0.00/0.00	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : appext
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : rpo6
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n041.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 07:47:24 CST 2018
221.92/222.17	% done 11367 iterations in 221.972s
221.92/222.17	% SZS status Theorem for 'stdin'
221.92/222.17	% SZS output start Refutation
221.92/222.17	tff(zf_stmt_31, axiom,
221.92/222.17	  (![M:int]:
221.92/222.17	     (app_encode_app(int,$o,zprime,
221.92/222.17	                     app_encode_app(int,int,
221.92/222.17	                                    app_encode_app(int,
221.92/222.17	                                                   app_encode_fun(int,int),
221.92/222.17	                                                   plus_plus(int),
221.92/222.17	                                                   app_encode_app(int,int,
221.92/222.17	                                                                  app_encode_app(
221.92/222.17	                                                                  int,
221.92/222.17	                                                                  app_encode_fun(
221.92/222.17	                                                                  int,int),
221.92/222.17	                                                                  times_times(
221.92/222.17	                                                                  int),
221.92/222.17	                                                                  app_encode_app(
221.92/222.17	                                                                  int,int,
221.92/222.17	                                                                  number_number_of(
221.92/222.17	                                                                  int),
221.92/222.17	                                                                  app_encode_app(
221.92/222.17	                                                                  int,int,
221.92/222.17	                                                                  bit0,
221.92/222.17	                                                                  app_encode_app(
221.92/222.17	                                                                  int,int,
221.92/222.17	                                                                  bit0,
221.92/222.17	                                                                  app_encode_app(
221.92/222.17	                                                                  int,int,
221.92/222.17	                                                                  bit1,pls))))),
221.92/222.17	                                                                  M)),
221.92/222.17	                                    one_one(int))) =>
221.92/222.17	      (app_encode_app(int,int,
221.92/222.17	                      app_encode_app(int,app_encode_fun(int,int),legendre,
221.92/222.17	                                     app_encode_app(int,int,
221.92/222.17	                                                    number_number_of(int),min)),
221.92/222.17	                      app_encode_app(int,int,
221.92/222.17	                                     app_encode_app(int,
221.92/222.17	                                                    app_encode_fun(int,int),
221.92/222.17	                                                    plus_plus(int),
221.92/222.17	                                                    app_encode_app(int,int,
221.92/222.17	                                                                   app_encode_app(
221.92/222.17	                                                                   int,
221.92/222.17	                                                                   app_encode_fun(
221.92/222.17	                                                                   int,int),
221.92/222.17	                                                                   times_times(
221.92/222.17	                                                                   int),
221.92/222.17	                                                                   app_encode_app(
221.92/222.17	                                                                   int,int,
221.92/222.17	                                                                   number_number_of(
221.92/222.17	                                                                   int),
221.92/222.17	                                                                   app_encode_app(
221.92/222.17	                                                                   int,int,
221.92/222.17	                                                                   bit0,
221.92/222.17	                                                                   app_encode_app(
221.92/222.17	                                                                   int,int,
221.92/222.17	                                                                   bit0,
221.92/222.17	                                                                   app_encode_app(
221.92/222.17	                                                                   int,int,
221.92/222.17	                                                                   bit1,pls))))),
221.92/222.17	                                                                   M)),
221.92/222.17	                                     one_one(int))) =
221.92/222.17	       one_one(int))))).
221.92/222.17	tff('0', plain,
221.92/222.17	    ![X9 : int]:
221.92/222.17	      (app_encode_app(int, int, 
221.92/222.17	         app_encode_app(int, app_encode_fun(int, int), legendre, 
221.92/222.17	           app_encode_app(int, int, number_number_of(int), min)), 
221.92/222.17	         app_encode_app(int, int, 
221.92/222.17	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
221.92/222.17	             app_encode_app(int, int, 
221.92/222.17	               app_encode_app(int, app_encode_fun(int, int), 
221.92/222.17	                 times_times(int), 
221.92/222.17	                 app_encode_app(int, int, number_number_of(int), 
221.92/222.17	                   app_encode_app(int, int, bit0, 
221.92/222.17	                     app_encode_app(int, int, bit0, 
221.92/222.17	                       app_encode_app(int, int, bit1, pls))))), X9)), 
221.92/222.17	           one_one(int)))
221.92/222.17	        = one_one(int)
221.92/222.17	       | ~ app_encode_app(int, $o, zprime, 
221.92/222.17	             app_encode_app(int, int, 
221.92/222.17	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
221.92/222.17	                 app_encode_app(int, int, 
221.92/222.17	                   app_encode_app(int, app_encode_fun(int, int), 
221.92/222.17	                     times_times(int), 
221.92/222.17	                     app_encode_app(int, int, number_number_of(int), 
221.92/222.17	                       app_encode_app(int, int, bit0, 
221.92/222.17	                         app_encode_app(int, int, bit0, 
221.92/222.17	                           app_encode_app(int, int, bit1, pls))))), X9)), 
221.92/222.17	               one_one(int)))),
221.92/222.17	    inference('cnf', [status(esa)], [zf_stmt_31])).
221.92/222.17	tff(zf_stmt_63, axiom,
221.92/222.17	  (![K1:int]: (app_encode_app(int,int,number_number_of(int),K1) = K1))).
221.92/222.17	tff('1', plain,
221.92/222.17	    ![X74 : int]: app_encode_app(int, int, number_number_of(int), X74) = X74,
221.92/222.17	    inference('cnf', [status(esa)], [zf_stmt_63])).
221.92/222.17	tff(zf_stmt_80, axiom,
221.92/222.17	  (one_one(int) =
221.92/222.17	   app_encode_app(int,int,number_number_of(int),
221.92/222.17	                  app_encode_app(int,int,bit1,pls)))).
221.92/222.17	tff('2', plain,
221.92/222.17	    one_one(int)
221.92/222.17	     = app_encode_app(int, int, number_number_of(int), 
221.92/222.17	         app_encode_app(int, int, bit1, pls)),
221.92/222.17	    inference('cnf', [status(esa)], [zf_stmt_80])).
221.92/222.17	tff('3', plain, one_one(int) = app_encode_app(int, int, bit1, pls),
221.92/222.17	    inference('demod', [status(thm)], ['2', '1'])).
