X8), X9))), X9),
1.98/2.22	    inference('cnf', [status(esa)], [zf_stmt_45])).
1.98/2.22	tff('16', plain,
1.98/2.22	    ![X0 : int]:
1.98/2.22	      app_encode_app(int, int, 
1.98/2.22	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.98/2.22	          app_encode_app(int, int, bit1, pls)), X0)
1.98/2.22	       = app_encode_app(int, int, 
1.98/2.22	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.98/2.22	             app_encode_app(int, int, bit0, pls)), X0),
1.98/2.22	    inference('sup+', [status(thm)], ['14', '15'])).
1.98/2.22	tff(zf_stmt_61, axiom, (app_encode_app(int,int,bit0,pls) = pls)).
1.98/2.22	tff('17', plain, app_encode_app(int, int, bit0, pls) = pls,
1.98/2.22	    inference('cnf', [status(esa)], [zf_stmt_61])).
1.98/2.22	tff(zf_stmt_117, axiom,
1.98/2.22	  (![K:int]:
1.98/2.22	     (app_encode_app(int,int,
1.98/2.22	                     app_encode_app(int,app_encode_fun(int,int),
1.98/2.22	                                    plus_plus(int),pls),
1.98/2.22	                     K) =
1.98/2.22	      K))).
1.98/2.22	tff('18', plain,
1.98/2.22	    ![X180 : int]:
1.98/2.22	      app_encode_app(int, int, 
1.98/2.22	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
1.98/2.22	        X180)
1.98/2.22	       = X180,
1.98/2.22	    inference('cnf', [status(esa)], [zf_stmt_117])).
1.98/2.22	tff('19', plain,
1.98/2.22	    ![X0 : int]:
1.98/2.22	      app_encode_app(int, int, 
1.98/2.22	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.98/2.22	          app_encode_app(int, int, bit1, pls)), X0)
1.98/2.22	       = X0,
1.98/2.22	    inference('demod', [status(thm)], ['16', '17', '18'])).
1.98/2.22	tff(zf_stmt_118, axiom,
1.98/2.22	  (![K:int]:
1.98/2.22	     (app_encode_app(int,int,bit0,K) =
1.98/2.22	      app_encode_app(int,int,
1.98/2.22	                     app_encode_app(int,app_encode_fun(int,int),
1.98/2.22	                                    plus_plus(int),K),
1.98/2.22	                     K)))).
1.98/2.22	tff('20', plain,
1.98/2.22	    ![X181 : int]:
1.98/2.22	      app_encode_app(int, int, bit0, X181)
1.98/2.22	       = app_encode_app(int, int, 
1.98/2.22	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.98/2.22	             X181), X181),
1.98/2.22	    inference('cnf', [status(esa)], [zf_stmt_118])).
1.98/2.22	tff(zf_stmt_136, axiom, (number_ring(int))).
1.98/2.22	tff('21', plain, number_ring(int),
1.98/2.22	    inference('cnf', [status(esa)], [zf_stmt_136])).
1.98/2.22	tff(zf_stmt_76, axiom,
1.98/2.22	  (![A:$tType]:
1.98/2.22	     (number_ring(A) =>
1.98/2.22	      (![Z3:A,W:int,V:int]:
1.98/2.22	         (app_encode_app(A,A,
1.98/2.22	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
1.98/2.22	                                        app_encode_app(int,A,
1.98/2.22	                                                       number_number_of(A),V)),
1.98/2.22	                         app_encode_app(A,A,
1.98/2.22	                                        app_encode_app(A,app_encode_fun(A,A),
1.98/2.22	                                                       plus_plus(A),
1.98/2.22	                                                       app_encode_app(
1.98/2.22	                                                       int,A,
1.98/2.22	                                                       number_number_of(A),W)),
1.98/2.22	                                        Z3)) =
1.98/2.22	          app_encode_app(A,A,
1.98/2.22	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
1.98/2.22	                                        app_encode_app(int,A,
1.98/2.22	                                                       number_number_of(A),
1.98/2.22	                                                       app_encode_app(
1.98/2.22	                                                       int,int,
1.98/2.22	                                                       app_encode_app(
1.98/2.22	                                                       int,
1.98/2.22	                                                       app_encode_fun(
1.98/2.22	                                                       int,int),
1.98/2.22	                                                       plus_plus(int),V),W))),
1.98/2.22	                         Z3)))))).
