0.00/0.00	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : app
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : kbo
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   : n161.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 08:01:54 CST 2018
2.42/2.67	% done 1279 iterations in 2.461s
2.42/2.67	% SZS status Theorem for 'stdin'
2.42/2.67	% SZS output start Refutation
2.50/2.67	tff(zf_stmt_85, axiom,
2.50/2.67	  (![K1:int]: (app_encode_app(int,int,number_number_of(int),K1) = K1))).
2.50/2.67	tff('0', plain,
2.50/2.67	    ![X78 : int]: app_encode_app(int, int, number_number_of(int), X78) = X78,
2.50/2.67	    inference('cnf', [status(esa)], [zf_stmt_85])).
2.50/2.67	tff(zf_stmt_51, axiom,
2.50/2.67	  (app_encode_app(int,int,
2.50/2.67	                  app_encode_app(int,app_encode_fun(int,int),plus_plus(int),
2.50/2.67	                                 app_encode_app(nat,int,
2.50/2.67	                                                app_encode_app(int,
2.50/2.67	                                                               app_encode_fun(
2.50/2.67	                                                               nat,int),
2.50/2.67	                                                               power_power(
2.50/2.67	                                                               int),s),
2.50/2.67	                                                app_encode_app(int,nat,
2.50/2.67	                                                               number_number_of(
2.50/2.67	                                                               nat),
2.50/2.67	                                                               app_encode_app(
2.50/2.67	                                                               int,int,bit0,
2.50/2.67	                                                               app_encode_app(
2.50/2.67	                                                               int,int,bit1,
2.50/2.67	                                                               pls))))),
2.50/2.67	                  one_one(int)) =
2.50/2.67	   app_encode_app(int,int,
2.50/2.67	                  app_encode_app(int,app_encode_fun(int,int),
2.50/2.67	                                 times_times(int),
2.50/2.67	                                 app_encode_app(int,int,
2.50/2.67	                                                app_encode_app(int,
2.50/2.67	                                                               app_encode_fun(
2.50/2.67	                                                               int,int),
2.50/2.67	                                                               plus_plus(int),
2.50/2.67	                                                               app_encode_app(
2.50/2.67	                                                               int,int,
2.50/2.67	                                                               app_encode_app(
2.50/2.67	                                                               int,
2.50/2.67	                                                               app_encode_fun(
2.50/2.67	                                                               int,int),
2.50/2.67	                                                               times_times(
2.50/2.67	                                                               int),
2.50/2.67	                                                               app_encode_app(
2.50/2.67	                                                               int,int,
2.50/2.67	                                                               number_number_of(
2.50/2.67	                                                               int),
2.50/2.67	                                                               app_encode_app(
2.50/2.67	                                                               int,int,bit0,
2.50/2.67	                                                               app_encode_app(
2.50/2.67	                                                               int,int,bit0,
2.50/2.67	                                                               app_encode_app(
2.50/2.67	                                                               int,int,bit1,
2.50/2.67	                                                               pls))))),m)),
2.50/2.67	                                                one_one(int))),
2.50/2.67	                  t))).
2.50/2.67	tff('1', plain,
2.50/2.67	    app_encode_app(int, int, 
2.50/2.67	      app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.50/2.67	        app_encode_app(nat, int, 
2.50/2.67	          app_encode_app(int, app_encode_fun(nat, int), power_power(int), s), 
2.50/2.67	          app_encode_app(int, nat, number_number_of(nat), 
2.50/2.67	            app_encode_app(int, int, bit0, 
2.50/2.67	              app_encode_app(int, int, bit1, pls))))), one_one(int))
2.50/2.67	     = app_encode_app(int, int, 
2.50/2.67	         app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.50/2.67	           app_encode_app(int, int, 
2.50/2.67	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.50/2.67	               app_encode_app(int, int, 
2.50/2.67	                 app_encode_app(int, app_encode_fun(int, int), 
2.50/2.67	                   times_times(int), 
2.50/2.67	                   app_encode_app(int, int, number_number_of(int), 
2.50/2.67	                     app_encode_app(int, int, bit0, 
2.50/2.67	                       app_encode_app(int, int, bit0, 
2.50/2.67	                         app_encode_app(int, int, bit1, pls))))), m)), 
2.50/2.67	             one_one(int))), t),
2.50/2.67	    inference('cnf', [status(esa)], [zf_stmt_51])).
2.50/2.67	tff(zf_stmt_105, axiom,
2.50/2.67	  (one_one(int) =
2.50/2.67	   app_encode_app(int,int,number_number_of(int),
2.50/2.67	                  app_encode_app(int,int,bit1,pls)))).
2.50/2.67	tff('2', plain,
2.50/2.67	    one_one(int)
2.50/2.67	     = app_encode_app(int, int, number_number_of(int), 
2.50/2.67	         app_encode_app(int, int, bit1, pls)),
2.50/2.67	    inference('cnf', [status(esa)], [zf_stmt_105])).
2.50/2.67	tff(zf_stmt_40, axiom, (t = one_one(int))).
2.50/2.67	tff('3', plain, t = one_one(int),
2.50/2.67	    inference('cnf', [status(esa)], [zf_stmt_40])).
