0.00/0.00	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : appext
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : rpo6
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.20	% Computer   : n139.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 07:49:08 CST 2018
2.99/3.16	% done 1213 iterations in 2.961s
2.99/3.16	% SZS status Theorem for 'stdin'
2.99/3.16	% SZS output start Refutation
2.99/3.17	tff(zf_stmt_31, axiom,
2.99/3.17	  (?[X1:int]:
2.99/3.17	     (app_encode_app(int,$o,
2.99/3.17	                     app_encode_app(int,app_encode_fun(int,$o),
2.99/3.17	                                    ord_less_eq(int),zero_zero(int)),
2.99/3.17	                     X1) & 
2.99/3.17	      app_encode_app(int,$o,
2.99/3.17	                     app_encode_app(int,app_encode_fun(int,$o),ord_less(int),
2.99/3.17	                                    X1),
2.99/3.17	                     app_encode_app(int,int,
2.99/3.17	                                    app_encode_app(int,
2.99/3.17	                                                   app_encode_fun(int,int),
2.99/3.17	                                                   plus_plus(int),
2.99/3.17	                                                   app_encode_app(int,int,
2.99/3.17	                                                                  app_encode_app(
2.99/3.17	                                                                  int,
2.99/3.17	                                                                  app_encode_fun(
2.99/3.17	                                                                  int,int),
2.99/3.17	                                                                  times_times(
2.99/3.17	                                                                  int),
2.99/3.17	                                                                  app_encode_app(
2.99/3.17	                                                                  int,int,
2.99/3.17	                                                                  number_number_of(
2.99/3.17	                                                                  int),
2.99/3.17	                                                                  app_encode_app(
2.99/3.17	                                                                  int,int,
2.99/3.17	                                                                  bit0,
2.99/3.17	                                                                  app_encode_app(
2.99/3.17	                                                                  int,int,
2.99/3.17	                                                                  bit0,
2.99/3.17	                                                                  app_encode_app(
2.99/3.17	                                                                  int,int,
2.99/3.17	                                                                  bit1,pls))))),
2.99/3.17	                                                                  m)),
2.99/3.17	                                    one_one(int))) & 
2.99/3.17	      app_encode_app(int,$o,
2.99/3.17	                     app_encode_app(int,app_encode_fun(int,$o),
2.99/3.17	                                    app_encode_app(int,
2.99/3.17	                                                   app_encode_fun(int,
2.99/3.17	                                                                  app_encode_fun(
2.99/3.17	                                                                  int,$o)),
2.99/3.17	                                                   zcong,s1),
2.99/3.17	                                    X1),
2.99/3.17	                     app_encode_app(int,int,
2.99/3.17	                                    app_encode_app(int,
2.99/3.17	                                                   app_encode_fun(int,int),
2.99/3.17	                                                   plus_plus(int),
2.99/3.17	                                                   app_encode_app(int,int,
2.99/3.17	                                                                  app_encode_app(
2.99/3.17	                                                                  int,
2.99/3.17	                                                                  app_encode_fun(
2.99/3.17	                                                                  int,int),
2.99/3.17	                                                                  times_times(
2.99/3.17	                                                                  int),
2.99/3.17	                                                                  app_encode_app(
2.99/3.17	                                                                  int,int,
2.99/3.17	                                                                  number_number_of(
2.99/3.17	                                                                  int),
2.99/3.17	                                                                  app_encode_app(
2.99/3.17	                                                                  int,int,
2.99/3.17	                                                                  bit0,
2.99/3.17	                                                                  app_encode_app(
2.99/3.17	                                                                  int,int,
2.99/3.17	                                                                  bit0,
2.99/3.17	                                                                  app_encode_app(
2.99/3.17	                                                                  int,int,
2.99/3.17	                                                                  bit1,pls))))),
2.99/3.17	                                                                  m)),
2.99/3.17	                                    one_one(int))) & 
2.99/3.17	      (![Y1:int]:
2.99/3.17	         ((app_encode_app(int,$o,
2.99/3.17	                          app_encode_app(int,app_encode_fun(int,$o),
2.99/3.17	                                         ord_less_eq(int),zero_zero(int)),
2.99/3.17	                          Y1) & 
2.99/3.17	           app_encode_app(int,$o,
2.99/3.17	                          app_encode_app(int,app_encode_fun(int,$o),
2.99/3.17	                                         ord_less(int),Y1),
2.99/3.17	                          app_encode_app(int,int,
2.99/3.17	                                         app_encode_app(int,
2.99/3.17	                                                        app_encode_fun(
2.99/3.17	                                                        int,int),
2.99/3.17	                                                        plus_plus(int),
2.99/3.17	                                                        app_encode_app(
2.99/3.17	                                                        int,int,
2.99/3.17	                                                        app_encode_app(
2.99/3.17	                                                        int,
2.99/3.17	                                                        app_encode_fun(
