0.00/0.00	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : app
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : kbo
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.20	% Computer   : n094.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 07:47:24 CST 2018
18.34/18.54	% done 1724 iterations in 18.339s
18.34/18.54	% SZS status Theorem for 'stdin'
18.34/18.54	% SZS output start Refutation
18.34/18.55	tff(zf_stmt_30, axiom,
18.34/18.55	  (![M:int]:
18.34/18.55	     (app_encode_app(int,$o,zprime,
18.34/18.55	                     app_encode_app(int,int,
18.34/18.55	                                    app_encode_app(int,
18.34/18.55	                                                   app_encode_fun(int,int),
18.34/18.55	                                                   plus_plus(int),
18.34/18.55	                                                   app_encode_app(int,int,
18.34/18.55	                                                                  app_encode_app(
18.34/18.55	                                                                  int,
18.34/18.55	                                                                  app_encode_fun(
18.34/18.55	                                                                  int,int),
18.34/18.55	                                                                  times_times(
18.34/18.55	                                                                  int),
18.34/18.55	                                                                  app_encode_app(
18.34/18.55	                                                                  int,int,
18.34/18.55	                                                                  number_number_of(
18.34/18.55	                                                                  int),
18.34/18.55	                                                                  app_encode_app(
18.34/18.55	                                                                  int,int,
18.34/18.55	                                                                  bit0,
18.34/18.55	                                                                  app_encode_app(
18.34/18.55	                                                                  int,int,
18.34/18.55	                                                                  bit0,
18.34/18.55	                                                                  app_encode_app(
18.34/18.55	                                                                  int,int,
18.34/18.55	                                                                  bit1,pls))))),
18.34/18.55	                                                                  M)),
18.34/18.55	                                    one_one(int))) =>
18.34/18.55	      (app_encode_app(int,int,
18.34/18.55	                      app_encode_app(int,app_encode_fun(int,int),legendre,
18.34/18.55	                                     app_encode_app(int,int,
18.34/18.55	                                                    number_number_of(int),min)),
18.34/18.55	                      app_encode_app(int,int,
18.34/18.55	                                     app_encode_app(int,
18.34/18.55	                                                    app_encode_fun(int,int),
18.34/18.55	                                                    plus_plus(int),
18.34/18.55	                                                    app_encode_app(int,int,
18.34/18.55	                                                                   app_encode_app(
18.34/18.55	                                                                   int,
18.34/18.55	                                                                   app_encode_fun(
18.34/18.55	                                                                   int,int),
18.34/18.55	                                                                   times_times(
18.34/18.55	                                                                   int),
18.34/18.55	                                                                   app_encode_app(
18.34/18.55	                                                                   int,int,
18.34/18.55	                                                                   number_number_of(
18.34/18.55	                                                                   int),
18.34/18.55	                                                                   app_encode_app(
18.34/18.55	                                                                   int,int,
18.34/18.55	                                                                   bit0,
18.34/18.55	                                                                   app_encode_app(
18.34/18.55	                                                                   int,int,
18.34/18.55	                                                                   bit0,
18.34/18.55	                                                                   app_encode_app(
18.34/18.55	                                                                   int,int,
18.34/18.55	                                                                   bit1,pls))))),
18.34/18.55	                                                                   M)),
18.34/18.55	                                     one_one(int))) =
18.34/18.55	       one_one(int))))).