2.50/2.67	tff('4', plain, t = app_encode_app(int, int, bit1, pls),
2.50/2.67	    inference('demod', [status(thm)], ['2', '3', '0'])).
2.50/2.67	tff(zf_stmt_66, axiom,
2.50/2.67	  (![L1:int,K1:int]:
2.50/2.67	     (app_encode_app(int,int,
2.50/2.67	                     app_encode_app(int,app_encode_fun(int,int),
2.50/2.67	                                    times_times(int),
2.50/2.67	                                    app_encode_app(int,int,bit0,K1)),
2.50/2.67	                     L1) =
2.50/2.67	      app_encode_app(int,int,bit0,
2.50/2.67	                     app_encode_app(int,int,
2.50/2.67	                                    app_encode_app(int,
2.50/2.67	                                                   app_encode_fun(int,int),
2.50/2.67	                                                   times_times(int),K1),
2.50/2.67	                                    L1))))).
2.50/2.67	tff('5', plain,
2.50/2.67	    ![X39 : int, X40 : int]:
2.50/2.67	      app_encode_app(int, int, 
2.50/2.67	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.50/2.67	          app_encode_app(int, int, bit0, X39)), X40)
2.50/2.67	       = app_encode_app(int, int, bit0, 
2.50/2.67	           app_encode_app(int, int, 
2.50/2.67	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.50/2.67	               X39), X40)),
2.50/2.67	    inference('cnf', [status(esa)], [zf_stmt_66])).
2.50/2.67	tff(zf_stmt_65, axiom,
2.50/2.67	  (![W:int]:
2.50/2.67	     (app_encode_app(int,int,
2.50/2.67	                     app_encode_app(int,app_encode_fun(int,int),
2.50/2.67	                                    times_times(int),pls),
2.50/2.67	                     W) =
2.50/2.67	      pls))).
2.50/2.67	tff('6', plain,
2.50/2.67	    ![X38 : int]:
2.50/2.67	      app_encode_app(int, int, 
2.50/2.67	        app_encode_app(int, app_encode_fun(int, int), times_times(int), pls), 
2.50/2.67	        X38)
2.50/2.67	       = pls,
2.50/2.67	    inference('cnf', [status(esa)], [zf_stmt_65])).
2.50/2.67	tff(zf_stmt_49, axiom,
2.50/2.67	  (![L1:int,K1:int]:
2.50/2.67	     (app_encode_app(int,int,
2.50/2.67	                     app_encode_app(int,app_encode_fun(int,int),
2.50/2.67	                                    times_times(int),
2.50/2.67	                                    app_encode_app(int,int,bit1,K1)),
2.50/2.67	                     L1) =
2.50/2.67	      app_encode_app(int,int,
2.50/2.67	                     app_encode_app(int,app_encode_fun(int,int),
2.50/2.67	                                    plus_plus(int),
2.50/2.67	                                    app_encode_app(int,int,bit0,
2.50/2.67	                                                   app_encode_app(int,int,
2.50/2.67	                                                                  app_encode_app(
2.50/2.67	                                                                  int,
2.50/2.67	                                                                  app_encode_fun(
2.50/2.67	                                                                  int,int),
2.50/2.67	                                                                  times_times(
2.50/2.67	                                                                  int),K1),L1))),
2.50/2.67	                     L1)))).
2.50/2.67	tff('7', plain,
2.50/2.67	    ![X8 : int, X9 : int]:
2.50/2.67	      app_encode_app(int, int, 
2.50/2.67	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.50/2.67	          app_encode_app(int, int, bit1, X8)), X9)
2.50/2.67	       = app_encode_app(int, int, 
2.50/2.67	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.50/2.67	             app_encode_app(int, int, bit0, 
2.50/2.67	               app_encode_app(int, int, 
2.50/2.67	                 app_encode_app(int, app_encode_fun(int, int), 
2.50/2.67	                   times_times(int), X8), X9))), X9),
2.50/2.67	    inference('cnf', [status(esa)], [zf_stmt_49])).
2.50/2.67	tff('8', plain,
2.50/2.67	    ![X0 : int]:
2.50/2.67	      app_encode_app(int, int, 
2.50/2.67	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.50/2.67	          app_encode_app(int, int, bit1, pls)), X0)
2.50/2.67	       = app_encode_app(int, int, 
2.50/2.67	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.50/2.67	             app_encode_app(int, int, bit0, pls)), X0),
2.50/2.67	    inference('sup+', [status(thm)], ['6', '7'])).
2.50/2.67	tff(zf_stmt_64, axiom, (app_encode_app(int,int,bit0,pls) = pls)).
2.50/2.67	tff('9', plain, app_encode_app(int, int, bit0, pls) = pls,
2.50/2.67	    inference('cnf', [status(esa)], [zf_stmt_64])).
2.50/2.67	tff(zf_stmt_88, axiom,
2.50/2.67	  (![K1:int]:
2.50/2.67	     (app_encode_app(int,int,
2.50/2.67	                     app_encode_app(int,app_encode_fun(int,int),
2.50/2.67	                                    plus_plus(int),pls),
2.50/2.67	                     K1) =
2.50/2.67	      K1))).
