0.00/0.00	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : appext
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : rpo6
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.20	% Computer   : n110.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 07:53:09 CST 2018
2.04/2.26	% done 928 iterations in 2.058s
2.04/2.26	% SZS status Theorem for 'stdin'
2.04/2.26	% SZS output start Refutation
2.04/2.27	tff(zf_stmt_34, axiom,
2.04/2.27	  (app_encode_app(int,int,
2.04/2.27	                  app_encode_app(int,app_encode_fun(int,int),plus_plus(int),
2.04/2.27	                                 app_encode_app(nat,int,
2.04/2.27	                                                app_encode_app(int,
2.04/2.27	                                                               app_encode_fun(
2.04/2.27	                                                               nat,int),
2.04/2.27	                                                               power_power(
2.04/2.27	                                                               int),s),
2.04/2.27	                                                app_encode_app(int,nat,
2.04/2.27	                                                               number_number_of(
2.04/2.27	                                                               nat),
2.04/2.27	                                                               app_encode_app(
2.04/2.27	                                                               int,int,bit0,
2.04/2.27	                                                               app_encode_app(
2.04/2.27	                                                               int,int,bit1,
2.04/2.27	                                                               pls))))),
2.04/2.27	                  one_one(int)) =
2.04/2.27	   app_encode_app(int,int,
2.04/2.27	                  app_encode_app(int,app_encode_fun(int,int),
2.04/2.27	                                 times_times(int),
2.04/2.27	                                 app_encode_app(int,int,
2.04/2.27	                                                app_encode_app(int,
2.04/2.27	                                                               app_encode_fun(
2.04/2.27	                                                               int,int),
2.04/2.27	                                                               plus_plus(int),
2.04/2.27	                                                               app_encode_app(
2.04/2.27	                                                               int,int,
2.04/2.27	                                                               app_encode_app(
2.04/2.27	                                                               int,
2.04/2.27	                                                               app_encode_fun(
2.04/2.27	                                                               int,int),
2.04/2.27	                                                               times_times(
2.04/2.27	                                                               int),
2.04/2.27	                                                               app_encode_app(
2.04/2.27	                                                               int,int,
2.04/2.27	                                                               number_number_of(
2.04/2.27	                                                               int),
2.04/2.27	                                                               app_encode_app(
2.04/2.27	                                                               int,int,bit0,
2.04/2.27	                                                               app_encode_app(
2.04/2.27	                                                               int,int,bit0,
2.04/2.27	                                                               app_encode_app(
2.04/2.27	                                                               int,int,bit1,
2.04/2.27	                                                               pls))))),m)),
2.04/2.27	                                                one_one(int))),
2.04/2.27	                  t))).
2.04/2.27	tff('0', plain,
2.04/2.27	    app_encode_app(int, int, 
2.04/2.27	      app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.04/2.27	        app_encode_app(nat, int, 
2.04/2.27	          app_encode_app(int, app_encode_fun(nat, int), power_power(int), s), 
2.04/2.27	          app_encode_app(int, nat, number_number_of(nat), 
2.04/2.27	            app_encode_app(int, int, bit0, 
2.04/2.27	              app_encode_app(int, int, bit1, pls))))), one_one(int))
2.04/2.27	     = app_encode_app(int, int, 
2.04/2.27	         app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.04/2.27	           app_encode_app(int, int, 
2.04/2.27	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.04/2.27	               app_encode_app(int, int, 
2.04/2.27	                 app_encode_app(int, app_encode_fun(int, int), 
2.04/2.27	                   times_times(int), 
2.04/2.27	                   app_encode_app(int, int, number_number_of(int), 
2.04/2.27	                     app_encode_app(int, int, bit0, 
2.04/2.27	                       app_encode_app(int, int, bit0, 
2.04/2.27	                         app_encode_app(int, int, bit1, pls))))), m)), 
2.04/2.27	             one_one(int))), t),
2.04/2.27	    inference('cnf', [status(esa)], [zf_stmt_34])).
2.04/2.27	tff(zf_stmt_112, axiom,
2.04/2.27	  (![K:int]: (app_encode_app(int,int,number_number_of(int),K) = K))).
2.04/2.27	tff('1', plain,
2.04/2.27	    ![X169 : int]:
2.04/2.27	      app_encode_app(int, int, number_number_of(int), X169) = X169,
2.04/2.27	    inference('cnf', [status(esa)], [zf_stmt_112])).
