0.00/0.00	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : appext
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : rpo6
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n145.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 07:53:38 CST 2018
257.37/257.61	% done 14909 iterations in 257.412s
257.37/257.61	% SZS status Theorem for 'stdin'
257.37/257.61	% SZS output start Refutation
257.37/257.62	tff(zf_stmt_37, axiom,
257.37/257.62	  (app_encode_app(int,$o,
257.37/257.62	                  app_encode_app(int,app_encode_fun(int,$o),ord_less_eq(int),
257.37/257.62	                                 zero_zero(int)),
257.37/257.62	                  s) & 
257.37/257.62	   app_encode_app(int,$o,
257.37/257.62	                  app_encode_app(int,app_encode_fun(int,$o),ord_less(int),s),
257.37/257.62	                  app_encode_app(int,int,
257.37/257.62	                                 app_encode_app(int,app_encode_fun(int,int),
257.37/257.62	                                                plus_plus(int),
257.37/257.62	                                                app_encode_app(int,int,
257.37/257.62	                                                               app_encode_app(
257.37/257.62	                                                               int,
257.37/257.62	                                                               app_encode_fun(
257.37/257.62	                                                               int,int),
257.37/257.62	                                                               times_times(
257.37/257.62	                                                               int),
257.37/257.62	                                                               app_encode_app(
257.37/257.62	                                                               int,int,
257.37/257.62	                                                               number_number_of(
257.37/257.62	                                                               int),
257.37/257.62	                                                               app_encode_app(
257.37/257.62	                                                               int,int,bit0,
257.37/257.62	                                                               app_encode_app(
257.37/257.62	                                                               int,int,bit0,
257.37/257.62	                                                               app_encode_app(
257.37/257.62	                                                               int,int,bit1,
257.37/257.62	                                                               pls))))),m)),
257.37/257.62	                                 one_one(int))) & 
257.37/257.62	   app_encode_app(int,$o,
257.37/257.62	                  app_encode_app(int,app_encode_fun(int,$o),
257.37/257.62	                                 app_encode_app(int,
257.37/257.62	                                                app_encode_fun(int,
257.37/257.62	                                                               app_encode_fun(
257.37/257.62	                                                               int,$o)),
257.37/257.62	                                                zcong,s1),
257.37/257.62	                                 s),
257.37/257.62	                  app_encode_app(int,int,
257.37/257.62	                                 app_encode_app(int,app_encode_fun(int,int),
257.37/257.62	                                                plus_plus(int),
257.37/257.62	                                                app_encode_app(int,int,
257.37/257.62	                                                               app_encode_app(
257.37/257.62	                                                               int,
257.37/257.62	                                                               app_encode_fun(
257.37/257.62	                                                               int,int),
257.37/257.62	                                                               times_times(
257.37/257.62	                                                               int),
257.37/257.62	                                                               app_encode_app(
257.37/257.62	                                                               int,int,
257.37/257.62	                                                               number_number_of(
257.37/257.62	                                                               int),
257.37/257.62	                                                               app_encode_app(
257.37/257.62	                                                               int,int,bit0,
257.37/257.62	                                                               app_encode_app(
257.37/257.62	                                                               int,int,bit0,
257.37/257.62	                                                               app_encode_app(
257.37/257.62	                                                               int,int,bit1,
257.37/257.62	                                                               pls))))),m)),
257.37/257.62	                                 one_one(int))))).
257.37/257.62	tff('0', plain,
257.37/257.62	    app_encode_app(int, $o, 
257.37/257.62	      app_encode_app(int, app_encode_fun(int, $o), ord_less(int), s), 
257.37/257.62	      app_encode_app(int, int, 
257.37/257.62	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	          app_encode_app(int, int, 
257.37/257.62	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
257.37/257.62	              app_encode_app(int, int, number_number_of(int), 
257.37/257.62	                app_encode_app(int, int, bit0, 
257.37/257.62	                  app_encode_app(int, int, bit0, 
257.37/257.62	                    app_encode_app(int, int, bit1, pls))))), m)), 
257.37/257.62	        one_one(int))),
257.37/257.62	    inference('cnf', [status(esa)], [zf_stmt_37])).
257.37/257.62	tff(zf_stmt_127, axiom,
257.37/257.62	  (![K:int]: (app_encode_app(int,int,number_number_of(int),K) = K))).
257.37/257.62	tff('1', plain,
257.37/257.62	    ![X200 : int]:
257.37/257.62	      app_encode_app(int, int, number_number_of(int), X200) = X200,
257.37/257.62	    inference('cnf', [status(esa)], [zf_stmt_127])).
257.37/257.62	tff('2', plain,
257.37/257.62	    app_encode_app(int, $o, 
257.37/257.62	      app_encode_app(int, app_encode_fun(int, $o), ord_less(int), s), 
257.37/257.62	      app_encode_app(int, int, 
257.37/257.62	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	          app_encode_app(int, int, 
257.37/257.62	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
257.37/257.62	              app_encode_app(int, int, bit0, 
257.37/257.62	                app_encode_app(int, int, bit0, 
257.37/257.62	                  app_encode_app(int, int, bit1, pls)))), m)), one_one(int))),
257.37/257.62	    inference('demod', [status(thm)], ['0', '1'])).
257.37/257.62	tff(zf_stmt_71, axiom,
257.37/257.62	  (![L1:int,K:int]:
257.37/257.62	     (app_encode_app(int,int,
257.37/257.62	                     app_encode_app(int,app_encode_fun(int,int),
257.37/257.62	                                    times_times(int),
257.37/257.62	                                    app_encode_app(int,int,bit0,K)),
257.37/257.62	                     L1) =
257.37/257.62	      app_encode_app(int,int,bit0,
257.37/257.62	                     app_encode_app(int,int,
257.37/257.62	                                    app_encode_app(int,
257.37/257.62	                                                   app_encode_fun(int,int),
257.37/257.62	                                                   times_times(int),K),
257.37/257.62	                                    L1))))).
257.37/257.62	tff('3', plain,
257.37/257.62	    ![X59 : int, X60 : int]:
257.37/257.62	      app_encode_app(int, int, 
257.37/257.62	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
257.37/257.62	          app_encode_app(int, int, bit0, X59)), X60)
257.37/257.62	       = app_encode_app(int, int, bit0, 
257.37/257.62	           app_encode_app(int, int, 
257.37/257.62	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
257.37/257.62	               X59), X60)),
257.37/257.62	    inference('cnf', [status(esa)], [zf_stmt_71])).
257.37/257.62	tff(zf_stmt_70, axiom,
257.37/257.62	  (![W:int]:
257.37/257.62	     (app_encode_app(int,int,
257.37/257.62	                     app_encode_app(int,app_encode_fun(int,int),
257.37/257.62	                                    times_times(int),pls),
257.37/257.62	                     W) =
257.37/257.62	      pls))).
257.37/257.62	tff('4', plain,
257.37/257.62	    ![X58 : int]:
257.37/257.62	      app_encode_app(int, int, 
257.37/257.62	        app_encode_app(int, app_encode_fun(int, int), times_times(int), pls), 
257.37/257.62	        X58)
257.37/257.62	       = pls,
257.37/257.62	    inference('cnf', [status(esa)], [zf_stmt_70])).
257.37/257.62	tff(zf_stmt_46, axiom,
257.37/257.62	  (![L1:int,K:int]:
257.37/257.62	     (app_encode_app(int,int,
257.37/257.62	                     app_encode_app(int,app_encode_fun(int,int),
257.37/257.62	                                    times_times(int),
257.37/257.62	                                    app_encode_app(int,int,bit1,K)),
257.37/257.62	                     L1) =
257.37/257.62	      app_encode_app(int,int,
257.37/257.62	                     app_encode_app(int,app_encode_fun(int,int),
257.37/257.62	                                    plus_plus(int),
257.37/257.62	                                    app_encode_app(int,int,bit0,
257.37/257.62	                                                   app_encode_app(int,int,
257.37/257.62	                                                                  app_encode_app(
257.37/257.62	                                                                  int,
257.37/257.62	                                                                  app_encode_fun(
257.37/257.62	                                                                  int,int),
257.37/257.62	                                                                  times_times(
257.37/257.62	                                                                  int),K),L1))),
257.37/257.62	                     L1)))).
257.37/257.62	tff('5', plain,
257.37/257.62	    ![X15 : int, X16 : int]:
257.37/257.62	      app_encode_app(int, int, 
257.37/257.62	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
257.37/257.62	          app_encode_app(int, int, bit1, X15)), X16)
257.37/257.62	       = app_encode_app(int, int, 
257.37/257.62	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	             app_encode_app(int, int, bit0, 
257.37/257.62	               app_encode_app(int, int, 
257.37/257.62	                 app_encode_app(int, app_encode_fun(int, int), 
257.37/257.62	                   times_times(int), X15), X16))), X16),
257.37/257.62	    inference('cnf', [status(esa)], [zf_stmt_46])).
257.37/257.62	tff('6', plain,
257.37/257.62	    ![X0 : int]:
257.37/257.62	      app_encode_app(int, int, 
257.37/257.62	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
257.37/257.62	          app_encode_app(int, int, bit1, pls)), X0)
257.37/257.62	       = app_encode_app(int, int, 
257.37/257.62	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	             app_encode_app(int, int, bit0, pls)), X0),
257.37/257.62	    inference('sup+', [status(thm)], ['4', '5'])).
257.37/257.62	tff(zf_stmt_63, axiom, (app_encode_app(int,int,bit0,pls) = pls)).
257.37/257.62	tff('7', plain, app_encode_app(int, int, bit0, pls) = pls,
257.37/257.62	    inference('cnf', [status(esa)], [zf_stmt_63])).
257.37/257.62	tff('8', plain,
257.37/257.62	    ![X0 : int]:
257.37/257.62	      app_encode_app(int, int, 
257.37/257.62	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
257.37/257.62	          app_encode_app(int, int, bit1, pls)), X0)
257.37/257.62	       = app_encode_app(int, int, 
257.37/257.62	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
257.37/257.62	           X0),
257.37/257.62	    inference('demod', [status(thm)], ['6', '7'])).
257.37/257.62	tff(zf_stmt_140, axiom, (number_ring(int))).
257.37/257.62	tff('9', plain, number_ring(int),
257.37/257.62	    inference('cnf', [status(esa)], [zf_stmt_140])).
257.37/257.62	tff(zf_stmt_47, axiom,
257.37/257.62	  (![A:$tType]:
257.37/257.62	     (number_ring(A) =>
257.37/257.62	      (app_encode_app(int,A,number_number_of(A),
257.37/257.62	                      app_encode_app(int,int,bit1,pls)) =
257.37/257.62	       one_one(A))))).
257.37/257.62	tff('10', plain,
257.37/257.62	    ![X17 : $tType]:
257.37/257.62	      (app_encode_app(int, X17, number_number_of(X17), 
257.37/257.62	         app_encode_app(int, int, bit1, pls))
257.37/257.62	        = one_one(X17)
257.37/257.62	       | ~ number_ring(X17)),
257.37/257.62	    inference('cnf', [status(esa)], [zf_stmt_47])).
257.37/257.62	tff('11', plain,
257.37/257.62	    (~ $true
257.37/257.62	     | app_encode_app(int, int, number_number_of(int), 
257.37/257.62	         app_encode_app(int, int, bit1, pls))
257.37/257.62	        = one_one(int)),
257.37/257.62	    inference('sup-', [status(thm)], ['9', '10'])).