18.34/18.55	tff('0', plain,
18.34/18.55	    ![X5 : int]:
18.34/18.55	      (app_encode_app(int, int, 
18.34/18.55	         app_encode_app(int, app_encode_fun(int, int), legendre, 
18.34/18.55	           app_encode_app(int, int, number_number_of(int), min)), 
18.34/18.55	         app_encode_app(int, int, 
18.34/18.55	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
18.34/18.55	             app_encode_app(int, int, 
18.34/18.55	               app_encode_app(int, app_encode_fun(int, int), 
18.34/18.55	                 times_times(int), 
18.34/18.55	                 app_encode_app(int, int, number_number_of(int), 
18.34/18.55	                   app_encode_app(int, int, bit0, 
18.34/18.55	                     app_encode_app(int, int, bit0, 
18.34/18.55	                       app_encode_app(int, int, bit1, pls))))), X5)), 
18.34/18.55	           one_one(int)))
18.34/18.55	        = one_one(int)
18.34/18.55	       | ~ app_encode_app(int, $o, zprime, 
18.34/18.55	             app_encode_app(int, int, 
18.34/18.55	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
18.34/18.55	                 app_encode_app(int, int, 
18.34/18.55	                   app_encode_app(int, app_encode_fun(int, int), 
18.34/18.55	                     times_times(int), 
18.34/18.55	                     app_encode_app(int, int, number_number_of(int), 
18.34/18.55	                       app_encode_app(int, int, bit0, 
18.34/18.55	                         app_encode_app(int, int, bit0, 
18.34/18.55	                           app_encode_app(int, int, bit1, pls))))), X5)), 
18.34/18.55	               one_one(int)))),
18.34/18.55	    inference('cnf', [status(esa)], [zf_stmt_30])).
18.34/18.55	tff(zf_stmt_62, axiom,
18.34/18.55	  (![K1:int]: (app_encode_app(int,int,number_number_of(int),K1) = K1))).
18.34/18.55	tff('1', plain,
18.34/18.55	    ![X70 : int]: app_encode_app(int, int, number_number_of(int), X70) = X70,
18.34/18.55	    inference('cnf', [status(esa)], [zf_stmt_62])).
18.34/18.55	tff(zf_stmt_79, axiom,
18.34/18.55	  (one_one(int) =
18.34/18.55	   app_encode_app(int,int,number_number_of(int),
18.34/18.55	                  app_encode_app(int,int,bit1,pls)))).
18.34/18.55	tff('2', plain,
18.34/18.55	    one_one(int)
18.34/18.55	     = app_encode_app(int, int, number_number_of(int), 
18.34/18.55	         app_encode_app(int, int, bit1, pls)),
18.34/18.55	    inference('cnf', [status(esa)], [zf_stmt_79])).
18.34/18.55	tff('3', plain, one_one(int) = app_encode_app(int, int, bit1, pls),
18.34/18.55	    inference('demod', [status(thm)], ['2', '1'])).
18.34/18.55	tff('4', plain,
18.34/18.55	    ![X5 : int]:
18.34/18.55	      (app_encode_app(int, int, 
18.34/18.55	         app_encode_app(int, app_encode_fun(int, int), legendre, min), 
18.34/18.55	         app_encode_app(int, int, 
18.34/18.55	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
18.34/18.55	             app_encode_app(int, int, 
18.34/18.55	               app_encode_app(int, app_encode_fun(int, int), 
18.34/18.55	                 times_times(int), 
18.34/18.55	                 app_encode_app(int, int, bit0, 
18.34/18.55	                   app_encode_app(int, int, bit0, one_one(int)))), X5)), 
18.34/18.55	           one_one(int)))
18.34/18.55	        = one_one(int)
18.34/18.55	       | ~ app_encode_app(int, $o, zprime, 
18.34/18.55	             app_encode_app(int, int, 
18.34/18.55	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
18.34/18.55	                 app_encode_app(int, int, 
18.34/18.55	                   app_encode_app(int, app_encode_fun(int, int), 
18.34/18.55	                     times_times(int), 
18.34/18.55	                     app_encode_app(int, int, bit0, 
18.34/18.55	                       app_encode_app(int, int, bit0, one_one(int)))), X5)), 
18.34/18.55	               one_one(int)))),
18.34/18.55	    inference('demod', [status(thm)], ['0', '1', '3', '1', '3', '1'])).