221.92/222.17	tff('4', plain,
221.92/222.17	    ![X9 : int]:
221.92/222.17	      (app_encode_app(int, int, 
221.92/222.17	         app_encode_app(int, app_encode_fun(int, int), legendre, min), 
221.92/222.17	         app_encode_app(int, int, 
221.92/222.17	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
221.92/222.17	             app_encode_app(int, int, 
221.92/222.17	               app_encode_app(int, app_encode_fun(int, int), 
221.92/222.17	                 times_times(int), 
221.92/222.17	                 app_encode_app(int, int, bit0, 
221.92/222.17	                   app_encode_app(int, int, bit0, one_one(int)))), X9)), 
221.92/222.17	           one_one(int)))
221.92/222.17	        = one_one(int)
221.92/222.17	       | ~ app_encode_app(int, $o, zprime, 
221.92/222.17	             app_encode_app(int, int, 
221.92/222.17	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
221.92/222.17	                 app_encode_app(int, int, 
221.92/222.17	                   app_encode_app(int, app_encode_fun(int, int), 
221.92/222.17	                     times_times(int), 
221.92/222.17	                     app_encode_app(int, int, bit0, 
221.92/222.17	                       app_encode_app(int, int, bit0, one_one(int)))), X9)), 
221.92/222.17	               one_one(int)))),
221.92/222.17	    inference('demod', [status(thm)], ['0', '1', '3', '1', '3', '1'])).
221.92/222.17	tff(zf_stmt_66, axiom,
221.92/222.17	  (![K1:int]:
221.92/222.17	     (app_encode_app(int,int,bit0,K1) =
221.92/222.17	      app_encode_app(int,int,
221.92/222.17	                     app_encode_app(int,app_encode_fun(int,int),
221.92/222.17	                                    plus_plus(int),K1),
221.92/222.17	                     K1)))).
221.92/222.17	tff('5', plain,
221.92/222.17	    ![X77 : int]:
221.92/222.17	      app_encode_app(int, int, bit0, X77)
221.92/222.17	       = app_encode_app(int, int, 
221.92/222.17	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X77), 
221.92/222.17	           X77),
221.92/222.17	    inference('cnf', [status(esa)], [zf_stmt_66])).
221.92/222.17	tff('6', plain,
221.92/222.17	    ![X9 : int]:
221.92/222.17	      (app_encode_app(int, int, 
221.92/222.17	         app_encode_app(int, app_encode_fun(int, int), legendre, min), 
221.92/222.17	         app_encode_app(int, int, 
221.92/222.17	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
221.92/222.17	             app_encode_app(int, int, 
221.92/222.17	               app_encode_app(int, app_encode_fun(int, int), 
221.92/222.17	                 times_times(int), 
221.92/222.17	                 app_encode_app(int, int, 
221.92/222.17	                   app_encode_app(int, app_encode_fun(int, int), 
221.92/222.17	                     plus_plus(int), 
221.92/222.17	                     app_encode_app(int, int, 
221.92/222.17	                       app_encode_app(int, app_encode_fun(int, int), 
221.92/222.17	                         plus_plus(int), one_one(int)), one_one(int))), 
221.92/222.17	                   app_encode_app(int, int, 
221.92/222.17	                     app_encode_app(int, app_encode_fun(int, int), 
221.92/222.17	                       plus_plus(int), one_one(int)), one_one(int)))), X9)), 
221.92/222.17	           one_one(int)))
221.92/222.17	        = one_one(int)
221.92/222.17	       | ~ app_encode_app(int, $o, zprime, 
221.92/222.17	             app_encode_app(int, int, 
221.92/222.17	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
221.92/222.17	                 app_encode_app(int, int, 
221.92/222.17	                   app_encode_app(int, app_encode_fun(int, int), 
221.92/222.17	                     times_times(int), 
221.92/222.17	                     app_encode_app(int, int, 
221.92/222.18	                       app_encode_app(int, app_encode_fun(int, int), 
221.92/222.18	                         plus_plus(int), 
221.92/222.18	                         app_encode_app(int, int, 
221.92/222.18	                           app_encode_app(int, app_encode_fun(int, int), 
221.92/222.18	                             plus_plus(int), one_one(int)), one_one(int))), 
221.92/222.18	                       app_encode_app(int, int, 
221.92/222.18	                         app_encode_app(int, app_encode_fun(int, int), 
221.92/222.18	                           plus_plus(int), one_one(int)), one_one(int)))), 
221.92/222.18	                   X9)), one_one(int)))),
221.92/222.18	    inference('demod', [status(thm)], ['4', '5', '5', '5', '5'])).
221.92/222.18	tff(zf_stmt_126, axiom, (number_semiring(int))).
221.92/222.18	tff('7', plain, number_semiring(int),
221.92/222.18	    inference('cnf', [status(esa)], [zf_stmt_126])).
221.92/222.18	tff(zf_stmt_86, axiom,
221.92/222.18	  (![A:$tType]:
221.92/222.18	     (number_semiring(A) =>
221.92/222.18	      (![Z1:A]:
221.92/222.18	         (app_encode_app(A,A,
221.92/222.18	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
221.92/222.18	                                        Z1),
221.92/222.18	                         app_encode_app(int,A,number_number_of(A),
221.92/222.18	                                        app_encode_app(int,int,bit0,
221.92/222.18	                                                       app_encode_app(
221.92/222.18	                                                       int,int,bit1,pls)))) =
221.92/222.18	          app_encode_app(A,A,
221.92/222.18	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),Z1),
221.92/222.18	                         Z1)))))).
221.92/222.18	tff('8', plain,
221.92/222.18	    ![X117 : $tType, X118 : X117]:
221.92/222.18	      (app_encode_app(X117, X117, 
221.92/222.18	         app_encode_app(X117, app_encode_fun(X117, X117), times_times(X117), 
221.92/222.18	           X118), 
221.92/222.18	         app_encode_app(int, X117, number_number_of(X117), 
221.92/222.18	           app_encode_app(int, int, bit0, 
221.92/222.18	             app_encode_app(int, int, bit1, pls))))
221.92/222.18	        = app_encode_app(X117, X117, 
221.92/222.18	            app_encode_app(X117, app_encode_fun(X117, X117), 
221.92/222.18	              plus_plus(X117), X118), X118)
221.92/222.18	       | ~ number_semiring(X117)),
221.92/222.18	    inference('cnf', [status(esa)], [zf_stmt_86])).