2.50/2.67	tff('10', plain,
2.50/2.67	    ![X83 : int]:
2.50/2.67	      app_encode_app(int, int, 
2.50/2.67	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
2.50/2.67	        X83)
2.50/2.67	       = X83,
2.50/2.67	    inference('cnf', [status(esa)], [zf_stmt_88])).
2.50/2.67	tff('11', plain,
2.50/2.67	    ![X0 : int]:
2.50/2.67	      app_encode_app(int, int, 
2.50/2.67	        app_encode_app(int, app_encode_fun(int, int), times_times(int), t), 
2.50/2.67	        X0)
2.50/2.67	       = X0,
2.50/2.67	    inference('demod', [status(thm)], ['8', '4', '9', '10'])).
2.50/2.67	tff('12', plain,
2.50/2.67	    app_encode_app(int, int, 
2.50/2.67	      app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.50/2.67	        app_encode_app(nat, int, 
2.50/2.67	          app_encode_app(int, app_encode_fun(nat, int), power_power(int), s), 
2.50/2.67	          app_encode_app(int, nat, number_number_of(nat), 
2.50/2.67	            app_encode_app(int, int, bit0, t)))), t)
2.50/2.67	     = app_encode_app(int, int, 
2.50/2.67	         app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.50/2.67	           app_encode_app(int, int, 
2.50/2.67	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.50/2.67	               app_encode_app(int, int, bit0, 
2.50/2.67	                 app_encode_app(int, int, bit0, m))), t)), t),
2.50/2.67	    inference('demod', [status(thm)],
2.50/2.67	              ['1', '4', '3', '4', '0', '5', '5', '11', '3'])).
2.50/2.67	tff(zf_stmt_47, axiom,
2.50/2.67	  (![A:$tType]:
2.50/2.67	     (number_ring(A) =>
2.50/2.67	      (![V:int]:
2.50/2.67	         (app_encode_app(A,A,
2.50/2.67	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
2.50/2.67	                                        app_encode_app(int,A,
2.50/2.67	                                                       number_number_of(A),V)),
2.50/2.67	                         one_one(A)) =
2.50/2.67	          app_encode_app(int,A,number_number_of(A),
2.50/2.67	                         app_encode_app(int,int,
2.50/2.67	                                        app_encode_app(int,
2.50/2.67	                                                       app_encode_fun(
2.50/2.67	                                                       int,int),
2.50/2.67	                                                       plus_plus(int),V),
2.50/2.67	                                        app_encode_app(int,int,bit1,pls)))))))).
2.50/2.67	tff('13', plain,
2.50/2.67	    ![X5 : $tType, X6 : int]:
2.50/2.67	      (app_encode_app(X5, X5, 
2.50/2.67	         app_encode_app(X5, app_encode_fun(X5, X5), plus_plus(X5), 
2.50/2.67	           app_encode_app(int, X5, number_number_of(X5), X6)), one_one(X5))
2.50/2.67	        = app_encode_app(int, X5, number_number_of(X5), 
2.50/2.67	            app_encode_app(int, int, 
2.50/2.67	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.50/2.67	                X6), app_encode_app(int, int, bit1, pls)))
2.50/2.67	       | ~ number_ring(X5)),
2.50/2.67	    inference('cnf', [status(esa)], [zf_stmt_47])).
2.50/2.67	tff('14', plain,
2.50/2.67	    ![X5 : $tType, X6 : int]:
2.50/2.67	      (app_encode_app(X5, X5, 
2.50/2.67	         app_encode_app(X5, app_encode_fun(X5, X5), plus_plus(X5), 
2.50/2.67	           app_encode_app(int, X5, number_number_of(X5), X6)), one_one(X5))
2.50/2.67	        = app_encode_app(int, X5, number_number_of(X5), 
2.50/2.67	            app_encode_app(int, int, 
2.50/2.67	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.50/2.67	                X6), t))
2.50/2.67	       | ~ number_ring(X5)),
2.50/2.67	    inference('demod', [status(thm)], ['13', '4'])).
2.50/2.67	tff('15', plain,
2.50/2.67	    ![X0 : $tType]:
2.50/2.67	      (app_encode_app(X0, X0, 
2.50/2.67	         app_encode_app(X0, app_encode_fun(X0, X0), plus_plus(X0), 
2.50/2.67	           app_encode_app(int, X0, number_number_of(X0), 
2.50/2.67	             app_encode_app(nat, int, 
2.50/2.67	               app_encode_app(int, app_encode_fun(nat, int), 
2.50/2.67	                 power_power(int), s), 
2.50/2.67	               app_encode_app(int, nat, number_number_of(nat), 
2.50/2.67	                 app_encode_app(int, int, bit0, t))))), one_one(X0))
2.50/2.67	        = app_encode_app(int, X0, number_number_of(X0), 
2.50/2.67	            app_encode_app(int, int, 
2.50/2.67	              app_encode_app(int, app_encode_fun(int, int), 
2.50/2.67	                times_times(int), 
2.50/2.67	                app_encode_app(int, int, 
2.50/2.67	                  app_encode_app(int, app_encode_fun(int, int), 
2.50/2.67	                    plus_plus(int), 
2.50/2.67	                    app_encode_app(int, int, bit0, 
2.50/2.67	                      app_encode_app(int, int, bit0, m))), t)), t))
2.50/2.67	       | ~ number_ring(X0)),
2.50/2.67	    inference('sup+', [status(thm)], ['12', '14'])).