18.34/18.55	tff(zf_stmt_50, axiom,
18.34/18.55	  (![L:int,K1:int]:
18.34/18.55	     (app_encode_app(int,int,
18.34/18.55	                     app_encode_app(int,app_encode_fun(int,int),
18.34/18.55	                                    times_times(int),
18.34/18.55	                                    app_encode_app(int,int,bit0,K1)),
18.34/18.55	                     L) =
18.34/18.55	      app_encode_app(int,int,bit0,
18.34/18.55	                     app_encode_app(int,int,
18.34/18.55	                                    app_encode_app(int,
18.34/18.55	                                                   app_encode_fun(int,int),
18.34/18.55	                                                   times_times(int),K1),
18.34/18.55	                                    L))))).
18.34/18.55	tff('5', plain,
18.34/18.55	    ![X48 : int, X49 : int]:
18.34/18.55	      app_encode_app(int, int, 
18.34/18.55	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
18.34/18.55	          app_encode_app(int, int, bit0, X48)), X49)
18.34/18.55	       = app_encode_app(int, int, bit0, 
18.34/18.55	           app_encode_app(int, int, 
18.34/18.55	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
18.34/18.55	               X48), X49)),
18.34/18.55	    inference('cnf', [status(esa)], [zf_stmt_50])).
18.34/18.55	tff(zf_stmt_49, axiom,
18.34/18.55	  (![W1:int]:
18.34/18.55	     (app_encode_app(int,int,
18.34/18.55	                     app_encode_app(int,app_encode_fun(int,int),
18.34/18.55	                                    times_times(int),pls),
18.34/18.55	                     W1) =
18.34/18.55	      pls))).
18.34/18.55	tff('6', plain,
18.34/18.55	    ![X47 : int]:
18.34/18.55	      app_encode_app(int, int, 
18.34/18.55	        app_encode_app(int, app_encode_fun(int, int), times_times(int), pls), 
18.34/18.55	        X47)
18.34/18.55	       = pls,
18.34/18.55	    inference('cnf', [status(esa)], [zf_stmt_49])).
18.34/18.55	tff(zf_stmt_31, axiom,
18.34/18.55	  (![L:int,K1:int]:
18.34/18.55	     (app_encode_app(int,int,
18.34/18.55	                     app_encode_app(int,app_encode_fun(int,int),
18.34/18.55	                                    times_times(int),
18.34/18.55	                                    app_encode_app(int,int,bit1,K1)),
18.34/18.55	                     L) =
18.34/18.55	      app_encode_app(int,int,
18.34/18.55	                     app_encode_app(int,app_encode_fun(int,int),
18.34/18.55	                                    plus_plus(int),
18.34/18.55	                                    app_encode_app(int,int,bit0,
18.34/18.55	                                                   app_encode_app(int,int,
18.34/18.55	                                                                  app_encode_app(
18.34/18.55	                                                                  int,
18.34/18.55	                                                                  app_encode_fun(
18.34/18.55	                                                                  int,int),
18.34/18.55	                                                                  times_times(
18.34/18.55	                                                                  int),K1),L))),
18.34/18.55	                     L)))).
18.34/18.55	tff('7', plain,
18.34/18.55	    ![X6 : int, X7 : int]:
18.34/18.55	      app_encode_app(int, int, 
18.34/18.55	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
18.34/18.55	          app_encode_app(int, int, bit1, X6)), X7)
18.34/18.55	       = app_encode_app(int, int, 
18.34/18.55	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
18.34/18.55	             app_encode_app(int, int, bit0, 
18.34/18.55	               app_encode_app(int, int, 
18.34/18.55	                 app_encode_app(int, app_encode_fun(int, int), 
18.34/18.55	                   times_times(int), X6), X7))), X7),
18.34/18.55	    inference('cnf', [status(esa)], [zf_stmt_31])).