221.92/222.18	tff(zf_stmt_35, axiom,
221.92/222.18	  (![L:int,K1:int]:
221.92/222.18	     (app_encode_app(int,int,
221.92/222.18	                     app_encode_app(int,app_encode_fun(int,int),
221.92/222.18	                                    plus_plus(int),
221.92/222.18	                                    app_encode_app(int,int,bit1,K1)),
221.92/222.18	                     app_encode_app(int,int,bit0,L)) =
221.92/222.18	      app_encode_app(int,int,bit1,
221.92/222.18	                     app_encode_app(int,int,
221.92/222.18	                                    app_encode_app(int,
221.92/222.18	                                                   app_encode_fun(int,int),
221.92/222.18	                                                   plus_plus(int),K1),
221.92/222.18	                                    L))))).
221.92/222.18	tff('9', plain,
221.92/222.18	    ![X15 : int, X16 : int]:
221.92/222.18	      app_encode_app(int, int, 
221.92/222.18	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
221.92/222.18	          app_encode_app(int, int, bit1, X15)), 
221.92/222.18	        app_encode_app(int, int, bit0, X16))
221.92/222.18	       = app_encode_app(int, int, bit1, 
221.92/222.18	           app_encode_app(int, int, 
221.92/222.18	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
221.92/222.18	               X15), X16)),
221.92/222.18	    inference('cnf', [status(esa)], [zf_stmt_35])).
221.92/222.18	tff('10', plain,
221.92/222.18	    ![X0 : int]:
221.92/222.18	      app_encode_app(int, int, 
221.92/222.18	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
221.92/222.18	          one_one(int)), app_encode_app(int, int, bit0, X0))
221.92/222.18	       = app_encode_app(int, int, bit1, 
221.92/222.18	           app_encode_app(int, int, 
221.92/222.18	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
221.92/222.18	               pls), X0)),
221.92/222.18	    inference('sup+', [status(thm)], ['3', '9'])).
221.92/222.18	tff(zf_stmt_50, axiom,
221.92/222.18	  (![W1:int]:
221.92/222.18	     (app_encode_app(int,int,
221.92/222.18	                     app_encode_app(int,app_encode_fun(int,int),
221.92/222.18	                                    times_times(int),pls),
221.92/222.18	                     W1) =
221.92/222.18	      pls))).
221.92/222.18	tff('11', plain,
221.92/222.18	    ![X51 : int]:
221.92/222.18	      app_encode_app(int, int, 
221.92/222.18	        app_encode_app(int, app_encode_fun(int, int), times_times(int), pls), 
221.92/222.18	        X51)
221.92/222.18	       = pls,
221.92/222.18	    inference('cnf', [status(esa)], [zf_stmt_50])).
221.92/222.18	tff(zf_stmt_32, axiom,
221.92/222.18	  (![L:int,K1:int]:
221.92/222.18	     (app_encode_app(int,int,
221.92/222.18	                     app_encode_app(int,app_encode_fun(int,int),
221.92/222.18	                                    times_times(int),
221.92/222.18	                                    app_encode_app(int,int,bit1,K1)),
221.92/222.18	                     L) =
221.92/222.18	      app_encode_app(int,int,
221.92/222.18	                     app_encode_app(int,app_encode_fun(int,int),
221.92/222.18	                                    plus_plus(int),
221.92/222.18	                                    app_encode_app(int,int,bit0,
221.92/222.18	                                                   app_encode_app(int,int,
221.92/222.18	                                                                  app_encode_app(
221.92/222.18	                                                                  int,
221.92/222.18	                                                                  app_encode_fun(
221.92/222.18	                                                                  int,int),
221.92/222.18	                                                                  times_times(
221.92/222.18	                                                                  int),K1),L))),
221.92/222.18	                     L)))).
221.92/222.18	tff('12', plain,
221.92/222.18	    ![X10 : int, X11 : int]:
221.92/222.18	      app_encode_app(int, int, 
221.92/222.18	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
221.92/222.18	          app_encode_app(int, int, bit1, X10)), X11)
221.92/222.18	       = app_encode_app(int, int, 
221.92/222.18	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
221.92/222.18	             app_encode_app(int, int, bit0, 
221.92/222.18	               app_encode_app(int, int, 
221.92/222.18	                 app_encode_app(int, app_encode_fun(int, int), 
221.92/222.18	                   times_times(int), X10), X11))), X11),
221.92/222.18	    inference('cnf', [status(esa)], [zf_stmt_32])).
221.92/222.18	tff('13', plain,
221.92/222.18	    ![X0 : int]:
221.92/222.18	      app_encode_app(int, int, 
221.92/222.18	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
221.92/222.18	          app_encode_app(int, int, bit1, pls)), X0)
221.92/222.18	       = app_encode_app(int, int, 
221.92/222.18	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
221.92/222.18	             app_encode_app(int, int, bit0, pls)), X0),
221.92/222.18	    inference('sup+', [status(thm)], ['11', '12'])).
221.92/222.18	tff(zf_stmt_65, axiom,
221.92/222.18	  (![K1:int]:
221.92/222.18	     (app_encode_app(int,int,
221.92/222.18	                     app_encode_app(int,app_encode_fun(int,int),
221.92/222.18	                                    plus_plus(int),pls),
221.92/222.18	                     K1) =
221.92/222.18	      K1))).
221.92/222.18	tff('14', plain,
221.92/222.18	    ![X76 : int]:
221.92/222.18	      app_encode_app(int, int, 
221.92/222.18	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
221.92/222.18	        X76)
221.92/222.18	       = X76,
221.92/222.18	    inference('cnf', [status(esa)], [zf_stmt_65])).
221.92/222.18	tff('15', plain,
221.92/222.18	    ![X0 : int]:
221.92/222.18	      app_encode_app(int, int, 
221.92/222.18	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
221.92/222.18	          one_one(int)), X0)
221.92/222.18	       = app_encode_app(int, int, 
221.92/222.18	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
221.92/222.18	           X0),
221.92/222.18	    inference('demod', [status(thm)], ['13', '3', '5', '14'])).
221.92/222.18	tff('16', plain,
221.92/222.18	    ![X0 : int]:
221.92/222.18	      app_encode_app(int, int, 
221.92/222.18	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
221.92/222.18	          one_one(int)), app_encode_app(int, int, bit0, X0))
221.92/222.18	       = app_encode_app(int, int, bit1, 
221.92/222.18	           app_encode_app(int, int, 
221.92/222.18	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
221.92/222.18	               one_one(int)), X0)),
221.92/222.18	    inference('demod', [status(thm)], ['10', '15'])).
221.92/222.18	tff('17', plain,
221.92/222.18	    ![X0 : int]:
221.92/222.18	      app_encode_app(int, int, 
221.92/222.18	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
221.92/222.18	          one_one(int)), X0)
221.92/222.18	       = X0,
221.92/222.18	    inference('sup+', [status(thm)], ['15', '14'])).