2.50/2.67	tff(zf_stmt_43, axiom,
2.50/2.67	  (![B1:$tType]:
2.50/2.67	     ((monoid_mult(B1) & number(B1)) =>
2.50/2.67	      (![W:int]:
2.50/2.67	         (app_encode_app(nat,B1,
2.50/2.67	                         app_encode_app(B1,app_encode_fun(nat,B1),
2.50/2.67	                                        power_power(B1),
2.50/2.67	                                        app_encode_app(int,B1,
2.50/2.67	                                                       number_number_of(B1),W)),
2.50/2.67	                         app_encode_app(int,nat,number_number_of(nat),
2.50/2.67	                                        app_encode_app(int,int,bit0,
2.50/2.67	                                                       app_encode_app(
2.50/2.67	                                                       int,int,bit1,pls)))) =
2.50/2.67	          app_encode_app(B1,B1,
2.50/2.67	                         app_encode_app(B1,app_encode_fun(B1,B1),
2.50/2.67	                                        times_times(B1),
2.50/2.67	                                        app_encode_app(int,B1,
2.50/2.67	                                                       number_number_of(B1),W)),
2.50/2.67	                         app_encode_app(int,B1,number_number_of(B1),W))))))).
2.50/2.67	tff('16', plain,
2.50/2.67	    ![X0 : $tType, X1 : int]:
2.50/2.67	      (app_encode_app(nat, X0, 
2.50/2.67	         app_encode_app(X0, app_encode_fun(nat, X0), power_power(X0), 
2.50/2.67	           app_encode_app(int, X0, number_number_of(X0), X1)), 
2.50/2.67	         app_encode_app(int, nat, number_number_of(nat), 
2.50/2.67	           app_encode_app(int, int, bit0, 
2.50/2.67	             app_encode_app(int, int, bit1, pls))))
2.50/2.67	        = app_encode_app(X0, X0, 
2.50/2.67	            app_encode_app(X0, app_encode_fun(X0, X0), times_times(X0), 
2.50/2.67	              app_encode_app(int, X0, number_number_of(X0), X1)), 
2.50/2.67	            app_encode_app(int, X0, number_number_of(X0), X1))
2.50/2.67	       | ~ number(X0)
2.50/2.67	       | ~ monoid_mult(X0)),
2.50/2.67	    inference('cnf', [status(esa)], [zf_stmt_43])).
2.50/2.67	tff('17', plain,
2.50/2.67	    ![X0 : int]:
2.50/2.67	      (app_encode_app(nat, int, 
2.50/2.67	         app_encode_app(int, app_encode_fun(nat, int), power_power(int), X0), 
2.50/2.67	         app_encode_app(int, nat, number_number_of(nat), 
2.50/2.67	           app_encode_app(int, int, bit0, 
2.50/2.67	             app_encode_app(int, int, bit1, pls))))
2.50/2.67	        = app_encode_app(int, int, 
2.50/2.67	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.50/2.67	              app_encode_app(int, int, number_number_of(int), X0)), 
2.50/2.67	            app_encode_app(int, int, number_number_of(int), X0))
2.50/2.67	       | ~ monoid_mult(int)
2.50/2.67	       | ~ number(int)),
2.50/2.67	    inference('sup+', [status(thm)], ['0', '16'])).
2.50/2.67	tff(zf_stmt_142, axiom, (monoid_mult(int))).
2.50/2.67	tff('18', plain, monoid_mult(int),
2.50/2.67	    inference('cnf', [status(esa)], [zf_stmt_142])).
2.50/2.67	tff(zf_stmt_147, axiom, (number(int))).
2.50/2.67	tff('19', plain, number(int), inference('cnf', [status(esa)], [zf_stmt_147])).
2.50/2.67	tff('20', plain,
2.50/2.67	    ![X0 : int]:
2.50/2.67	      (app_encode_app(nat, int, 
2.50/2.67	         app_encode_app(int, app_encode_fun(nat, int), power_power(int), X0), 
2.50/2.67	         app_encode_app(int, nat, number_number_of(nat), 
2.50/2.67	           app_encode_app(int, int, bit0, 
2.50/2.67	             app_encode_app(int, int, bit1, pls))))
2.50/2.67	        = app_encode_app(int, int, 
2.50/2.67	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.50/2.67	              X0), X0)
2.50/2.67	       | ~ $true
2.50/2.67	       | ~ $true),
2.50/2.67	    inference('demod', [status(thm)], ['17', '0', '0', '18', '19'])).
2.50/2.67	tff('21', plain,
2.50/2.67	    ![X0 : int]:
2.50/2.67	      app_encode_app(nat, int, 
2.50/2.67	        app_encode_app(int, app_encode_fun(nat, int), power_power(int), X0), 
2.50/2.67	        app_encode_app(int, nat, number_number_of(nat), 
2.50/2.67	          app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls))))
2.50/2.67	       = app_encode_app(int, int, 
2.50/2.67	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.50/2.67	             X0), X0),
2.50/2.67	    inference('simplify', [status(thm)], ['20'])).