18.34/18.55	tff('8', plain,
18.34/18.55	    ![X0 : int]:
18.34/18.55	      app_encode_app(int, int, 
18.34/18.55	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
18.34/18.55	          app_encode_app(int, int, bit1, pls)), X0)
18.34/18.55	       = app_encode_app(int, int, 
18.34/18.55	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
18.34/18.55	             app_encode_app(int, int, bit0, pls)), X0),
18.34/18.55	    inference('sup+', [status(thm)], ['6', '7'])).
18.34/18.55	tff(zf_stmt_48, axiom, (app_encode_app(int,int,bit0,pls) = pls)).
18.34/18.55	tff('9', plain, app_encode_app(int, int, bit0, pls) = pls,
18.34/18.55	    inference('cnf', [status(esa)], [zf_stmt_48])).
18.34/18.55	tff('10', plain,
18.34/18.55	    ![X0 : int]:
18.34/18.55	      app_encode_app(int, int, 
18.34/18.55	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
18.34/18.55	          one_one(int)), X0)
18.34/18.55	       = app_encode_app(int, int, 
18.34/18.55	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
18.34/18.55	           X0),
18.34/18.55	    inference('demod', [status(thm)], ['8', '3', '9'])).
18.34/18.55	tff(zf_stmt_64, axiom,
18.34/18.55	  (![K1:int]:
18.34/18.55	     (app_encode_app(int,int,
18.34/18.55	                     app_encode_app(int,app_encode_fun(int,int),
18.34/18.55	                                    plus_plus(int),pls),
18.34/18.55	                     K1) =
18.34/18.55	      K1))).
18.34/18.55	tff('11', plain,
18.34/18.55	    ![X72 : int]:
18.34/18.55	      app_encode_app(int, int, 
18.34/18.55	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
18.34/18.55	        X72)
18.34/18.55	       = X72,
18.34/18.55	    inference('cnf', [status(esa)], [zf_stmt_64])).
18.34/18.55	tff('12', plain,
18.34/18.55	    ![X0 : int]:
18.34/18.55	      app_encode_app(int, int, 
18.34/18.55	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
18.34/18.55	          one_one(int)), X0)
18.34/18.55	       = X0,
18.34/18.55	    inference('demod', [status(thm)], ['10', '11'])).
18.34/18.55	tff(zf_stmt_33, axiom,
18.34/18.55	  (![L:int,K1:int]:
18.34/18.55	     (app_encode_app(int,int,
18.34/18.55	                     app_encode_app(int,app_encode_fun(int,int),
18.34/18.55	                                    plus_plus(int),
18.34/18.55	                                    app_encode_app(int,int,bit0,K1)),
18.34/18.55	                     app_encode_app(int,int,bit1,L)) =
18.34/18.55	      app_encode_app(int,int,bit1,
18.34/18.55	                     app_encode_app(int,int,
18.34/18.55	                                    app_encode_app(int,
18.34/18.55	                                                   app_encode_fun(int,int),
18.34/18.55	                                                   plus_plus(int),K1),
18.34/18.55	                                    L))))).
18.34/18.55	tff('13', plain,
18.34/18.55	    ![X9 : int, X10 : int]:
18.34/18.55	      app_encode_app(int, int, 
18.34/18.55	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
18.34/18.55	          app_encode_app(int, int, bit0, X9)), 
18.34/18.55	        app_encode_app(int, int, bit1, X10))
18.34/18.55	       = app_encode_app(int, int, bit1, 
18.34/18.55	           app_encode_app(int, int, 
18.34/18.55	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
18.34/18.55	               X9), X10)),
18.34/18.55	    inference('cnf', [status(esa)], [zf_stmt_33])).
18.34/18.55	tff('14', plain,
18.34/18.55	    ![X0 : int]:
18.34/18.55	      app_encode_app(int, int, 
18.34/18.55	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
18.34/18.55	          app_encode_app(int, int, bit0, X0)), one_one(int))
18.34/18.55	       = app_encode_app(int, int, bit1, 
18.34/18.55	           app_encode_app(int, int, 
18.34/18.55	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
18.34/18.55	               X0), pls)),
18.34/18.55	    inference('sup+', [status(thm)], ['3', '13'])).