2.04/2.27	tff('2', plain,
2.04/2.27	    app_encode_app(int, int, 
2.04/2.27	      app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.04/2.27	        app_encode_app(nat, int, 
2.04/2.27	          app_encode_app(int, app_encode_fun(nat, int), power_power(int), s), 
2.04/2.27	          app_encode_app(int, nat, number_number_of(nat), 
2.04/2.27	            app_encode_app(int, int, bit0, 
2.04/2.27	              app_encode_app(int, int, bit1, pls))))), one_one(int))
2.04/2.27	     = app_encode_app(int, int, 
2.04/2.27	         app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.04/2.27	           app_encode_app(int, int, 
2.04/2.27	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.04/2.27	               app_encode_app(int, int, 
2.04/2.27	                 app_encode_app(int, app_encode_fun(int, int), 
2.04/2.27	                   times_times(int), 
2.04/2.27	                   app_encode_app(int, int, bit0, 
2.04/2.27	                     app_encode_app(int, int, bit0, 
2.04/2.27	                       app_encode_app(int, int, bit1, pls)))), m)), 
2.04/2.27	             one_one(int))), t),
2.04/2.27	    inference('demod', [status(thm)], ['0', '1'])).
2.04/2.27	tff(zf_stmt_134, axiom, (monoid_mult(int))).
2.04/2.27	tff('3', plain, monoid_mult(int),
2.04/2.27	    inference('cnf', [status(esa)], [zf_stmt_134])).
2.04/2.27	tff(zf_stmt_41, axiom,
2.04/2.27	  (![B1:$tType]:
2.04/2.27	     ((monoid_mult(B1) & number(B1)) =>
2.04/2.27	      (![W:int]:
2.04/2.27	         (app_encode_app(nat,B1,
2.04/2.27	                         app_encode_app(B1,app_encode_fun(nat,B1),
2.04/2.27	                                        power_power(B1),
2.04/2.27	                                        app_encode_app(int,B1,
2.04/2.27	                                                       number_number_of(B1),W)),
2.04/2.27	                         app_encode_app(int,nat,number_number_of(nat),
2.04/2.27	                                        app_encode_app(int,int,bit0,
2.04/2.27	                                                       app_encode_app(
2.04/2.27	                                                       int,int,bit1,pls)))) =
2.04/2.27	          app_encode_app(B1,B1,
2.04/2.27	                         app_encode_app(B1,app_encode_fun(B1,B1),
2.04/2.27	                                        times_times(B1),
2.04/2.27	                                        app_encode_app(int,B1,
2.04/2.27	                                                       number_number_of(B1),W)),
2.04/2.27	                         app_encode_app(int,B1,number_number_of(B1),W))))))).
2.04/2.27	tff('4', plain,
2.04/2.27	    ![X4 : $tType, X5 : int]:
2.04/2.27	      (app_encode_app(nat, X4, 
2.04/2.27	         app_encode_app(X4, app_encode_fun(nat, X4), power_power(X4), 
2.04/2.27	           app_encode_app(int, X4, number_number_of(X4), X5)), 
2.04/2.27	         app_encode_app(int, nat, number_number_of(nat), 
2.04/2.27	           app_encode_app(int, int, bit0, 
2.04/2.27	             app_encode_app(int, int, bit1, pls))))
2.04/2.27	        = app_encode_app(X4, X4, 
2.04/2.27	            app_encode_app(X4, app_encode_fun(X4, X4), times_times(X4), 
2.04/2.27	              app_encode_app(int, X4, number_number_of(X4), X5)), 
2.04/2.27	            app_encode_app(int, X4, number_number_of(X4), X5))
2.04/2.27	       | ~ number(X4)
2.04/2.27	       | ~ monoid_mult(X4)),
2.04/2.27	    inference('cnf', [status(esa)], [zf_stmt_41])).
2.04/2.27	tff('5', plain,
2.04/2.27	    ![X0 : int]:
2.04/2.27	      (~ $true
2.04/2.27	       | ~ number(int)
2.04/2.27	       | app_encode_app(nat, int, 
2.04/2.27	           app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
2.04/2.27	             app_encode_app(int, int, number_number_of(int), X0)), 
2.04/2.27	           app_encode_app(int, nat, number_number_of(nat), 
2.04/2.27	             app_encode_app(int, int, bit0, 
2.04/2.27	               app_encode_app(int, int, bit1, pls))))
2.04/2.27	          = app_encode_app(int, int, 
2.04/2.27	              app_encode_app(int, app_encode_fun(int, int), 
2.04/2.27	                times_times(int), 
2.04/2.27	                app_encode_app(int, int, number_number_of(int), X0)), 
2.04/2.27	              app_encode_app(int, int, number_number_of(int), X0))),
2.04/2.27	    inference('sup-', [status(thm)], ['3', '4'])).
2.04/2.27	tff(zf_stmt_140, axiom, (number(int))).
2.04/2.27	tff('6', plain, number(int), inference('cnf', [status(esa)], [zf_stmt_140])).