2.99/3.17	                                                        int,int),
2.99/3.17	                                                        times_times(int),
2.99/3.17	                                                        app_encode_app(
2.99/3.17	                                                        int,int,
2.99/3.17	                                                        number_number_of(int),
2.99/3.17	                                                        app_encode_app(
2.99/3.17	                                                        int,int,bit0,
2.99/3.17	                                                        app_encode_app(
2.99/3.17	                                                        int,int,bit0,
2.99/3.17	                                                        app_encode_app(
2.99/3.17	                                                        int,int,bit1,pls))))),
2.99/3.17	                                                        m)),
2.99/3.17	                                         one_one(int))) & 
2.99/3.17	           app_encode_app(int,$o,
2.99/3.17	                          app_encode_app(int,app_encode_fun(int,$o),
2.99/3.17	                                         app_encode_app(int,
2.99/3.17	                                                        app_encode_fun(
2.99/3.17	                                                        int,
2.99/3.17	                                                        app_encode_fun(
2.99/3.17	                                                        int,$o)),zcong,s1),
2.99/3.17	                                         Y1),
2.99/3.17	                          app_encode_app(int,int,
2.99/3.17	                                         app_encode_app(int,
2.99/3.17	                                                        app_encode_fun(
2.99/3.17	                                                        int,int),
2.99/3.17	                                                        plus_plus(int),
2.99/3.17	                                                        app_encode_app(
2.99/3.17	                                                        int,int,
2.99/3.17	                                                        app_encode_app(
2.99/3.17	                                                        int,
2.99/3.17	                                                        app_encode_fun(
2.99/3.17	                                                        int,int),
2.99/3.17	                                                        times_times(int),
2.99/3.17	                                                        app_encode_app(
2.99/3.17	                                                        int,int,
2.99/3.17	                                                        number_number_of(int),
2.99/3.17	                                                        app_encode_app(
2.99/3.17	                                                        int,int,bit0,
2.99/3.17	                                                        app_encode_app(
2.99/3.17	                                                        int,int,bit0,
2.99/3.17	                                                        app_encode_app(
2.99/3.17	                                                        int,int,bit1,pls))))),
2.99/3.17	                                                        m)),
2.99/3.17	                                         one_one(int)))) =>
2.99/3.17	          (Y1 = X1)))))).
2.99/3.17	tff('0', plain,
2.99/3.17	    app_encode_app(int, $o, 
2.99/3.17	      app_encode_app(int, app_encode_fun(int, $o), 
2.99/3.17	        app_encode_app(int, app_encode_fun(int, app_encode_fun(int, $o)), 
2.99/3.17	          zcong, s1), sk_X1), 
2.99/3.17	      app_encode_app(int, int, 
2.99/3.17	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.99/3.17	          app_encode_app(int, int, 
2.99/3.17	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.99/3.17	              app_encode_app(int, int, number_number_of(int), 
2.99/3.17	                app_encode_app(int, int, bit0, 
2.99/3.17	                  app_encode_app(int, int, bit0, 
2.99/3.17	                    app_encode_app(int, int, bit1, pls))))), m)), 
2.99/3.17	        one_one(int))),
2.99/3.17	    inference('cnf', [status(esa)], [zf_stmt_31])).
2.99/3.17	tff(zf_stmt_92, axiom,
2.99/3.17	  (![K:int]: (app_encode_app(int,int,number_number_of(int),K) = K))).
2.99/3.17	tff('1', plain,
2.99/3.17	    ![X147 : int]:
2.99/3.17	      app_encode_app(int, int, number_number_of(int), X147) = X147,
2.99/3.17	    inference('cnf', [status(esa)], [zf_stmt_92])).
2.99/3.17	tff('2', plain,
2.99/3.17	    app_encode_app(int, $o, 
2.99/3.17	      app_encode_app(int, app_encode_fun(int, $o), 
2.99/3.17	        app_encode_app(int, app_encode_fun(int, app_encode_fun(int, $o)), 
2.99/3.17	          zcong, s1), sk_X1), 
2.99/3.17	      app_encode_app(int, int, 
2.99/3.17	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.99/3.17	          app_encode_app(int, int, 
2.99/3.17	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.99/3.17	              app_encode_app(int, int, bit0, 
2.99/3.17	                app_encode_app(int, int, bit0, 
2.99/3.17	                  app_encode_app(int, int, bit1, pls)))), m)), one_one(int))),
2.99/3.17	    inference('demod', [status(thm)], ['0', '1'])).
2.99/3.17	tff(zf_stmt_99, axiom,
2.99/3.17	  (![K:int]:
2.99/3.17	     (app_encode_app(int,int,
2.99/3.17	                     app_encode_app(int,app_encode_fun(int,int),
2.99/3.17	                                    plus_plus(int),K),
2.99/3.17	                     pls) =
2.99/3.17	      K))).
2.99/3.17	tff('3', plain,
2.99/3.17	    ![X163 : int]:
2.99/3.17	      app_encode_app(int, int, 
2.99/3.17	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X163), 
2.99/3.17	        pls)
2.99/3.17	       = X163,
2.99/3.17	    inference('cnf', [status(esa)], [zf_stmt_99])).
2.99/3.17	tff(zf_stmt_122, axiom,
2.99/3.17	  (![K:int]:
2.99/3.17	     (app_encode_app(int,int,bit1,K) =
2.99/3.17	      app_encode_app(int,int,
2.99/3.17	                     app_encode_app(int,app_encode_fun(int,int),
2.99/3.17	                                    plus_plus(int),
2.99/3.17	                                    app_encode_app(int,int,
2.99/3.17	                                                   app_encode_app(int,
2.99/3.17	                                                                  app_encode_fun(
2.99/3.17	                                                                  int,int),
2.99/3.17	                                                                  plus_plus(
2.99/3.17	                                                                  int),
2.99/3.17	                                                                  one_one(
2.99/3.17	                                                                  int)),
2.99/3.17	                                                   K)),
2.99/3.17	                     K)))).
