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    : 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
0.00/0.19	% Computer   : n188.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 08:18:23 CST 2018
2.27/2.45	% done 945 iterations in 2.247s
2.27/2.45	% SZS status Theorem for 'stdin'
2.27/2.45	% SZS output start Refutation
2.27/2.45	tff(zf_stmt_146, conjecture,
2.27/2.45	  (app_encode_app(int,int,
2.27/2.45	                  app_encode_app(int,app_encode_fun(int,int),
2.27/2.45	                                 times_times(int),
2.27/2.45	                                 app_encode_app(int,int,
2.27/2.45	                                                app_encode_app(int,
2.27/2.45	                                                               app_encode_fun(
2.27/2.45	                                                               int,int),
2.27/2.45	                                                               times_times(
2.27/2.45	                                                               int),
2.27/2.45	                                                               app_encode_app(
2.27/2.45	                                                               int,int,
2.27/2.45	                                                               number_number_of(
2.27/2.45	                                                               int),
2.27/2.45	                                                               app_encode_app(
2.27/2.45	                                                               int,int,bit0,
2.27/2.45	                                                               app_encode_app(
2.27/2.45	                                                               int,int,bit0,
2.27/2.45	                                                               app_encode_app(
2.27/2.45	                                                               int,int,bit1,
2.27/2.45	                                                               pls))))),
2.27/2.45	                                                app_encode_app(int,int,
2.27/2.45	                                                               app_encode_app(
2.27/2.45	                                                               int,
2.27/2.45	                                                               app_encode_fun(
2.27/2.45	                                                               int,int),
2.27/2.45	                                                               plus_plus(int),
2.27/2.45	                                                               one_one(int)),
2.27/2.45	                                                               app_encode_app(
2.27/2.45	                                                               nat,int,
2.27/2.45	                                                               semiring_1_of_nat(
2.27/2.45	                                                               int),n)))),
2.27/2.45	                  m1) =
2.27/2.45	   app_encode_app(int,int,
2.27/2.45	                  app_encode_app(int,app_encode_fun(int,int),plus_plus(int),
2.27/2.45	                                 app_encode_app(int,int,
2.27/2.45	                                                app_encode_app(int,
2.27/2.45	                                                               app_encode_fun(
2.27/2.45	                                                               int,int),
2.27/2.45	                                                               times_times(
2.27/2.45	                                                               int),
2.27/2.45	                                                               app_encode_app(
2.27/2.45	                                                               int,int,
2.27/2.45	                                                               number_number_of(
2.27/2.45	                                                               int),
2.27/2.45	                                                               app_encode_app(
2.27/2.45	                                                               int,int,bit0,
2.27/2.45	                                                               app_encode_app(
2.27/2.45	                                                               int,int,bit0,
2.27/2.45	                                                               app_encode_app(
2.27/2.45	                                                               int,int,bit1,
2.27/2.45	                                                               pls))))),
2.27/2.45	                                                app_encode_app(nat,int,
2.27/2.45	                                                               app_encode_app(
2.27/2.45	                                                               int,
2.27/2.45	                                                               app_encode_fun(
2.27/2.45	                                                               nat,int),
2.27/2.45	                                                               power_power(
2.27/2.45	                                                               int),v),
2.27/2.45	                                                               app_encode_app(
2.27/2.45	                                                               int,nat,
2.27/2.45	                                                               number_number_of(
2.27/2.45	                                                               nat),
2.27/2.45	                                                               app_encode_app(
2.27/2.45	                                                               int,int,bit0,
2.27/2.45	                                                               app_encode_app(
2.27/2.45	                                                               int,int,bit1,
2.27/2.45	                                                               pls)))))),
2.27/2.45	                  app_encode_app(int,int,
2.27/2.45	                                 app_encode_app(int,app_encode_fun(int,int),
2.27/2.45	                                                times_times(int),
2.27/2.45	                                                app_encode_app(int,int,
2.27/2.45	                                                               number_number_of(
2.27/2.45	                                                               int),
2.27/2.45	                                                               app_encode_app(
2.27/2.45	                                                               int,int,bit0,
2.27/2.45	                                                               app_encode_app(
2.27/2.45	                                                               int,int,bit0,
2.27/2.45	                                                               app_encode_app(
2.27/2.45	                                                               int,int,bit1,
2.27/2.45	                                                               pls))))),
2.27/2.45	                                 app_encode_app(nat,int,
2.27/2.45	                                                app_encode_app(int,
2.27/2.45	                                                               app_encode_fun(
2.27/2.45	                                                               nat,int),
2.27/2.45	                                                               power_power(
2.27/2.45	                                                               int),w),
2.27/2.45	                                                app_encode_app(int,nat,
2.27/2.45	                                                               number_number_of(
2.27/2.45	                                                               nat),
2.27/2.45	                                                               app_encode_app(
2.27/2.45	                                                               int,int,bit0,
2.27/2.45	                                                               app_encode_app(
2.27/2.45	                                                               int,int,bit1,
2.27/2.45	                                                               pls)))))))).