2.04/2.27	tff('7', plain,
2.04/2.27	    ![X0 : int]:
2.04/2.27	      (~ $true
2.04/2.27	       | ~ $true
2.04/2.27	       | app_encode_app(nat, int, 
2.04/2.27	           app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
2.04/2.27	             X0), 
2.04/2.27	           app_encode_app(int, nat, number_number_of(nat), 
2.04/2.27	             app_encode_app(int, int, bit0, 
2.04/2.27	               app_encode_app(int, int, bit1, pls))))
2.04/2.27	          = app_encode_app(int, int, 
2.04/2.27	              app_encode_app(int, app_encode_fun(int, int), 
2.04/2.27	                times_times(int), X0), X0)),
2.04/2.27	    inference('demod', [status(thm)], ['5', '6', '1', '1', '1'])).
2.04/2.27	tff('8', plain,
2.04/2.27	    ![X0 : int]:
2.04/2.27	      app_encode_app(nat, int, 
2.04/2.27	        app_encode_app(int, app_encode_fun(nat, int), power_power(int), X0), 
2.04/2.27	        app_encode_app(int, nat, number_number_of(nat), 
2.04/2.27	          app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls))))
2.04/2.27	       = app_encode_app(int, int, 
2.04/2.27	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.04/2.27	             X0), X0),
2.04/2.27	    inference('simplify', [status(thm)], ['7'])).
2.04/2.27	tff(zf_stmt_117, axiom,
2.04/2.27	  (![K:int]:
2.04/2.27	     (app_encode_app(int,int,
2.04/2.27	                     app_encode_app(int,app_encode_fun(int,int),
2.04/2.27	                                    plus_plus(int),K),
2.04/2.27	                     pls) =
2.04/2.27	      K))).
2.04/2.27	tff('9', plain,
2.04/2.27	    ![X183 : int]:
2.04/2.27	      app_encode_app(int, int, 
2.04/2.27	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X183), 
2.04/2.27	        pls)
2.04/2.27	       = X183,
2.04/2.27	    inference('cnf', [status(esa)], [zf_stmt_117])).
2.04/2.27	tff(zf_stmt_128, axiom,
2.04/2.27	  (![K:int]:
2.04/2.27	     (app_encode_app(int,int,bit1,K) =
2.04/2.27	      app_encode_app(int,int,
2.04/2.27	                     app_encode_app(int,app_encode_fun(int,int),
2.04/2.27	                                    plus_plus(int),
2.04/2.27	                                    app_encode_app(int,int,
2.04/2.27	                                                   app_encode_app(int,
2.04/2.27	                                                                  app_encode_fun(
2.04/2.27	                                                                  int,int),
2.04/2.27	                                                                  plus_plus(
2.04/2.27	                                                                  int),
2.04/2.27	                                                                  one_one(
2.04/2.27	                                                                  int)),
2.04/2.27	                                                   K)),
2.04/2.27	                     K)))).
2.04/2.27	tff('10', plain,
2.04/2.27	    ![X206 : int]:
2.04/2.27	      app_encode_app(int, int, bit1, X206)
2.04/2.27	       = app_encode_app(int, int, 
2.04/2.27	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.04/2.27	             app_encode_app(int, int, 
2.04/2.27	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.04/2.27	                 one_one(int)), X206)), X206),
2.04/2.27	    inference('cnf', [status(esa)], [zf_stmt_128])).
2.04/2.27	tff('11', plain,
2.04/2.27	    app_encode_app(int, int, bit1, pls)
2.04/2.27	     = app_encode_app(int, int, 
2.04/2.27	         app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.04/2.27	           one_one(int)), pls),
2.04/2.27	    inference('sup+', [status(thm)], ['9', '10'])).
2.04/2.27	tff('12', plain, app_encode_app(int, int, bit1, pls) = one_one(int),
2.04/2.27	    inference('demod', [status(thm)], ['11', '9'])).
2.04/2.27	tff(zf_stmt_67, axiom,
2.04/2.27	  (![L1:int,K:int]:
2.04/2.27	     (app_encode_app(int,int,
2.04/2.27	                     app_encode_app(int,app_encode_fun(int,int),
2.04/2.27	                                    times_times(int),
2.04/2.27	                                    app_encode_app(int,int,bit0,K)),
2.04/2.27	                     L1) =
2.04/2.27	      app_encode_app(int,int,bit0,
2.04/2.27	                     app_encode_app(int,int,
2.04/2.27	                                    app_encode_app(int,
2.04/2.27	                                                   app_encode_fun(int,int),
2.04/2.27	                                                   times_times(int),K),
2.04/2.27	                                    L1))))).