257.37/257.62	tff('12', plain,
257.37/257.62	    (~ $true | app_encode_app(int, int, bit1, pls) = one_one(int)),
257.37/257.62	    inference('demod', [status(thm)], ['11', '1'])).
257.37/257.62	tff('13', plain, app_encode_app(int, int, bit1, pls) = one_one(int),
257.37/257.62	    inference('simplify', [status(thm)], ['12'])).
257.37/257.62	tff(zf_stmt_94, axiom,
257.37/257.62	  (![L1:int,K:int]:
257.37/257.62	     (app_encode_app(int,int,
257.37/257.62	                     app_encode_app(int,app_encode_fun(int,int),
257.37/257.62	                                    plus_plus(int),
257.37/257.62	                                    app_encode_app(int,int,bit0,K)),
257.37/257.62	                     app_encode_app(int,int,bit1,L1)) =
257.37/257.62	      app_encode_app(int,int,bit1,
257.37/257.62	                     app_encode_app(int,int,
257.37/257.62	                                    app_encode_app(int,
257.37/257.62	                                                   app_encode_fun(int,int),
257.37/257.62	                                                   plus_plus(int),K),
257.37/257.62	                                    L1))))).
257.37/257.62	tff('14', plain,
257.37/257.62	    ![X124 : int, X125 : int]:
257.37/257.62	      app_encode_app(int, int, 
257.37/257.62	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	          app_encode_app(int, int, bit0, X124)), 
257.37/257.62	        app_encode_app(int, int, bit1, X125))
257.37/257.62	       = app_encode_app(int, int, bit1, 
257.37/257.62	           app_encode_app(int, int, 
257.37/257.62	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	               X124), X125)),
257.37/257.62	    inference('cnf', [status(esa)], [zf_stmt_94])).
257.37/257.62	tff(zf_stmt_72, axiom,
257.37/257.62	  (![L1:int,K:int]:
257.37/257.62	     (app_encode_app(int,int,
257.37/257.62	                     app_encode_app(int,app_encode_fun(int,int),
257.37/257.62	                                    plus_plus(int),
257.37/257.62	                                    app_encode_app(int,int,bit0,K)),
257.37/257.62	                     app_encode_app(int,int,bit0,L1)) =
257.37/257.62	      app_encode_app(int,int,bit0,
257.37/257.62	                     app_encode_app(int,int,
257.37/257.62	                                    app_encode_app(int,
257.37/257.62	                                                   app_encode_fun(int,int),
257.37/257.62	                                                   plus_plus(int),K),
257.37/257.62	                                    L1))))).
257.37/257.62	tff('15', plain,
257.37/257.62	    ![X61 : int, X62 : int]:
257.37/257.62	      app_encode_app(int, int, 
257.37/257.62	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	          app_encode_app(int, int, bit0, X61)), 
257.37/257.62	        app_encode_app(int, int, bit0, X62))
257.37/257.62	       = app_encode_app(int, int, bit0, 
257.37/257.62	           app_encode_app(int, int, 
257.37/257.62	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	               X61), X62)),
257.37/257.62	    inference('cnf', [status(esa)], [zf_stmt_72])).
257.37/257.62	tff('16', plain,
257.37/257.62	    ![X0 : int]:
257.37/257.62	      app_encode_app(int, int, 
257.37/257.62	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	          app_encode_app(int, int, bit0, X0)), pls)
257.37/257.62	       = app_encode_app(int, int, bit0, 
257.37/257.62	           app_encode_app(int, int, 
257.37/257.62	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	               X0), pls)),
257.37/257.62	    inference('sup+', [status(thm)], ['7', '15'])).
257.37/257.62	tff('17', plain,
257.37/257.62	    app_encode_app(int, $o, 
257.37/257.62	      app_encode_app(int, app_encode_fun(int, $o), ord_less(int), s), 
257.37/257.62	      app_encode_app(int, int, bit1, 
257.37/257.62	        app_encode_app(int, int, bit0, 
257.37/257.62	          app_encode_app(int, int, 
257.37/257.62	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	              app_encode_app(int, int, 
257.37/257.62	                app_encode_app(int, app_encode_fun(int, int), 
257.37/257.62	                  plus_plus(int), pls), m)), pls)))),
257.37/257.62	    inference('demod', [status(thm)], ['2', '3', '3', '8', '13', '14', '16'])).
257.37/257.62	tff(zf_stmt_141, axiom, (semiring(int))).
257.37/257.62	tff('18', plain, semiring(int),
257.37/257.62	    inference('cnf', [status(esa)], [zf_stmt_141])).
257.37/257.62	tff(zf_stmt_74, axiom,
257.37/257.62	  (![B:$tType]:
257.37/257.62	     ((number(B) & semiring(B)) =>
257.37/257.62	      (![V1:int,B1:B,A2:B]:
257.37/257.62	         (app_encode_app(B,B,
257.37/257.62	                         app_encode_app(B,app_encode_fun(B,B),times_times(B),
257.37/257.62	                                        app_encode_app(B,B,
257.37/257.62	                                                       app_encode_app(
257.37/257.62	                                                       B,app_encode_fun(B,B),
257.37/257.62	                                                       plus_plus(B),A2),B1)),
257.37/257.62	                         app_encode_app(int,B,number_number_of(B),V1)) =
257.37/257.62	          app_encode_app(B,B,
257.37/257.62	                         app_encode_app(B,app_encode_fun(B,B),plus_plus(B),
257.37/257.62	                                        app_encode_app(B,B,
257.37/257.62	                                                       app_encode_app(
257.37/257.62	                                                       B,app_encode_fun(B,B),
257.37/257.62	                                                       times_times(B),A2),
257.37/257.62	                                                       app_encode_app(
257.37/257.62	                                                       int,B,
257.37/257.62	                                                       number_number_of(B),V1))),
257.37/257.62	                         app_encode_app(B,B,
257.37/257.62	                                        app_encode_app(B,app_encode_fun(B,B),
257.37/257.62	                                                       times_times(B),B1),
257.37/257.62	                                        app_encode_app(int,B,
257.37/257.62	                                                       number_number_of(B),V1)))))))).
257.37/257.62	tff('19', plain,
257.37/257.62	    ![X65 : $tType, X66 : X65, X67 : int, X68 : X65]:
257.37/257.62	      (app_encode_app(X65, X65, 
257.37/257.62	         app_encode_app(X65, app_encode_fun(X65, X65), times_times(X65), 
257.37/257.62	           app_encode_app(X65, X65, 
257.37/257.62	             app_encode_app(X65, app_encode_fun(X65, X65), plus_plus(X65), 
257.37/257.62	               X66), X68)), 
257.37/257.62	         app_encode_app(int, X65, number_number_of(X65), X67))
257.37/257.62	        = app_encode_app(X65, X65, 
257.37/257.62	            app_encode_app(X65, app_encode_fun(X65, X65), plus_plus(X65), 
257.37/257.62	              app_encode_app(X65, X65, 
257.37/257.62	                app_encode_app(X65, app_encode_fun(X65, X65), 
257.37/257.62	                  times_times(X65), X66), 
257.37/257.62	                app_encode_app(int, X65, number_number_of(X65), X67))), 
257.37/257.62	            app_encode_app(X65, X65, 
257.37/257.62	              app_encode_app(X65, app_encode_fun(X65, X65), 
257.37/257.62	                times_times(X65), X68), 
257.37/257.62	              app_encode_app(int, X65, number_number_of(X65), X67)))
257.37/257.62	       | ~ semiring(X65)
257.37/257.62	       | ~ number(X65)),
257.37/257.62	    inference('cnf', [status(esa)], [zf_stmt_74])).
257.37/257.62	tff('20', plain,
257.37/257.62	    ![X0 : int, X1 : int, X2 : int]:
257.37/257.62	      (~ $true
257.37/257.62	       | ~ number(int)
257.37/257.62	       | app_encode_app(int, int, 
257.37/257.62	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
257.37/257.62	             app_encode_app(int, int, 
257.37/257.62	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	                 X2), X1)), 
257.37/257.62	           app_encode_app(int, int, number_number_of(int), X0))
257.37/257.62	          = app_encode_app(int, int, 
257.37/257.62	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	                app_encode_app(int, int, 
257.37/257.62	                  app_encode_app(int, app_encode_fun(int, int), 
257.37/257.62	                    times_times(int), X2), 
257.37/257.62	                  app_encode_app(int, int, number_number_of(int), X0))), 
257.37/257.62	              app_encode_app(int, int, 
257.37/257.62	                app_encode_app(int, app_encode_fun(int, int), 
257.37/257.62	                  times_times(int), X1), 
257.37/257.62	                app_encode_app(int, int, number_number_of(int), X0)))),
257.37/257.62	    inference('sup-', [status(thm)], ['18', '19'])).
257.37/257.62	tff(zf_stmt_143, axiom, (number(int))).
257.37/257.62	tff('21', plain, number(int), inference('cnf', [status(esa)], [zf_stmt_143])).
257.37/257.62	tff('22', plain,
257.37/257.62	    ![X0 : int, X1 : int, X2 : int]:
257.37/257.62	      (~ $true
257.37/257.62	       | ~ $true
257.37/257.62	       | app_encode_app(int, int, 
257.37/257.62	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
257.37/257.62	             app_encode_app(int, int, 
257.37/257.62	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	                 X2), X1)), X0)
257.37/257.62	          = app_encode_app(int, int, 
257.37/257.62	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	                app_encode_app(int, int, 
257.37/257.62	                  app_encode_app(int, app_encode_fun(int, int), 
257.37/257.62	                    times_times(int), X2), X0)), 
257.37/257.62	              app_encode_app(int, int, 
257.37/257.62	                app_encode_app(int, app_encode_fun(int, int), 
257.37/257.62	                  times_times(int), X1), X0))),
257.37/257.62	    inference('demod', [status(thm)], ['20', '21', '1', '1', '1'])).
257.37/257.62	tff('23', plain,
257.37/257.62	    ![X0 : int, X1 : int, X2 : int]:
257.37/257.62	      app_encode_app(int, int, 
257.37/257.62	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
257.37/257.62	          app_encode_app(int, int, 
257.37/257.62	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X2), 
257.37/257.62	            X1)), X0)
257.37/257.62	       = app_encode_app(int, int, 
257.37/257.62	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	             app_encode_app(int, int, 
257.37/257.62	               app_encode_app(int, app_encode_fun(int, int), 
257.37/257.62	                 times_times(int), X2), X0)), 
257.37/257.62	           app_encode_app(int, int, 
257.37/257.62	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
257.37/257.62	               X1), X0)),
257.37/257.62	    inference('simplify', [status(thm)], ['22'])).
257.37/257.62	tff('24', plain,
257.37/257.62	    ![X0 : int, X1 : int]:
257.37/257.62	      app_encode_app(int, int, 
257.37/257.62	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
257.37/257.62	          app_encode_app(int, int, 
257.37/257.62	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X1), 
257.37/257.62	            pls)), X0)
257.37/257.62	       = app_encode_app(int, int, 
257.37/257.62	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	             app_encode_app(int, int, 
257.37/257.62	               app_encode_app(int, app_encode_fun(int, int), 
257.37/257.62	                 times_times(int), X1), X0)), pls),
257.37/257.62	    inference('sup+', [status(thm)], ['4', '23'])).