2.27/2.45	tff(zf_stmt_0, negated_conjecture,
2.27/2.45	  (app_encode_app(int,int,
2.27/2.45	                  app_encode_app(int,app_encode_fun(int,int),
2.27/2.45	                                 times_times(int),
2.27/2.45	                                 app_encode_app(int,int,
2.27/2.45	                                                app_encode_app(int,
2.27/2.45	                                                               app_encode_fun(
2.27/2.45	                                                               int,int),
2.27/2.45	                                                               times_times(
2.27/2.45	                                                               int),
2.27/2.45	                                                               app_encode_app(
2.27/2.45	                                                               int,int,
2.27/2.45	                                                               number_number_of(
2.27/2.45	                                                               int),
2.27/2.45	                                                               app_encode_app(
2.27/2.45	                                                               int,int,bit0,
2.27/2.45	                                                               app_encode_app(
2.27/2.45	                                                               int,int,bit0,
2.27/2.45	                                                               app_encode_app(
2.27/2.45	                                                               int,int,bit1,
2.27/2.45	                                                               pls))))),
2.27/2.45	                                                app_encode_app(int,int,
2.27/2.45	                                                               app_encode_app(
2.27/2.45	                                                               int,
2.27/2.45	                                                               app_encode_fun(
2.27/2.45	                                                               int,int),
2.27/2.45	                                                               plus_plus(int),
2.27/2.45	                                                               one_one(int)),
2.27/2.45	                                                               app_encode_app(
2.27/2.45	                                                               nat,int,
2.27/2.45	                                                               semiring_1_of_nat(
2.27/2.45	                                                               int),n)))),
2.27/2.45	                  m1) !=
2.27/2.45	   app_encode_app(int,int,
2.27/2.45	                  app_encode_app(int,app_encode_fun(int,int),plus_plus(int),
2.27/2.45	                                 app_encode_app(int,int,
2.27/2.45	                                                app_encode_app(int,
2.27/2.45	                                                               app_encode_fun(
2.27/2.45	                                                               int,int),
2.27/2.45	                                                               times_times(
2.27/2.45	                                                               int),
2.27/2.45	                                                               app_encode_app(
2.27/2.45	                                                               int,int,
2.27/2.45	                                                               number_number_of(
2.27/2.45	                                                               int),
2.27/2.45	                                                               app_encode_app(
2.27/2.45	                                                               int,int,bit0,
2.27/2.45	                                                               app_encode_app(
2.27/2.45	                                                               int,int,bit0,
2.27/2.45	                                                               app_encode_app(
2.27/2.45	                                                               int,int,bit1,
2.27/2.45	                                                               pls))))),
2.27/2.45	                                                app_encode_app(nat,int,
2.27/2.45	                                                               app_encode_app(
2.27/2.45	                                                               int,
2.27/2.45	                                                               app_encode_fun(
2.27/2.45	                                                               nat,int),
2.27/2.45	                                                               power_power(
2.27/2.45	                                                               int),v),
2.27/2.45	                                                               app_encode_app(
2.27/2.45	                                                               int,nat,
2.27/2.45	                                                               number_number_of(
2.27/2.45	                                                               nat),
2.27/2.45	                                                               app_encode_app(
2.27/2.45	                                                               int,int,bit0,
2.27/2.45	                                                               app_encode_app(
2.27/2.45	                                                               int,int,bit1,
2.27/2.45	                                                               pls)))))),
2.27/2.45	                  app_encode_app(int,int,
2.27/2.45	                                 app_encode_app(int,app_encode_fun(int,int),
2.27/2.45	                                                times_times(int),
2.27/2.45	                                                app_encode_app(int,int,
2.27/2.45	                                                               number_number_of(
2.27/2.45	                                                               int),
2.27/2.45	                                                               app_encode_app(
2.27/2.45	                                                               int,int,bit0,
2.27/2.45	                                                               app_encode_app(
2.27/2.45	                                                               int,int,bit0,
2.27/2.45	                                                               app_encode_app(
2.27/2.45	                                                               int,int,bit1,
2.27/2.45	                                                               pls))))),
2.27/2.45	                                 app_encode_app(nat,int,
2.27/2.45	                                                app_encode_app(int,
2.27/2.45	                                                               app_encode_fun(
2.27/2.45	                                                               nat,int),
2.27/2.45	                                                               power_power(
2.27/2.45	                                                               int),w),
2.27/2.45	                                                app_encode_app(int,nat,
2.27/2.45	                                                               number_number_of(
2.27/2.45	                                                               nat),
2.27/2.45	                                                               app_encode_app(
2.27/2.45	                                                               int,int,bit0,
2.27/2.45	                                                               app_encode_app(
2.27/2.45	                                                               int,int,bit1,
2.27/2.45	                                                               pls)))))))).