2.99/3.17	tff('4', plain,
2.99/3.17	    ![X213 : int]:
2.99/3.17	      app_encode_app(int, int, bit1, X213)
2.99/3.17	       = app_encode_app(int, int, 
2.99/3.17	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.99/3.17	             app_encode_app(int, int, 
2.99/3.17	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.99/3.17	                 one_one(int)), X213)), X213),
2.99/3.17	    inference('cnf', [status(esa)], [zf_stmt_122])).
2.99/3.17	tff('5', plain,
2.99/3.17	    app_encode_app(int, int, bit1, pls)
2.99/3.17	     = app_encode_app(int, int, 
2.99/3.17	         app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.99/3.17	           one_one(int)), pls),
2.99/3.17	    inference('sup+', [status(thm)], ['3', '4'])).
2.99/3.17	tff('6', plain, app_encode_app(int, int, bit1, pls) = one_one(int),
2.99/3.17	    inference('demod', [status(thm)], ['5', '3'])).
2.99/3.17	tff('7', plain,
2.99/3.17	    app_encode_app(int, $o, 
2.99/3.17	      app_encode_app(int, app_encode_fun(int, $o), 
2.99/3.17	        app_encode_app(int, app_encode_fun(int, app_encode_fun(int, $o)), 
2.99/3.17	          zcong, s1), sk_X1), 
2.99/3.17	      app_encode_app(int, int, 
2.99/3.17	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.99/3.17	          app_encode_app(int, int, 
2.99/3.17	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.99/3.17	              app_encode_app(int, int, bit0, 
2.99/3.17	                app_encode_app(int, int, bit0, 
2.99/3.17	                  app_encode_app(int, int, bit1, pls)))), m)), 
2.99/3.17	        app_encode_app(int, int, bit1, pls))),
2.99/3.17	    inference('demod', [status(thm)], ['2', '6'])).
2.99/3.17	tff(zf_stmt_64, axiom,
2.99/3.17	  (![L1:int,K:int]:
2.99/3.17	     (app_encode_app(int,int,
2.99/3.17	                     app_encode_app(int,app_encode_fun(int,int),
2.99/3.17	                                    times_times(int),
2.99/3.17	                                    app_encode_app(int,int,bit0,K)),
2.99/3.17	                     L1) =
2.99/3.17	      app_encode_app(int,int,bit0,
2.99/3.17	                     app_encode_app(int,int,
2.99/3.17	                                    app_encode_app(int,
2.99/3.17	                                                   app_encode_fun(int,int),
2.99/3.17	                                                   times_times(int),K),
2.99/3.17	                                    L1))))).
2.99/3.17	tff('8', plain,
2.99/3.17	    ![X73 : int, X74 : int]:
2.99/3.17	      app_encode_app(int, int, 
2.99/3.17	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.99/3.17	          app_encode_app(int, int, bit0, X73)), X74)
2.99/3.17	       = app_encode_app(int, int, bit0, 
2.99/3.17	           app_encode_app(int, int, 
2.99/3.17	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.99/3.17	               X73), X74)),
2.99/3.17	    inference('cnf', [status(esa)], [zf_stmt_64])).
2.99/3.17	tff(zf_stmt_63, axiom,
2.99/3.17	  (![W:int]:
2.99/3.17	     (app_encode_app(int,int,
2.99/3.17	                     app_encode_app(int,app_encode_fun(int,int),
2.99/3.17	                                    times_times(int),pls),
2.99/3.17	                     W) =
2.99/3.17	      pls))).
2.99/3.17	tff('9', plain,
2.99/3.17	    ![X72 : int]:
2.99/3.17	      app_encode_app(int, int, 
2.99/3.17	        app_encode_app(int, app_encode_fun(int, int), times_times(int), pls), 
2.99/3.17	        X72)
2.99/3.17	       = pls,
2.99/3.17	    inference('cnf', [status(esa)], [zf_stmt_63])).
2.99/3.17	tff(zf_stmt_90, axiom,
2.99/3.17	  (![L1:int,K:int]:
2.99/3.17	     (app_encode_app(int,int,
2.99/3.17	                     app_encode_app(int,app_encode_fun(int,int),
2.99/3.17	                                    times_times(int),
2.99/3.17	                                    app_encode_app(int,int,bit1,K)),
2.99/3.17	                     L1) =
2.99/3.17	      app_encode_app(int,int,
2.99/3.17	                     app_encode_app(int,app_encode_fun(int,int),
2.99/3.17	                                    plus_plus(int),
2.99/3.17	                                    app_encode_app(int,int,bit0,
2.99/3.17	                                                   app_encode_app(int,int,
2.99/3.17	                                                                  app_encode_app(
2.99/3.17	                                                                  int,
2.99/3.17	                                                                  app_encode_fun(
2.99/3.17	                                                                  int,int),
2.99/3.17	                                                                  times_times(
2.99/3.17	                                                                  int),K),L1))),
2.99/3.17	                     L1)))).