221.92/222.18	tff('18', plain,
221.92/222.18	    ![X0 : int]:
221.92/222.18	      app_encode_app(int, int, 
221.92/222.18	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
221.92/222.18	          one_one(int)), app_encode_app(int, int, bit0, X0))
221.92/222.18	       = app_encode_app(int, int, bit1, X0),
221.92/222.18	    inference('demod', [status(thm)], ['16', '17'])).
221.92/222.18	tff(zf_stmt_51, axiom,
221.92/222.18	  (![L:int,K1:int]:
221.92/222.18	     (app_encode_app(int,int,
221.92/222.18	                     app_encode_app(int,app_encode_fun(int,int),
221.92/222.18	                                    times_times(int),
221.92/222.18	                                    app_encode_app(int,int,bit0,K1)),
221.92/222.18	                     L) =
221.92/222.18	      app_encode_app(int,int,bit0,
221.92/222.18	                     app_encode_app(int,int,
221.92/222.18	                                    app_encode_app(int,
221.92/222.18	                                                   app_encode_fun(int,int),
221.92/222.18	                                                   times_times(int),K1),
221.92/222.18	                                    L))))).
221.92/222.18	tff('19', plain,
221.92/222.18	    ![X52 : int, X53 : int]:
221.92/222.18	      app_encode_app(int, int, 
221.92/222.18	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
221.92/222.18	          app_encode_app(int, int, bit0, X52)), X53)
221.92/222.18	       = app_encode_app(int, int, bit0, 
221.92/222.18	           app_encode_app(int, int, 
221.92/222.18	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
221.92/222.18	               X52), X53)),
221.92/222.18	    inference('cnf', [status(esa)], [zf_stmt_51])).
221.92/222.18	tff('20', plain,
221.92/222.18	    ![X0 : int, X1 : int]:
221.92/222.18	      app_encode_app(int, int, 
221.92/222.18	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
221.92/222.18	          app_encode_app(int, int, 
221.92/222.18	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
221.92/222.18	            X0)), X1)
221.92/222.18	       = app_encode_app(int, int, bit0, 
221.92/222.18	           app_encode_app(int, int, 
221.92/222.18	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
221.92/222.18	               X0), X1)),
221.92/222.18	    inference('sup+', [status(thm)], ['5', '19'])).
221.92/222.18	tff('21', plain,
221.92/222.18	    ![X0 : int]:
221.92/222.18	      app_encode_app(int, int, 
221.92/222.18	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
221.92/222.18	          app_encode_app(int, int, 
221.92/222.18	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
221.92/222.18	              one_one(int)), one_one(int))), X0)
221.92/222.18	       = app_encode_app(int, int, bit0, X0),
221.92/222.18	    inference('sup+', [status(thm)], ['17', '20'])).
221.92/222.18	tff('22', plain,
221.92/222.18	    ![X0 : int]:
221.92/222.18	      app_encode_app(int, int, 
221.92/222.18	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
221.92/222.18	          one_one(int)), 
221.92/222.18	        app_encode_app(int, int, 
221.92/222.18	          app_encode_app(int, app_encode_fun(int, int), times_times(int), 
221.92/222.18	            app_encode_app(int, int, 
221.92/222.18	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
221.92/222.18	                one_one(int)), one_one(int))), X0))
221.92/222.18	       = app_encode_app(int, int, bit1, X0),
221.92/222.18	    inference('demod', [status(thm)], ['18', '21'])).
221.92/222.18	tff('23', plain,
221.92/222.18	    ![X77 : int]:
221.92/222.18	      app_encode_app(int, int, 
221.92/222.18	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
221.92/222.18	          app_encode_app(int, int, 
221.92/222.18	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
221.92/222.18	              one_one(int)), one_one(int))), X77)
221.92/222.18	       = app_encode_app(int, int, 
221.92/222.18	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X77), 
221.92/222.18	           X77),
221.92/222.18	    inference('demod', [status(thm)], ['5', '21'])).
221.92/222.18	tff(zf_stmt_64, axiom,
221.92/222.18	  (![K1:int]:
221.92/222.18	     (app_encode_app(int,int,
221.92/222.18	                     app_encode_app(int,app_encode_fun(int,int),
221.92/222.18	                                    plus_plus(int),K1),
221.92/222.18	                     pls) =
221.92/222.18	      K1))).
221.92/222.18	tff('24', plain,
221.92/222.18	    ![X75 : int]:
221.92/222.18	      app_encode_app(int, int, 
221.92/222.18	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X75), 
221.92/222.18	        pls)
221.92/222.18	       = X75,
221.92/222.18	    inference('cnf', [status(esa)], [zf_stmt_64])).
221.92/222.18	tff('25', plain,
221.92/222.18	    app_encode_app(int, int, 
221.92/222.18	      app_encode_app(int, app_encode_fun(int, int), times_times(int), 
221.92/222.18	        app_encode_app(int, int, 
221.92/222.18	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
221.92/222.18	            one_one(int)), one_one(int))), pls)
221.92/222.18	     = pls,
221.92/222.18	    inference('sup+', [status(thm)], ['23', '24'])).
221.92/222.18	tff('26', plain,
221.92/222.18	    ![X117 : $tType, X118 : X117]:
221.92/222.18	      (app_encode_app(X117, X117, 
221.92/222.18	         app_encode_app(X117, app_encode_fun(X117, X117), times_times(X117), 
221.92/222.18	           X118), 
221.92/222.18	         app_encode_app(int, X117, number_number_of(X117), 
221.92/222.18	           app_encode_app(int, int, 
221.92/222.18	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
221.92/222.18	               one_one(int)), one_one(int))))
221.92/222.18	        = app_encode_app(X117, X117, 
221.92/222.18	            app_encode_app(X117, app_encode_fun(X117, X117), 
221.92/222.18	              plus_plus(X117), X118), X118)
221.92/222.18	       | ~ number_semiring(X117)),
221.92/222.18	    inference('demod', [status(thm)], ['8', '22', '25', '24', '21', '23'])).
221.92/222.18	tff('27', plain,
221.92/222.18	    ![X0 : int]:
221.92/222.18	      (~ $true
221.92/222.18	       | app_encode_app(int, int, 
221.92/222.18	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
221.92/222.18	             X0), 
221.92/222.18	           app_encode_app(int, int, number_number_of(int), 
221.92/222.18	             app_encode_app(int, int, 
221.92/222.18	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
221.92/222.18	                 one_one(int)), one_one(int))))
221.92/222.18	          = app_encode_app(int, int, 
221.92/222.18	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
221.92/222.18	                X0), X0)),
221.92/222.18	    inference('sup-', [status(thm)], ['7', '26'])).