2.27/2.45	tff('0', plain,
2.27/2.45	    app_encode_app(int, int, 
2.27/2.45	      app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.27/2.45	        app_encode_app(int, int, 
2.27/2.45	          app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.27/2.45	            app_encode_app(int, int, number_number_of(int), 
2.27/2.45	              app_encode_app(int, int, bit0, 
2.27/2.45	                app_encode_app(int, int, bit0, 
2.27/2.45	                  app_encode_app(int, int, bit1, pls))))), 
2.27/2.45	          app_encode_app(int, int, 
2.27/2.45	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.27/2.45	              one_one(int)), 
2.27/2.45	            app_encode_app(nat, int, semiring_1_of_nat(int), n)))), m1)
2.27/2.45	     != app_encode_app(int, int, 
2.27/2.45	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.27/2.45	            app_encode_app(int, int, 
2.27/2.45	              app_encode_app(int, app_encode_fun(int, int), 
2.27/2.45	                times_times(int), 
2.27/2.45	                app_encode_app(int, int, number_number_of(int), 
2.27/2.45	                  app_encode_app(int, int, bit0, 
2.27/2.45	                    app_encode_app(int, int, bit0, 
2.27/2.45	                      app_encode_app(int, int, bit1, pls))))), 
2.27/2.45	              app_encode_app(nat, int, 
2.27/2.45	                app_encode_app(int, app_encode_fun(nat, int), 
2.27/2.45	                  power_power(int), v), 
2.27/2.45	                app_encode_app(int, nat, number_number_of(nat), 
2.27/2.45	                  app_encode_app(int, int, bit0, 
2.27/2.45	                    app_encode_app(int, int, bit1, pls)))))), 
2.27/2.45	          app_encode_app(int, int, 
2.27/2.45	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.27/2.45	              app_encode_app(int, int, number_number_of(int), 
2.27/2.45	                app_encode_app(int, int, bit0, 
2.27/2.45	                  app_encode_app(int, int, bit0, 
2.27/2.45	                    app_encode_app(int, int, bit1, pls))))), 
2.27/2.45	            app_encode_app(nat, int, 
2.27/2.45	              app_encode_app(int, app_encode_fun(nat, int), 
2.27/2.45	                power_power(int), w), 
2.27/2.45	              app_encode_app(int, nat, number_number_of(nat), 
2.27/2.45	                app_encode_app(int, int, bit0, 
2.27/2.45	                  app_encode_app(int, int, bit1, pls)))))),
2.27/2.45	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.27/2.45	tff(zf_stmt_122, axiom,
2.27/2.45	  (one_one(int) =
2.27/2.45	   app_encode_app(int,int,number_number_of(int),
2.27/2.45	                  app_encode_app(int,int,bit1,pls)))).
2.27/2.45	tff('1', plain,
2.27/2.45	    one_one(int)
2.27/2.45	     = app_encode_app(int, int, number_number_of(int), 
2.27/2.45	         app_encode_app(int, int, bit1, pls)),
2.27/2.45	    inference('cnf', [status(esa)], [zf_stmt_122])).
2.27/2.45	tff(zf_stmt_101, axiom,
2.27/2.45	  (![K:int]: (app_encode_app(int,int,number_number_of(int),K) = K))).
2.27/2.45	tff('2', plain,
2.27/2.45	    ![X147 : int]:
2.27/2.45	      app_encode_app(int, int, number_number_of(int), X147) = X147,
2.27/2.45	    inference('cnf', [status(esa)], [zf_stmt_101])).
2.27/2.45	tff('3', plain, one_one(int) = app_encode_app(int, int, bit1, pls),
2.27/2.45	    inference('demod', [status(thm)], ['1', '2'])).
2.27/2.45	tff(zf_stmt_63, axiom,
2.27/2.45	  (![L1:int,K:int]:
2.27/2.45	     (app_encode_app(int,int,
2.27/2.45	                     app_encode_app(int,app_encode_fun(int,int),
2.27/2.45	                                    times_times(int),
2.27/2.45	                                    app_encode_app(int,int,bit0,K)),
2.27/2.45	                     L1) =
2.27/2.45	      app_encode_app(int,int,bit0,
2.27/2.45	                     app_encode_app(int,int,
2.27/2.45	                                    app_encode_app(int,
2.27/2.45	                                                   app_encode_fun(int,int),
2.27/2.45	                                                   times_times(int),K),
2.27/2.45	                                    L1))))).
2.27/2.45	tff('4', plain,
2.27/2.45	    ![X51 : int, X52 : int]:
2.27/2.45	      app_encode_app(int, int, 
2.27/2.45	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.27/2.45	          app_encode_app(int, int, bit0, X51)), X52)
2.27/2.45	       = app_encode_app(int, int, bit0, 
2.27/2.45	           app_encode_app(int, int, 
2.27/2.45	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.27/2.45	               X51), X52)),
2.27/2.45	    inference('cnf', [status(esa)], [zf_stmt_63])).
2.27/2.45	tff(zf_stmt_62, axiom,
2.27/2.45	  (![W:int]:
2.27/2.45	     (app_encode_app(int,int,
2.27/2.45	                     app_encode_app(int,app_encode_fun(int,int),
2.27/2.45	                                    times_times(int),pls),
2.27/2.45	                     W) =
2.27/2.45	      pls))).
2.27/2.45	tff('5', plain,
2.27/2.45	    ![X50 : int]:
2.27/2.45	      app_encode_app(int, int, 
2.27/2.45	        app_encode_app(int, app_encode_fun(int, int), times_times(int), pls), 
2.27/2.45	        X50)
2.27/2.45	       = pls,
2.27/2.45	    inference('cnf', [status(esa)], [zf_stmt_62])).