2.04/2.27	tff('13', plain,
2.04/2.27	    ![X51 : int, X52 : int]:
2.04/2.27	      app_encode_app(int, int, 
2.04/2.27	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.04/2.27	          app_encode_app(int, int, bit0, X51)), X52)
2.04/2.27	       = app_encode_app(int, int, bit0, 
2.04/2.27	           app_encode_app(int, int, 
2.04/2.27	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.04/2.27	               X51), X52)),
2.04/2.27	    inference('cnf', [status(esa)], [zf_stmt_67])).
2.04/2.27	tff(zf_stmt_66, axiom,
2.04/2.27	  (![W:int]:
2.04/2.27	     (app_encode_app(int,int,
2.04/2.27	                     app_encode_app(int,app_encode_fun(int,int),
2.04/2.27	                                    times_times(int),pls),
2.04/2.27	                     W) =
2.04/2.27	      pls))).
2.04/2.27	tff('14', plain,
2.04/2.27	    ![X50 : int]:
2.04/2.27	      app_encode_app(int, int, 
2.04/2.27	        app_encode_app(int, app_encode_fun(int, int), times_times(int), pls), 
2.04/2.27	        X50)
2.04/2.27	       = pls,
2.04/2.27	    inference('cnf', [status(esa)], [zf_stmt_66])).
2.04/2.27	tff(zf_stmt_46, axiom,
2.04/2.27	  (![L1:int,K:int]:
2.04/2.27	     (app_encode_app(int,int,
2.04/2.27	                     app_encode_app(int,app_encode_fun(int,int),
2.04/2.27	                                    times_times(int),
2.04/2.27	                                    app_encode_app(int,int,bit1,K)),
2.04/2.27	                     L1) =
2.04/2.27	      app_encode_app(int,int,
2.04/2.27	                     app_encode_app(int,app_encode_fun(int,int),
2.04/2.27	                                    plus_plus(int),
2.04/2.27	                                    app_encode_app(int,int,bit0,
2.04/2.27	                                                   app_encode_app(int,int,
2.04/2.27	                                                                  app_encode_app(
2.04/2.27	                                                                  int,
2.04/2.27	                                                                  app_encode_fun(
2.04/2.27	                                                                  int,int),
2.04/2.27	                                                                  times_times(
2.04/2.27	                                                                  int),K),L1))),
2.04/2.27	                     L1)))).
2.04/2.27	tff('15', plain,
2.04/2.27	    ![X12 : int, X13 : int]:
2.04/2.27	      app_encode_app(int, int, 
2.04/2.27	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.04/2.27	          app_encode_app(int, int, bit1, X12)), X13)
2.04/2.27	       = app_encode_app(int, int, 
2.04/2.27	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.04/2.27	             app_encode_app(int, int, bit0, 
2.04/2.27	               app_encode_app(int, int, 
2.04/2.27	                 app_encode_app(int, app_encode_fun(int, int), 
2.04/2.27	                   times_times(int), X12), X13))), X13),
2.04/2.27	    inference('cnf', [status(esa)], [zf_stmt_46])).
2.04/2.27	tff('16', plain,
2.04/2.27	    ![X0 : int]:
2.04/2.27	      app_encode_app(int, int, 
2.04/2.27	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.04/2.27	          app_encode_app(int, int, bit1, pls)), X0)
2.04/2.27	       = app_encode_app(int, int, 
2.04/2.27	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.04/2.27	             app_encode_app(int, int, bit0, pls)), X0),
2.04/2.27	    inference('sup+', [status(thm)], ['14', '15'])).
2.04/2.27	tff(zf_stmt_62, axiom, (app_encode_app(int,int,bit0,pls) = pls)).
2.04/2.27	tff('17', plain, app_encode_app(int, int, bit0, pls) = pls,
2.04/2.27	    inference('cnf', [status(esa)], [zf_stmt_62])).
2.04/2.27	tff(zf_stmt_118, axiom,
2.04/2.27	  (![K:int]:
2.04/2.27	     (app_encode_app(int,int,
2.04/2.27	                     app_encode_app(int,app_encode_fun(int,int),
2.04/2.27	                                    plus_plus(int),pls),
2.04/2.27	                     K) =
2.04/2.27	      K))).
2.04/2.27	tff('18', plain,
2.04/2.27	    ![X184 : int]:
2.04/2.27	      app_encode_app(int, int, 
2.04/2.27	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
2.04/2.27	        X184)
2.04/2.27	       = X184,
2.04/2.27	    inference('cnf', [status(esa)], [zf_stmt_118])).
2.04/2.27	tff('19', plain,
2.04/2.27	    ![X0 : int]:
2.04/2.27	      app_encode_app(int, int, 
2.04/2.27	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.04/2.27	          app_encode_app(int, int, bit1, pls)), X0)
2.04/2.27	       = X0,
2.04/2.27	    inference('demod', [status(thm)], ['16', '17', '18'])).