2.50/2.67	tff('22', plain,
2.50/2.67	    ![X0 : int]:
2.50/2.67	      app_encode_app(nat, int, 
2.50/2.67	        app_encode_app(int, app_encode_fun(nat, int), power_power(int), X0), 
2.50/2.67	        app_encode_app(int, nat, number_number_of(nat), 
2.50/2.67	          app_encode_app(int, int, bit0, t)))
2.50/2.67	       = app_encode_app(int, int, 
2.50/2.67	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.50/2.67	             X0), X0),
2.50/2.67	    inference('demod', [status(thm)], ['21', '4'])).
2.50/2.67	tff(zf_stmt_76, axiom,
2.50/2.67	  (![L1:int,K1:int]:
2.50/2.67	     (app_encode_app(int,int,
2.50/2.67	                     app_encode_app(int,app_encode_fun(int,int),
2.50/2.67	                                    plus_plus(int),
2.50/2.67	                                    app_encode_app(int,int,bit0,K1)),
2.50/2.67	                     app_encode_app(int,int,bit1,L1)) =
2.50/2.67	      app_encode_app(int,int,bit1,
2.50/2.67	                     app_encode_app(int,int,
2.50/2.67	                                    app_encode_app(int,
2.50/2.67	                                                   app_encode_fun(int,int),
2.50/2.67	                                                   plus_plus(int),K1),
2.50/2.67	                                    L1))))).
2.50/2.67	tff('23', plain,
2.50/2.67	    ![X67 : int, X68 : int]:
2.50/2.67	      app_encode_app(int, int, 
2.50/2.67	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.50/2.67	          app_encode_app(int, int, bit0, X67)), 
2.50/2.67	        app_encode_app(int, int, bit1, X68))
2.50/2.67	       = app_encode_app(int, int, bit1, 
2.50/2.67	           app_encode_app(int, int, 
2.50/2.67	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.50/2.67	               X67), X68)),
2.50/2.67	    inference('cnf', [status(esa)], [zf_stmt_76])).
2.50/2.67	tff('24', plain,
2.50/2.67	    ![X0 : int]:
2.50/2.67	      app_encode_app(int, int, 
2.50/2.67	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.50/2.67	          app_encode_app(int, int, bit0, X0)), t)
2.50/2.67	       = app_encode_app(int, int, bit1, 
2.50/2.67	           app_encode_app(int, int, 
2.50/2.67	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.50/2.67	               X0), pls)),
2.50/2.67	    inference('sup+', [status(thm)], ['4', '23'])).
2.50/2.67	tff(zf_stmt_87, axiom,
2.50/2.67	  (![K1:int]:
2.50/2.67	     (app_encode_app(int,int,
2.50/2.67	                     app_encode_app(int,app_encode_fun(int,int),
2.50/2.67	                                    plus_plus(int),K1),
2.50/2.67	                     pls) =
2.50/2.67	      K1))).
2.50/2.67	tff('25', plain,
2.50/2.67	    ![X82 : int]:
2.50/2.67	      app_encode_app(int, int, 
2.50/2.67	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X82), 
2.50/2.67	        pls)
2.50/2.67	       = X82,
2.50/2.67	    inference('cnf', [status(esa)], [zf_stmt_87])).
2.50/2.67	tff('26', plain,
2.50/2.67	    ![X0 : int]:
2.50/2.67	      app_encode_app(int, int, 
2.50/2.67	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.50/2.67	          app_encode_app(int, int, bit0, X0)), t)
2.50/2.67	       = app_encode_app(int, int, bit1, X0),
2.50/2.67	    inference('demod', [status(thm)], ['24', '25'])).
2.50/2.67	tff(zf_stmt_102, axiom,
2.50/2.67	  (![A:$tType]:
2.50/2.67	     (number_ring(A) =>
2.50/2.67	      (![A1:A]:
2.50/2.67	         (app_encode_app(A,A,
2.50/2.67	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
2.50/2.67	                                        A1),
2.50/2.67	                         app_encode_app(int,A,number_number_of(A),
2.50/2.67	                                        app_encode_app(int,int,bit1,pls))) =
2.50/2.67	          A1))))).
2.50/2.67	tff('27', plain,
2.50/2.67	    ![X112 : $tType, X113 : X112]:
2.50/2.67	      (app_encode_app(X112, X112, 
2.50/2.67	         app_encode_app(X112, app_encode_fun(X112, X112), times_times(X112), 
2.50/2.67	           X113), 
2.50/2.67	         app_encode_app(int, X112, number_number_of(X112), 
2.50/2.67	           app_encode_app(int, int, bit1, pls)))
2.50/2.67	        = X113
2.50/2.67	       | ~ number_ring(X112)),
2.50/2.67	    inference('cnf', [status(esa)], [zf_stmt_102])).
2.50/2.67	tff('28', plain,
2.50/2.67	    ![X112 : $tType, X113 : X112]:
2.50/2.67	      (app_encode_app(X112, X112, 
2.50/2.67	         app_encode_app(X112, app_encode_fun(X112, X112), times_times(X112), 
2.50/2.67	           X113), app_encode_app(int, X112, number_number_of(X112), t))
2.50/2.67	        = X113
2.50/2.67	       | ~ number_ring(X112)),
2.50/2.67	    inference('demod', [status(thm)], ['27', '4'])).