2.27/2.45	tff(zf_stmt_41, axiom,
2.27/2.45	  (![L1:int,K:int]:
2.27/2.45	     (app_encode_app(int,int,
2.27/2.45	                     app_encode_app(int,app_encode_fun(int,int),
2.27/2.45	                                    times_times(int),
2.27/2.45	                                    app_encode_app(int,int,bit1,K)),
2.27/2.45	                     L1) =
2.27/2.45	      app_encode_app(int,int,
2.27/2.45	                     app_encode_app(int,app_encode_fun(int,int),
2.27/2.45	                                    plus_plus(int),
2.27/2.45	                                    app_encode_app(int,int,bit0,
2.27/2.45	                                                   app_encode_app(int,int,
2.27/2.45	                                                                  app_encode_app(
2.27/2.45	                                                                  int,
2.27/2.45	                                                                  app_encode_fun(
2.27/2.45	                                                                  int,int),
2.27/2.45	                                                                  times_times(
2.27/2.45	                                                                  int),K),L1))),
2.27/2.45	                     L1)))).
2.27/2.45	tff('6', plain,
2.27/2.45	    ![X12 : int, X13 : int]:
2.27/2.45	      app_encode_app(int, int, 
2.27/2.45	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.27/2.45	          app_encode_app(int, int, bit1, X12)), X13)
2.27/2.45	       = app_encode_app(int, int, 
2.27/2.45	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.27/2.45	             app_encode_app(int, int, bit0, 
2.27/2.45	               app_encode_app(int, int, 
2.27/2.45	                 app_encode_app(int, app_encode_fun(int, int), 
2.27/2.45	                   times_times(int), X12), X13))), X13),
2.27/2.45	    inference('cnf', [status(esa)], [zf_stmt_41])).
2.27/2.45	tff('7', plain,
2.27/2.45	    ![X0 : int]:
2.27/2.45	      app_encode_app(int, int, 
2.27/2.45	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.27/2.45	          app_encode_app(int, int, bit1, pls)), X0)
2.27/2.45	       = app_encode_app(int, int, 
2.27/2.45	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.27/2.45	             app_encode_app(int, int, bit0, pls)), X0),
2.27/2.45	    inference('sup+', [status(thm)], ['5', '6'])).
2.27/2.45	tff(zf_stmt_58, axiom, (app_encode_app(int,int,bit0,pls) = pls)).
2.27/2.45	tff('8', plain, app_encode_app(int, int, bit0, pls) = pls,
2.27/2.45	    inference('cnf', [status(esa)], [zf_stmt_58])).
2.27/2.45	tff(zf_stmt_105, axiom,
2.27/2.45	  (![K:int]:
2.27/2.45	     (app_encode_app(int,int,
2.27/2.45	                     app_encode_app(int,app_encode_fun(int,int),
2.27/2.45	                                    plus_plus(int),pls),
2.27/2.45	                     K) =
2.27/2.45	      K))).
2.27/2.45	tff('9', plain,
2.27/2.45	    ![X155 : int]:
2.27/2.45	      app_encode_app(int, int, 
2.27/2.45	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
2.27/2.45	        X155)
2.27/2.45	       = X155,
2.27/2.45	    inference('cnf', [status(esa)], [zf_stmt_105])).
2.27/2.45	tff('10', plain,
2.27/2.45	    ![X0 : int]:
2.27/2.45	      app_encode_app(int, int, 
2.27/2.45	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.27/2.45	          one_one(int)), X0)
2.27/2.45	       = X0,
2.27/2.45	    inference('demod', [status(thm)], ['7', '3', '8', '9'])).
2.27/2.45	tff(zf_stmt_2, axiom,
2.27/2.45	  (![X:app_encode_fun(Alpha,Beta),Y:app_encode_fun(Alpha,Beta)]:
2.27/2.45	     ((![Z:Alpha]:
2.27/2.45	         (app_encode_app(Alpha,Beta,X,Z) = app_encode_app(Alpha,Beta,Y,Z))) =>
2.27/2.45	      (X = Y)))).
2.27/2.45	tff('11', plain,
2.27/2.45	    ![X0 : $tType, X1 : $tType, X2 : app_encode_fun(X0, X1), 
2.27/2.45	      X3 : app_encode_fun(X0, X1)]:
2.27/2.45	      (X3 = X2
2.27/2.45	       | app_encode_app(X0, X1, X3, sk_Z(X1, X0, X2, X3))
2.27/2.45	          != app_encode_app(X0, X1, X2, sk_Z(X1, X0, X2, X3))),
2.27/2.45	    inference('cnf', [status(esa)], [zf_stmt_2])).
2.27/2.45	tff('12', plain,
2.27/2.45	    ![X0 : app_encode_fun(int, int)]:
2.27/2.45	      (app_encode_app(int, int, X0, 
2.27/2.45	         sk_Z(int, int, number_number_of(int), X0))
2.27/2.45	        != sk_Z(int, int, number_number_of(int), X0)
2.27/2.45	       | X0 = number_number_of(int)),
2.27/2.45	    inference('sup-', [status(thm)], ['2', '11'])).
2.27/2.45	tff('13', plain,
2.27/2.45	    (sk_Z(int, int, number_number_of(int), 
2.27/2.45	       app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.27/2.45	         one_one(int)))
2.27/2.45	      != sk_Z(int, int, number_number_of(int), 
2.27/2.45	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.27/2.45	             one_one(int)))
2.27/2.45	     | app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.27/2.45	         one_one(int))
2.27/2.45	        = number_number_of(int)),
2.27/2.45	    inference('sup-', [status(thm)], ['10', '12'])).
2.27/2.45	tff('14', plain,
2.27/2.45	    app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.27/2.45	      one_one(int))
2.27/2.45	     = number_number_of(int),
2.27/2.45	    inference('simplify', [status(thm)], ['13'])).