1.98/2.22	tff('22', plain,
1.98/2.22	    ![X80 : $tType, X81 : int, X82 : int, X83 : X80]:
1.98/2.22	      (app_encode_app(X80, X80, 
1.98/2.22	         app_encode_app(X80, app_encode_fun(X80, X80), plus_plus(X80), 
1.98/2.22	           app_encode_app(int, X80, number_number_of(X80), X81)), 
1.98/2.22	         app_encode_app(X80, X80, 
1.98/2.22	           app_encode_app(X80, app_encode_fun(X80, X80), plus_plus(X80), 
1.98/2.22	             app_encode_app(int, X80, number_number_of(X80), X82)), X83))
1.98/2.22	        = app_encode_app(X80, X80, 
1.98/2.22	            app_encode_app(X80, app_encode_fun(X80, X80), plus_plus(X80), 
1.98/2.22	              app_encode_app(int, X80, number_number_of(X80), 
1.98/2.22	                app_encode_app(int, int, 
1.98/2.22	                  app_encode_app(int, app_encode_fun(int, int), 
1.98/2.22	                    plus_plus(int), X81), X82))), X83)
1.98/2.22	       | ~ number_ring(X80)),
1.98/2.22	    inference('cnf', [status(esa)], [zf_stmt_76])).
1.98/2.22	tff('23', plain,
1.98/2.22	    ![X0 : int, X1 : int, X2 : int]:
1.98/2.22	      (~ $true
1.98/2.22	       | app_encode_app(int, int, 
1.98/2.22	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.98/2.22	             app_encode_app(int, int, number_number_of(int), X2)), 
1.98/2.22	           app_encode_app(int, int, 
1.98/2.22	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.98/2.22	               app_encode_app(int, int, number_number_of(int), X1)), X0))
1.98/2.22	          = app_encode_app(int, int, 
1.98/2.22	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.98/2.22	                app_encode_app(int, int, number_number_of(int), 
1.98/2.22	                  app_encode_app(int, int, 
1.98/2.22	                    app_encode_app(int, app_encode_fun(int, int), 
1.98/2.22	                      plus_plus(int), X2), X1))), X0)),
1.98/2.22	    inference('sup-', [status(thm)], ['21', '22'])).
1.98/2.22	tff('24', plain,
1.98/2.22	    ![X0 : int, X1 : int, X2 : int]:
1.98/2.22	      (~ $true
1.98/2.22	       | app_encode_app(int, int, 
1.98/2.22	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X2), 
1.98/2.22	           app_encode_app(int, int, 
1.98/2.22	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.98/2.22	               X1), X0))
1.98/2.22	          = app_encode_app(int, int, 
1.98/2.22	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.98/2.22	                app_encode_app(int, int, 
1.98/2.22	                  app_encode_app(int, app_encode_fun(int, int), 
1.98/2.22	                    plus_plus(int), X2), X1)), X0)),
1.98/2.22	    inference('demod', [status(thm)], ['23', '1', '1', '1'])).
1.98/2.22	tff('25', plain,
1.98/2.22	    ![X0 : int, X1 : int, X2 : int]:
1.98/2.22	      app_encode_app(int, int, 
1.98/2.22	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X2), 
1.98/2.22	        app_encode_app(int, int, 
1.98/2.22	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X1), 
1.98/2.22	          X0))
1.98/2.22	       = app_encode_app(int, int, 
1.98/2.22	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.98/2.22	             app_encode_app(int, int, 
1.98/2.22	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.98/2.22	                 X2), X1)), X0),
1.98/2.22	    inference('simplify', [status(thm)], ['24'])).
1.98/2.22	tff('26', plain,
1.98/2.22	    ![X0 : int, X1 : int]:
1.98/2.22	      app_encode_app(int, int, 
1.98/2.22	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
1.98/2.22	        app_encode_app(int, int, 
1.98/2.22	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
1.98/2.22	          X1))
1.98/2.22	       = app_encode_app(int, int, 
1.98/2.22	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.98/2.22	             app_encode_app(int, int, bit0, X0)), X1),
1.98/2.22	    inference('sup+', [status(thm)], ['20', '25'])).
1.98/2.22	tff(zf_stmt_51, axiom,
1.98/2.22	  (![L1:int,K:int]:
1.98/2.22	     (app_encode_app(int,int,
1.98/2.22	                     app_encode_app(int,app_encode_fun(int,int),
1.98/2.22	                                    plus_plus(int),
1.98/2.22	                                    app_encode_app(int,int,bit0,K)),
1.98/2.22	                     app_encode_app(int,int,bit1,L1)) =
1.98/2.22	      app_encode_app(int,int,bit1,
1.98/2.22	                     app_encode_app(int,int,
1.98/2.22	                                    app_encode_app(int,
1.98/2.22	                                                   app_encode_fun(int,int),
1.98/2.22	                                                   plus_plus(int),K),
1.98/2.22	                                    L1))))).