257.37/257.62	tff('25', plain,
257.37/257.62	    ![X0 : int]:
257.37/257.62	      app_encode_app(int, int, 
257.37/257.62	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
257.37/257.62	          app_encode_app(int, int, 
257.37/257.62	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	              app_encode_app(int, int, bit1, pls)), pls)), X0)
257.37/257.62	       = app_encode_app(int, int, 
257.37/257.62	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	             app_encode_app(int, int, 
257.37/257.62	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	                 pls), X0)), pls),
257.37/257.62	    inference('sup+', [status(thm)], ['8', '24'])).
257.37/257.62	tff(zf_stmt_93, axiom,
257.37/257.62	  (![L1:int,K:int]:
257.37/257.62	     (app_encode_app(int,int,
257.37/257.62	                     app_encode_app(int,app_encode_fun(int,int),
257.37/257.62	                                    plus_plus(int),
257.37/257.62	                                    app_encode_app(int,int,bit1,K)),
257.37/257.62	                     app_encode_app(int,int,bit0,L1)) =
257.37/257.62	      app_encode_app(int,int,bit1,
257.37/257.62	                     app_encode_app(int,int,
257.37/257.62	                                    app_encode_app(int,
257.37/257.62	                                                   app_encode_fun(int,int),
257.37/257.62	                                                   plus_plus(int),K),
257.37/257.62	                                    L1))))).
257.37/257.62	tff('26', plain,
257.37/257.62	    ![X122 : int, X123 : int]:
257.37/257.62	      app_encode_app(int, int, 
257.37/257.62	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	          app_encode_app(int, int, bit1, X122)), 
257.37/257.62	        app_encode_app(int, int, bit0, X123))
257.37/257.62	       = app_encode_app(int, int, bit1, 
257.37/257.62	           app_encode_app(int, int, 
257.37/257.62	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	               X122), X123)),
257.37/257.62	    inference('cnf', [status(esa)], [zf_stmt_93])).
257.37/257.62	tff('27', plain,
257.37/257.62	    ![X0 : int]:
257.37/257.62	      app_encode_app(int, int, 
257.37/257.62	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	          app_encode_app(int, int, bit1, X0)), pls)
257.37/257.62	       = app_encode_app(int, int, bit1, 
257.37/257.62	           app_encode_app(int, int, 
257.37/257.62	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	               X0), pls)),
257.37/257.62	    inference('sup+', [status(thm)], ['7', '26'])).
257.37/257.62	tff(zf_stmt_135, axiom, (linord219039673up_add(int))).
257.37/257.62	tff('28', plain, linord219039673up_add(int),
257.37/257.62	    inference('cnf', [status(esa)], [zf_stmt_135])).
257.37/257.62	tff(zf_stmt_56, axiom,
257.37/257.62	  (![A:$tType]:
257.37/257.62	     (linord219039673up_add(A) =>
257.37/257.62	      (![A1:A]:
257.37/257.62	         ((app_encode_app(A,A,
257.37/257.62	                          app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
257.37/257.62	                                         A1),
257.37/257.62	                          A1) =
257.37/257.62	           zero_zero(A)) <=>
257.37/257.62	          (A1 = zero_zero(A))))))).
257.37/257.62	tff('29', plain,
257.37/257.62	    ![X33 : $tType, X34 : X33]:
257.37/257.62	      (X34 != zero_zero(X33)
257.37/257.62	       | app_encode_app(X33, X33, 
257.37/257.62	           app_encode_app(X33, app_encode_fun(X33, X33), plus_plus(X33), X34), 
257.37/257.62	           X34)
257.37/257.62	          = zero_zero(X33)
257.37/257.62	       | ~ linord219039673up_add(X33)),
257.37/257.62	    inference('cnf', [status(esa)], [zf_stmt_56])).
257.37/257.62	tff('30', plain,
257.37/257.62	    ![X33 : $tType]:
257.37/257.62	      (~ linord219039673up_add(X33)
257.37/257.62	       | app_encode_app(X33, X33, 
257.37/257.62	           app_encode_app(X33, app_encode_fun(X33, X33), plus_plus(X33), 
257.37/257.62	             zero_zero(X33)), zero_zero(X33))
257.37/257.62	          = zero_zero(X33)),
257.37/257.62	    inference('simplify', [status(thm)], ['29'])).
257.37/257.62	tff('31', plain,
257.37/257.62	    (~ $true
257.37/257.62	     | app_encode_app(int, int, 
257.37/257.62	         app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	           zero_zero(int)), zero_zero(int))
257.37/257.62	        = zero_zero(int)),
257.37/257.62	    inference('sup-', [status(thm)], ['28', '30'])).
257.37/257.62	tff(zf_stmt_120, axiom, (pls = zero_zero(int))).
257.37/257.62	tff('32', plain, pls = zero_zero(int),
257.37/257.62	    inference('cnf', [status(esa)], [zf_stmt_120])).
257.37/257.62	tff('33', plain,
257.37/257.62	    (~ $true
257.37/257.62	     | app_encode_app(int, int, 
257.37/257.62	         app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
257.37/257.62	         pls)
257.37/257.62	        = pls),
257.37/257.62	    inference('demod', [status(thm)], ['31', '32', '32', '32'])).
257.37/257.62	tff('34', plain,
257.37/257.62	    app_encode_app(int, int, 
257.37/257.62	      app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
257.37/257.62	      pls)
257.37/257.62	     = pls,
257.37/257.62	    inference('simplify', [status(thm)], ['33'])).
257.37/257.62	tff('35', plain,
257.37/257.62	    ![X0 : int]:
257.37/257.62	      app_encode_app(int, int, 
257.37/257.62	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
257.37/257.62	        X0)
257.37/257.62	       = app_encode_app(int, int, 
257.37/257.62	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	             app_encode_app(int, int, 
257.37/257.62	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	                 pls), X0)), pls),
257.37/257.62	    inference('demod', [status(thm)], ['25', '27', '34', '8'])).
257.37/257.62	tff('36', plain,
257.37/257.62	    app_encode_app(int, $o, 
257.37/257.62	      app_encode_app(int, app_encode_fun(int, $o), ord_less(int), s), 
257.37/257.62	      app_encode_app(int, int, bit1, 
257.37/257.62	        app_encode_app(int, int, bit0, 
257.37/257.62	          app_encode_app(int, int, 
257.37/257.62	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	              pls), m)))),
257.37/257.62	    inference('demod', [status(thm)], ['17', '35'])).
257.37/257.62	tff(zf_stmt_134, axiom,
257.37/257.62	  (![A:$tType]:
257.37/257.62	     (number_ring(A) =>
257.37/257.62	      (![W:int]:
257.37/257.62	         (app_encode_app(int,A,number_number_of(A),
257.37/257.62	                         app_encode_app(int,int,bit0,W)) =
257.37/257.62	          app_encode_app(A,A,
257.37/257.62	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
257.37/257.62	                                        app_encode_app(A,A,
257.37/257.62	                                                       app_encode_app(
257.37/257.62	                                                       A,app_encode_fun(A,A),
257.37/257.62	                                                       plus_plus(A),
257.37/257.62	                                                       zero_zero(A)),
257.37/257.62	                                                       app_encode_app(
257.37/257.62	                                                       int,A,
257.37/257.62	                                                       number_number_of(A),W))),
257.37/257.62	                         app_encode_app(int,A,number_number_of(A),W))))))).
257.37/257.62	tff('37', plain,
257.37/257.62	    ![X210 : $tType, X211 : int]:
257.37/257.62	      (app_encode_app(int, X210, number_number_of(X210), 
257.37/257.62	         app_encode_app(int, int, bit0, X211))
257.37/257.62	        = app_encode_app(X210, X210, 
257.37/257.62	            app_encode_app(X210, app_encode_fun(X210, X210), 
257.37/257.62	              plus_plus(X210), 
257.37/257.62	              app_encode_app(X210, X210, 
257.37/257.62	                app_encode_app(X210, app_encode_fun(X210, X210), 
257.37/257.62	                  plus_plus(X210), zero_zero(X210)), 
257.37/257.62	                app_encode_app(int, X210, number_number_of(X210), X211))), 
257.37/257.62	            app_encode_app(int, X210, number_number_of(X210), X211))
257.37/257.62	       | ~ number_ring(X210)),
257.37/257.62	    inference('cnf', [status(esa)], [zf_stmt_134])).
257.37/257.62	tff('38', plain,
257.37/257.62	    ![X0 : int]:
257.37/257.62	      (~ $true
257.37/257.62	       | app_encode_app(int, int, number_number_of(int), 
257.37/257.62	           app_encode_app(int, int, bit0, X0))
257.37/257.62	          = app_encode_app(int, int, 
257.37/257.62	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	                app_encode_app(int, int, 
257.37/257.62	                  app_encode_app(int, app_encode_fun(int, int), 
257.37/257.62	                    plus_plus(int), zero_zero(int)), 
257.37/257.62	                  app_encode_app(int, int, number_number_of(int), X0))), 
257.37/257.62	              app_encode_app(int, int, number_number_of(int), X0))),
257.37/257.62	    inference('sup-', [status(thm)], ['9', '37'])).
257.37/257.62	tff(zf_stmt_83, axiom,
257.37/257.62	  (![A:$tType]:
257.37/257.62	     (number_ring(A) =>
257.37/257.62	      (![Z:A,W:int,V1:int]:
257.37/257.62	         (app_encode_app(A,A,
257.37/257.62	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
257.37/257.62	                                        app_encode_app(int,A,
257.37/257.62	                                                       number_number_of(A),V1)),
257.37/257.62	                         app_encode_app(A,A,
257.37/257.62	                                        app_encode_app(A,app_encode_fun(A,A),
257.37/257.62	                                                       plus_plus(A),
257.37/257.62	                                                       app_encode_app(
257.37/257.62	                                                       int,A,
257.37/257.62	                                                       number_number_of(A),W)),
257.37/257.62	                                        Z)) =
257.37/257.62	          app_encode_app(A,A,
257.37/257.62	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
257.37/257.62	                                        app_encode_app(int,A,
257.37/257.62	                                                       number_number_of(A),
257.37/257.62	                                                       app_encode_app(
257.37/257.62	                                                       int,int,
257.37/257.62	                                                       app_encode_app(
257.37/257.62	                                                       int,
257.37/257.62	                                                       app_encode_fun(
257.37/257.62	                                                       int,int),
257.37/257.62	                                                       plus_plus(int),V1),W))),
257.37/257.62	                         Z)))))).
257.37/257.62	tff('39', plain,
257.37/257.62	    ![X97 : $tType, X98 : int, X99 : int, X100 : X97]:
257.37/257.62	      (app_encode_app(X97, X97, 
257.37/257.62	         app_encode_app(X97, app_encode_fun(X97, X97), plus_plus(X97), 
257.37/257.62	           app_encode_app(int, X97, number_number_of(X97), X98)), 
257.37/257.62	         app_encode_app(X97, X97, 
257.37/257.62	           app_encode_app(X97, app_encode_fun(X97, X97), plus_plus(X97), 
257.37/257.62	             app_encode_app(int, X97, number_number_of(X97), X99)), X100))
257.37/257.62	        = app_encode_app(X97, X97, 
257.37/257.62	            app_encode_app(X97, app_encode_fun(X97, X97), plus_plus(X97), 
257.37/257.62	              app_encode_app(int, X97, number_number_of(X97), 
257.37/257.62	                app_encode_app(int, int, 
257.37/257.62	                  app_encode_app(int, app_encode_fun(int, int), 
257.37/257.62	                    plus_plus(int), X98), X99))), X100)
257.37/257.62	       | ~ number_ring(X97)),
257.37/257.62	    inference('cnf', [status(esa)], [zf_stmt_83])).