2.27/2.45	tff(zf_stmt_65, axiom,
2.27/2.45	  (![B:$tType]:
2.27/2.45	     ((number(B) & semiring(B)) =>
2.27/2.45	      (![V:int,B1:B,A1:B]:
2.27/2.45	         (app_encode_app(B,B,
2.27/2.45	                         app_encode_app(B,app_encode_fun(B,B),times_times(B),
2.27/2.45	                                        app_encode_app(B,B,
2.27/2.45	                                                       app_encode_app(
2.27/2.45	                                                       B,app_encode_fun(B,B),
2.27/2.45	                                                       plus_plus(B),A1),B1)),
2.27/2.45	                         app_encode_app(int,B,number_number_of(B),V)) =
2.27/2.45	          app_encode_app(B,B,
2.27/2.45	                         app_encode_app(B,app_encode_fun(B,B),plus_plus(B),
2.27/2.45	                                        app_encode_app(B,B,
2.27/2.45	                                                       app_encode_app(
2.27/2.45	                                                       B,app_encode_fun(B,B),
2.27/2.45	                                                       times_times(B),A1),
2.27/2.45	                                                       app_encode_app(
2.27/2.45	                                                       int,B,
2.27/2.45	                                                       number_number_of(B),V))),
2.27/2.45	                         app_encode_app(B,B,
2.27/2.45	                                        app_encode_app(B,app_encode_fun(B,B),
2.27/2.45	                                                       times_times(B),B1),
2.27/2.45	                                        app_encode_app(int,B,
2.27/2.45	                                                       number_number_of(B),V)))))))).
2.27/2.45	tff('15', plain,
2.27/2.45	    ![X55 : $tType, X56 : X55, X57 : int, X58 : X55]:
2.27/2.45	      (app_encode_app(X55, X55, 
2.27/2.45	         app_encode_app(X55, app_encode_fun(X55, X55), times_times(X55), 
2.27/2.45	           app_encode_app(X55, X55, 
2.27/2.45	             app_encode_app(X55, app_encode_fun(X55, X55), plus_plus(X55), 
2.27/2.45	               X56), X58)), 
2.27/2.45	         app_encode_app(int, X55, number_number_of(X55), X57))
2.27/2.45	        = app_encode_app(X55, X55, 
2.27/2.45	            app_encode_app(X55, app_encode_fun(X55, X55), plus_plus(X55), 
2.27/2.45	              app_encode_app(X55, X55, 
2.27/2.45	                app_encode_app(X55, app_encode_fun(X55, X55), 
2.27/2.45	                  times_times(X55), X56), 
2.27/2.45	                app_encode_app(int, X55, number_number_of(X55), X57))), 
2.27/2.45	            app_encode_app(X55, X55, 
2.27/2.45	              app_encode_app(X55, app_encode_fun(X55, X55), 
2.27/2.45	                times_times(X55), X58), 
2.27/2.45	              app_encode_app(int, X55, number_number_of(X55), X57)))
2.27/2.45	       | ~ semiring(X55)
2.27/2.45	       | ~ number(X55)),
2.27/2.45	    inference('cnf', [status(esa)], [zf_stmt_65])).
2.27/2.45	tff('16', plain,
2.27/2.45	    ![X0 : int, X1 : int]:
2.27/2.45	      (app_encode_app(int, int, 
2.27/2.45	         app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.27/2.45	           app_encode_app(int, int, 
2.27/2.45	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.27/2.45	               one_one(int)), X1)), 
2.27/2.45	         app_encode_app(int, int, number_number_of(int), X0))
2.27/2.45	        = app_encode_app(int, int, 
2.27/2.45	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.27/2.45	              app_encode_app(int, int, number_number_of(int), 
2.27/2.45	                app_encode_app(int, int, number_number_of(int), X0))), 
2.27/2.45	            app_encode_app(int, int, 
2.27/2.45	              app_encode_app(int, app_encode_fun(int, int), 
2.27/2.45	                times_times(int), X1), 
2.27/2.45	              app_encode_app(int, int, number_number_of(int), X0)))
2.27/2.45	       | ~ number(int)
2.27/2.45	       | ~ semiring(int)),
2.27/2.45	    inference('sup+', [status(thm)], ['14', '15'])).
2.27/2.45	tff(zf_stmt_138, axiom, (number(int))).
2.27/2.45	tff('17', plain, number(int), inference('cnf', [status(esa)], [zf_stmt_138])).
2.27/2.45	tff(zf_stmt_137, axiom, (semiring(int))).
2.27/2.45	tff('18', plain, semiring(int),
2.27/2.45	    inference('cnf', [status(esa)], [zf_stmt_137])).
2.27/2.45	tff('19', plain,
2.27/2.45	    ![X0 : int, X1 : int]:
2.27/2.45	      (app_encode_app(int, int, 
2.27/2.45	         app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.27/2.45	           app_encode_app(int, int, 
2.27/2.45	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.27/2.45	               one_one(int)), X1)), X0)
2.27/2.45	        = app_encode_app(int, int, 
2.27/2.45	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
2.27/2.45	            app_encode_app(int, int, 
2.27/2.45	              app_encode_app(int, app_encode_fun(int, int), 
2.27/2.45	                times_times(int), X1), X0))
2.27/2.45	       | ~ $true
2.27/2.45	       | ~ $true),
2.27/2.45	    inference('demod', [status(thm)], ['16', '2', '2', '2', '2', '17', '18'])).