18.34/18.55	tff(zf_stmt_63, axiom,
18.34/18.55	  (![K1:int]:
18.34/18.55	     (app_encode_app(int,int,
18.34/18.55	                     app_encode_app(int,app_encode_fun(int,int),
18.34/18.55	                                    plus_plus(int),K1),
18.34/18.55	                     pls) =
18.34/18.55	      K1))).
18.34/18.55	tff('15', plain,
18.34/18.55	    ![X71 : int]:
18.34/18.55	      app_encode_app(int, int, 
18.34/18.55	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X71), 
18.34/18.55	        pls)
18.34/18.55	       = X71,
18.34/18.55	    inference('cnf', [status(esa)], [zf_stmt_63])).
18.34/18.55	tff('16', plain,
18.34/18.55	    ![X0 : int]:
18.34/18.55	      app_encode_app(int, int, 
18.34/18.55	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
18.34/18.55	          app_encode_app(int, int, bit0, X0)), one_one(int))
18.34/18.55	       = app_encode_app(int, int, bit1, X0),
18.34/18.55	    inference('demod', [status(thm)], ['14', '15'])).
18.34/18.55	tff('17', plain,
18.34/18.55	    ![X5 : int]:
18.34/18.55	      (app_encode_app(int, int, 
18.34/18.55	         app_encode_app(int, app_encode_fun(int, int), legendre, min), 
18.34/18.55	         app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, X5)))
18.34/18.55	        = one_one(int)
18.34/18.55	       | ~ app_encode_app(int, $o, zprime, 
18.34/18.55	             app_encode_app(int, int, bit1, 
18.34/18.55	               app_encode_app(int, int, bit0, X5)))),
18.34/18.55	    inference('demod', [status(thm)],
18.34/18.55	              ['4', '5', '5', '12', '16', '5', '5', '12', '16'])).
18.34/18.55	tff(zf_stmt_137, conjecture,
18.34/18.55	  (app_encode_app(int,int,
18.34/18.55	                  app_encode_app(int,app_encode_fun(int,int),legendre,
18.34/18.55	                                 app_encode_app(int,int,
18.34/18.55	                                                number_number_of(int),min)),
18.34/18.55	                  app_encode_app(int,int,
18.34/18.55	                                 app_encode_app(int,app_encode_fun(int,int),
18.34/18.55	                                                plus_plus(int),
18.34/18.55	                                                app_encode_app(int,int,
18.34/18.55	                                                               app_encode_app(
18.34/18.55	                                                               int,
18.34/18.55	                                                               app_encode_fun(
18.34/18.55	                                                               int,int),
18.34/18.55	                                                               times_times(
18.34/18.55	                                                               int),
18.34/18.55	                                                               app_encode_app(
18.34/18.55	                                                               int,int,
18.34/18.55	                                                               number_number_of(
18.34/18.55	                                                               int),
18.34/18.55	                                                               app_encode_app(
18.34/18.55	                                                               int,int,bit0,
18.34/18.55	                                                               app_encode_app(
18.34/18.55	                                                               int,int,bit0,
18.34/18.55	                                                               app_encode_app(
18.34/18.55	                                                               int,int,bit1,
18.34/18.55	                                                               pls))))),m)),
18.34/18.55	                                 one_one(int))) =
18.34/18.55	   one_one(int))).