2.04/2.27	tff(zf_stmt_2, axiom,
2.04/2.27	  (![X:app_encode_fun(Alpha,Beta),Y:app_encode_fun(Alpha,Beta)]:
2.04/2.27	     ((![Z:Alpha]:
2.04/2.27	         (app_encode_app(Alpha,Beta,X,Z) = app_encode_app(Alpha,Beta,Y,Z))) =>
2.04/2.27	      (X = Y)))).
2.04/2.27	tff('20', plain,
2.04/2.27	    ![X0 : $tType, X1 : $tType, X2 : app_encode_fun(X0, X1), 
2.04/2.27	      X3 : app_encode_fun(X0, X1)]:
2.04/2.27	      (X3 = X2
2.04/2.27	       | app_encode_app(X0, X1, X3, sk_Z(X1, X0, X2, X3))
2.04/2.27	          != app_encode_app(X0, X1, X2, sk_Z(X1, X0, X2, X3))),
2.04/2.27	    inference('cnf', [status(esa)], [zf_stmt_2])).
2.04/2.27	tff('21', plain,
2.04/2.27	    ![X0 : app_encode_fun(int, int)]:
2.04/2.27	      (app_encode_app(int, int, X0, 
2.04/2.27	         sk_Z(int, int, number_number_of(int), X0))
2.04/2.27	        != sk_Z(int, int, number_number_of(int), X0)
2.04/2.27	       | X0 = number_number_of(int)),
2.04/2.27	    inference('sup-', [status(thm)], ['1', '20'])).
2.04/2.27	tff('22', plain,
2.04/2.27	    (sk_Z(int, int, number_number_of(int), 
2.04/2.27	       app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.04/2.27	         app_encode_app(int, int, bit1, pls)))
2.04/2.27	      != sk_Z(int, int, number_number_of(int), 
2.04/2.27	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.04/2.27	             app_encode_app(int, int, bit1, pls)))
2.04/2.27	     | app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.04/2.27	         app_encode_app(int, int, bit1, pls))
2.04/2.27	        = number_number_of(int)),
2.04/2.27	    inference('sup-', [status(thm)], ['19', '21'])).
2.04/2.27	tff('23', plain,
2.04/2.27	    app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.04/2.27	      app_encode_app(int, int, bit1, pls))
2.04/2.27	     = number_number_of(int),
2.04/2.27	    inference('simplify', [status(thm)], ['22'])).
2.04/2.27	tff(zf_stmt_119, axiom,
2.04/2.27	  (![K:int]:
2.04/2.27	     (app_encode_app(int,int,bit0,K) =
2.04/2.27	      app_encode_app(int,int,
2.04/2.27	                     app_encode_app(int,app_encode_fun(int,int),
2.04/2.27	                                    plus_plus(int),K),
2.04/2.27	                     K)))).
2.04/2.27	tff('24', plain,
2.04/2.27	    ![X185 : int]:
2.04/2.27	      app_encode_app(int, int, bit0, X185)
2.04/2.27	       = app_encode_app(int, int, 
2.04/2.27	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.04/2.27	             X185), X185),
2.04/2.27	    inference('cnf', [status(esa)], [zf_stmt_119])).
2.04/2.27	tff(zf_stmt_137, axiom, (number_ring(int))).
2.04/2.27	tff('25', plain, number_ring(int),
2.04/2.27	    inference('cnf', [status(esa)], [zf_stmt_137])).
2.04/2.27	tff(zf_stmt_77, axiom,
2.04/2.27	  (![A:$tType]:
2.04/2.27	     (number_ring(A) =>
2.04/2.27	      (![Z3:A,W:int,V:int]:
2.04/2.27	         (app_encode_app(A,A,
2.04/2.27	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
2.04/2.27	                                        app_encode_app(int,A,
2.04/2.27	                                                       number_number_of(A),V)),
2.04/2.27	                         app_encode_app(A,A,
2.04/2.27	                                        app_encode_app(A,app_encode_fun(A,A),
2.04/2.27	                                                       plus_plus(A),
2.04/2.27	                                                       app_encode_app(
2.04/2.27	                                                       int,A,
2.04/2.27	                                                       number_number_of(A),W)),
2.04/2.27	                                        Z3)) =
2.04/2.27	          app_encode_app(A,A,
2.04/2.27	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
2.04/2.27	                                        app_encode_app(int,A,
2.04/2.27	                                                       number_number_of(A),
2.04/2.27	                                                       app_encode_app(
2.04/2.27	                                                       int,int,
2.04/2.27	                                                       app_encode_app(
2.04/2.27	                                                       int,
2.04/2.27	                                                       app_encode_fun(
2.04/2.27	                                                       int,int),
2.04/2.27	                                                       plus_plus(int),V),W))),
2.04/2.27	                         Z3)))))).