2.50/2.67	tff('29', plain,
2.50/2.67	    ![X0 : int]:
2.50/2.67	      (app_encode_app(int, int, 
2.50/2.67	         app_encode_app(int, app_encode_fun(int, int), times_times(int), X0), 
2.50/2.67	         t)
2.50/2.67	        = X0
2.50/2.67	       | ~ number_ring(int)),
2.50/2.67	    inference('sup+', [status(thm)], ['0', '28'])).
2.50/2.67	tff(zf_stmt_145, axiom, (number_ring(int))).
2.50/2.67	tff('30', plain, number_ring(int),
2.50/2.67	    inference('cnf', [status(esa)], [zf_stmt_145])).
2.50/2.67	tff('31', plain,
2.50/2.67	    ![X0 : int]:
2.50/2.67	      (app_encode_app(int, int, 
2.50/2.67	         app_encode_app(int, app_encode_fun(int, int), times_times(int), X0), 
2.50/2.67	         t)
2.50/2.67	        = X0
2.50/2.67	       | ~ $true),
2.50/2.67	    inference('demod', [status(thm)], ['29', '30'])).
2.50/2.67	tff('32', plain,
2.50/2.67	    ![X0 : int]:
2.50/2.67	      app_encode_app(int, int, 
2.50/2.67	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X0), 
2.50/2.67	        t)
2.50/2.67	       = X0,
2.50/2.67	    inference('simplify', [status(thm)], ['31'])).
2.50/2.67	tff('33', plain,
2.50/2.67	    ![X0 : $tType]:
2.50/2.67	      (app_encode_app(X0, X0, 
2.50/2.67	         app_encode_app(X0, app_encode_fun(X0, X0), plus_plus(X0), 
2.50/2.67	           app_encode_app(int, X0, number_number_of(X0), 
2.50/2.67	             app_encode_app(int, int, 
2.50/2.67	               app_encode_app(int, app_encode_fun(int, int), 
2.50/2.67	                 times_times(int), s), s))), one_one(X0))
2.50/2.67	        = app_encode_app(int, X0, number_number_of(X0), 
2.50/2.67	            app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m)))
2.50/2.67	       | ~ number_ring(X0)),
2.50/2.67	    inference('demod', [status(thm)], ['15', '22', '26', '32'])).
2.50/2.67	tff('34', plain,
2.50/2.67	    (app_encode_app(int, int, 
2.50/2.67	       app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.50/2.67	         app_encode_app(int, int, 
2.50/2.67	           app_encode_app(int, app_encode_fun(int, int), times_times(int), s), 
2.50/2.67	           s)), one_one(int))
2.50/2.67	      = app_encode_app(int, int, number_number_of(int), 
2.50/2.67	          app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m)))
2.50/2.67	     | ~ number_ring(int)),
2.50/2.67	    inference('sup+', [status(thm)], ['0', '33'])).
2.50/2.67	tff('35', plain,
2.50/2.67	    (app_encode_app(int, int, 
2.50/2.67	       app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.50/2.67	         app_encode_app(int, int, 
2.50/2.67	           app_encode_app(int, app_encode_fun(int, int), times_times(int), s), 
2.50/2.67	           s)), t)
2.50/2.67	      = app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m))
2.50/2.67	     | ~ $true),
2.50/2.67	    inference('demod', [status(thm)], ['34', '3', '0', '30'])).
2.50/2.67	tff('36', plain,
2.50/2.67	    app_encode_app(int, int, 
2.50/2.67	      app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.50/2.67	        app_encode_app(int, int, 
2.50/2.67	          app_encode_app(int, app_encode_fun(int, int), times_times(int), s), 
2.50/2.67	          s)), t)
2.50/2.67	     = app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m)),
2.50/2.67	    inference('simplify', [status(thm)], ['35'])).
2.50/2.67	tff(zf_stmt_120, axiom,
2.50/2.67	  (![A:$tType]:
2.50/2.67	     (monoid_mult(A) =>
2.50/2.67	      (![N:nat]:
2.50/2.67	         (app_encode_app(nat,A,
2.50/2.67	                         app_encode_app(A,app_encode_fun(nat,A),
2.50/2.67	                                        power_power(A),one_one(A)),
2.50/2.67	                         N) =
2.50/2.67	          one_one(A)))))).
2.50/2.67	tff('37', plain,
2.50/2.67	    ![X138 : $tType, X139 : nat]:
2.50/2.67	      (app_encode_app(nat, X138, 
2.50/2.67	         app_encode_app(X138, app_encode_fun(nat, X138), power_power(X138), 
2.50/2.67	           one_one(X138)), X139)
2.50/2.67	        = one_one(X138)
2.50/2.67	       | ~ monoid_mult(X138)),
2.50/2.67	    inference('cnf', [status(esa)], [zf_stmt_120])).
2.50/2.67	tff('38', plain,
2.50/2.67	    ![X0 : nat]:
2.50/2.67	      (app_encode_app(nat, int, 
2.50/2.67	         app_encode_app(int, app_encode_fun(nat, int), power_power(int), t), 
2.50/2.67	         X0)
2.50/2.67	        = one_one(int)
2.50/2.67	       | ~ monoid_mult(int)),
2.50/2.67	    inference('sup+', [status(thm)], ['3', '37'])).