2.27/2.45	tff('20', plain,
2.27/2.45	    ![X0 : int, X1 : int]:
2.27/2.45	      app_encode_app(int, int, 
2.27/2.45	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.27/2.45	          app_encode_app(int, int, 
2.27/2.45	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.27/2.45	              one_one(int)), X1)), X0)
2.27/2.45	       = app_encode_app(int, int, 
2.27/2.45	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
2.27/2.45	           app_encode_app(int, int, 
2.27/2.45	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.27/2.45	               X1), X0)),
2.27/2.45	    inference('simplify', [status(thm)], ['19'])).
2.27/2.45	tff(zf_stmt_36, axiom,
2.27/2.45	  (![B:$tType]:
2.27/2.45	     ((monoid_mult(B) & number(B)) =>
2.27/2.45	      (![W:int]:
2.27/2.45	         (app_encode_app(nat,B,
2.27/2.45	                         app_encode_app(B,app_encode_fun(nat,B),
2.27/2.45	                                        power_power(B),
2.27/2.45	                                        app_encode_app(int,B,
2.27/2.45	                                                       number_number_of(B),W)),
2.27/2.45	                         app_encode_app(int,nat,number_number_of(nat),
2.27/2.45	                                        app_encode_app(int,int,bit0,
2.27/2.45	                                                       app_encode_app(
2.27/2.45	                                                       int,int,bit1,pls)))) =
2.27/2.45	          app_encode_app(B,B,
2.27/2.45	                         app_encode_app(B,app_encode_fun(B,B),times_times(B),
2.27/2.45	                                        app_encode_app(int,B,
2.27/2.45	                                                       number_number_of(B),W)),
2.27/2.45	                         app_encode_app(int,B,number_number_of(B),W))))))).
2.27/2.45	tff('21', plain,
2.27/2.45	    ![X4 : $tType, X5 : int]:
2.27/2.45	      (app_encode_app(nat, X4, 
2.27/2.45	         app_encode_app(X4, app_encode_fun(nat, X4), power_power(X4), 
2.27/2.45	           app_encode_app(int, X4, number_number_of(X4), X5)), 
2.27/2.45	         app_encode_app(int, nat, number_number_of(nat), 
2.27/2.45	           app_encode_app(int, int, bit0, 
2.27/2.45	             app_encode_app(int, int, bit1, pls))))
2.27/2.45	        = app_encode_app(X4, X4, 
2.27/2.45	            app_encode_app(X4, app_encode_fun(X4, X4), times_times(X4), 
2.27/2.45	              app_encode_app(int, X4, number_number_of(X4), X5)), 
2.27/2.45	            app_encode_app(int, X4, number_number_of(X4), X5))
2.27/2.45	       | ~ number(X4)
2.27/2.45	       | ~ monoid_mult(X4)),
2.27/2.45	    inference('cnf', [status(esa)], [zf_stmt_36])).
2.27/2.45	tff('22', plain,
2.27/2.45	    ![X4 : $tType, X5 : int]:
2.27/2.45	      (app_encode_app(nat, X4, 
2.27/2.45	         app_encode_app(X4, app_encode_fun(nat, X4), power_power(X4), 
2.27/2.45	           app_encode_app(int, X4, number_number_of(X4), X5)), 
2.27/2.45	         app_encode_app(int, nat, number_number_of(nat), 
2.27/2.45	           app_encode_app(int, int, bit0, one_one(int))))
2.27/2.45	        = app_encode_app(X4, X4, 
2.27/2.45	            app_encode_app(X4, app_encode_fun(X4, X4), times_times(X4), 
2.27/2.45	              app_encode_app(int, X4, number_number_of(X4), X5)), 
2.27/2.45	            app_encode_app(int, X4, number_number_of(X4), X5))
2.27/2.45	       | ~ number(X4)
2.27/2.45	       | ~ monoid_mult(X4)),
2.27/2.45	    inference('demod', [status(thm)], ['21', '3'])).
2.27/2.45	tff('23', plain,
2.27/2.45	    ![X0 : int]:
2.27/2.45	      (app_encode_app(nat, int, 
2.27/2.45	         app_encode_app(int, app_encode_fun(nat, int), power_power(int), X0), 
2.27/2.45	         app_encode_app(int, nat, number_number_of(nat), 
2.27/2.45	           app_encode_app(int, int, bit0, one_one(int))))
2.27/2.45	        = app_encode_app(int, int, 
2.27/2.45	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.27/2.45	              app_encode_app(int, int, number_number_of(int), X0)), 
2.27/2.45	            app_encode_app(int, int, number_number_of(int), X0))
2.27/2.45	       | ~ monoid_mult(int)
2.27/2.45	       | ~ number(int)),
2.27/2.45	    inference('sup+', [status(thm)], ['2', '22'])).
2.27/2.45	tff(zf_stmt_133, axiom, (monoid_mult(int))).
2.27/2.45	tff('24', plain, monoid_mult(int),
2.27/2.45	    inference('cnf', [status(esa)], [zf_stmt_133])).