221.92/222.18	tff('28', plain,
221.92/222.18	    ![X0 : int]:
221.92/222.18	      (~ $true
221.92/222.18	       | app_encode_app(int, int, 
221.92/222.18	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
221.92/222.18	             X0), 
221.92/222.18	           app_encode_app(int, int, 
221.92/222.18	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
221.92/222.18	               one_one(int)), one_one(int)))
221.92/222.18	          = app_encode_app(int, int, 
221.92/222.18	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
221.92/222.18	                X0), X0)),
221.92/222.18	    inference('demod', [status(thm)], ['27', '1'])).
221.92/222.18	tff('29', plain,
221.92/222.18	    ![X0 : int]:
221.92/222.18	      app_encode_app(int, int, 
221.92/222.18	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X0), 
221.92/222.18	        app_encode_app(int, int, 
221.92/222.18	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
221.92/222.18	            one_one(int)), one_one(int)))
221.92/222.18	       = app_encode_app(int, int, 
221.92/222.18	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
221.92/222.18	           X0),
221.92/222.18	    inference('simplify', [status(thm)], ['28'])).
221.92/222.18	tff('30', plain,
221.92/222.18	    ![X0 : int, X1 : int]:
221.92/222.18	      app_encode_app(int, int, 
221.92/222.18	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
221.92/222.18	          app_encode_app(int, int, bit0, X0)), X1)
221.92/222.18	       = app_encode_app(int, int, bit0, 
221.92/222.18	           app_encode_app(int, int, 
221.92/222.18	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
221.92/222.18	               X0), X1)),
221.92/222.18	    inference('sup+', [status(thm)], ['5', '20'])).
221.92/222.18	tff('31', plain,
221.92/222.18	    ![X0 : int, X1 : int]:
221.92/222.18	      app_encode_app(int, int, 
221.92/222.18	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
221.92/222.18	          app_encode_app(int, int, 
221.92/222.18	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
221.92/222.18	              app_encode_app(int, int, 
221.92/222.18	                app_encode_app(int, app_encode_fun(int, int), 
221.92/222.18	                  plus_plus(int), one_one(int)), one_one(int))), X0)), X1)
221.92/222.18	       = app_encode_app(int, int, 
221.92/222.18	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
221.92/222.18	             app_encode_app(int, int, 
221.92/222.18	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
221.92/222.18	                 one_one(int)), one_one(int))), 
221.92/222.18	           app_encode_app(int, int, 
221.92/222.18	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
221.92/222.18	               X0), X1)),
221.92/222.18	    inference('demod', [status(thm)], ['30', '21', '21'])).
221.92/222.18	tff(zf_stmt_125, axiom, (comm_semiring_1(int))).
221.92/222.18	tff('32', plain, comm_semiring_1(int),
221.92/222.18	    inference('cnf', [status(esa)], [zf_stmt_125])).
221.92/222.18	tff(zf_stmt_106, axiom,
221.92/222.18	  (![A:$tType]:
221.92/222.18	     (comm_semiring_1(A) =>
221.92/222.18	      (![C:A,A1:A]:
221.92/222.18	         (app_encode_app(A,A,
221.92/222.18	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),A1),
221.92/222.18	                         C) =
221.92/222.18	          app_encode_app(A,A,
221.92/222.18	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),C),
221.92/222.18	                         A1)))))).
221.92/222.18	tff('33', plain,
221.92/222.18	    ![X165 : $tType, X166 : X165, X167 : X165]:
221.92/222.18	      (app_encode_app(X165, X165, 
221.92/222.18	         app_encode_app(X165, app_encode_fun(X165, X165), plus_plus(X165), 
221.92/222.18	           X167), X166)
221.92/222.18	        = app_encode_app(X165, X165, 
221.92/222.18	            app_encode_app(X165, app_encode_fun(X165, X165), 
221.92/222.18	              plus_plus(X165), X166), X167)
221.92/222.18	       | ~ comm_semiring_1(X165)),
221.92/222.18	    inference('cnf', [status(esa)], [zf_stmt_106])).
221.92/222.18	tff('34', plain,
221.92/222.18	    ![X0 : int, X1 : int]:
221.92/222.18	      (~ $true
221.92/222.18	       | app_encode_app(int, int, 
221.92/222.18	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X1), 
221.92/222.18	           X0)
221.92/222.18	          = app_encode_app(int, int, 
221.92/222.18	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
221.92/222.18	                X0), X1)),
221.92/222.18	    inference('sup-', [status(thm)], ['32', '33'])).
221.92/222.18	tff('35', plain,
221.92/222.18	    ![X0 : int, X1 : int]:
221.92/222.18	      app_encode_app(int, int, 
221.92/222.18	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X1), 
221.92/222.18	        X0)
221.92/222.18	       = app_encode_app(int, int, 
221.92/222.18	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
221.92/222.18	           X1),
221.92/222.18	    inference('simplify', [status(thm)], ['34'])).
221.92/222.18	tff('36', plain,
221.92/222.18	    ![X9 : int]:
221.92/222.18	      (app_encode_app(int, int, 
221.92/222.18	         app_encode_app(int, app_encode_fun(int, int), legendre, min), 
221.92/222.18	         app_encode_app(int, int, 
221.92/222.18	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
221.92/222.18	             one_one(int)), 
221.92/222.18	           app_encode_app(int, int, 
221.92/222.18	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
221.92/222.18	               app_encode_app(int, int, 
221.92/222.18	                 app_encode_app(int, app_encode_fun(int, int), 
221.92/222.18	                   plus_plus(int), one_one(int)), one_one(int))), 
221.92/222.18	             app_encode_app(int, int, 
221.92/222.18	               app_encode_app(int, app_encode_fun(int, int), 
221.92/222.18	                 times_times(int), 
221.92/222.18	                 app_encode_app(int, int, 
221.92/222.18	                   app_encode_app(int, app_encode_fun(int, int), 
221.92/222.18	                     plus_plus(int), one_one(int)), one_one(int))), X9))))
221.92/222.18	        = one_one(int)
221.92/222.18	       | ~ app_encode_app(int, $o, zprime, 
221.92/222.18	             app_encode_app(int, int, 
221.92/222.18	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
221.92/222.18	                 one_one(int)), 
221.92/222.18	               app_encode_app(int, int, 
221.92/222.18	                 app_encode_app(int, app_encode_fun(int, int), 
221.92/222.18	                   times_times(int), 
221.92/222.18	                   app_encode_app(int, int, 
221.92/222.18	                     app_encode_app(int, app_encode_fun(int, int), 
221.92/222.18	                       plus_plus(int), one_one(int)), one_one(int))), 
221.92/222.18	                 app_encode_app(int, int, 
221.92/222.18	                   app_encode_app(int, app_encode_fun(int, int), 
221.92/222.18	                     times_times(int), 
221.92/222.18	                     app_encode_app(int, int, 
221.92/222.18	                       app_encode_app(int, app_encode_fun(int, int), 
221.92/222.18	                         plus_plus(int), one_one(int)), one_one(int))), X9))))),
221.92/222.18	    inference('demod', [status(thm)],
221.92/222.18	              ['6', '29', '31', '35', '29', '31', '35'])).