18.34/18.55	tff(zf_stmt_0, negated_conjecture,
18.34/18.55	  (app_encode_app(int,int,
18.34/18.55	                  app_encode_app(int,app_encode_fun(int,int),legendre,
18.34/18.55	                                 app_encode_app(int,int,
18.34/18.55	                                                number_number_of(int),min)),
18.34/18.55	                  app_encode_app(int,int,
18.34/18.55	                                 app_encode_app(int,app_encode_fun(int,int),
18.34/18.55	                                                plus_plus(int),
18.34/18.55	                                                app_encode_app(int,int,
18.34/18.55	                                                               app_encode_app(
18.34/18.55	                                                               int,
18.34/18.55	                                                               app_encode_fun(
18.34/18.55	                                                               int,int),
18.34/18.55	                                                               times_times(
18.34/18.55	                                                               int),
18.34/18.55	                                                               app_encode_app(
18.34/18.55	                                                               int,int,
18.34/18.55	                                                               number_number_of(
18.34/18.55	                                                               int),
18.34/18.55	                                                               app_encode_app(
18.34/18.55	                                                               int,int,bit0,
18.34/18.55	                                                               app_encode_app(
18.34/18.55	                                                               int,int,bit0,
18.34/18.55	                                                               app_encode_app(
18.34/18.55	                                                               int,int,bit1,
18.34/18.55	                                                               pls))))),m)),
18.34/18.55	                                 one_one(int))) !=
18.34/18.55	   one_one(int))).
18.34/18.55	tff('18', plain,
18.34/18.55	    app_encode_app(int, int, 
18.34/18.55	      app_encode_app(int, app_encode_fun(int, int), legendre, 
18.34/18.55	        app_encode_app(int, int, number_number_of(int), min)), 
18.34/18.55	      app_encode_app(int, int, 
18.34/18.55	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
18.34/18.55	          app_encode_app(int, int, 
18.34/18.55	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
18.34/18.55	              app_encode_app(int, int, number_number_of(int), 
18.34/18.55	                app_encode_app(int, int, bit0, 
18.34/18.55	                  app_encode_app(int, int, bit0, 
18.34/18.55	                    app_encode_app(int, int, bit1, pls))))), m)), 
18.34/18.55	        one_one(int)))
18.34/18.55	     != one_one(int),
18.34/18.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
18.34/18.55	tff(zf_stmt_106, axiom,
18.34/18.55	  (![A:$tType]:
18.34/18.55	     (comm_semiring_1(A) =>
18.34/18.55	      (![D1:A,C:A,A1:A]:
18.34/18.55	         (app_encode_app(A,A,
18.34/18.55	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),A1),
18.34/18.55	                         app_encode_app(A,A,
18.34/18.55	                                        app_encode_app(A,app_encode_fun(A,A),
18.34/18.55	                                                       plus_plus(A),C),
18.34/18.55	                                        D1)) =
18.34/18.55	          app_encode_app(A,A,
18.34/18.55	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),C),
18.34/18.55	                         app_encode_app(A,A,
18.34/18.55	                                        app_encode_app(A,app_encode_fun(A,A),
18.34/18.55	                                                       plus_plus(A),A1),
18.34/18.55	                                        D1))))))).
18.34/18.55	tff('19', plain,
18.34/18.55	    ![X164 : $tType, X165 : X164, X166 : X164, X167 : X164]:
18.34/18.55	      (app_encode_app(X164, X164, 
18.34/18.55	         app_encode_app(X164, app_encode_fun(X164, X164), plus_plus(X164), 
18.34/18.55	           X166), 
18.34/18.55	         app_encode_app(X164, X164, 
18.34/18.55	           app_encode_app(X164, app_encode_fun(X164, X164), plus_plus(X164), 
18.34/18.55	             X165), X167))
18.34/18.55	        = app_encode_app(X164, X164, 
18.34/18.55	            app_encode_app(X164, app_encode_fun(X164, X164), 
18.34/18.55	              plus_plus(X164), X165), 
18.34/18.55	            app_encode_app(X164, X164, 
18.34/18.55	              app_encode_app(X164, app_encode_fun(X164, X164), 
18.34/18.55	                plus_plus(X164), X166), X167))
18.34/18.55	       | ~ comm_semiring_1(X164)),
18.34/18.55	    inference('cnf', [status(esa)], [zf_stmt_106])).