1.98/2.22	tff('27', plain,
1.98/2.22	    ![X18 : int, X19 : int]:
1.98/2.22	      app_encode_app(int, int, 
1.98/2.22	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.98/2.22	          app_encode_app(int, int, bit0, X18)), 
1.98/2.22	        app_encode_app(int, int, bit1, X19))
1.98/2.22	       = app_encode_app(int, int, bit1, 
1.98/2.22	           app_encode_app(int, int, 
1.98/2.22	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.98/2.22	               X18), X19)),
1.98/2.22	    inference('cnf', [status(esa)], [zf_stmt_51])).
1.98/2.22	tff('28', plain,
1.98/2.22	    ![X18 : int, X19 : int]:
1.98/2.22	      app_encode_app(int, int, 
1.98/2.22	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X18), 
1.98/2.22	        app_encode_app(int, int, 
1.98/2.22	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X18), 
1.98/2.22	          app_encode_app(int, int, bit1, X19)))
1.98/2.22	       = app_encode_app(int, int, bit1, 
1.98/2.22	           app_encode_app(int, int, 
1.98/2.22	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.98/2.22	               X18), X19)),
1.98/2.22	    inference('demod', [status(thm)], ['27', '26'])).
1.98/2.22	tff('29', plain,
1.98/2.22	    app_encode_app(int, int, 
1.98/2.22	      app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.98/2.22	        app_encode_app(int, int, 
1.98/2.22	          app_encode_app(int, app_encode_fun(int, int), times_times(int), s), 
1.98/2.22	          s)), app_encode_app(int, int, bit1, pls))
1.98/2.22	     = app_encode_app(int, int, 
1.98/2.22	         app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.98/2.22	           app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m))), 
1.98/2.22	         t),
1.98/2.22	    inference('demod', [status(thm)],
1.98/2.22	              ['2', '8', '12', '13', '13', '19', '12', '26', '26', '28', 
1.98/2.22	               '9', '26', '28', '20'])).
1.98/2.22	tff(zf_stmt_147, conjecture,
1.98/2.22	  (app_encode_app(int,int,
1.98/2.22	                  app_encode_app(int,app_encode_fun(int,int),
1.98/2.22	                                 times_times(int),
1.98/2.22	                                 app_encode_app(int,int,
1.98/2.22	                                                app_encode_app(int,
1.98/2.22	                                                               app_encode_fun(
1.98/2.22	                                                               int,int),
1.98/2.22	                                                               plus_plus(int),
1.98/2.22	                                                               app_encode_app(
1.98/2.22	                                                               int,int,
1.98/2.22	                                                               app_encode_app(
1.98/2.22	                                                               int,
1.98/2.22	                                                               app_encode_fun(
1.98/2.22	                                                               int,int),
1.98/2.22	                                                               times_times(
1.98/2.22	                                                               int),
1.98/2.22	                                                               app_encode_app(
1.98/2.22	                                                               int,int,
1.98/2.22	                                                               number_number_of(
1.98/2.22	                                                               int),
1.98/2.22	                                                               app_encode_app(
1.98/2.22	                                                               int,int,bit0,
1.98/2.22	                                                               app_encode_app(
1.98/2.22	                                                               int,int,bit0,
1.98/2.22	                                                               app_encode_app(
1.98/2.22	                                                               int,int,bit1,
1.98/2.22	                                                               pls))))),m)),
1.98/2.22	                                                one_one(int))),
1.98/2.22	                  t) =
1.98/2.22	   app_encode_app(int,int,
1.98/2.22	                  app_encode_app(int,app_encode_fun(int,int),plus_plus(int),
1.98/2.22	                                 app_encode_app(nat,int,
1.98/2.22	                                                app_encode_app(int,
1.98/2.22	                                                               app_encode_fun(
1.98/2.22	                                                               nat,int),
1.98/2.22	                                                               power_power(
1.98/2.22	                                                               int),s),
1.98/2.22	                                                app_encode_app(int,nat,
1.98/2.22	                                                               number_number_of(
1.98/2.22	                                                               nat),
1.98/2.22	                                                               app_encode_app(
1.98/2.22	                                                               int,int,bit0,
1.98/2.22	                                                               app_encode_app(
1.98/2.22	                                                               int,int,bit1,
1.98/2.22	                                                               pls))))),
1.98/2.22	                  one_one(int)))).