2.04/2.27	tff('26', plain,
2.04/2.27	    ![X84 : $tType, X85 : int, X86 : int, X87 : X84]:
2.04/2.27	      (app_encode_app(X84, X84, 
2.04/2.27	         app_encode_app(X84, app_encode_fun(X84, X84), plus_plus(X84), 
2.04/2.27	           app_encode_app(int, X84, number_number_of(X84), X85)), 
2.04/2.27	         app_encode_app(X84, X84, 
2.04/2.27	           app_encode_app(X84, app_encode_fun(X84, X84), plus_plus(X84), 
2.04/2.27	             app_encode_app(int, X84, number_number_of(X84), X86)), X87))
2.04/2.27	        = app_encode_app(X84, X84, 
2.04/2.27	            app_encode_app(X84, app_encode_fun(X84, X84), plus_plus(X84), 
2.04/2.27	              app_encode_app(int, X84, number_number_of(X84), 
2.04/2.27	                app_encode_app(int, int, 
2.04/2.27	                  app_encode_app(int, app_encode_fun(int, int), 
2.04/2.27	                    plus_plus(int), X85), X86))), X87)
2.04/2.27	       | ~ number_ring(X84)),
2.04/2.27	    inference('cnf', [status(esa)], [zf_stmt_77])).
2.04/2.27	tff('27', plain,
2.04/2.27	    ![X0 : int, X1 : int, X2 : int]:
2.04/2.27	      (~ $true
2.04/2.27	       | app_encode_app(int, int, 
2.04/2.27	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.04/2.27	             app_encode_app(int, int, number_number_of(int), X2)), 
2.04/2.27	           app_encode_app(int, int, 
2.04/2.27	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.04/2.27	               app_encode_app(int, int, number_number_of(int), X1)), X0))
2.04/2.27	          = app_encode_app(int, int, 
2.04/2.27	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.04/2.27	                app_encode_app(int, int, number_number_of(int), 
2.04/2.27	                  app_encode_app(int, int, 
2.04/2.27	                    app_encode_app(int, app_encode_fun(int, int), 
2.04/2.27	                      plus_plus(int), X2), X1))), X0)),
2.04/2.27	    inference('sup-', [status(thm)], ['25', '26'])).
2.04/2.27	tff('28', plain,
2.04/2.27	    ![X0 : int, X1 : int, X2 : int]:
2.04/2.27	      (~ $true
2.04/2.27	       | app_encode_app(int, int, 
2.04/2.27	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X2), 
2.04/2.27	           app_encode_app(int, int, 
2.04/2.27	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.04/2.27	               X1), X0))
2.04/2.27	          = app_encode_app(int, int, 
2.04/2.27	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.04/2.27	                app_encode_app(int, int, 
2.04/2.27	                  app_encode_app(int, app_encode_fun(int, int), 
2.04/2.27	                    plus_plus(int), X2), X1)), X0)),
2.04/2.27	    inference('demod', [status(thm)], ['27', '1', '1', '1'])).
2.04/2.27	tff('29', plain,
2.04/2.27	    ![X0 : int, X1 : int, X2 : int]:
2.04/2.27	      app_encode_app(int, int, 
2.04/2.27	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X2), 
2.04/2.27	        app_encode_app(int, int, 
2.04/2.27	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X1), 
2.04/2.27	          X0))
2.04/2.27	       = app_encode_app(int, int, 
2.04/2.27	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.04/2.27	             app_encode_app(int, int, 
2.04/2.27	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.04/2.27	                 X2), X1)), X0),
2.04/2.27	    inference('simplify', [status(thm)], ['28'])).
2.04/2.27	tff('30', plain,
2.04/2.27	    ![X0 : int, X1 : int]:
2.04/2.27	      app_encode_app(int, int, 
2.04/2.27	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
2.04/2.27	        app_encode_app(int, int, 
2.04/2.27	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
2.04/2.27	          X1))
2.04/2.27	       = app_encode_app(int, int, 
2.04/2.27	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.04/2.27	             app_encode_app(int, int, bit0, X0)), X1),
2.04/2.27	    inference('sup+', [status(thm)], ['24', '29'])).