2.99/3.17	tff('10', plain,
2.99/3.17	    ![X141 : int, X142 : int]:
2.99/3.17	      app_encode_app(int, int, 
2.99/3.17	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.99/3.17	          app_encode_app(int, int, bit1, X141)), X142)
2.99/3.17	       = app_encode_app(int, int, 
2.99/3.17	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.99/3.17	             app_encode_app(int, int, bit0, 
2.99/3.17	               app_encode_app(int, int, 
2.99/3.17	                 app_encode_app(int, app_encode_fun(int, int), 
2.99/3.17	                   times_times(int), X141), X142))), X142),
2.99/3.17	    inference('cnf', [status(esa)], [zf_stmt_90])).
2.99/3.17	tff('11', plain,
2.99/3.17	    ![X0 : int]:
2.99/3.17	      app_encode_app(int, int, 
2.99/3.17	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.99/3.17	          app_encode_app(int, int, bit1, pls)), X0)
2.99/3.17	       = app_encode_app(int, int, 
2.99/3.17	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.99/3.17	             app_encode_app(int, int, bit0, pls)), X0),
2.99/3.17	    inference('sup+', [status(thm)], ['9', '10'])).
2.99/3.17	tff(zf_stmt_56, axiom, (app_encode_app(int,int,bit0,pls) = pls)).
2.99/3.17	tff('12', plain, app_encode_app(int, int, bit0, pls) = pls,
2.99/3.17	    inference('cnf', [status(esa)], [zf_stmt_56])).
2.99/3.17	tff(zf_stmt_100, axiom,
2.99/3.17	  (![K:int]:
2.99/3.17	     (app_encode_app(int,int,
2.99/3.17	                     app_encode_app(int,app_encode_fun(int,int),
2.99/3.17	                                    plus_plus(int),pls),
2.99/3.17	                     K) =
2.99/3.17	      K))).
2.99/3.17	tff('13', plain,
2.99/3.17	    ![X164 : int]:
2.99/3.17	      app_encode_app(int, int, 
2.99/3.17	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
2.99/3.17	        X164)
2.99/3.17	       = X164,
2.99/3.17	    inference('cnf', [status(esa)], [zf_stmt_100])).
2.99/3.17	tff('14', plain,
2.99/3.17	    ![X0 : int]:
2.99/3.17	      app_encode_app(int, int, 
2.99/3.17	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.99/3.17	          app_encode_app(int, int, bit1, pls)), X0)
2.99/3.17	       = X0,
2.99/3.17	    inference('demod', [status(thm)], ['11', '12', '13'])).
2.99/3.17	tff(zf_stmt_2, axiom,
2.99/3.17	  (![X:app_encode_fun(Alpha,Beta),Y:app_encode_fun(Alpha,Beta)]:
2.99/3.17	     ((![Z:Alpha]:
2.99/3.17	         (app_encode_app(Alpha,Beta,X,Z) = app_encode_app(Alpha,Beta,Y,Z))) =>
2.99/3.17	      (X = Y)))).
2.99/3.17	tff('15', plain,
2.99/3.17	    ![X0 : $tType, X1 : $tType, X2 : app_encode_fun(X0, X1), 
2.99/3.17	      X3 : app_encode_fun(X0, X1)]:
2.99/3.17	      (X3 = X2
2.99/3.17	       | app_encode_app(X0, X1, X3, sk_Z(X1, X0, X2, X3))
2.99/3.17	          != app_encode_app(X0, X1, X2, sk_Z(X1, X0, X2, X3))),
2.99/3.17	    inference('cnf', [status(esa)], [zf_stmt_2])).
2.99/3.17	tff('16', plain,
2.99/3.17	    ![X0 : app_encode_fun(int, int)]:
2.99/3.17	      (app_encode_app(int, int, X0, 
2.99/3.17	         sk_Z(int, int, number_number_of(int), X0))
2.99/3.17	        != sk_Z(int, int, number_number_of(int), X0)
2.99/3.17	       | X0 = number_number_of(int)),
2.99/3.17	    inference('sup-', [status(thm)], ['1', '15'])).
2.99/3.17	tff('17', plain,
2.99/3.17	    (sk_Z(int, int, number_number_of(int), 
2.99/3.17	       app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.99/3.17	         app_encode_app(int, int, bit1, pls)))
2.99/3.17	      != sk_Z(int, int, number_number_of(int), 
2.99/3.17	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.99/3.17	             app_encode_app(int, int, bit1, pls)))
2.99/3.17	     | app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.99/3.17	         app_encode_app(int, int, bit1, pls))
2.99/3.17	        = number_number_of(int)),
2.99/3.17	    inference('sup-', [status(thm)], ['14', '16'])).
2.99/3.17	tff('18', plain,
2.99/3.17	    app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.99/3.17	      app_encode_app(int, int, bit1, pls))
2.99/3.17	     = number_number_of(int),
2.99/3.17	    inference('simplify', [status(thm)], ['17'])).
2.99/3.17	tff(zf_stmt_101, axiom,
2.99/3.17	  (![K:int]:
2.99/3.17	     (app_encode_app(int,int,bit0,K) =
2.99/3.17	      app_encode_app(int,int,
2.99/3.17	                     app_encode_app(int,app_encode_fun(int,int),
2.99/3.17	                                    plus_plus(int),K),
2.99/3.17	                     K)))).