257.37/257.62	tff('40', plain,
257.37/257.62	    ![X0 : int, X1 : int, X2 : int]:
257.37/257.62	      (~ $true
257.37/257.62	       | app_encode_app(int, int, 
257.37/257.62	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	             app_encode_app(int, int, number_number_of(int), X2)), 
257.37/257.62	           app_encode_app(int, int, 
257.37/257.62	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	               app_encode_app(int, int, number_number_of(int), X1)), X0))
257.37/257.62	          = app_encode_app(int, int, 
257.37/257.62	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	                app_encode_app(int, int, number_number_of(int), 
257.37/257.62	                  app_encode_app(int, int, 
257.37/257.62	                    app_encode_app(int, app_encode_fun(int, int), 
257.37/257.62	                      plus_plus(int), X2), X1))), X0)),
257.37/257.62	    inference('sup-', [status(thm)], ['9', '39'])).
257.37/257.62	tff('41', plain,
257.37/257.62	    ![X0 : int, X1 : int, X2 : int]:
257.37/257.62	      (~ $true
257.37/257.62	       | app_encode_app(int, int, 
257.37/257.62	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X2), 
257.37/257.62	           app_encode_app(int, int, 
257.37/257.62	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	               X1), X0))
257.37/257.62	          = app_encode_app(int, int, 
257.37/257.62	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	                app_encode_app(int, int, 
257.37/257.62	                  app_encode_app(int, app_encode_fun(int, int), 
257.37/257.62	                    plus_plus(int), X2), X1)), X0)),
257.37/257.62	    inference('demod', [status(thm)], ['40', '1', '1', '1'])).
257.37/257.62	tff('42', plain,
257.37/257.62	    ![X0 : int, X1 : int, X2 : int]:
257.37/257.62	      app_encode_app(int, int, 
257.37/257.62	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X2), 
257.37/257.62	        app_encode_app(int, int, 
257.37/257.62	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X1), 
257.37/257.62	          X0))
257.37/257.62	       = app_encode_app(int, int, 
257.37/257.62	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	             app_encode_app(int, int, 
257.37/257.62	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	                 X2), X1)), X0),
257.37/257.62	    inference('simplify', [status(thm)], ['41'])).
257.37/257.62	tff('43', plain,
257.37/257.62	    ![X0 : int]:
257.37/257.62	      (~ $true
257.37/257.62	       | app_encode_app(int, int, bit0, X0)
257.37/257.62	          = app_encode_app(int, int, 
257.37/257.62	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	                pls), 
257.37/257.62	              app_encode_app(int, int, 
257.37/257.62	                app_encode_app(int, app_encode_fun(int, int), 
257.37/257.62	                  plus_plus(int), X0), X0))),
257.37/257.62	    inference('demod', [status(thm)], ['38', '1', '32', '1', '1', '42'])).
257.37/257.62	tff('44', plain,
257.37/257.62	    ![X0 : int]:
257.37/257.62	      app_encode_app(int, int, bit0, X0)
257.37/257.62	       = app_encode_app(int, int, 
257.37/257.62	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
257.37/257.62	           app_encode_app(int, int, 
257.37/257.62	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	               X0), X0)),
257.37/257.62	    inference('simplify', [status(thm)], ['43'])).
257.37/257.62	tff('45', plain,
257.37/257.62	    ![X0 : int]:
257.37/257.62	      app_encode_app(int, int, 
257.37/257.62	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
257.37/257.62	        app_encode_app(int, int, bit1, X0))
257.37/257.62	       = app_encode_app(int, int, bit1, 
257.37/257.62	           app_encode_app(int, int, 
257.37/257.62	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	               pls), X0)),
257.37/257.62	    inference('sup+', [status(thm)], ['7', '14'])).
257.37/257.62	tff('46', plain,
257.37/257.62	    ![X0 : int, X1 : int]:
257.37/257.62	      app_encode_app(int, int, 
257.37/257.62	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	          app_encode_app(int, int, bit1, X0)), 
257.37/257.62	        app_encode_app(int, int, 
257.37/257.62	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
257.37/257.62	          X1))
257.37/257.62	       = app_encode_app(int, int, 
257.37/257.62	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	             app_encode_app(int, int, bit1, 
257.37/257.62	               app_encode_app(int, int, 
257.37/257.62	                 app_encode_app(int, app_encode_fun(int, int), 
257.37/257.62	                   plus_plus(int), X0), pls))), X1),
257.37/257.62	    inference('sup+', [status(thm)], ['27', '42'])).
257.37/257.62	tff('47', plain,
257.37/257.62	    ![X0 : int]:
257.37/257.62	      app_encode_app(int, int, 
257.37/257.62	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	          app_encode_app(int, int, bit1, pls)), 
257.37/257.62	        app_encode_app(int, int, 
257.37/257.62	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
257.37/257.62	          X0))
257.37/257.62	       = app_encode_app(int, int, 
257.37/257.62	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	             app_encode_app(int, int, bit1, pls)), X0),
257.37/257.62	    inference('sup+', [status(thm)], ['34', '46'])).
257.37/257.62	tff('48', plain,
257.37/257.62	    ![X0 : int]:
257.37/257.62	      app_encode_app(int, int, 
257.37/257.62	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	          app_encode_app(int, int, bit1, pls)), 
257.37/257.62	        app_encode_app(int, int, bit1, 
257.37/257.62	          app_encode_app(int, int, 
257.37/257.62	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	              pls), X0)))
257.37/257.62	       = app_encode_app(int, int, 
257.37/257.62	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	             app_encode_app(int, int, bit1, pls)), 
257.37/257.62	           app_encode_app(int, int, bit1, X0)),
257.37/257.62	    inference('sup+', [status(thm)], ['45', '47'])).
257.37/257.62	tff(zf_stmt_45, axiom,
257.37/257.62	  (![A:$tType]:
257.37/257.62	     (number_ring(A) =>
257.37/257.62	      (app_encode_app(A,A,
257.37/257.62	                      app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
257.37/257.62	                                     one_one(A)),
257.37/257.62	                      one_one(A)) =
257.37/257.62	       app_encode_app(int,A,number_number_of(A),
257.37/257.62	                      app_encode_app(int,int,bit0,
257.37/257.62	                                     app_encode_app(int,int,bit1,pls))))))).
257.37/257.62	tff('49', plain,
257.37/257.62	    ![X14 : $tType]:
257.37/257.62	      (app_encode_app(X14, X14, 
257.37/257.62	         app_encode_app(X14, app_encode_fun(X14, X14), plus_plus(X14), 
257.37/257.62	           one_one(X14)), one_one(X14))
257.37/257.62	        = app_encode_app(int, X14, number_number_of(X14), 
257.37/257.62	            app_encode_app(int, int, bit0, 
257.37/257.62	              app_encode_app(int, int, bit1, pls)))
257.37/257.62	       | ~ number_ring(X14)),
257.37/257.62	    inference('cnf', [status(esa)], [zf_stmt_45])).
257.37/257.62	tff('50', plain,
257.37/257.62	    (~ $true
257.37/257.62	     | app_encode_app(int, int, 
257.37/257.62	         app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	           one_one(int)), one_one(int))
257.37/257.62	        = app_encode_app(int, int, number_number_of(int), 
257.37/257.62	            app_encode_app(int, int, bit0, 
257.37/257.62	              app_encode_app(int, int, bit1, pls)))),
257.37/257.62	    inference('sup-', [status(thm)], ['9', '49'])).
257.37/257.62	tff('51', plain,
257.37/257.62	    (~ $true
257.37/257.62	     | app_encode_app(int, int, 
257.37/257.62	         app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	           app_encode_app(int, int, bit1, pls)), 
257.37/257.62	         app_encode_app(int, int, bit1, pls))
257.37/257.62	        = app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls))),
257.37/257.62	    inference('demod', [status(thm)], ['50', '13', '13', '1'])).
257.37/257.62	tff('52', plain,
257.37/257.62	    app_encode_app(int, int, 
257.37/257.62	      app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	        app_encode_app(int, int, bit1, pls)), 
257.37/257.62	      app_encode_app(int, int, bit1, pls))
257.37/257.62	     = app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls)),
257.37/257.62	    inference('simplify', [status(thm)], ['51'])).
257.37/257.62	tff('53', plain,
257.37/257.62	    ![X0 : int]:
257.37/257.62	      app_encode_app(int, int, 
257.37/257.62	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	          app_encode_app(int, int, bit1, pls)), 
257.37/257.62	        app_encode_app(int, int, 
257.37/257.62	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	            app_encode_app(int, int, bit1, pls)), X0))
257.37/257.62	       = app_encode_app(int, int, 
257.37/257.62	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	             app_encode_app(int, int, bit0, 
257.37/257.62	               app_encode_app(int, int, bit1, pls))), X0),
257.37/257.62	    inference('sup+', [status(thm)], ['52', '42'])).
257.37/257.62	tff('54', plain,
257.37/257.62	    ![X0 : int]:
257.37/257.62	      app_encode_app(int, int, 
257.37/257.62	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	          app_encode_app(int, int, bit1, pls)), 
257.37/257.62	        app_encode_app(int, int, 
257.37/257.62	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	            app_encode_app(int, int, bit1, pls)), 
257.37/257.62	          app_encode_app(int, int, bit0, X0)))
257.37/257.62	       = app_encode_app(int, int, bit0, 
257.37/257.62	           app_encode_app(int, int, 
257.37/257.62	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	               app_encode_app(int, int, bit1, pls)), X0)),
257.37/257.62	    inference('sup+', [status(thm)], ['15', '53'])).
257.37/257.62	tff('55', plain,
257.37/257.62	    ![X0 : int]:
257.37/257.62	      app_encode_app(int, int, 
257.37/257.62	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	          app_encode_app(int, int, bit1, pls)), 
257.37/257.62	        app_encode_app(int, int, bit1, 
257.37/257.62	          app_encode_app(int, int, 
257.37/257.62	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	              pls), X0)))
257.37/257.62	       = app_encode_app(int, int, bit0, 
257.37/257.62	           app_encode_app(int, int, 
257.37/257.62	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	               app_encode_app(int, int, bit1, pls)), X0)),
257.37/257.62	    inference('demod', [status(thm)], ['54', '26'])).
257.37/257.62	tff('56', plain,
257.37/257.62	    ![X0 : int]:
257.37/257.62	      app_encode_app(int, int, 
257.37/257.62	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	          app_encode_app(int, int, bit1, pls)), 
257.37/257.62	        app_encode_app(int, int, bit1, X0))
257.37/257.62	       = app_encode_app(int, int, bit0, 
257.37/257.62	           app_encode_app(int, int, 
257.37/257.62	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	               app_encode_app(int, int, bit1, pls)), X0)),
257.37/257.62	    inference('sup+', [status(thm)], ['48', '55'])).