18.34/18.55	tff('20', plain,
18.34/18.55	    ![X0 : int, X1 : int]:
18.34/18.55	      (app_encode_app(int, int, 
18.34/18.55	         app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X1), 
18.34/18.55	         X0)
18.34/18.55	        = app_encode_app(int, int, 
18.34/18.55	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
18.34/18.55	            app_encode_app(int, int, 
18.34/18.55	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
18.34/18.55	                X1), pls))
18.34/18.55	       | ~ comm_semiring_1(int)),
18.34/18.55	    inference('sup+', [status(thm)], ['15', '19'])).
18.34/18.55	tff(zf_stmt_124, axiom, (comm_semiring_1(int))).
18.34/18.55	tff('21', plain, comm_semiring_1(int),
18.34/18.55	    inference('cnf', [status(esa)], [zf_stmt_124])).
18.34/18.55	tff('22', plain,
18.34/18.55	    ![X0 : int, X1 : int]:
18.34/18.55	      (app_encode_app(int, int, 
18.34/18.55	         app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X1), 
18.34/18.55	         X0)
18.34/18.55	        = app_encode_app(int, int, 
18.34/18.55	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
18.34/18.55	            X1)
18.34/18.55	       | ~ $true),
18.34/18.55	    inference('demod', [status(thm)], ['20', '15', '21'])).
18.34/18.55	tff('23', plain,
18.34/18.55	    ![X0 : int, X1 : int]:
18.34/18.55	      app_encode_app(int, int, 
18.34/18.55	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X1), 
18.34/18.55	        X0)
18.34/18.55	       = app_encode_app(int, int, 
18.34/18.55	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
18.34/18.55	           X1),
18.34/18.55	    inference('simplify', [status(thm)], ['22'])).
18.34/18.55	tff(zf_stmt_34, axiom,
18.34/18.55	  (![L:int,K1:int]:
18.34/18.55	     (app_encode_app(int,int,
18.34/18.55	                     app_encode_app(int,app_encode_fun(int,int),
18.34/18.55	                                    plus_plus(int),
18.34/18.55	                                    app_encode_app(int,int,bit1,K1)),
18.34/18.55	                     app_encode_app(int,int,bit0,L)) =
18.34/18.55	      app_encode_app(int,int,bit1,
18.34/18.55	                     app_encode_app(int,int,
18.34/18.55	                                    app_encode_app(int,
18.34/18.55	                                                   app_encode_fun(int,int),
18.34/18.55	                                                   plus_plus(int),K1),
18.34/18.55	                                    L))))).
18.34/18.55	tff('24', plain,
18.34/18.55	    ![X11 : int, X12 : int]:
18.34/18.55	      app_encode_app(int, int, 
18.34/18.55	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
18.34/18.55	          app_encode_app(int, int, bit1, X11)), 
18.34/18.55	        app_encode_app(int, int, bit0, X12))
18.34/18.55	       = app_encode_app(int, int, bit1, 
18.34/18.55	           app_encode_app(int, int, 
18.34/18.55	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
18.34/18.55	               X11), X12)),
18.34/18.55	    inference('cnf', [status(esa)], [zf_stmt_34])).
18.34/18.55	tff('25', plain,
18.34/18.55	    ![X0 : int]:
18.34/18.55	      app_encode_app(int, int, 
18.34/18.55	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
18.34/18.55	          one_one(int)), app_encode_app(int, int, bit0, X0))
18.34/18.55	       = app_encode_app(int, int, bit1, 
18.34/18.55	           app_encode_app(int, int, 
18.34/18.55	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
18.34/18.55	               pls), X0)),
18.34/18.55	    inference('sup+', [status(thm)], ['3', '24'])).
18.34/18.55	tff('26', plain,
18.34/18.55	    ![X0 : int]:
18.34/18.55	      app_encode_app(int, int, 
18.34/18.55	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
18.34/18.55	          one_one(int)), app_encode_app(int, int, bit0, X0))
18.34/18.55	       = app_encode_app(int, int, bit1, X0),
18.34/18.55	    inference('demod', [status(thm)], ['25', '11'])).