2.99/3.17	tff('19', plain,
2.99/3.17	    ![X165 : int]:
2.99/3.17	      app_encode_app(int, int, bit0, X165)
2.99/3.17	       = app_encode_app(int, int, 
2.99/3.17	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.99/3.17	             X165), X165),
2.99/3.17	    inference('cnf', [status(esa)], [zf_stmt_101])).
2.99/3.17	tff(zf_stmt_134, axiom, (number_ring(int))).
2.99/3.17	tff('20', plain, number_ring(int),
2.99/3.17	    inference('cnf', [status(esa)], [zf_stmt_134])).
2.99/3.17	tff(zf_stmt_73, axiom,
2.99/3.17	  (![A:$tType]:
2.99/3.17	     (number_ring(A) =>
2.99/3.17	      (![Z1:A,W:int,V:int]:
2.99/3.17	         (app_encode_app(A,A,
2.99/3.17	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
2.99/3.17	                                        app_encode_app(int,A,
2.99/3.17	                                                       number_number_of(A),V)),
2.99/3.17	                         app_encode_app(A,A,
2.99/3.17	                                        app_encode_app(A,app_encode_fun(A,A),
2.99/3.17	                                                       plus_plus(A),
2.99/3.17	                                                       app_encode_app(
2.99/3.17	                                                       int,A,
2.99/3.17	                                                       number_number_of(A),W)),
2.99/3.17	                                        Z1)) =
2.99/3.17	          app_encode_app(A,A,
2.99/3.17	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
2.99/3.17	                                        app_encode_app(int,A,
2.99/3.17	                                                       number_number_of(A),
2.99/3.17	                                                       app_encode_app(
2.99/3.17	                                                       int,int,
2.99/3.17	                                                       app_encode_app(
2.99/3.17	                                                       int,
2.99/3.17	                                                       app_encode_fun(
2.99/3.17	                                                       int,int),
2.99/3.17	                                                       plus_plus(int),V),W))),
2.99/3.17	                         Z1)))))).
2.99/3.17	tff('21', plain,
2.99/3.17	    ![X101 : $tType, X102 : int, X103 : int, X104 : X101]:
2.99/3.17	      (app_encode_app(X101, X101, 
2.99/3.17	         app_encode_app(X101, app_encode_fun(X101, X101), plus_plus(X101), 
2.99/3.17	           app_encode_app(int, X101, number_number_of(X101), X102)), 
2.99/3.17	         app_encode_app(X101, X101, 
2.99/3.17	           app_encode_app(X101, app_encode_fun(X101, X101), plus_plus(X101), 
2.99/3.17	             app_encode_app(int, X101, number_number_of(X101), X103)), X104))
2.99/3.17	        = app_encode_app(X101, X101, 
2.99/3.17	            app_encode_app(X101, app_encode_fun(X101, X101), 
2.99/3.17	              plus_plus(X101), 
2.99/3.17	              app_encode_app(int, X101, number_number_of(X101), 
2.99/3.17	                app_encode_app(int, int, 
2.99/3.17	                  app_encode_app(int, app_encode_fun(int, int), 
2.99/3.17	                    plus_plus(int), X102), X103))), X104)
2.99/3.17	       | ~ number_ring(X101)),
2.99/3.17	    inference('cnf', [status(esa)], [zf_stmt_73])).
2.99/3.17	tff('22', plain,
2.99/3.17	    ![X0 : int, X1 : int, X2 : int]:
2.99/3.17	      (~ $true
2.99/3.17	       | app_encode_app(int, int, 
2.99/3.17	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.99/3.17	             app_encode_app(int, int, number_number_of(int), X2)), 
2.99/3.17	           app_encode_app(int, int, 
2.99/3.17	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.99/3.17	               app_encode_app(int, int, number_number_of(int), X1)), X0))
2.99/3.17	          = app_encode_app(int, int, 
2.99/3.17	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.99/3.17	                app_encode_app(int, int, number_number_of(int), 
2.99/3.17	                  app_encode_app(int, int, 
2.99/3.17	                    app_encode_app(int, app_encode_fun(int, int), 
2.99/3.17	                      plus_plus(int), X2), X1))), X0)),
2.99/3.17	    inference('sup-', [status(thm)], ['20', '21'])).
2.99/3.17	tff('23', plain,
2.99/3.17	    ![X0 : int, X1 : int, X2 : int]:
2.99/3.17	      (~ $true
2.99/3.17	       | app_encode_app(int, int, 
2.99/3.17	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X2), 
2.99/3.17	           app_encode_app(int, int, 
2.99/3.17	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.99/3.17	               X1), X0))
2.99/3.17	          = app_encode_app(int, int, 
2.99/3.17	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.99/3.17	                app_encode_app(int, int, 
2.99/3.17	                  app_encode_app(int, app_encode_fun(int, int), 
2.99/3.17	                    plus_plus(int), X2), X1)), X0)),
2.99/3.17	    inference('demod', [status(thm)], ['22', '1', '1', '1'])).
2.99/3.17	tff('24', plain,
2.99/3.17	    ![X0 : int, X1 : int, X2 : int]:
2.99/3.17	      app_encode_app(int, int, 
2.99/3.17	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X2), 
2.99/3.17	        app_encode_app(int, int, 
2.99/3.17	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X1), 
2.99/3.17	          X0))
2.99/3.17	       = app_encode_app(int, int, 
2.99/3.17	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.99/3.17	             app_encode_app(int, int, 
2.99/3.17	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.99/3.17	                 X2), X1)), X0),
2.99/3.17	    inference('simplify', [status(thm)], ['23'])).