2.27/2.45	tff('25', plain,
2.27/2.45	    ![X0 : int]:
2.27/2.45	      (app_encode_app(nat, int, 
2.27/2.45	         app_encode_app(int, app_encode_fun(nat, int), power_power(int), X0), 
2.27/2.45	         app_encode_app(int, nat, number_number_of(nat), 
2.27/2.45	           app_encode_app(int, int, bit0, one_one(int))))
2.27/2.45	        = app_encode_app(int, int, 
2.27/2.45	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.27/2.45	              X0), X0)
2.27/2.45	       | ~ $true
2.27/2.45	       | ~ $true),
2.27/2.45	    inference('demod', [status(thm)], ['23', '2', '2', '24', '17'])).
2.27/2.45	tff('26', plain,
2.27/2.45	    ![X0 : int]:
2.27/2.45	      app_encode_app(nat, int, 
2.27/2.45	        app_encode_app(int, app_encode_fun(nat, int), power_power(int), X0), 
2.27/2.45	        app_encode_app(int, nat, number_number_of(nat), 
2.27/2.45	          app_encode_app(int, int, bit0, one_one(int))))
2.27/2.45	       = app_encode_app(int, int, 
2.27/2.45	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.27/2.45	             X0), X0),
2.27/2.45	    inference('simplify', [status(thm)], ['25'])).
2.27/2.45	tff(zf_stmt_64, axiom,
2.27/2.45	  (![L1:int,K:int]:
2.27/2.45	     (app_encode_app(int,int,
2.27/2.45	                     app_encode_app(int,app_encode_fun(int,int),
2.27/2.45	                                    plus_plus(int),
2.27/2.45	                                    app_encode_app(int,int,bit0,K)),
2.27/2.45	                     app_encode_app(int,int,bit0,L1)) =
2.27/2.45	      app_encode_app(int,int,bit0,
2.27/2.45	                     app_encode_app(int,int,
2.27/2.45	                                    app_encode_app(int,
2.27/2.45	                                                   app_encode_fun(int,int),
2.27/2.45	                                                   plus_plus(int),K),
2.27/2.45	                                    L1))))).
2.27/2.45	tff('27', plain,
2.27/2.45	    ![X53 : int, X54 : int]:
2.27/2.45	      app_encode_app(int, int, 
2.27/2.45	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.27/2.45	          app_encode_app(int, int, bit0, X53)), 
2.27/2.45	        app_encode_app(int, int, bit0, X54))
2.27/2.45	       = app_encode_app(int, int, bit0, 
2.27/2.45	           app_encode_app(int, int, 
2.27/2.45	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.27/2.45	               X53), X54)),
2.27/2.45	    inference('cnf', [status(esa)], [zf_stmt_64])).
2.27/2.45	tff('28', plain,
2.27/2.45	    app_encode_app(int, int, bit0, 
2.27/2.45	      app_encode_app(int, int, bit0, 
2.27/2.45	        app_encode_app(int, int, 
2.27/2.45	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), m1), 
2.27/2.45	          app_encode_app(int, int, 
2.27/2.45	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.27/2.45	              app_encode_app(nat, int, semiring_1_of_nat(int), n)), m1))))
2.27/2.45	     != app_encode_app(int, int, bit0, 
2.27/2.45	          app_encode_app(int, int, bit0, 
2.27/2.45	            app_encode_app(int, int, 
2.27/2.45	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.27/2.45	                app_encode_app(int, int, 
2.27/2.45	                  app_encode_app(int, app_encode_fun(int, int), 
2.27/2.45	                    times_times(int), v), v)), 
2.27/2.45	              app_encode_app(int, int, 
2.27/2.45	                app_encode_app(int, app_encode_fun(int, int), 
2.27/2.45	                  times_times(int), w), w)))),
2.27/2.45	    inference('demod', [status(thm)],
2.27/2.45	              ['0', '3', '2', '4', '4', '14', '2', '4', '4', '20', '3', '2', 
2.27/2.45	               '3', '26', '4', '4', '14', '2', '3', '2', '3', '26', '4', 
2.27/2.45	               '4', '14', '2', '27', '27'])).
2.27/2.45	tff(zf_stmt_33, axiom,
2.27/2.45	  (app_encode_app(int,int,
2.27/2.45	                  app_encode_app(int,app_encode_fun(int,int),plus_plus(int),
2.27/2.45	                                 app_encode_app(nat,int,
2.27/2.45	                                                app_encode_app(int,
2.27/2.45	                                                               app_encode_fun(
2.27/2.45	                                                               nat,int),
2.27/2.45	                                                               power_power(
2.27/2.45	                                                               int),v),
2.27/2.45	                                                app_encode_app(int,nat,
2.27/2.45	                                                               number_number_of(
2.27/2.45	                                                               nat),
2.27/2.45	                                                               app_encode_app(
2.27/2.45	                                                               int,int,bit0,
2.27/2.45	                                                               app_encode_app(
2.27/2.45	                                                               int,int,bit1,
2.27/2.45	                                                               pls))))),
2.27/2.45	                  app_encode_app(nat,int,
2.27/2.45	                                 app_encode_app(int,app_encode_fun(nat,int),
2.27/2.45	                                                power_power(int),w),
2.27/2.45	                                 app_encode_app(int,nat,
2.27/2.45	                                                number_number_of(nat),
2.27/2.45	                                                app_encode_app(int,int,bit0,
2.27/2.45	                                                               app_encode_app(
2.27/2.45	                                                               int,int,bit1,
2.27/2.45	                                                               pls))))) =
2.27/2.45	   app_encode_app(int,int,
2.27/2.45	                  app_encode_app(int,app_encode_fun(int,int),
2.27/2.45	                                 times_times(int),
2.27/2.45	                                 app_encode_app(int,int,
2.27/2.45	                                                app_encode_app(int,
2.27/2.45	                                                               app_encode_fun(
2.27/2.45	                                                               int,int),
2.27/2.45	                                                               plus_plus(int),
2.27/2.45	                                                               one_one(int)),
2.27/2.45	                                                app_encode_app(nat,int,
2.27/2.45	                                                               semiring_1_of_nat(
2.27/2.45	                                                               int),n))),
2.27/2.45	                  m1))).