2.04/2.27	tff(zf_stmt_52, axiom,
2.04/2.27	  (![L1:int,K:int]:
2.04/2.27	     (app_encode_app(int,int,
2.04/2.27	                     app_encode_app(int,app_encode_fun(int,int),
2.04/2.27	                                    plus_plus(int),
2.04/2.27	                                    app_encode_app(int,int,bit0,K)),
2.04/2.27	                     app_encode_app(int,int,bit1,L1)) =
2.04/2.27	      app_encode_app(int,int,bit1,
2.04/2.27	                     app_encode_app(int,int,
2.04/2.27	                                    app_encode_app(int,
2.04/2.27	                                                   app_encode_fun(int,int),
2.04/2.27	                                                   plus_plus(int),K),
2.04/2.27	                                    L1))))).
2.04/2.27	tff('31', plain,
2.04/2.27	    ![X22 : int, X23 : int]:
2.04/2.27	      app_encode_app(int, int, 
2.04/2.27	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.04/2.27	          app_encode_app(int, int, bit0, X22)), 
2.04/2.27	        app_encode_app(int, int, bit1, X23))
2.04/2.27	       = app_encode_app(int, int, bit1, 
2.04/2.27	           app_encode_app(int, int, 
2.04/2.27	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.04/2.27	               X22), X23)),
2.04/2.27	    inference('cnf', [status(esa)], [zf_stmt_52])).
2.04/2.27	tff('32', plain,
2.04/2.27	    ![X22 : int, X23 : int]:
2.04/2.27	      app_encode_app(int, int, 
2.04/2.27	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X22), 
2.04/2.27	        app_encode_app(int, int, 
2.04/2.27	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X22), 
2.04/2.27	          app_encode_app(int, int, bit1, X23)))
2.04/2.27	       = app_encode_app(int, int, bit1, 
2.04/2.27	           app_encode_app(int, int, 
2.04/2.27	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.04/2.27	               X22), X23)),
2.04/2.27	    inference('demod', [status(thm)], ['31', '30'])).
2.04/2.27	tff('33', plain,
2.04/2.27	    app_encode_app(int, int, 
2.04/2.27	      app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.04/2.27	        app_encode_app(int, int, 
2.04/2.27	          app_encode_app(int, app_encode_fun(int, int), times_times(int), s), 
2.04/2.27	          s)), app_encode_app(int, int, bit1, pls))
2.04/2.27	     = app_encode_app(int, int, 
2.04/2.27	         app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.04/2.27	           app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m))), 
2.04/2.27	         t),
2.04/2.27	    inference('demod', [status(thm)],
2.04/2.27	              ['2', '8', '12', '13', '13', '23', '1', '12', '30', '30', 
2.04/2.27	               '32', '9', '30', '32', '24'])).
2.04/2.27	tff(zf_stmt_148, conjecture,
2.04/2.27	  (app_encode_app(int,int,
2.04/2.27	                  app_encode_app(int,app_encode_fun(int,int),
2.04/2.27	                                 times_times(int),
2.04/2.27	                                 app_encode_app(int,int,
2.04/2.27	                                                app_encode_app(int,
2.04/2.27	                                                               app_encode_fun(
2.04/2.27	                                                               int,int),
2.04/2.27	                                                               plus_plus(int),
2.04/2.27	                                                               app_encode_app(
2.04/2.27	                                                               int,int,
2.04/2.27	                                                               app_encode_app(
2.04/2.27	                                                               int,
2.04/2.27	                                                               app_encode_fun(
2.04/2.27	                                                               int,int),
2.04/2.27	                                                               times_times(
2.04/2.27	                                                               int),
2.04/2.27	                                                               app_encode_app(
2.04/2.27	                                                               int,int,
2.04/2.27	                                                               number_number_of(
2.04/2.27	                                                               int),
2.04/2.27	                                                               app_encode_app(
2.04/2.27	                                                               int,int,bit0,
2.04/2.27	                                                               app_encode_app(
2.04/2.27	                                                               int,int,bit0,
2.04/2.27	                                                               app_encode_app(
2.04/2.27	                                                               int,int,bit1,
2.04/2.27	                                                               pls))))),m)),
2.04/2.27	                                                one_one(int))),
2.04/2.27	                  t) =
2.04/2.27	   app_encode_app(int,int,
2.04/2.27	                  app_encode_app(int,app_encode_fun(int,int),plus_plus(int),
2.04/2.27	                                 app_encode_app(nat,int,
2.04/2.27	                                                app_encode_app(int,
2.04/2.27	                                                               app_encode_fun(
2.04/2.27	                                                               nat,int),
2.04/2.27	                                                               power_power(
2.04/2.27	                                                               int),s),
2.04/2.27	                                                app_encode_app(int,nat,
2.04/2.27	                                                               number_number_of(
2.04/2.27	                                                               nat),
2.04/2.27	                                                               app_encode_app(
2.04/2.27	                                                               int,int,bit0,
2.04/2.27	                                                               app_encode_app(
2.04/2.27	                                                               int,int,bit1,
2.04/2.27	                                                               pls))))),
2.04/2.27	                  one_one(int)))).