2.99/3.17	tff('25', plain,
2.99/3.17	    ![X0 : int, X1 : int]:
2.99/3.17	      app_encode_app(int, int, 
2.99/3.17	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
2.99/3.17	        app_encode_app(int, int, 
2.99/3.17	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
2.99/3.17	          X1))
2.99/3.17	       = app_encode_app(int, int, 
2.99/3.17	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.99/3.17	             app_encode_app(int, int, bit0, X0)), X1),
2.99/3.17	    inference('sup+', [status(thm)], ['19', '24'])).
2.99/3.17	tff(zf_stmt_84, axiom,
2.99/3.17	  (![L1:int,K:int]:
2.99/3.17	     (app_encode_app(int,int,
2.99/3.17	                     app_encode_app(int,app_encode_fun(int,int),
2.99/3.17	                                    plus_plus(int),
2.99/3.17	                                    app_encode_app(int,int,bit0,K)),
2.99/3.17	                     app_encode_app(int,int,bit1,L1)) =
2.99/3.17	      app_encode_app(int,int,bit1,
2.99/3.17	                     app_encode_app(int,int,
2.99/3.17	                                    app_encode_app(int,
2.99/3.17	                                                   app_encode_fun(int,int),
2.99/3.17	                                                   plus_plus(int),K),
2.99/3.17	                                    L1))))).
2.99/3.17	tff('26', plain,
2.99/3.17	    ![X128 : int, X129 : int]:
2.99/3.17	      app_encode_app(int, int, 
2.99/3.17	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.99/3.17	          app_encode_app(int, int, bit0, X128)), 
2.99/3.17	        app_encode_app(int, int, bit1, X129))
2.99/3.17	       = app_encode_app(int, int, bit1, 
2.99/3.17	           app_encode_app(int, int, 
2.99/3.17	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.99/3.17	               X128), X129)),
2.99/3.17	    inference('cnf', [status(esa)], [zf_stmt_84])).
2.99/3.17	tff('27', plain,
2.99/3.17	    ![X128 : int, X129 : int]:
2.99/3.17	      app_encode_app(int, int, 
2.99/3.17	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X128), 
2.99/3.17	        app_encode_app(int, int, 
2.99/3.17	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X128), 
2.99/3.17	          app_encode_app(int, int, bit1, X129)))
2.99/3.17	       = app_encode_app(int, int, bit1, 
2.99/3.17	           app_encode_app(int, int, 
2.99/3.17	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.99/3.17	               X128), X129)),
2.99/3.17	    inference('demod', [status(thm)], ['26', '25'])).
2.99/3.17	tff('28', plain,
2.99/3.17	    app_encode_app(int, $o, 
2.99/3.17	      app_encode_app(int, app_encode_fun(int, $o), 
2.99/3.17	        app_encode_app(int, app_encode_fun(int, app_encode_fun(int, $o)), 
2.99/3.17	          zcong, s1), sk_X1), 
2.99/3.17	      app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m))),
2.99/3.17	    inference('demod', [status(thm)],
2.99/3.17	              ['7', '8', '8', '18', '1', '25', '25', '27', '3', '25', '27', 
2.99/3.17	               '19'])).
2.99/3.17	tff(zf_stmt_140, axiom,
2.99/3.17	  (![S:int]:
2.99/3.17	     ((app_encode_app(int,$o,
2.99/3.17	                      app_encode_app(int,app_encode_fun(int,$o),
2.99/3.17	                                     ord_less_eq(int),zero_zero(int)),
2.99/3.17	                      S) & 
2.99/3.17	       app_encode_app(int,$o,
2.99/3.17	                      app_encode_app(int,app_encode_fun(int,$o),
2.99/3.17	                                     ord_less(int),S),
2.99/3.17	                      app_encode_app(int,int,
2.99/3.17	                                     app_encode_app(int,
2.99/3.17	                                                    app_encode_fun(int,int),
2.99/3.17	                                                    plus_plus(int),
2.99/3.17	                                                    app_encode_app(int,int,
2.99/3.17	                                                                   app_encode_app(
2.99/3.17	                                                                   int,
2.99/3.17	                                                                   app_encode_fun(
2.99/3.17	                                                                   int,int),
2.99/3.17	                                                                   times_times(
2.99/3.17	                                                                   int),
2.99/3.17	                                                                   app_encode_app(
2.99/3.17	                                                                   int,int,
2.99/3.17	                                                                   number_number_of(
2.99/3.17	                                                                   int),
2.99/3.17	                                                                   app_encode_app(
2.99/3.17	                                                                   int,int,
2.99/3.17	                                                                   bit0,
2.99/3.17	                                                                   app_encode_app(
2.99/3.17	                                                                   int,int,
2.99/3.17	                                                                   bit0,
2.99/3.17	                                                                   app_encode_app(
2.99/3.17	                                                                   int,int,
2.99/3.17	                                                                   bit1,pls))))),
2.99/3.17	                                                                   m)),
2.99/3.17	                                     one_one(int))) & 
2.99/3.17	       app_encode_app(int,$o,
2.99/3.17	                      app_encode_app(int,app_encode_fun(int,$o),
2.99/3.17	                                     app_encode_app(int,
2.99/3.17	                                                    app_encode_fun(int,