2.50/2.67	tff('39', plain,
2.50/2.67	    ![X0 : nat]:
2.50/2.67	      (app_encode_app(nat, int, 
2.50/2.67	         app_encode_app(int, app_encode_fun(nat, int), power_power(int), t), 
2.50/2.67	         X0)
2.50/2.67	        = t
2.50/2.67	       | ~ $true),
2.50/2.67	    inference('demod', [status(thm)], ['38', '3', '18'])).
2.50/2.67	tff('40', plain,
2.50/2.67	    ![X0 : nat]:
2.50/2.67	      app_encode_app(nat, int, 
2.50/2.67	        app_encode_app(int, app_encode_fun(nat, int), power_power(int), t), 
2.50/2.67	        X0)
2.50/2.67	       = t,
2.50/2.67	    inference('simplify', [status(thm)], ['39'])).
2.50/2.67	tff(zf_stmt_167, conjecture,
2.50/2.67	  (?[X:int,Y:int]:
2.50/2.67	     (app_encode_app(int,int,
2.50/2.67	                     app_encode_app(int,app_encode_fun(int,int),
2.50/2.67	                                    plus_plus(int),
2.50/2.67	                                    app_encode_app(nat,int,
2.50/2.67	                                                   app_encode_app(int,
2.50/2.67	                                                                  app_encode_fun(
2.50/2.67	                                                                  nat,int),
2.50/2.67	                                                                  power_power(
2.50/2.67	                                                                  int),X),
2.50/2.67	                                                   app_encode_app(int,nat,
2.50/2.67	                                                                  number_number_of(
2.50/2.67	                                                                  nat),
2.50/2.67	                                                                  app_encode_app(
2.50/2.67	                                                                  int,int,
2.50/2.67	                                                                  bit0,
2.50/2.67	                                                                  app_encode_app(
2.50/2.67	                                                                  int,int,
2.50/2.67	                                                                  bit1,pls))))),
2.50/2.67	                     app_encode_app(nat,int,
2.50/2.67	                                    app_encode_app(int,
2.50/2.67	                                                   app_encode_fun(nat,int),
2.50/2.67	                                                   power_power(int),Y),
2.50/2.67	                                    app_encode_app(int,nat,
2.50/2.67	                                                   number_number_of(nat),
2.50/2.67	                                                   app_encode_app(int,int,
2.50/2.67	                                                                  bit0,
2.50/2.67	                                                                  app_encode_app(
2.50/2.67	                                                                  int,int,
2.50/2.67	                                                                  bit1,pls))))) =
2.50/2.67	      app_encode_app(int,int,
2.50/2.67	                     app_encode_app(int,app_encode_fun(int,int),
2.50/2.67	                                    plus_plus(int),
2.50/2.67	                                    app_encode_app(int,int,
2.50/2.67	                                                   app_encode_app(int,
2.50/2.67	                                                                  app_encode_fun(
2.50/2.67	                                                                  int,int),
2.50/2.67	                                                                  times_times(
2.50/2.67	                                                                  int),
2.50/2.67	                                                                  app_encode_app(
2.50/2.67	                                                                  int,int,
2.50/2.67	                                                                  number_number_of(
2.50/2.67	                                                                  int),
2.50/2.67	                                                                  app_encode_app(
2.50/2.67	                                                                  int,int,
2.50/2.67	                                                                  bit0,
2.50/2.67	                                                                  app_encode_app(
2.50/2.67	                                                                  int,int,
2.50/2.67	                                                                  bit0,
2.50/2.67	                                                                  app_encode_app(
2.50/2.67	                                                                  int,int,
2.50/2.67	                                                                  bit1,pls))))),
2.50/2.67	                                                   m)),
2.50/2.67	                     one_one(int))))).