2.04/2.27	tff(zf_stmt_0, negated_conjecture,
2.04/2.27	  (app_encode_app(int,int,
2.04/2.27	                  app_encode_app(int,app_encode_fun(int,int),
2.04/2.27	                                 times_times(int),
2.04/2.27	                                 app_encode_app(int,int,
2.04/2.27	                                                app_encode_app(int,
2.04/2.27	                                                               app_encode_fun(
2.04/2.27	                                                               int,int),
2.04/2.27	                                                               plus_plus(int),
2.04/2.27	                                                               app_encode_app(
2.04/2.27	                                                               int,int,
2.04/2.27	                                                               app_encode_app(
2.04/2.27	                                                               int,
2.04/2.27	                                                               app_encode_fun(
2.04/2.27	                                                               int,int),
2.04/2.27	                                                               times_times(
2.04/2.27	                                                               int),
2.04/2.27	                                                               app_encode_app(
2.04/2.27	                                                               int,int,
2.04/2.27	                                                               number_number_of(
2.04/2.27	                                                               int),
2.04/2.27	                                                               app_encode_app(
2.04/2.27	                                                               int,int,bit0,
2.04/2.27	                                                               app_encode_app(
2.04/2.27	                                                               int,int,bit0,
2.04/2.27	                                                               app_encode_app(
2.04/2.27	                                                               int,int,bit1,
2.04/2.27	                                                               pls))))),m)),
2.04/2.27	                                                one_one(int))),
2.04/2.27	                  t) !=
2.04/2.27	   app_encode_app(int,int,
2.04/2.27	                  app_encode_app(int,app_encode_fun(int,int),plus_plus(int),
2.04/2.27	                                 app_encode_app(nat,int,
2.04/2.27	                                                app_encode_app(int,
2.04/2.27	                                                               app_encode_fun(
2.04/2.27	                                                               nat,int),
2.04/2.27	                                                               power_power(
2.04/2.27	                                                               int),s),
2.04/2.27	                                                app_encode_app(int,nat,
2.04/2.27	                                                               number_number_of(
2.04/2.27	                                                               nat),
2.04/2.27	                                                               app_encode_app(
2.04/2.27	                                                               int,int,bit0,
2.04/2.27	                                                               app_encode_app(
2.04/2.27	                                                               int,int,bit1,
2.04/2.27	                                                               pls))))),
2.04/2.27	                  one_one(int)))).
2.04/2.27	tff('34', plain,
2.04/2.27	    app_encode_app(int, int, 
2.04/2.27	      app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.04/2.27	        app_encode_app(int, int, 
2.04/2.27	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.04/2.27	            app_encode_app(int, int, 
2.04/2.27	              app_encode_app(int, app_encode_fun(int, int), 
2.04/2.27	                times_times(int), 
2.04/2.27	                app_encode_app(int, int, number_number_of(int), 
2.04/2.27	                  app_encode_app(int, int, bit0, 
2.04/2.27	                    app_encode_app(int, int, bit0, 
2.04/2.27	                      app_encode_app(int, int, bit1, pls))))), m)), 
2.04/2.27	          one_one(int))), t)
2.04/2.27	     != app_encode_app(int, int, 
2.04/2.27	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.04/2.27	            app_encode_app(nat, int, 
2.04/2.27	              app_encode_app(int, app_encode_fun(nat, int), 
2.04/2.27	                power_power(int), s), 
2.04/2.27	              app_encode_app(int, nat, number_number_of(nat), 
2.04/2.27	                app_encode_app(int, int, bit0, 
2.04/2.27	                  app_encode_app(int, int, bit1, pls))))), one_one(int)),
2.04/2.27	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.04/2.27	tff('35', plain,
2.04/2.27	    app_encode_app(int, int, 
2.04/2.27	      app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.04/2.27	        app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m))), 
2.04/2.27	      t)
2.04/2.27	     != app_encode_app(int, int, 
2.04/2.27	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.04/2.27	            app_encode_app(int, int, 
2.04/2.27	              app_encode_app(int, app_encode_fun(int, int), 
2.04/2.27	                times_times(int), s), s)), 
2.04/2.27	          app_encode_app(int, int, bit1, pls)),
2.04/2.27	    inference('demod', [status(thm)],
2.04/2.27	              ['34', '1', '13', '13', '23', '1', '12', '30', '30', '32', 
2.04/2.27	               '9', '30', '32', '24', '8', '12'])).
2.04/2.27	tff('36', plain, $false,
2.04/2.27	    inference('simplify_reflect-', [status(thm)], ['33', '35'])).
2.04/2.27	
2.04/2.27	% SZS output end Refutation
2.04/2.27	EOF