2.99/3.17	                                                                   app_encode_fun(
2.99/3.17	                                                                   int,$o)),
2.99/3.17	                                                    zcong,s1),
2.99/3.17	                                     S),
2.99/3.17	                      app_encode_app(int,int,
2.99/3.17	                                     app_encode_app(int,
2.99/3.17	                                                    app_encode_fun(int,int),
2.99/3.17	                                                    plus_plus(int),
2.99/3.17	                                                    app_encode_app(int,int,
2.99/3.17	                                                                   app_encode_app(
2.99/3.17	                                                                   int,
2.99/3.17	                                                                   app_encode_fun(
2.99/3.17	                                                                   int,int),
2.99/3.17	                                                                   times_times(
2.99/3.17	                                                                   int),
2.99/3.17	                                                                   app_encode_app(
2.99/3.17	                                                                   int,int,
2.99/3.17	                                                                   number_number_of(
2.99/3.17	                                                                   int),
2.99/3.17	                                                                   app_encode_app(
2.99/3.17	                                                                   int,int,
2.99/3.17	                                                                   bit0,
2.99/3.17	                                                                   app_encode_app(
2.99/3.17	                                                                   int,int,
2.99/3.17	                                                                   bit0,
2.99/3.17	                                                                   app_encode_app(
2.99/3.17	                                                                   int,int,
2.99/3.17	                                                                   bit1,pls))))),
2.99/3.17	                                                                   m)),
2.99/3.17	                                     one_one(int)))) =>
2.99/3.17	      thesis))).
2.99/3.17	tff('29', plain,
2.99/3.17	    ![X226 : int]:
2.99/3.17	      (thesis
2.99/3.17	       | ~ app_encode_app(int, $o, 
2.99/3.17	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
2.99/3.17	               zero_zero(int)), X226)
2.99/3.17	       | ~ app_encode_app(int, $o, 
2.99/3.17	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
2.99/3.17	               X226), 
2.99/3.17	             app_encode_app(int, int, 
2.99/3.17	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.99/3.17	                 app_encode_app(int, int, 
2.99/3.17	                   app_encode_app(int, app_encode_fun(int, int), 
2.99/3.17	                     times_times(int), 
2.99/3.17	                     app_encode_app(int, int, number_number_of(int), 
2.99/3.17	                       app_encode_app(int, int, bit0, 
2.99/3.17	                         app_encode_app(int, int, bit0, 
2.99/3.17	                           app_encode_app(int, int, bit1, pls))))), m)), 
2.99/3.17	               one_one(int)))
2.99/3.17	       | ~ app_encode_app(int, $o, 
2.99/3.17	             app_encode_app(int, app_encode_fun(int, $o), 
2.99/3.17	               app_encode_app(int, 
2.99/3.17	                 app_encode_fun(int, app_encode_fun(int, $o)), zcong, s1), 
2.99/3.17	               X226), 
2.99/3.17	             app_encode_app(int, int, 
2.99/3.17	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.99/3.17	                 app_encode_app(int, int, 
2.99/3.17	                   app_encode_app(int, app_encode_fun(int, int), 
2.99/3.17	                     times_times(int), 
2.99/3.17	                     app_encode_app(int, int, number_number_of(int), 
2.99/3.17	                       app_encode_app(int, int, bit0, 
2.99/3.17	                         app_encode_app(int, int, bit0, 
2.99/3.17	                           app_encode_app(int, int, bit1, pls))))), m)), 
2.99/3.17	               one_one(int)))),
2.99/3.17	    inference('cnf', [status(esa)], [zf_stmt_140])).
2.99/3.17	tff(zf_stmt_93, axiom, (pls = zero_zero(int))).
2.99/3.17	tff('30', plain, pls = zero_zero(int),
2.99/3.17	    inference('cnf', [status(esa)], [zf_stmt_93])).
2.99/3.17	tff('31', plain,
2.99/3.17	    ![X226 : int]:
2.99/3.17	      (thesis
2.99/3.17	       | ~ app_encode_app(int, $o, 
2.99/3.17	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
2.99/3.17	               pls), X226)
2.99/3.17	       | ~ app_encode_app(int, $o, 
2.99/3.17	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
2.99/3.17	               X226), 
2.99/3.17	             app_encode_app(int, int, bit1, 
2.99/3.17	               app_encode_app(int, int, bit0, m)))
2.99/3.17	       | ~ app_encode_app(int, $o, 
2.99/3.17	             app_encode_app(int, app_encode_fun(int, $o), 
2.99/3.17	               app_encode_app(int, 
2.99/3.17	                 app_encode_fun(int, app_encode_fun(int, $o)), zcong, s1), 
2.99/3.17	               X226), 
2.99/3.17	             app_encode_app(int, int, bit1, 
2.99/3.17	               app_encode_app(int, int, bit0, m)))),
2.99/3.17	    inference('demod', [status(thm)],
2.99/3.17	              ['29', '30', '1', '8', '8', '18', '1', '6', '25', '25', '27', 
2.99/3.17	               '3', '25', '27', '19', '1', '8', '8', '18', '1', '6', '25', 
2.99/3.17	               '25', '27', '3', '25', '27', '19'])).