221.92/222.18	tff(zf_stmt_138, conjecture,
221.92/222.18	  (app_encode_app(int,int,
221.92/222.18	                  app_encode_app(int,app_encode_fun(int,int),legendre,
221.92/222.18	                                 app_encode_app(int,int,
221.92/222.18	                                                number_number_of(int),min)),
221.92/222.18	                  app_encode_app(int,int,
221.92/222.18	                                 app_encode_app(int,app_encode_fun(int,int),
221.92/222.18	                                                plus_plus(int),
221.92/222.18	                                                app_encode_app(int,int,
221.92/222.18	                                                               app_encode_app(
221.92/222.18	                                                               int,
221.92/222.18	                                                               app_encode_fun(
221.92/222.18	                                                               int,int),
221.92/222.18	                                                               times_times(
221.92/222.18	                                                               int),
221.92/222.18	                                                               app_encode_app(
221.92/222.18	                                                               int,int,
221.92/222.18	                                                               number_number_of(
221.92/222.18	                                                               int),
221.92/222.18	                                                               app_encode_app(
221.92/222.18	                                                               int,int,bit0,
221.92/222.18	                                                               app_encode_app(
221.92/222.18	                                                               int,int,bit0,
221.92/222.18	                                                               app_encode_app(
221.92/222.18	                                                               int,int,bit1,
221.92/222.18	                                                               pls))))),m)),
221.92/222.18	                                 one_one(int))) =
221.92/222.18	   one_one(int))).
221.92/222.18	tff(zf_stmt_0, negated_conjecture,
221.92/222.18	  (app_encode_app(int,int,
221.92/222.18	                  app_encode_app(int,app_encode_fun(int,int),legendre,
221.92/222.18	                                 app_encode_app(int,int,
221.92/222.18	                                                number_number_of(int),min)),
221.92/222.18	                  app_encode_app(int,int,
221.92/222.18	                                 app_encode_app(int,app_encode_fun(int,int),
221.92/222.18	                                                plus_plus(int),
221.92/222.18	                                                app_encode_app(int,int,
221.92/222.18	                                                               app_encode_app(
221.92/222.18	                                                               int,
221.92/222.18	                                                               app_encode_fun(
221.92/222.18	                                                               int,int),
221.92/222.18	                                                               times_times(
221.92/222.18	                                                               int),
221.92/222.18	                                                               app_encode_app(
221.92/222.18	                                                               int,int,
221.92/222.18	                                                               number_number_of(
221.92/222.18	                                                               int),
221.92/222.18	                                                               app_encode_app(
221.92/222.18	                                                               int,int,bit0,
221.92/222.18	                                                               app_encode_app(
221.92/222.18	                                                               int,int,bit0,
221.92/222.18	                                                               app_encode_app(
221.92/222.18	                                                               int,int,bit1,
221.92/222.18	                                                               pls))))),m)),
221.92/222.18	                                 one_one(int))) !=
221.92/222.18	   one_one(int))).
221.92/222.18	tff('37', plain,
221.92/222.18	    app_encode_app(int, int, 
221.92/222.18	      app_encode_app(int, app_encode_fun(int, int), legendre, 
221.92/222.18	        app_encode_app(int, int, number_number_of(int), min)), 
221.92/222.18	      app_encode_app(int, int, 
221.92/222.18	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
221.92/222.18	          app_encode_app(int, int, 
221.92/222.18	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
221.92/222.18	              app_encode_app(int, int, number_number_of(int), 
221.92/222.18	                app_encode_app(int, int, bit0, 
221.92/222.18	                  app_encode_app(int, int, bit0, 
221.92/222.18	                    app_encode_app(int, int, bit1, pls))))), m)), 
221.92/222.18	        one_one(int)))
221.92/222.18	     != one_one(int),
221.92/222.18	    inference('cnf', [status(esa)], [zf_stmt_0])).
221.92/222.18	tff(zf_stmt_98, axiom,
221.92/222.18	  (![A:$tType]:
221.92/222.18	     (comm_semiring_1(A) =>
221.92/222.18	      (![B:A,A1:A]:
221.92/222.18	         (app_encode_app(A,A,
221.92/222.18	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
221.92/222.18	                                        A1),
221.92/222.18	                         B) =
221.92/222.18	          app_encode_app(A,A,
221.92/222.18	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
221.92/222.18	                                        B),
221.92/222.18	                         A1)))))).
221.92/222.18	tff('38', plain,
221.92/222.18	    ![X131 : $tType, X132 : X131, X133 : X131]:
221.92/222.18	      (app_encode_app(X131, X131, 
221.92/222.18	         app_encode_app(X131, app_encode_fun(X131, X131), times_times(X131), 
221.92/222.18	           X133), X132)
221.92/222.18	        = app_encode_app(X131, X131, 
221.92/222.18	            app_encode_app(X131, app_encode_fun(X131, X131), 
221.92/222.18	              times_times(X131), X132), X133)
221.92/222.18	       | ~ comm_semiring_1(X131)),
221.92/222.18	    inference('cnf', [status(esa)], [zf_stmt_98])).
221.92/222.18	tff('39', plain,
221.92/222.18	    ![X0 : int, X1 : int]:
221.92/222.18	      (~ $true
221.92/222.18	       | app_encode_app(int, int, 
221.92/222.18	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
221.92/222.18	             X1), X0)
221.92/222.18	          = app_encode_app(int, int, 
221.92/222.18	              app_encode_app(int, app_encode_fun(int, int), 
221.92/222.18	                times_times(int), X0), X1)),
221.92/222.18	    inference('sup-', [status(thm)], ['32', '38'])).