2.27/2.45	tff('29', plain,
2.27/2.45	    app_encode_app(int, int, 
2.27/2.45	      app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.27/2.45	        app_encode_app(nat, int, 
2.27/2.45	          app_encode_app(int, app_encode_fun(nat, int), power_power(int), v), 
2.27/2.45	          app_encode_app(int, nat, number_number_of(nat), 
2.27/2.45	            app_encode_app(int, int, bit0, 
2.27/2.45	              app_encode_app(int, int, bit1, pls))))), 
2.27/2.45	      app_encode_app(nat, int, 
2.27/2.45	        app_encode_app(int, app_encode_fun(nat, int), power_power(int), w), 
2.27/2.45	        app_encode_app(int, nat, number_number_of(nat), 
2.27/2.45	          app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls)))))
2.27/2.45	     = app_encode_app(int, int, 
2.27/2.45	         app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.27/2.45	           app_encode_app(int, int, 
2.27/2.45	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.27/2.45	               one_one(int)), 
2.27/2.45	             app_encode_app(nat, int, semiring_1_of_nat(int), n))), m1),
2.27/2.45	    inference('cnf', [status(esa)], [zf_stmt_33])).
2.27/2.45	tff('30', plain,
2.27/2.45	    app_encode_app(int, int, 
2.27/2.45	      app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.27/2.45	        app_encode_app(nat, int, 
2.27/2.45	          app_encode_app(int, app_encode_fun(nat, int), power_power(int), v), 
2.27/2.45	          app_encode_app(int, nat, number_number_of(nat), 
2.27/2.45	            app_encode_app(int, int, bit0, one_one(int))))), 
2.27/2.45	      app_encode_app(nat, int, 
2.27/2.45	        app_encode_app(int, app_encode_fun(nat, int), power_power(int), w), 
2.27/2.45	        app_encode_app(int, nat, number_number_of(nat), 
2.27/2.45	          app_encode_app(int, int, bit0, one_one(int)))))
2.27/2.45	     = app_encode_app(int, int, 
2.27/2.45	         app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.27/2.45	           app_encode_app(int, int, 
2.27/2.45	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.27/2.45	               one_one(int)), 
2.27/2.45	             app_encode_app(nat, int, semiring_1_of_nat(int), n))), m1),
2.27/2.45	    inference('demod', [status(thm)], ['29', '3', '3'])).
2.27/2.45	tff('31', plain,
2.27/2.45	    app_encode_app(int, int, 
2.27/2.45	      app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.27/2.45	        app_encode_app(int, int, 
2.27/2.45	          app_encode_app(int, app_encode_fun(int, int), times_times(int), v), 
2.27/2.45	          v)), 
2.27/2.45	      app_encode_app(int, int, 
2.27/2.45	        app_encode_app(int, app_encode_fun(int, int), times_times(int), w), 
2.27/2.45	        w))
2.27/2.45	     = app_encode_app(int, int, 
2.27/2.45	         app_encode_app(int, app_encode_fun(int, int), plus_plus(int), m1), 
2.27/2.45	         app_encode_app(int, int, 
2.27/2.45	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.27/2.45	             app_encode_app(nat, int, semiring_1_of_nat(int), n)), m1)),
2.27/2.45	    inference('demod', [status(thm)], ['30', '26', '26', '20'])).
2.27/2.45	tff('32', plain,
2.27/2.45	    app_encode_app(int, int, bit0, 
2.27/2.45	      app_encode_app(int, int, bit0, 
2.27/2.45	        app_encode_app(int, int, 
2.27/2.45	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), m1), 
2.27/2.45	          app_encode_app(int, int, 
2.27/2.45	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.27/2.45	              app_encode_app(nat, int, semiring_1_of_nat(int), n)), m1))))
2.27/2.45	     != app_encode_app(int, int, bit0, 
2.27/2.45	          app_encode_app(int, int, bit0, 
2.27/2.45	            app_encode_app(int, int, 
2.27/2.45	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.27/2.45	                m1), 
2.27/2.45	              app_encode_app(int, int, 
2.27/2.45	                app_encode_app(int, app_encode_fun(int, int), 
2.27/2.45	                  times_times(int), 
2.27/2.45	                  app_encode_app(nat, int, semiring_1_of_nat(int), n)), m1)))),
2.27/2.45	    inference('demod', [status(thm)], ['28', '31'])).
2.27/2.45	tff('33', plain, $false, inference('simplify', [status(thm)], ['32'])).
2.27/2.45	
2.27/2.45	% SZS output end Refutation
2.27/2.45	EOF