257.37/257.62	tff(zf_stmt_75, axiom,
257.37/257.62	  (![B:$tType]:
257.37/257.62	     ((number(B) & semiring(B)) =>
257.37/257.62	      (![C:B,B1:B,V1:int]:
257.37/257.62	         (app_encode_app(B,B,
257.37/257.62	                         app_encode_app(B,app_encode_fun(B,B),times_times(B),
257.37/257.62	                                        app_encode_app(int,B,
257.37/257.62	                                                       number_number_of(B),V1)),
257.37/257.62	                         app_encode_app(B,B,
257.37/257.62	                                        app_encode_app(B,app_encode_fun(B,B),
257.37/257.62	                                                       plus_plus(B),B1),
257.37/257.62	                                        C)) =
257.37/257.62	          app_encode_app(B,B,
257.37/257.62	                         app_encode_app(B,app_encode_fun(B,B),plus_plus(B),
257.37/257.62	                                        app_encode_app(B,B,
257.37/257.62	                                                       app_encode_app(
257.37/257.62	                                                       B,app_encode_fun(B,B),
257.37/257.62	                                                       times_times(B),
257.37/257.62	                                                       app_encode_app(
257.37/257.62	                                                       int,B,
257.37/257.62	                                                       number_number_of(B),V1)),
257.37/257.62	                                                       B1)),
257.37/257.62	                         app_encode_app(B,B,
257.37/257.62	                                        app_encode_app(B,app_encode_fun(B,B),
257.37/257.62	                                                       times_times(B),
257.37/257.62	                                                       app_encode_app(
257.37/257.62	                                                       int,B,
257.37/257.62	                                                       number_number_of(B),V1)),
257.37/257.62	                                        C))))))).
257.37/257.62	tff('57', plain,
257.37/257.62	    ![X69 : $tType, X70 : int, X71 : X69, X72 : X69]:
257.37/257.62	      (app_encode_app(X69, X69, 
257.37/257.62	         app_encode_app(X69, app_encode_fun(X69, X69), times_times(X69), 
257.37/257.62	           app_encode_app(int, X69, number_number_of(X69), X70)), 
257.37/257.62	         app_encode_app(X69, X69, 
257.37/257.62	           app_encode_app(X69, app_encode_fun(X69, X69), plus_plus(X69), X71), 
257.37/257.62	           X72))
257.37/257.62	        = app_encode_app(X69, X69, 
257.37/257.62	            app_encode_app(X69, app_encode_fun(X69, X69), plus_plus(X69), 
257.37/257.62	              app_encode_app(X69, X69, 
257.37/257.62	                app_encode_app(X69, app_encode_fun(X69, X69), 
257.37/257.62	                  times_times(X69), 
257.37/257.62	                  app_encode_app(int, X69, number_number_of(X69), X70)), X71)), 
257.37/257.62	            app_encode_app(X69, X69, 
257.37/257.62	              app_encode_app(X69, app_encode_fun(X69, X69), 
257.37/257.62	                times_times(X69), 
257.37/257.62	                app_encode_app(int, X69, number_number_of(X69), X70)), X72))
257.37/257.62	       | ~ semiring(X69)
257.37/257.62	       | ~ number(X69)),
257.37/257.62	    inference('cnf', [status(esa)], [zf_stmt_75])).
257.37/257.62	tff('58', plain,
257.37/257.62	    ![X0 : int, X1 : int, X2 : int]:
257.37/257.62	      (~ $true
257.37/257.62	       | ~ number(int)
257.37/257.62	       | app_encode_app(int, int, 
257.37/257.62	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
257.37/257.62	             app_encode_app(int, int, number_number_of(int), X2)), 
257.37/257.62	           app_encode_app(int, int, 
257.37/257.62	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	               X1), X0))
257.37/257.62	          = app_encode_app(int, int, 
257.37/257.62	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	                app_encode_app(int, int, 
257.37/257.62	                  app_encode_app(int, app_encode_fun(int, int), 
257.37/257.62	                    times_times(int), 
257.37/257.62	                    app_encode_app(int, int, number_number_of(int), X2)), X1)), 
257.37/257.62	              app_encode_app(int, int, 
257.37/257.62	                app_encode_app(int, app_encode_fun(int, int), 
257.37/257.62	                  times_times(int), 
257.37/257.62	                  app_encode_app(int, int, number_number_of(int), X2)), X0))),
257.37/257.62	    inference('sup-', [status(thm)], ['18', '57'])).
257.37/257.62	tff('59', plain,
257.37/257.62	    ![X0 : int, X1 : int, X2 : int]:
257.37/257.62	      (~ $true
257.37/257.62	       | ~ $true
257.37/257.62	       | app_encode_app(int, int, 
257.37/257.62	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
257.37/257.62	             X2), 
257.37/257.62	           app_encode_app(int, int, 
257.37/257.62	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	               X1), X0))
257.37/257.62	          = app_encode_app(int, int, 
257.37/257.62	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	                app_encode_app(int, int, 
257.37/257.62	                  app_encode_app(int, app_encode_fun(int, int), 
257.37/257.62	                    times_times(int), X2), X1)), 
257.37/257.62	              app_encode_app(int, int, 
257.37/257.62	                app_encode_app(int, app_encode_fun(int, int), 
257.37/257.62	                  times_times(int), X2), X0))),
257.37/257.62	    inference('demod', [status(thm)], ['58', '21', '1', '1', '1'])).
257.37/257.62	tff('60', plain,
257.37/257.62	    ![X0 : int, X1 : int, X2 : int]:
257.37/257.62	      app_encode_app(int, int, 
257.37/257.62	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X2), 
257.37/257.62	        app_encode_app(int, int, 
257.37/257.62	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X1), 
257.37/257.62	          X0))
257.37/257.62	       = app_encode_app(int, int, 
257.37/257.62	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	             app_encode_app(int, int, 
257.37/257.62	               app_encode_app(int, app_encode_fun(int, int), 
257.37/257.62	                 times_times(int), X2), X1)), 
257.37/257.62	           app_encode_app(int, int, 
257.37/257.62	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
257.37/257.62	               X2), X0)),
257.37/257.62	    inference('simplify', [status(thm)], ['59'])).
257.37/257.62	tff('61', plain,
257.37/257.62	    ![X0 : int, X1 : int]:
257.37/257.62	      app_encode_app(int, int, 
257.37/257.62	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
257.37/257.62	          app_encode_app(int, int, 
257.37/257.62	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X1), 
257.37/257.62	            X1)), X0)
257.37/257.62	       = app_encode_app(int, int, 
257.37/257.62	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
257.37/257.62	             X1), 
257.37/257.62	           app_encode_app(int, int, 
257.37/257.62	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	               X0), X0)),
257.37/257.62	    inference('sup+', [status(thm)], ['60', '23'])).
257.37/257.62	tff('62', plain,
257.37/257.62	    ![X0 : int]:
257.37/257.62	      app_encode_app(int, int, 
257.37/257.62	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
257.37/257.62	          app_encode_app(int, int, bit0, 
257.37/257.62	            app_encode_app(int, int, 
257.37/257.62	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	                app_encode_app(int, int, bit1, pls)), pls))), X0)
257.37/257.62	       = app_encode_app(int, int, 
257.37/257.62	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
257.37/257.62	             app_encode_app(int, int, bit1, pls)), 
257.37/257.62	           app_encode_app(int, int, 
257.37/257.62	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	               X0), X0)),
257.37/257.62	    inference('sup+', [status(thm)], ['56', '61'])).
257.37/257.62	tff('63', plain,
257.37/257.62	    ![X0 : int]:
257.37/257.62	      app_encode_app(int, int, bit0, 
257.37/257.62	        app_encode_app(int, int, 
257.37/257.62	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
257.37/257.62	          X0))
257.37/257.62	       = app_encode_app(int, int, 
257.37/257.62	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
257.37/257.62	           app_encode_app(int, int, 
257.37/257.62	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	               X0), X0)),
257.37/257.62	    inference('demod', [status(thm)], ['62', '27', '34', '3', '8', '8'])).
257.37/257.62	tff('64', plain,
257.37/257.62	    ![X0 : int]:
257.37/257.62	      app_encode_app(int, int, bit0, 
257.37/257.62	        app_encode_app(int, int, 
257.37/257.62	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
257.37/257.62	          X0))
257.37/257.62	       = app_encode_app(int, int, bit0, X0),
257.37/257.62	    inference('sup+', [status(thm)], ['44', '63'])).
257.37/257.62	tff('65', plain,
257.37/257.62	    app_encode_app(int, $o, 
257.37/257.62	      app_encode_app(int, app_encode_fun(int, $o), ord_less(int), s), 
257.37/257.62	      app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m))),
257.37/257.62	    inference('demod', [status(thm)], ['36', '64'])).
257.37/257.62	tff(zf_stmt_52, axiom,
257.37/257.62	  (![L1:int,K:int]:
257.37/257.62	     (app_encode_app(int,int,
257.37/257.62	                     app_encode_app(int,app_encode_fun(int,int),
257.37/257.62	                                    minus_minus(int),
257.37/257.62	                                    app_encode_app(int,int,bit1,K)),
257.37/257.62	                     app_encode_app(int,int,bit1,L1)) =
257.37/257.62	      app_encode_app(int,int,bit0,
257.37/257.62	                     app_encode_app(int,int,
257.37/257.62	                                    app_encode_app(int,
257.37/257.62	                                                   app_encode_fun(int,int),
257.37/257.62	                                                   minus_minus(int),K),
257.37/257.62	                                    L1))))).
257.37/257.62	tff('66', plain,
257.37/257.62	    ![X21 : int, X22 : int]:
257.37/257.62	      app_encode_app(int, int, 
257.37/257.62	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
257.37/257.62	          app_encode_app(int, int, bit1, X21)), 
257.37/257.62	        app_encode_app(int, int, bit1, X22))
257.37/257.62	       = app_encode_app(int, int, bit0, 
257.37/257.62	           app_encode_app(int, int, 
257.37/257.62	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
257.37/257.62	               X21), X22)),
257.37/257.62	    inference('cnf', [status(esa)], [zf_stmt_52])).
257.37/257.62	tff(zf_stmt_100, axiom,
257.37/257.62	  (![Z1:int,W1:int]:
257.37/257.62	     (app_encode_app(int,$o,
257.37/257.62	                     app_encode_app(int,app_encode_fun(int,$o),
257.37/257.62	                                    ord_less_eq(int),W1),
257.37/257.62	                     app_encode_app(int,int,
257.37/257.62	                                    app_encode_app(int,
257.37/257.62	                                                   app_encode_fun(int,int),
257.37/257.62	                                                   minus_minus(int),Z1),
257.37/257.62	                                    one_one(int))) <=>
257.37/257.62	      app_encode_app(int,$o,
257.37/257.62	                     app_encode_app(int,app_encode_fun(int,$o),ord_less(int),
257.37/257.62	                                    W1),
257.37/257.62	                     Z1)))).
257.37/257.62	tff('67', plain,
257.37/257.62	    ![X140 : int, X141 : int]:
257.37/257.62	      (app_encode_app(int, $o, 
257.37/257.62	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), X141), 
257.37/257.62	         app_encode_app(int, int, 
257.37/257.62	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
257.37/257.62	             X140), one_one(int)))
257.37/257.62	       | ~ app_encode_app(int, $o, 
257.37/257.62	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
257.37/257.62	               X141), X140)),
257.37/257.62	    inference('cnf', [status(esa)], [zf_stmt_100])).
257.37/257.62	tff('68', plain,
257.37/257.62	    ![X140 : int, X141 : int]:
257.37/257.62	      (app_encode_app(int, $o, 
257.37/257.62	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), X141), 
257.37/257.62	         app_encode_app(int, int, 
257.37/257.62	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
257.37/257.62	             X140), app_encode_app(int, int, bit1, pls)))
257.37/257.62	       | ~ app_encode_app(int, $o, 
257.37/257.62	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
257.37/257.62	               X141), X140)),
257.37/257.62	    inference('demod', [status(thm)], ['67', '13'])).