2.50/2.67	tff(zf_stmt_0, negated_conjecture,
2.50/2.67	  (~
2.50/2.67	    (?[X:int,Y:int]:
2.50/2.67	       (app_encode_app(int,int,
2.50/2.67	                       app_encode_app(int,app_encode_fun(int,int),
2.50/2.67	                                      plus_plus(int),
2.50/2.67	                                      app_encode_app(nat,int,
2.50/2.67	                                                     app_encode_app(int,
2.50/2.67	                                                                    app_encode_fun(
2.50/2.67	                                                                    nat,int),
2.50/2.67	                                                                    power_power(
2.50/2.67	                                                                    int),X),
2.50/2.67	                                                     app_encode_app(int,nat,
2.50/2.67	                                                                    number_number_of(
2.50/2.67	                                                                    nat),
2.50/2.67	                                                                    app_encode_app(
2.50/2.67	                                                                    int,int,
2.50/2.67	                                                                    bit0,
2.50/2.67	                                                                    app_encode_app(
2.50/2.67	                                                                    int,int,
2.50/2.67	                                                                    bit1,pls))))),
2.50/2.67	                       app_encode_app(nat,int,
2.50/2.67	                                      app_encode_app(int,
2.50/2.67	                                                     app_encode_fun(nat,int),
2.50/2.67	                                                     power_power(int),Y),
2.50/2.67	                                      app_encode_app(int,nat,
2.50/2.67	                                                     number_number_of(nat),
2.50/2.67	                                                     app_encode_app(int,int,
2.50/2.67	                                                                    bit0,
2.50/2.67	                                                                    app_encode_app(
2.50/2.67	                                                                    int,int,
2.50/2.67	                                                                    bit1,pls))))) =
2.50/2.67	        app_encode_app(int,int,
2.50/2.67	                       app_encode_app(int,app_encode_fun(int,int),
2.50/2.67	                                      plus_plus(int),
2.50/2.67	                                      app_encode_app(int,int,
2.50/2.67	                                                     app_encode_app(int,
2.50/2.67	                                                                    app_encode_fun(
2.50/2.67	                                                                    int,int),
2.50/2.67	                                                                    times_times(
2.50/2.67	                                                                    int),
2.50/2.67	                                                                    app_encode_app(
2.50/2.67	                                                                    int,int,
2.50/2.67	                                                                    number_number_of(
2.50/2.67	                                                                    int),
2.50/2.67	                                                                    app_encode_app(
2.50/2.67	                                                                    int,int,
2.50/2.67	                                                                    bit0,
2.50/2.67	                                                                    app_encode_app(
2.50/2.67	                                                                    int,int,
2.50/2.67	                                                                    bit0,
2.50/2.67	                                                                    app_encode_app(
2.50/2.67	                                                                    int,int,
2.50/2.67	                                                                    bit1,pls))))),
2.50/2.67	                                                     m)),
2.50/2.67	                       one_one(int)))))).
2.50/2.67	tff('41', plain,
2.50/2.67	    ![X177 : int, X178 : int]:
2.50/2.67	      app_encode_app(int, int, 
2.50/2.67	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.50/2.67	          app_encode_app(nat, int, 
2.50/2.67	            app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
2.50/2.67	              X177), 
2.50/2.67	            app_encode_app(int, nat, number_number_of(nat), 
2.50/2.67	              app_encode_app(int, int, bit0, 
2.50/2.67	                app_encode_app(int, int, bit1, pls))))), 
2.50/2.67	        app_encode_app(nat, int, 
2.50/2.67	          app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
2.50/2.67	            X178), 
2.50/2.67	          app_encode_app(int, nat, number_number_of(nat), 
2.50/2.67	            app_encode_app(int, int, bit0, 
2.50/2.67	              app_encode_app(int, int, bit1, pls)))))
2.50/2.67	       != app_encode_app(int, int, 
2.50/2.67	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.50/2.67	              app_encode_app(int, int, 
2.50/2.67	                app_encode_app(int, app_encode_fun(int, int), 
2.50/2.67	                  times_times(int), 
2.50/2.67	                  app_encode_app(int, int, number_number_of(int), 
2.50/2.67	                    app_encode_app(int, int, bit0, 
2.50/2.67	                      app_encode_app(int, int, bit0, 
2.50/2.67	                        app_encode_app(int, int, bit1, pls))))), m)), 
2.50/2.67	            one_one(int)),
2.50/2.67	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.50/2.67	tff('42', plain,
2.50/2.67	    ![X177 : int, X178 : int]:
2.50/2.67	      app_encode_app(int, int, 
2.50/2.67	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.50/2.67	          app_encode_app(nat, int, 
2.50/2.67	            app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
2.50/2.67	              X177), 
2.50/2.67	            app_encode_app(int, nat, number_number_of(nat), 
2.50/2.67	              app_encode_app(int, int, bit0, t)))), 
2.50/2.67	        app_encode_app(nat, int, 
2.50/2.67	          app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
2.50/2.67	            X178), 
2.50/2.67	          app_encode_app(int, nat, number_number_of(nat), 
2.50/2.67	            app_encode_app(int, int, bit0, t))))
2.50/2.67	       != app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m)),
2.50/2.67	    inference('demod', [status(thm)],
2.50/2.67	              ['41', '4', '4', '4', '0', '5', '5', '11', '3', '26'])).
2.50/2.67	tff('43', plain,
2.50/2.67	    ![X0 : int]:
2.50/2.67	      app_encode_app(int, int, 
2.50/2.67	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.50/2.67	          app_encode_app(nat, int, 
2.50/2.67	            app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
2.50/2.67	              X0), 
2.50/2.67	            app_encode_app(int, nat, number_number_of(nat), 
2.50/2.67	              app_encode_app(int, int, bit0, t)))), t)
2.50/2.67	       != app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m)),
2.50/2.67	    inference('sup-', [status(thm)], ['40', '42'])).
2.50/2.67	tff('44', plain,
2.50/2.67	    ![X0 : int]:
2.50/2.67	      app_encode_app(int, int, 
2.50/2.67	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.50/2.67	          app_encode_app(int, int, 
2.50/2.67	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.50/2.67	              X0), X0)), t)
2.50/2.67	       != app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m)),
2.50/2.67	    inference('sup-', [status(thm)], ['22', '43'])).
2.50/2.67	tff('45', plain, $false,
2.50/2.67	    inference('simplify_reflect-', [status(thm)], ['36', '44'])).
2.50/2.67	
2.50/2.67	% SZS output end Refutation
2.50/2.67	EOF