221.92/222.18	tff('40', plain,
221.92/222.18	    ![X0 : int, X1 : int]:
221.92/222.18	      app_encode_app(int, int, 
221.92/222.18	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X1), 
221.92/222.18	        X0)
221.92/222.18	       = app_encode_app(int, int, 
221.92/222.18	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
221.92/222.18	             X0), X1),
221.92/222.18	    inference('simplify', [status(thm)], ['39'])).
221.92/222.18	tff('41', plain,
221.92/222.18	    ![X0 : int]:
221.92/222.18	      app_encode_app(int, int, 
221.92/222.18	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X0), 
221.92/222.18	        pls)
221.92/222.18	       = pls,
221.92/222.18	    inference('sup+', [status(thm)], ['40', '11'])).
221.92/222.18	tff('42', plain,
221.92/222.18	    app_encode_app(int, int, 
221.92/222.18	      app_encode_app(int, app_encode_fun(int, int), legendre, min), 
221.92/222.18	      app_encode_app(int, int, 
221.92/222.18	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
221.92/222.18	          one_one(int)), 
221.92/222.18	        app_encode_app(int, int, 
221.92/222.18	          app_encode_app(int, app_encode_fun(int, int), times_times(int), 
221.92/222.18	            app_encode_app(int, int, 
221.92/222.18	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
221.92/222.18	                one_one(int)), one_one(int))), 
221.92/222.18	          app_encode_app(int, int, 
221.92/222.18	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
221.92/222.18	              app_encode_app(int, int, 
221.92/222.18	                app_encode_app(int, app_encode_fun(int, int), 
221.92/222.18	                  plus_plus(int), one_one(int)), one_one(int))), m))))
221.92/222.18	     != one_one(int),
221.92/222.18	    inference('demod', [status(thm)],
221.92/222.18	              ['37', '1', '22', '41', '24', '21', '23', '21', '1', '31', '35'])).
221.92/222.18	tff('43', plain,
221.92/222.18	    (one_one(int) != one_one(int)
221.92/222.18	     | ~ app_encode_app(int, $o, zprime, 
221.92/222.18	           app_encode_app(int, int, 
221.92/222.18	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
221.92/222.18	               one_one(int)), 
221.92/222.18	             app_encode_app(int, int, 
221.92/222.18	               app_encode_app(int, app_encode_fun(int, int), 
221.92/222.18	                 times_times(int), 
221.92/222.18	                 app_encode_app(int, int, 
221.92/222.18	                   app_encode_app(int, app_encode_fun(int, int), 
221.92/222.18	                     plus_plus(int), one_one(int)), one_one(int))), 
221.92/222.18	               app_encode_app(int, int, 
221.92/222.18	                 app_encode_app(int, app_encode_fun(int, int), 
221.92/222.18	                   times_times(int), 
221.92/222.18	                   app_encode_app(int, int, 
221.92/222.18	                     app_encode_app(int, app_encode_fun(int, int), 
221.92/222.18	                       plus_plus(int), one_one(int)), one_one(int))), m))))),
221.92/222.18	    inference('sup-', [status(thm)], ['36', '42'])).
221.92/222.18	tff('44', plain,
221.92/222.18	    ~ app_encode_app(int, $o, zprime, 
221.92/222.18	        app_encode_app(int, int, 
221.92/222.18	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
221.92/222.18	            one_one(int)), 
221.92/222.18	          app_encode_app(int, int, 
221.92/222.18	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
221.92/222.18	              app_encode_app(int, int, 
221.92/222.18	                app_encode_app(int, app_encode_fun(int, int), 
221.92/222.18	                  plus_plus(int), one_one(int)), one_one(int))), 
221.92/222.18	            app_encode_app(int, int, 
221.92/222.18	              app_encode_app(int, app_encode_fun(int, int), 
221.92/222.18	                times_times(int), 
221.92/222.18	                app_encode_app(int, int, 
221.92/222.18	                  app_encode_app(int, app_encode_fun(int, int), 
221.92/222.18	                    plus_plus(int), one_one(int)), one_one(int))), m)))),
221.92/222.18	    inference('simplify', [status(thm)], ['43'])).
221.92/222.18	tff(zf_stmt_27, axiom,
221.92/222.18	  (app_encode_app(int,$o,zprime,
221.92/222.18	                  app_encode_app(int,int,
221.92/222.18	                                 app_encode_app(int,app_encode_fun(int,int),
221.92/222.18	                                                plus_plus(int),
221.92/222.18	                                                app_encode_app(int,int,
221.92/222.18	                                                               app_encode_app(
221.92/222.18	                                                               int,
221.92/222.18	                                                               app_encode_fun(
221.92/222.18	                                                               int,int),
221.92/222.18	                                                               times_times(
221.92/222.18	                                                               int),
221.92/222.18	                                                               app_encode_app(
221.92/222.18	                                                               int,int,
221.92/222.18	                                                               number_number_of(
221.92/222.18	                                                               int),
221.92/222.18	                                                               app_encode_app(
221.92/222.18	                                                               int,int,bit0,
221.92/222.18	                                                               app_encode_app(
221.92/222.18	                                                               int,int,bit0,
221.92/222.18	                                                               app_encode_app(
221.92/222.18	                                                               int,int,bit1,
221.92/222.18	                                                               pls))))),m)),
221.92/222.18	                                 one_one(int))))).
221.92/222.18	tff('45', plain,
221.92/222.18	    app_encode_app(int, $o, zprime, 
221.92/222.18	      app_encode_app(int, int, 
221.92/222.18	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
221.92/222.18	          app_encode_app(int, int, 
221.92/222.18	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
221.92/222.18	              app_encode_app(int, int, number_number_of(int), 
221.92/222.18	                app_encode_app(int, int, bit0, 
221.92/222.18	                  app_encode_app(int, int, bit0, 
221.92/222.18	                    app_encode_app(int, int, bit1, pls))))), m)), 
221.92/222.18	        one_one(int))),
221.92/222.18	    inference('cnf', [status(esa)], [zf_stmt_27])).
221.92/222.18	tff('46', plain,
221.92/222.18	    app_encode_app(int, $o, zprime, 
221.92/222.18	      app_encode_app(int, int, 
221.92/222.18	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
221.92/222.18	          app_encode_app(int, int, 
221.92/222.18	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
221.92/222.18	              app_encode_app(int, int, bit0, 
221.92/222.18	                app_encode_app(int, int, bit0, 
221.92/222.18	                  app_encode_app(int, int, bit1, pls)))), m)), one_one(int))),
221.92/222.18	    inference('demod', [status(thm)], ['45', '1'])).