2.99/3.17	tff(zf_stmt_141, conjecture, (thesis)).
2.99/3.17	tff(zf_stmt_0, negated_conjecture, (~thesis)).
2.99/3.17	tff('32', plain, ~ thesis, inference('cnf', [status(esa)], [zf_stmt_0])).
2.99/3.17	tff('33', plain,
2.99/3.17	    ![X226 : int]:
2.99/3.17	      (~ app_encode_app(int, $o, 
2.99/3.17	           app_encode_app(int, app_encode_fun(int, $o), 
2.99/3.17	             app_encode_app(int, 
2.99/3.17	               app_encode_fun(int, app_encode_fun(int, $o)), zcong, s1), 
2.99/3.17	             X226), 
2.99/3.17	           app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m)))
2.99/3.17	       | ~ app_encode_app(int, $o, 
2.99/3.17	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
2.99/3.17	               X226), 
2.99/3.17	             app_encode_app(int, int, bit1, 
2.99/3.17	               app_encode_app(int, int, bit0, m)))
2.99/3.17	       | ~ app_encode_app(int, $o, 
2.99/3.17	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
2.99/3.17	               pls), X226)),
2.99/3.17	    inference('clc', [status(thm)], ['31', '32'])).
2.99/3.17	tff('34', plain,
2.99/3.17	    (~ $true
2.99/3.17	     | ~ app_encode_app(int, $o, 
2.99/3.17	           app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
2.99/3.17	             pls), sk_X1)
2.99/3.17	     | ~ app_encode_app(int, $o, 
2.99/3.17	           app_encode_app(int, app_encode_fun(int, $o), ord_less(int), sk_X1), 
2.99/3.17	           app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m)))),
2.99/3.17	    inference('sup-', [status(thm)], ['28', '33'])).
2.99/3.17	tff('35', plain,
2.99/3.17	    app_encode_app(int, $o, 
2.99/3.17	      app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
2.99/3.17	        zero_zero(int)), sk_X1),
2.99/3.17	    inference('cnf', [status(esa)], [zf_stmt_31])).
2.99/3.17	tff('36', plain,
2.99/3.17	    app_encode_app(int, $o, 
2.99/3.17	      app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), pls), 
2.99/3.17	      sk_X1),
2.99/3.17	    inference('demod', [status(thm)], ['35', '30'])).
2.99/3.17	tff('37', plain,
2.99/3.17	    app_encode_app(int, $o, 
2.99/3.17	      app_encode_app(int, app_encode_fun(int, $o), ord_less(int), sk_X1), 
2.99/3.17	      app_encode_app(int, int, 
2.99/3.17	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.99/3.17	          app_encode_app(int, int, 
2.99/3.17	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.99/3.17	              app_encode_app(int, int, number_number_of(int), 
2.99/3.17	                app_encode_app(int, int, bit0, 
2.99/3.17	                  app_encode_app(int, int, bit0, 
2.99/3.17	                    app_encode_app(int, int, bit1, pls))))), m)), 
2.99/3.17	        one_one(int))),
2.99/3.17	    inference('cnf', [status(esa)], [zf_stmt_31])).
2.99/3.17	tff('38', plain,
2.99/3.17	    app_encode_app(int, $o, 
2.99/3.17	      app_encode_app(int, app_encode_fun(int, $o), ord_less(int), sk_X1), 
2.99/3.17	      app_encode_app(int, int, 
2.99/3.17	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.99/3.17	          app_encode_app(int, int, 
2.99/3.17	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.99/3.17	              app_encode_app(int, int, bit0, 
2.99/3.17	                app_encode_app(int, int, bit0, 
2.99/3.17	                  app_encode_app(int, int, bit1, pls)))), m)), one_one(int))),
2.99/3.17	    inference('demod', [status(thm)], ['37', '1'])).
2.99/3.17	tff('39', plain,
2.99/3.17	    app_encode_app(int, $o, 
2.99/3.17	      app_encode_app(int, app_encode_fun(int, $o), ord_less(int), sk_X1), 
2.99/3.17	      app_encode_app(int, int, 
2.99/3.17	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.99/3.17	          app_encode_app(int, int, 
2.99/3.17	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.99/3.17	              app_encode_app(int, int, bit0, 
2.99/3.17	                app_encode_app(int, int, bit0, 
2.99/3.17	                  app_encode_app(int, int, bit1, pls)))), m)), 
2.99/3.17	        app_encode_app(int, int, bit1, pls))),
2.99/3.17	    inference('demod', [status(thm)], ['38', '6'])).
2.99/3.17	tff('40', plain,
2.99/3.17	    app_encode_app(int, $o, 
2.99/3.17	      app_encode_app(int, app_encode_fun(int, $o), ord_less(int), sk_X1), 
2.99/3.17	      app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m))),
2.99/3.17	    inference('demod', [status(thm)], ['39', '8', '8', '18', '1', '26', '3'])).
2.99/3.17	tff('41', plain, (~ $true | ~ $true | ~ $true),
2.99/3.17	    inference('demod', [status(thm)], ['34', '36', '40'])).
2.99/3.17	tff('42', plain, $false, inference('simplify', [status(thm)], ['41'])).
2.99/3.17	
2.99/3.17	% SZS output end Refutation
2.99/3.17	EOF