257.37/257.62	tff('69', plain,
257.37/257.62	    ![X0 : int, X1 : int]:
257.37/257.62	      (app_encode_app(int, $o, 
257.37/257.62	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), X1), 
257.37/257.62	         app_encode_app(int, int, bit0, 
257.37/257.62	           app_encode_app(int, int, 
257.37/257.62	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
257.37/257.62	               X0), pls)))
257.37/257.62	       | ~ app_encode_app(int, $o, 
257.37/257.62	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X1), 
257.37/257.62	             app_encode_app(int, int, bit1, X0))),
257.37/257.62	    inference('sup+', [status(thm)], ['66', '68'])).
257.37/257.62	tff(zf_stmt_2, axiom,
257.37/257.62	  (![X:app_encode_fun(Alpha,Beta),Y:app_encode_fun(Alpha,Beta)]:
257.37/257.62	     ((![Z:Alpha]:
257.37/257.62	         (app_encode_app(Alpha,Beta,X,Z) = app_encode_app(Alpha,Beta,Y,Z))) =>
257.37/257.62	      (X = Y)))).
257.37/257.62	tff('70', plain,
257.37/257.62	    ![X0 : $tType, X1 : $tType, X2 : app_encode_fun(X0, X1), 
257.37/257.62	      X3 : app_encode_fun(X0, X1)]:
257.37/257.62	      (X3 = X2
257.37/257.62	       | app_encode_app(X0, X1, X3, sk_Z(X1, X0, X2, X3))
257.37/257.62	          != app_encode_app(X0, X1, X2, sk_Z(X1, X0, X2, X3))),
257.37/257.62	    inference('cnf', [status(esa)], [zf_stmt_2])).
257.37/257.62	tff('71', plain,
257.37/257.62	    ![X0 : app_encode_fun(int, int)]:
257.37/257.62	      (app_encode_app(int, int, X0, 
257.37/257.62	         sk_Z(int, int, 
257.37/257.62	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
257.37/257.62	             app_encode_app(int, int, bit1, pls)), X0))
257.37/257.62	        != app_encode_app(int, int, 
257.37/257.62	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	               pls), 
257.37/257.62	             sk_Z(int, int, 
257.37/257.62	               app_encode_app(int, app_encode_fun(int, int), 
257.37/257.62	                 times_times(int), app_encode_app(int, int, bit1, pls)), X0))
257.37/257.62	       | X0
257.37/257.62	          = app_encode_app(int, app_encode_fun(int, int), times_times(int), 
257.37/257.62	              app_encode_app(int, int, bit1, pls))),
257.37/257.62	    inference('sup-', [status(thm)], ['8', '70'])).
257.37/257.62	tff('72', plain,
257.37/257.62	    app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls)
257.37/257.62	     = app_encode_app(int, app_encode_fun(int, int), times_times(int), 
257.37/257.62	         app_encode_app(int, int, bit1, pls)),
257.37/257.62	    inference('eq_res', [status(thm)], ['71'])).
257.37/257.62	tff(zf_stmt_142, axiom, (ring(int))).
257.37/257.62	tff('73', plain, ring(int), inference('cnf', [status(esa)], [zf_stmt_142])).
257.37/257.62	tff(zf_stmt_77, axiom,
257.37/257.62	  (![B:$tType]:
257.37/257.62	     ((number(B) & ring(B)) =>
257.37/257.62	      (![V1:int,B1:B,A2:B]:
257.37/257.62	         (app_encode_app(B,B,
257.37/257.62	                         app_encode_app(B,app_encode_fun(B,B),times_times(B),
257.37/257.62	                                        app_encode_app(B,B,
257.37/257.62	                                                       app_encode_app(
257.37/257.62	                                                       B,app_encode_fun(B,B),
257.37/257.62	                                                       minus_minus(B),A2),B1)),
257.37/257.62	                         app_encode_app(int,B,number_number_of(B),V1)) =
257.37/257.62	          app_encode_app(B,B,
257.37/257.62	                         app_encode_app(B,app_encode_fun(B,B),minus_minus(B),
257.37/257.62	                                        app_encode_app(B,B,
257.37/257.62	                                                       app_encode_app(
257.37/257.62	                                                       B,app_encode_fun(B,B),
257.37/257.62	                                                       times_times(B),A2),
257.37/257.62	                                                       app_encode_app(
257.37/257.62	                                                       int,B,
257.37/257.62	                                                       number_number_of(B),V1))),
257.37/257.62	                         app_encode_app(B,B,
257.37/257.62	                                        app_encode_app(B,app_encode_fun(B,B),
257.37/257.62	                                                       times_times(B),B1),
257.37/257.62	                                        app_encode_app(int,B,
257.37/257.62	                                                       number_number_of(B),V1)))))))).
257.37/257.62	tff('74', plain,
257.37/257.62	    ![X74 : $tType, X75 : X74, X76 : int, X77 : X74]:
257.37/257.62	      (app_encode_app(X74, X74, 
257.37/257.62	         app_encode_app(X74, app_encode_fun(X74, X74), times_times(X74), 
257.37/257.62	           app_encode_app(X74, X74, 
257.37/257.62	             app_encode_app(X74, app_encode_fun(X74, X74), minus_minus(X74), 
257.37/257.62	               X75), X77)), 
257.37/257.62	         app_encode_app(int, X74, number_number_of(X74), X76))
257.37/257.62	        = app_encode_app(X74, X74, 
257.37/257.62	            app_encode_app(X74, app_encode_fun(X74, X74), minus_minus(X74), 
257.37/257.62	              app_encode_app(X74, X74, 
257.37/257.62	                app_encode_app(X74, app_encode_fun(X74, X74), 
257.37/257.62	                  times_times(X74), X75), 
257.37/257.62	                app_encode_app(int, X74, number_number_of(X74), X76))), 
257.37/257.62	            app_encode_app(X74, X74, 
257.37/257.62	              app_encode_app(X74, app_encode_fun(X74, X74), 
257.37/257.62	                times_times(X74), X77), 
257.37/257.62	              app_encode_app(int, X74, number_number_of(X74), X76)))
257.37/257.62	       | ~ ring(X74)
257.37/257.62	       | ~ number(X74)),
257.37/257.62	    inference('cnf', [status(esa)], [zf_stmt_77])).
257.37/257.62	tff('75', plain,
257.37/257.62	    ![X0 : int, X1 : int, X2 : int]:
257.37/257.62	      (~ $true
257.37/257.62	       | ~ number(int)
257.37/257.62	       | app_encode_app(int, int, 
257.37/257.62	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
257.37/257.62	             app_encode_app(int, int, 
257.37/257.62	               app_encode_app(int, app_encode_fun(int, int), 
257.37/257.62	                 minus_minus(int), X2), X1)), 
257.37/257.62	           app_encode_app(int, int, number_number_of(int), X0))
257.37/257.62	          = app_encode_app(int, int, 
257.37/257.62	              app_encode_app(int, app_encode_fun(int, int), 
257.37/257.62	                minus_minus(int), 
257.37/257.62	                app_encode_app(int, int, 
257.37/257.62	                  app_encode_app(int, app_encode_fun(int, int), 
257.37/257.62	                    times_times(int), X2), 
257.37/257.62	                  app_encode_app(int, int, number_number_of(int), X0))), 
257.37/257.62	              app_encode_app(int, int, 
257.37/257.62	                app_encode_app(int, app_encode_fun(int, int), 
257.37/257.62	                  times_times(int), X1), 
257.37/257.62	                app_encode_app(int, int, number_number_of(int), X0)))),
257.37/257.62	    inference('sup-', [status(thm)], ['73', '74'])).
257.37/257.62	tff('76', plain,
257.37/257.62	    ![X0 : int, X1 : int, X2 : int]:
257.37/257.62	      (~ $true
257.37/257.62	       | ~ $true
257.37/257.62	       | app_encode_app(int, int, 
257.37/257.62	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
257.37/257.62	             app_encode_app(int, int, 
257.37/257.62	               app_encode_app(int, app_encode_fun(int, int), 
257.37/257.62	                 minus_minus(int), X2), X1)), X0)
257.37/257.62	          = app_encode_app(int, int, 
257.37/257.62	              app_encode_app(int, app_encode_fun(int, int), 
257.37/257.62	                minus_minus(int), 
257.37/257.62	                app_encode_app(int, int, 
257.37/257.62	                  app_encode_app(int, app_encode_fun(int, int), 
257.37/257.62	                    times_times(int), X2), X0)), 
257.37/257.62	              app_encode_app(int, int, 
257.37/257.62	                app_encode_app(int, app_encode_fun(int, int), 
257.37/257.62	                  times_times(int), X1), X0))),
257.37/257.62	    inference('demod', [status(thm)], ['75', '21', '1', '1', '1'])).
257.37/257.62	tff('77', plain,
257.37/257.62	    ![X0 : int, X1 : int, X2 : int]:
257.37/257.62	      app_encode_app(int, int, 
257.37/257.62	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
257.37/257.62	          app_encode_app(int, int, 
257.37/257.62	            app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
257.37/257.62	              X2), X1)), X0)
257.37/257.62	       = app_encode_app(int, int, 
257.37/257.62	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
257.37/257.62	             app_encode_app(int, int, 
257.37/257.62	               app_encode_app(int, app_encode_fun(int, int), 
257.37/257.62	                 times_times(int), X2), X0)), 
257.37/257.62	           app_encode_app(int, int, 
257.37/257.62	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
257.37/257.62	               X1), X0)),
257.37/257.62	    inference('simplify', [status(thm)], ['76'])).
257.37/257.62	tff('78', plain,
257.37/257.62	    ![X0 : int, X1 : int]:
257.37/257.62	      app_encode_app(int, int, 
257.37/257.62	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
257.37/257.62	          app_encode_app(int, int, 
257.37/257.62	            app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
257.37/257.62	              X1), pls)), X0)
257.37/257.62	       = app_encode_app(int, int, 
257.37/257.62	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
257.37/257.62	             app_encode_app(int, int, 
257.37/257.62	               app_encode_app(int, app_encode_fun(int, int), 
257.37/257.62	                 times_times(int), X1), X0)), pls),
257.37/257.62	    inference('sup+', [status(thm)], ['4', '77'])).
257.37/257.62	tff('79', plain,
257.37/257.62	    ![X0 : int]:
257.37/257.62	      app_encode_app(int, int, 
257.37/257.62	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
257.37/257.62	          app_encode_app(int, int, 
257.37/257.62	            app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
257.37/257.62	              app_encode_app(int, int, bit1, pls)), pls)), X0)
257.37/257.62	       = app_encode_app(int, int, 
257.37/257.62	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
257.37/257.62	             app_encode_app(int, int, 
257.37/257.62	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	                 pls), X0)), pls),
257.37/257.62	    inference('sup+', [status(thm)], ['72', '78'])).