1.98/2.22	tff(zf_stmt_0, negated_conjecture,
1.98/2.22	  (app_encode_app(int,int,
1.98/2.22	                  app_encode_app(int,app_encode_fun(int,int),
1.98/2.22	                                 times_times(int),
1.98/2.22	                                 app_encode_app(int,int,
1.98/2.22	                                                app_encode_app(int,
1.98/2.22	                                                               app_encode_fun(
1.98/2.22	                                                               int,int),
1.98/2.22	                                                               plus_plus(int),
1.98/2.22	                                                               app_encode_app(
1.98/2.22	                                                               int,int,
1.98/2.22	                                                               app_encode_app(
1.98/2.22	                                                               int,
1.98/2.22	                                                               app_encode_fun(
1.98/2.22	                                                               int,int),
1.98/2.22	                                                               times_times(
1.98/2.22	                                                               int),
1.98/2.22	                                                               app_encode_app(
1.98/2.22	                                                               int,int,
1.98/2.22	                                                               number_number_of(
1.98/2.22	                                                               int),
1.98/2.22	                                                               app_encode_app(
1.98/2.22	                                                               int,int,bit0,
1.98/2.22	                                                               app_encode_app(
1.98/2.22	                                                               int,int,bit0,
1.98/2.22	                                                               app_encode_app(
1.98/2.22	                                                               int,int,bit1,
1.98/2.22	                                                               pls))))),m)),
1.98/2.22	                                                one_one(int))),
1.98/2.22	                  t) !=
1.98/2.22	   app_encode_app(int,int,
1.98/2.22	                  app_encode_app(int,app_encode_fun(int,int),plus_plus(int),
1.98/2.22	                                 app_encode_app(nat,int,
1.98/2.22	                                                app_encode_app(int,
1.98/2.22	                                                               app_encode_fun(
1.98/2.22	                                                               nat,int),
1.98/2.22	                                                               power_power(
1.98/2.22	                                                               int),s),
1.98/2.22	                                                app_encode_app(int,nat,
1.98/2.22	                                                               number_number_of(
1.98/2.22	                                                               nat),
1.98/2.22	                                                               app_encode_app(
1.98/2.22	                                                               int,int,bit0,
1.98/2.22	                                                               app_encode_app(
1.98/2.22	                                                               int,int,bit1,
1.98/2.22	                                                               pls))))),
1.98/2.22	                  one_one(int)))).
1.98/2.22	tff('30', plain,
1.98/2.22	    app_encode_app(int, int, 
1.98/2.22	      app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.98/2.22	        app_encode_app(int, int, 
1.98/2.22	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.98/2.22	            app_encode_app(int, int, 
1.98/2.22	              app_encode_app(int, app_encode_fun(int, int), 
1.98/2.22	                times_times(int), 
1.98/2.22	                app_encode_app(int, int, number_number_of(int), 
1.98/2.22	                  app_encode_app(int, int, bit0, 
1.98/2.22	                    app_encode_app(int, int, bit0, 
1.98/2.22	                      app_encode_app(int, int, bit1, pls))))), m)), 
1.98/2.22	          one_one(int))), t)
1.98/2.22	     != app_encode_app(int, int, 
1.98/2.22	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.98/2.22	            app_encode_app(nat, int, 
1.98/2.22	              app_encode_app(int, app_encode_fun(nat, int), 
1.98/2.22	                power_power(int), s), 
1.98/2.22	              app_encode_app(int, nat, number_number_of(nat), 
1.98/2.22	                app_encode_app(int, int, bit0, 
1.98/2.22	                  app_encode_app(int, int, bit1, pls))))), one_one(int)),
1.98/2.22	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.98/2.22	tff('31', plain,
1.98/2.22	    app_encode_app(int, int, 
1.98/2.22	      app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.98/2.22	        app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m))), 
1.98/2.22	      t)
1.98/2.22	     != app_encode_app(int, int, 
1.98/2.22	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.98/2.22	            app_encode_app(int, int, 
1.98/2.22	              app_encode_app(int, app_encode_fun(int, int), 
1.98/2.22	                times_times(int), s), s)), 
1.98/2.22	          app_encode_app(int, int, bit1, pls)),
1.98/2.22	    inference('demod', [status(thm)],
1.98/2.22	              ['30', '1', '13', '13', '19', '12', '26', '26', '28', '9', 
1.98/2.22	               '26', '28', '20', '8', '12'])).
1.98/2.22	tff('32', plain, $false,
1.98/2.22	    inference('simplify_reflect-', [status(thm)], ['29', '31'])).
1.98/2.22	
1.98/2.22	% SZS output end Refutation
1.98/2.22	EOF