221.92/222.18	tff('47', plain,
221.92/222.18	    ![X0 : int]:
221.92/222.18	      app_encode_app(int, int, 
221.92/222.18	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
221.92/222.18	          one_one(int)), 
221.92/222.18	        app_encode_app(int, int, 
221.92/222.18	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
221.92/222.18	          X0))
221.92/222.18	       = app_encode_app(int, int, bit1, X0),
221.92/222.18	    inference('sup+', [status(thm)], ['5', '18'])).
221.92/222.18	tff('48', plain,
221.92/222.18	    app_encode_app(int, $o, zprime, 
221.92/222.18	      app_encode_app(int, int, 
221.92/222.18	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
221.92/222.18	          app_encode_app(int, int, 
221.92/222.18	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
221.92/222.18	              app_encode_app(int, int, 
221.92/222.18	                app_encode_app(int, app_encode_fun(int, int), 
221.92/222.18	                  plus_plus(int), one_one(int)), one_one(int))), 
221.92/222.18	            app_encode_app(int, int, 
221.92/222.18	              app_encode_app(int, app_encode_fun(int, int), 
221.92/222.18	                times_times(int), 
221.92/222.18	                app_encode_app(int, int, 
221.92/222.18	                  app_encode_app(int, app_encode_fun(int, int), 
221.92/222.18	                    plus_plus(int), one_one(int)), one_one(int))), m))), 
221.92/222.18	        one_one(int))),
221.92/222.18	    inference('demod', [status(thm)],
221.92/222.18	              ['46', '47', '14', '24', '21', '23', '21', '31'])).
221.92/222.18	tff(zf_stmt_34, axiom,
221.92/222.18	  (![L:int,K1:int]:
221.92/222.18	     (app_encode_app(int,int,
221.92/222.18	                     app_encode_app(int,app_encode_fun(int,int),
221.92/222.18	                                    plus_plus(int),
221.92/222.18	                                    app_encode_app(int,int,bit0,K1)),
221.92/222.18	                     app_encode_app(int,int,bit1,L)) =
221.92/222.18	      app_encode_app(int,int,bit1,
221.92/222.18	                     app_encode_app(int,int,
221.92/222.18	                                    app_encode_app(int,
221.92/222.18	                                                   app_encode_fun(int,int),
221.92/222.18	                                                   plus_plus(int),K1),
221.92/222.18	                                    L))))).
221.92/222.18	tff('49', plain,
221.92/222.18	    ![X13 : int, X14 : int]:
221.92/222.18	      app_encode_app(int, int, 
221.92/222.18	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
221.92/222.18	          app_encode_app(int, int, bit0, X13)), 
221.92/222.18	        app_encode_app(int, int, bit1, X14))
221.92/222.18	       = app_encode_app(int, int, bit1, 
221.92/222.18	           app_encode_app(int, int, 
221.92/222.18	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
221.92/222.18	               X13), X14)),
221.92/222.18	    inference('cnf', [status(esa)], [zf_stmt_34])).
221.92/222.18	tff('50', plain,
221.92/222.18	    ![X0 : int]:
221.92/222.18	      app_encode_app(int, int, 
221.92/222.18	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
221.92/222.18	          app_encode_app(int, int, bit0, X0)), one_one(int))
221.92/222.18	       = app_encode_app(int, int, bit1, 
221.92/222.18	           app_encode_app(int, int, 
221.92/222.18	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
221.92/222.18	               X0), pls)),
221.92/222.18	    inference('sup+', [status(thm)], ['3', '49'])).
221.92/222.18	tff('51', plain,
221.92/222.18	    ![X0 : int]:
221.92/222.18	      app_encode_app(int, int, 
221.92/222.18	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
221.92/222.18	          app_encode_app(int, int, bit0, X0)), one_one(int))
221.92/222.18	       = app_encode_app(int, int, bit1, X0),
221.92/222.18	    inference('demod', [status(thm)], ['50', '24'])).
221.92/222.18	tff('52', plain,
221.92/222.18	    ![X0 : int]:
221.92/222.18	      app_encode_app(int, int, 
221.92/222.18	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
221.92/222.18	          app_encode_app(int, int, 
221.92/222.18	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
221.92/222.18	              app_encode_app(int, int, 
221.92/222.18	                app_encode_app(int, app_encode_fun(int, int), 
221.92/222.18	                  plus_plus(int), one_one(int)), one_one(int))), X0)), 
221.92/222.18	        one_one(int))
221.92/222.18	       = app_encode_app(int, int, bit1, X0),
221.92/222.18	    inference('demod', [status(thm)], ['51', '21'])).
221.92/222.18	tff('53', plain,
221.92/222.18	    app_encode_app(int, $o, zprime, 
221.92/222.18	      app_encode_app(int, int, bit1, 
221.92/222.18	        app_encode_app(int, int, 
221.92/222.18	          app_encode_app(int, app_encode_fun(int, int), times_times(int), 
221.92/222.18	            app_encode_app(int, int, 
221.92/222.18	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
221.92/222.18	                one_one(int)), one_one(int))), m))),
221.92/222.18	    inference('demod', [status(thm)], ['48', '52'])).
221.92/222.18	tff('54', plain,
221.92/222.18	    app_encode_app(int, $o, zprime, 
221.92/222.18	      app_encode_app(int, int, 
221.92/222.18	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
221.92/222.18	          one_one(int)), 
221.92/222.18	        app_encode_app(int, int, 
221.92/222.18	          app_encode_app(int, app_encode_fun(int, int), times_times(int), 
221.92/222.18	            app_encode_app(int, int, 
221.92/222.18	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
221.92/222.18	                one_one(int)), one_one(int))), 
221.92/222.18	          app_encode_app(int, int, 
221.92/222.18	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
221.92/222.18	              app_encode_app(int, int, 
221.92/222.18	                app_encode_app(int, app_encode_fun(int, int), 
221.92/222.18	                  plus_plus(int), one_one(int)), one_one(int))), m)))),
221.92/222.18	    inference('demod', [status(thm)], ['53', '22'])).
221.92/222.18	tff('55', plain, ~ $true, inference('demod', [status(thm)], ['44', '54'])).
221.92/222.18	tff('56', plain, $false, inference('simplify', [status(thm)], ['55'])).
221.92/222.18	
221.92/222.18	% SZS output end Refutation
221.92/222.18	EOF