257.37/257.62	tff(zf_stmt_51, axiom,
257.37/257.62	  (![L1:int,K:int]:
257.37/257.62	     (app_encode_app(int,int,
257.37/257.62	                     app_encode_app(int,app_encode_fun(int,int),
257.37/257.62	                                    minus_minus(int),
257.37/257.62	                                    app_encode_app(int,int,bit1,K)),
257.37/257.62	                     app_encode_app(int,int,bit0,L1)) =
257.37/257.62	      app_encode_app(int,int,bit1,
257.37/257.62	                     app_encode_app(int,int,
257.37/257.62	                                    app_encode_app(int,
257.37/257.62	                                                   app_encode_fun(int,int),
257.37/257.62	                                                   minus_minus(int),K),
257.37/257.62	                                    L1))))).
257.37/257.62	tff('80', plain,
257.37/257.62	    ![X19 : int, X20 : int]:
257.37/257.62	      app_encode_app(int, int, 
257.37/257.62	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
257.37/257.62	          app_encode_app(int, int, bit1, X19)), 
257.37/257.62	        app_encode_app(int, int, bit0, X20))
257.37/257.62	       = app_encode_app(int, int, bit1, 
257.37/257.62	           app_encode_app(int, int, 
257.37/257.62	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
257.37/257.62	               X19), X20)),
257.37/257.62	    inference('cnf', [status(esa)], [zf_stmt_51])).
257.37/257.62	tff('81', plain,
257.37/257.62	    ![X0 : int]:
257.37/257.62	      app_encode_app(int, int, 
257.37/257.62	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
257.37/257.62	          app_encode_app(int, int, bit1, X0)), pls)
257.37/257.62	       = app_encode_app(int, int, bit1, 
257.37/257.62	           app_encode_app(int, int, 
257.37/257.62	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
257.37/257.62	               X0), pls)),
257.37/257.62	    inference('sup+', [status(thm)], ['7', '80'])).
257.37/257.62	tff(zf_stmt_78, axiom,
257.37/257.62	  (![B:$tType]:
257.37/257.62	     ((number(B) & ring(B)) =>
257.37/257.62	      (![C:B,B1:B,V1:int]:
257.37/257.62	         (app_encode_app(B,B,
257.37/257.62	                         app_encode_app(B,app_encode_fun(B,B),times_times(B),
257.37/257.62	                                        app_encode_app(int,B,
257.37/257.62	                                                       number_number_of(B),V1)),
257.37/257.62	                         app_encode_app(B,B,
257.37/257.62	                                        app_encode_app(B,app_encode_fun(B,B),
257.37/257.62	                                                       minus_minus(B),B1),
257.37/257.62	                                        C)) =
257.37/257.62	          app_encode_app(B,B,
257.37/257.62	                         app_encode_app(B,app_encode_fun(B,B),minus_minus(B),
257.37/257.62	                                        app_encode_app(B,B,
257.37/257.62	                                                       app_encode_app(
257.37/257.62	                                                       B,app_encode_fun(B,B),
257.37/257.62	                                                       times_times(B),
257.37/257.62	                                                       app_encode_app(
257.37/257.62	                                                       int,B,
257.37/257.62	                                                       number_number_of(B),V1)),
257.37/257.62	                                                       B1)),
257.37/257.62	                         app_encode_app(B,B,
257.37/257.62	                                        app_encode_app(B,app_encode_fun(B,B),
257.37/257.62	                                                       times_times(B),
257.37/257.62	                                                       app_encode_app(
257.37/257.62	                                                       int,B,
257.37/257.62	                                                       number_number_of(B),V1)),
257.37/257.62	                                        C))))))).
257.37/257.62	tff('82', plain,
257.37/257.62	    ![X78 : $tType, X79 : int, X80 : X78, X81 : X78]:
257.37/257.62	      (app_encode_app(X78, X78, 
257.37/257.62	         app_encode_app(X78, app_encode_fun(X78, X78), times_times(X78), 
257.37/257.62	           app_encode_app(int, X78, number_number_of(X78), X79)), 
257.37/257.62	         app_encode_app(X78, X78, 
257.37/257.62	           app_encode_app(X78, app_encode_fun(X78, X78), minus_minus(X78), 
257.37/257.62	             X80), X81))
257.37/257.62	        = app_encode_app(X78, X78, 
257.37/257.62	            app_encode_app(X78, app_encode_fun(X78, X78), minus_minus(X78), 
257.37/257.62	              app_encode_app(X78, X78, 
257.37/257.62	                app_encode_app(X78, app_encode_fun(X78, X78), 
257.37/257.62	                  times_times(X78), 
257.37/257.62	                  app_encode_app(int, X78, number_number_of(X78), X79)), X80)), 
257.37/257.62	            app_encode_app(X78, X78, 
257.37/257.62	              app_encode_app(X78, app_encode_fun(X78, X78), 
257.37/257.62	                times_times(X78), 
257.37/257.62	                app_encode_app(int, X78, number_number_of(X78), X79)), X81))
257.37/257.62	       | ~ ring(X78)
257.37/257.62	       | ~ number(X78)),
257.37/257.62	    inference('cnf', [status(esa)], [zf_stmt_78])).
257.37/257.62	tff('83', plain,
257.37/257.62	    ![X0 : int, X1 : int, X2 : int]:
257.37/257.62	      (~ $true
257.37/257.62	       | ~ number(int)
257.37/257.62	       | app_encode_app(int, int, 
257.37/257.62	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
257.37/257.62	             app_encode_app(int, int, number_number_of(int), X2)), 
257.37/257.62	           app_encode_app(int, int, 
257.37/257.62	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
257.37/257.62	               X1), X0))
257.37/257.62	          = app_encode_app(int, int, 
257.37/257.62	              app_encode_app(int, app_encode_fun(int, int), 
257.37/257.62	                minus_minus(int), 
257.37/257.62	                app_encode_app(int, int, 
257.37/257.62	                  app_encode_app(int, app_encode_fun(int, int), 
257.37/257.62	                    times_times(int), 
257.37/257.62	                    app_encode_app(int, int, number_number_of(int), X2)), X1)), 
257.37/257.62	              app_encode_app(int, int, 
257.37/257.62	                app_encode_app(int, app_encode_fun(int, int), 
257.37/257.62	                  times_times(int), 
257.37/257.62	                  app_encode_app(int, int, number_number_of(int), X2)), X0))),
257.37/257.62	    inference('sup-', [status(thm)], ['73', '82'])).
257.37/257.62	tff('84', plain,
257.37/257.62	    ![X0 : int, X1 : int, X2 : int]:
257.37/257.62	      (~ $true
257.37/257.62	       | ~ $true
257.37/257.62	       | app_encode_app(int, int, 
257.37/257.62	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
257.37/257.62	             X2), 
257.37/257.62	           app_encode_app(int, int, 
257.37/257.62	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
257.37/257.62	               X1), X0))
257.37/257.62	          = app_encode_app(int, int, 
257.37/257.62	              app_encode_app(int, app_encode_fun(int, int), 
257.37/257.62	                minus_minus(int), 
257.37/257.62	                app_encode_app(int, int, 
257.37/257.62	                  app_encode_app(int, app_encode_fun(int, int), 
257.37/257.62	                    times_times(int), X2), X1)), 
257.37/257.62	              app_encode_app(int, int, 
257.37/257.62	                app_encode_app(int, app_encode_fun(int, int), 
257.37/257.62	                  times_times(int), X2), X0))),
257.37/257.62	    inference('demod', [status(thm)], ['83', '21', '1', '1', '1'])).
257.37/257.62	tff('85', plain,
257.37/257.62	    ![X0 : int, X1 : int, X2 : int]:
257.37/257.62	      app_encode_app(int, int, 
257.37/257.62	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X2), 
257.37/257.62	        app_encode_app(int, int, 
257.37/257.62	          app_encode_app(int, app_encode_fun(int, int), minus_minus(int), X1), 
257.37/257.62	          X0))
257.37/257.62	       = app_encode_app(int, int, 
257.37/257.62	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
257.37/257.62	             app_encode_app(int, int, 
257.37/257.62	               app_encode_app(int, app_encode_fun(int, int), 
257.37/257.62	                 times_times(int), X2), X1)), 
257.37/257.62	           app_encode_app(int, int, 
257.37/257.62	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
257.37/257.62	               X2), X0)),
257.37/257.62	    inference('simplify', [status(thm)], ['84'])).
257.37/257.62	tff('86', plain,
257.37/257.62	    ![X0 : int, X1 : int]:
257.37/257.62	      app_encode_app(int, int, 
257.37/257.62	        app_encode_app(int, app_encode_fun(int, int), times_times(int), pls), 
257.37/257.62	        app_encode_app(int, int, 
257.37/257.62	          app_encode_app(int, app_encode_fun(int, int), minus_minus(int), X1), 
257.37/257.62	          X0))
257.37/257.62	       = app_encode_app(int, int, 
257.37/257.62	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
257.37/257.62	             pls), 
257.37/257.62	           app_encode_app(int, int, 
257.37/257.62	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
257.37/257.62	               pls), X0)),
257.37/257.62	    inference('sup+', [status(thm)], ['4', '85'])).
257.37/257.62	tff('87', plain,
257.37/257.62	    pls
257.37/257.62	     = app_encode_app(int, int, 
257.37/257.62	         app_encode_app(int, app_encode_fun(int, int), minus_minus(int), pls), 
257.37/257.62	         pls),
257.37/257.62	    inference('demod', [status(thm)], ['86', '4', '4'])).
257.37/257.62	tff('88', plain,
257.37/257.62	    ![X0 : int]:
257.37/257.62	      app_encode_app(int, int, 
257.37/257.62	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
257.37/257.62	        X0)
257.37/257.62	       = app_encode_app(int, int, 
257.37/257.62	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
257.37/257.62	             app_encode_app(int, int, 
257.37/257.62	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	                 pls), X0)), pls),
257.37/257.62	    inference('demod', [status(thm)], ['79', '81', '87', '72'])).
257.37/257.62	tff(zf_stmt_73, axiom,
257.37/257.62	  (![L1:int,K:int]:
257.37/257.62	     (app_encode_app(int,int,
257.37/257.62	                     app_encode_app(int,app_encode_fun(int,int),
257.37/257.62	                                    minus_minus(int),
257.37/257.62	                                    app_encode_app(int,int,bit0,K)),
257.37/257.62	                     app_encode_app(int,int,bit0,L1)) =
257.37/257.62	      app_encode_app(int,int,bit0,
257.37/257.62	                     app_encode_app(int,int,
257.37/257.62	                                    app_encode_app(int,
257.37/257.62	                                                   app_encode_fun(int,int),
257.37/257.62	                                                   minus_minus(int),K),
257.37/257.62	                                    L1))))).
257.37/257.62	tff('89', plain,
257.37/257.62	    ![X63 : int, X64 : int]:
257.37/257.62	      app_encode_app(int, int, 
257.37/257.62	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
257.37/257.62	          app_encode_app(int, int, bit0, X63)), 
257.37/257.62	        app_encode_app(int, int, bit0, X64))
257.37/257.62	       = app_encode_app(int, int, bit0, 
257.37/257.62	           app_encode_app(int, int, 
257.37/257.62	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
257.37/257.62	               X63), X64)),
257.37/257.62	    inference('cnf', [status(esa)], [zf_stmt_73])).
257.37/257.62	tff('90', plain,
257.37/257.62	    ![X0 : int, X1 : int]:
257.37/257.62	      app_encode_app(int, int, 
257.37/257.62	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
257.37/257.62	          app_encode_app(int, int, bit0, X0)), 
257.37/257.62	        app_encode_app(int, int, bit0, X1))
257.37/257.62	       = app_encode_app(int, int, bit0, 
257.37/257.62	           app_encode_app(int, int, 
257.37/257.62	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
257.37/257.62	               app_encode_app(int, int, 
257.37/257.62	                 app_encode_app(int, app_encode_fun(int, int), 
257.37/257.62	                   plus_plus(int), pls), X0)), X1)),
257.37/257.62	    inference('sup+', [status(thm)], ['64', '89'])).