18.34/18.55	tff('27', plain,
18.34/18.55	    app_encode_app(int, int, 
18.34/18.55	      app_encode_app(int, app_encode_fun(int, int), legendre, min), 
18.34/18.55	      app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m)))
18.34/18.55	     != one_one(int),
18.34/18.55	    inference('demod', [status(thm)],
18.34/18.55	              ['18', '1', '3', '1', '5', '5', '12', '23', '26'])).
18.34/18.55	tff('28', plain,
18.34/18.55	    (one_one(int) != one_one(int)
18.34/18.55	     | ~ app_encode_app(int, $o, zprime, 
18.34/18.55	           app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m)))),
18.34/18.55	    inference('sup-', [status(thm)], ['17', '27'])).
18.34/18.55	tff(zf_stmt_26, axiom,
18.34/18.55	  (app_encode_app(int,$o,zprime,
18.34/18.55	                  app_encode_app(int,int,
18.34/18.55	                                 app_encode_app(int,app_encode_fun(int,int),
18.34/18.55	                                                plus_plus(int),
18.34/18.55	                                                app_encode_app(int,int,
18.34/18.55	                                                               app_encode_app(
18.34/18.55	                                                               int,
18.34/18.55	                                                               app_encode_fun(
18.34/18.55	                                                               int,int),
18.34/18.55	                                                               times_times(
18.34/18.55	                                                               int),
18.34/18.55	                                                               app_encode_app(
18.34/18.55	                                                               int,int,
18.34/18.55	                                                               number_number_of(
18.34/18.55	                                                               int),
18.34/18.55	                                                               app_encode_app(
18.34/18.55	                                                               int,int,bit0,
18.34/18.55	                                                               app_encode_app(
18.34/18.55	                                                               int,int,bit0,
18.34/18.55	                                                               app_encode_app(
18.34/18.55	                                                               int,int,bit1,
18.34/18.55	                                                               pls))))),m)),
18.34/18.55	                                 one_one(int))))).
18.34/18.55	tff('29', plain,
18.34/18.55	    app_encode_app(int, $o, zprime, 
18.34/18.55	      app_encode_app(int, int, 
18.34/18.55	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
18.34/18.55	          app_encode_app(int, int, 
18.34/18.55	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
18.34/18.55	              app_encode_app(int, int, number_number_of(int), 
18.34/18.55	                app_encode_app(int, int, bit0, 
18.34/18.55	                  app_encode_app(int, int, bit0, 
18.34/18.55	                    app_encode_app(int, int, bit1, pls))))), m)), 
18.34/18.55	        one_one(int))),
18.34/18.55	    inference('cnf', [status(esa)], [zf_stmt_26])).
18.34/18.55	tff('30', plain,
18.34/18.55	    app_encode_app(int, $o, zprime, 
18.34/18.55	      app_encode_app(int, int, 
18.34/18.55	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
18.34/18.55	          app_encode_app(int, int, 
18.34/18.55	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
18.34/18.55	              app_encode_app(int, int, bit0, 
18.34/18.55	                app_encode_app(int, int, bit0, 
18.34/18.55	                  app_encode_app(int, int, bit1, pls)))), m)), one_one(int))),
18.34/18.55	    inference('demod', [status(thm)], ['29', '1'])).
18.34/18.55	tff('31', plain,
18.34/18.55	    app_encode_app(int, $o, zprime, 
18.34/18.55	      app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m))),
18.34/18.55	    inference('demod', [status(thm)], ['30', '3', '5', '5', '12', '16'])).
18.34/18.55	tff('32', plain, (one_one(int) != one_one(int) | ~ $true),
18.34/18.55	    inference('demod', [status(thm)], ['28', '31'])).
18.34/18.55	tff('33', plain, $false, inference('simplify', [status(thm)], ['32'])).
18.34/18.55	
18.34/18.55	% SZS output end Refutation
18.34/18.55	EOF