257.37/257.62	tff('91', plain,
257.37/257.62	    ![X0 : int, X1 : int]:
257.37/257.62	      app_encode_app(int, int, bit0, 
257.37/257.62	        app_encode_app(int, int, 
257.37/257.62	          app_encode_app(int, app_encode_fun(int, int), minus_minus(int), X0), 
257.37/257.62	          X1))
257.37/257.62	       = app_encode_app(int, int, bit0, 
257.37/257.62	           app_encode_app(int, int, 
257.37/257.62	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
257.37/257.62	               app_encode_app(int, int, 
257.37/257.62	                 app_encode_app(int, app_encode_fun(int, int), 
257.37/257.62	                   plus_plus(int), pls), X0)), X1)),
257.37/257.62	    inference('demod', [status(thm)], ['90', '89'])).
257.37/257.62	tff('92', plain,
257.37/257.62	    ![X0 : int]:
257.37/257.62	      app_encode_app(int, int, bit0, 
257.37/257.62	        app_encode_app(int, int, 
257.37/257.62	          app_encode_app(int, app_encode_fun(int, int), minus_minus(int), X0), 
257.37/257.62	          pls))
257.37/257.62	       = app_encode_app(int, int, bit0, 
257.37/257.62	           app_encode_app(int, int, 
257.37/257.62	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	               pls), X0)),
257.37/257.62	    inference('sup+', [status(thm)], ['88', '91'])).
257.37/257.62	tff('93', plain,
257.37/257.62	    ![X0 : int]:
257.37/257.62	      app_encode_app(int, int, bit0, 
257.37/257.62	        app_encode_app(int, int, 
257.37/257.62	          app_encode_app(int, app_encode_fun(int, int), minus_minus(int), X0), 
257.37/257.62	          pls))
257.37/257.62	       = app_encode_app(int, int, bit0, X0),
257.37/257.62	    inference('demod', [status(thm)], ['92', '64'])).
257.37/257.62	tff('94', plain,
257.37/257.62	    ![X0 : int, X1 : int]:
257.37/257.62	      (app_encode_app(int, $o, 
257.37/257.62	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), X1), 
257.37/257.62	         app_encode_app(int, int, bit0, X0))
257.37/257.62	       | ~ app_encode_app(int, $o, 
257.37/257.62	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X1), 
257.37/257.62	             app_encode_app(int, int, bit1, X0))),
257.37/257.62	    inference('demod', [status(thm)], ['69', '93'])).
257.37/257.62	tff('95', plain,
257.37/257.62	    (~ $true
257.37/257.62	     | app_encode_app(int, $o, 
257.37/257.62	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), s), 
257.37/257.62	         app_encode_app(int, int, bit0, app_encode_app(int, int, bit0, m)))),
257.37/257.62	    inference('sup-', [status(thm)], ['65', '94'])).
257.37/257.62	tff('96', plain,
257.37/257.62	    app_encode_app(int, $o, 
257.37/257.62	      app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), s), 
257.37/257.62	      app_encode_app(int, int, bit0, app_encode_app(int, int, bit0, m))),
257.37/257.62	    inference('simplify', [status(thm)], ['95'])).
257.37/257.62	tff(zf_stmt_151, conjecture,
257.37/257.62	  (app_encode_app(int,$o,
257.37/257.62	                  app_encode_app(int,app_encode_fun(int,$o),ord_less_eq(int),
257.37/257.62	                                 s),
257.37/257.62	                  app_encode_app(int,int,
257.37/257.62	                                 app_encode_app(int,app_encode_fun(int,int),
257.37/257.62	                                                minus_minus(int),
257.37/257.62	                                                app_encode_app(int,int,
257.37/257.62	                                                               app_encode_app(
257.37/257.62	                                                               int,
257.37/257.62	                                                               app_encode_fun(
257.37/257.62	                                                               int,int),
257.37/257.62	                                                               plus_plus(int),
257.37/257.62	                                                               app_encode_app(
257.37/257.62	                                                               int,int,
257.37/257.62	                                                               app_encode_app(
257.37/257.62	                                                               int,
257.37/257.62	                                                               app_encode_fun(
257.37/257.62	                                                               int,int),
257.37/257.62	                                                               times_times(
257.37/257.62	                                                               int),
257.37/257.62	                                                               app_encode_app(
257.37/257.62	                                                               int,int,
257.37/257.62	                                                               number_number_of(
257.37/257.62	                                                               int),
257.37/257.62	                                                               app_encode_app(
257.37/257.62	                                                               int,int,bit0,
257.37/257.62	                                                               app_encode_app(
257.37/257.62	                                                               int,int,bit0,
257.37/257.62	                                                               app_encode_app(
257.37/257.62	                                                               int,int,bit1,
257.37/257.62	                                                               pls))))),m)),
257.37/257.62	                                                               one_one(int))),
257.37/257.62	                                 one_one(int))))).
257.37/257.62	tff(zf_stmt_0, negated_conjecture,
257.37/257.62	  (~
257.37/257.62	    app_encode_app(int,$o,
257.37/257.62	                   app_encode_app(int,app_encode_fun(int,$o),
257.37/257.62	                                  ord_less_eq(int),s),
257.37/257.62	                   app_encode_app(int,int,
257.37/257.62	                                  app_encode_app(int,app_encode_fun(int,int),
257.37/257.62	                                                 minus_minus(int),
257.37/257.62	                                                 app_encode_app(int,int,
257.37/257.62	                                                                app_encode_app(
257.37/257.62	                                                                int,
257.37/257.62	                                                                app_encode_fun(
257.37/257.62	                                                                int,int),
257.37/257.62	                                                                plus_plus(
257.37/257.62	                                                                int),
257.37/257.62	                                                                app_encode_app(
257.37/257.62	                                                                int,int,
257.37/257.62	                                                                app_encode_app(
257.37/257.62	                                                                int,
257.37/257.62	                                                                app_encode_fun(
257.37/257.62	                                                                int,int),
257.37/257.62	                                                                times_times(
257.37/257.62	                                                                int),
257.37/257.62	                                                                app_encode_app(
257.37/257.62	                                                                int,int,
257.37/257.62	                                                                number_number_of(
257.37/257.62	                                                                int),
257.37/257.62	                                                                app_encode_app(
257.37/257.62	                                                                int,int,bit0,
257.37/257.62	                                                                app_encode_app(
257.37/257.62	                                                                int,int,bit0,
257.37/257.62	                                                                app_encode_app(
257.37/257.62	                                                                int,int,bit1,
257.37/257.62	                                                                pls))))),m)),
257.37/257.62	                                                                one_one(int))),
257.37/257.62	                                  one_one(int))))).
257.37/257.62	tff('97', plain,
257.37/257.62	    ~ app_encode_app(int, $o, 
257.37/257.62	        app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), s), 
257.37/257.62	        app_encode_app(int, int, 
257.37/257.62	          app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
257.37/257.62	            app_encode_app(int, int, 
257.37/257.62	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	                app_encode_app(int, int, 
257.37/257.62	                  app_encode_app(int, app_encode_fun(int, int), 
257.37/257.62	                    times_times(int), 
257.37/257.62	                    app_encode_app(int, int, number_number_of(int), 
257.37/257.62	                      app_encode_app(int, int, bit0, 
257.37/257.62	                        app_encode_app(int, int, bit0, 
257.37/257.62	                          app_encode_app(int, int, bit1, pls))))), m)), 
257.37/257.62	              one_one(int))), one_one(int))),
257.37/257.62	    inference('cnf', [status(esa)], [zf_stmt_0])).
257.37/257.62	tff('98', plain,
257.37/257.62	    ![X0 : int]:
257.37/257.62	      app_encode_app(int, int, 
257.37/257.62	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
257.37/257.62	        X0)
257.37/257.62	       = app_encode_app(int, int, 
257.37/257.62	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
257.37/257.62	           app_encode_app(int, int, 
257.37/257.62	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	               X0), pls)),
257.37/257.62	    inference('demod', [status(thm)], ['35', '42'])).
257.37/257.62	tff('99', plain,
257.37/257.62	    ![X0 : int]:
257.37/257.62	      app_encode_app(int, int, bit0, 
257.37/257.62	        app_encode_app(int, int, 
257.37/257.62	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
257.37/257.62	          X0))
257.37/257.62	       = app_encode_app(int, int, bit0, 
257.37/257.62	           app_encode_app(int, int, 
257.37/257.62	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	               X0), pls)),
257.37/257.62	    inference('sup+', [status(thm)], ['98', '64'])).
257.37/257.62	tff('100', plain,
257.37/257.62	    ![X0 : int]:
257.37/257.62	      app_encode_app(int, int, bit0, X0)
257.37/257.62	       = app_encode_app(int, int, bit0, 
257.37/257.62	           app_encode_app(int, int, 
257.37/257.62	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	               X0), pls)),
257.37/257.62	    inference('demod', [status(thm)], ['99', '64'])).
257.37/257.62	tff('101', plain,
257.37/257.62	    ![X0 : int]:
257.37/257.62	      app_encode_app(int, int, 
257.37/257.62	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
257.37/257.62	          app_encode_app(int, int, bit0, X0)), pls)
257.37/257.62	       = app_encode_app(int, int, bit0, X0),
257.37/257.62	    inference('demod', [status(thm)], ['16', '100'])).
257.37/257.62	tff('102', plain,
257.37/257.62	    ![X0 : int]:
257.37/257.62	      app_encode_app(int, int, 
257.37/257.62	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
257.37/257.62	          app_encode_app(int, int, bit0, X0)), pls)
257.37/257.62	       = app_encode_app(int, int, bit0, 
257.37/257.62	           app_encode_app(int, int, 
257.37/257.62	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
257.37/257.62	               X0), pls)),
257.37/257.62	    inference('sup+', [status(thm)], ['7', '89'])).
257.37/257.62	tff('103', plain,
257.37/257.62	    ~ app_encode_app(int, $o, 
257.37/257.62	        app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), s), 
257.37/257.62	        app_encode_app(int, int, bit0, 
257.37/257.62	          app_encode_app(int, int, bit0, 
257.37/257.62	            app_encode_app(int, int, 
257.37/257.62	              app_encode_app(int, app_encode_fun(int, int), 
257.37/257.62	                minus_minus(int), m), pls)))),
257.37/257.62	    inference('demod', [status(thm)],
257.37/257.62	              ['97', '1', '3', '3', '8', '64', '13', '14', '101', '13', 
257.37/257.62	               '66', '102'])).
257.37/257.62	tff('104', plain,
257.37/257.62	    ~ app_encode_app(int, $o, 
257.37/257.62	        app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), s), 
257.37/257.62	        app_encode_app(int, int, bit0, app_encode_app(int, int, bit0, m))),
257.37/257.62	    inference('demod', [status(thm)], ['103', '93'])).
257.37/257.62	tff('105', plain, ~ $true, inference('sup-', [status(thm)], ['96', '104'])).
257.37/257.62	tff('106', plain, $false, inference('simplify', [status(thm)], ['105'])).
257.37/257.62	
257.37/257.62	% SZS output end Refutation
257.37/257.63	EOF
