0.00/0.00	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : app
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 $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n133.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 07:53:38 CST 2018
277.71/277.95	% done 14963 iterations in 277.752s
277.71/277.95	% SZS status Theorem for 'stdin'
277.71/277.95	% SZS output start Refutation
277.71/277.96	tff(zf_stmt_36, axiom,
277.71/277.96	  (app_encode_app(int,$o,
277.71/277.96	                  app_encode_app(int,app_encode_fun(int,$o),ord_less_eq(int),
277.71/277.96	                                 zero_zero(int)),
277.71/277.96	                  s) & 
277.71/277.96	   app_encode_app(int,$o,
277.71/277.96	                  app_encode_app(int,app_encode_fun(int,$o),ord_less(int),s),
277.71/277.96	                  app_encode_app(int,int,
277.71/277.96	                                 app_encode_app(int,app_encode_fun(int,int),
277.71/277.96	                                                plus_plus(int),
277.71/277.96	                                                app_encode_app(int,int,
277.71/277.96	                                                               app_encode_app(
277.71/277.96	                                                               int,
277.71/277.96	                                                               app_encode_fun(
277.71/277.96	                                                               int,int),
277.71/277.96	                                                               times_times(
277.71/277.96	                                                               int),
277.71/277.96	                                                               app_encode_app(
277.71/277.96	                                                               int,int,
277.71/277.96	                                                               number_number_of(
277.71/277.96	                                                               int),
277.71/277.96	                                                               app_encode_app(
277.71/277.96	                                                               int,int,bit0,
277.71/277.96	                                                               app_encode_app(
277.71/277.96	                                                               int,int,bit0,
277.71/277.96	                                                               app_encode_app(
277.71/277.96	                                                               int,int,bit1,
277.71/277.96	                                                               pls))))),m)),
277.71/277.96	                                 one_one(int))) & 
277.71/277.96	   app_encode_app(int,$o,
277.71/277.96	                  app_encode_app(int,app_encode_fun(int,$o),
277.71/277.96	                                 app_encode_app(int,
277.71/277.96	                                                app_encode_fun(int,
277.71/277.96	                                                               app_encode_fun(
277.71/277.96	                                                               int,$o)),
277.71/277.96	                                                zcong,s1),
277.71/277.96	                                 s),
277.71/277.96	                  app_encode_app(int,int,
277.71/277.96	                                 app_encode_app(int,app_encode_fun(int,int),
277.71/277.96	                                                plus_plus(int),
277.71/277.96	                                                app_encode_app(int,int,
277.71/277.96	                                                               app_encode_app(
277.71/277.96	                                                               int,
277.71/277.96	                                                               app_encode_fun(
277.71/277.96	                                                               int,int),
277.71/277.96	                                                               times_times(
277.71/277.96	                                                               int),
277.71/277.96	                                                               app_encode_app(
277.71/277.96	                                                               int,int,
277.71/277.96	                                                               number_number_of(
277.71/277.96	                                                               int),
277.71/277.96	                                                               app_encode_app(
277.71/277.96	                                                               int,int,bit0,
277.71/277.96	                                                               app_encode_app(
277.71/277.96	                                                               int,int,bit0,
277.71/277.96	                                                               app_encode_app(
277.71/277.96	                                                               int,int,bit1,
277.71/277.96	                                                               pls))))),m)),
277.71/277.96	                                 one_one(int))))).
277.71/277.96	tff('0', plain,
277.71/277.96	    app_encode_app(int, $o, 
277.71/277.96	      app_encode_app(int, app_encode_fun(int, $o), ord_less(int), s), 
277.71/277.96	      app_encode_app(int, int, 
277.71/277.96	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	          app_encode_app(int, int, 
277.71/277.96	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
277.71/277.96	              app_encode_app(int, int, number_number_of(int), 
277.71/277.96	                app_encode_app(int, int, bit0, 
277.71/277.96	                  app_encode_app(int, int, bit0, 
277.71/277.96	                    app_encode_app(int, int, bit1, pls))))), m)), 
277.71/277.96	        one_one(int))),
277.71/277.96	    inference('cnf', [status(esa)], [zf_stmt_36])).
277.71/277.96	tff(zf_stmt_126, axiom,
277.71/277.96	  (![K:int]: (app_encode_app(int,int,number_number_of(int),K) = K))).
277.71/277.96	tff('1', plain,
277.71/277.96	    ![X196 : int]:
277.71/277.96	      app_encode_app(int, int, number_number_of(int), X196) = X196,
277.71/277.96	    inference('cnf', [status(esa)], [zf_stmt_126])).
277.71/277.96	tff('2', plain,
277.71/277.96	    app_encode_app(int, $o, 
277.71/277.96	      app_encode_app(int, app_encode_fun(int, $o), ord_less(int), s), 
277.71/277.96	      app_encode_app(int, int, 
277.71/277.96	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	          app_encode_app(int, int, 
277.71/277.96	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
277.71/277.96	              app_encode_app(int, int, bit0, 
277.71/277.96	                app_encode_app(int, int, bit0, 
277.71/277.96	                  app_encode_app(int, int, bit1, pls)))), m)), one_one(int))),
277.71/277.96	    inference('demod', [status(thm)], ['0', '1'])).
277.71/277.96	tff(zf_stmt_70, axiom,
277.71/277.96	  (![L1:int,K:int]:
277.71/277.96	     (app_encode_app(int,int,
277.71/277.96	                     app_encode_app(int,app_encode_fun(int,int),
277.71/277.96	                                    times_times(int),
277.71/277.96	                                    app_encode_app(int,int,bit0,K)),
277.71/277.96	                     L1) =
277.71/277.96	      app_encode_app(int,int,bit0,
277.71/277.96	                     app_encode_app(int,int,
277.71/277.96	                                    app_encode_app(int,
277.71/277.96	                                                   app_encode_fun(int,int),
277.71/277.96	                                                   times_times(int),K),
277.71/277.96	                                    L1))))).
277.71/277.96	tff('3', plain,
277.71/277.96	    ![X55 : int, X56 : int]:
277.71/277.96	      app_encode_app(int, int, 
277.71/277.96	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
277.71/277.96	          app_encode_app(int, int, bit0, X55)), X56)
277.71/277.96	       = app_encode_app(int, int, bit0, 
277.71/277.96	           app_encode_app(int, int, 
277.71/277.96	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
277.71/277.96	               X55), X56)),
277.71/277.96	    inference('cnf', [status(esa)], [zf_stmt_70])).
277.71/277.96	tff(zf_stmt_69, axiom,
277.71/277.96	  (![W:int]:
277.71/277.96	     (app_encode_app(int,int,
277.71/277.96	                     app_encode_app(int,app_encode_fun(int,int),
277.71/277.96	                                    times_times(int),pls),
277.71/277.96	                     W) =
277.71/277.96	      pls))).
277.71/277.96	tff('4', plain,
277.71/277.96	    ![X54 : int]:
277.71/277.96	      app_encode_app(int, int, 
277.71/277.96	        app_encode_app(int, app_encode_fun(int, int), times_times(int), pls), 
277.71/277.96	        X54)
277.71/277.96	       = pls,
277.71/277.96	    inference('cnf', [status(esa)], [zf_stmt_69])).
277.71/277.96	tff(zf_stmt_45, axiom,
277.71/277.96	  (![L1:int,K:int]:
277.71/277.96	     (app_encode_app(int,int,
277.71/277.96	                     app_encode_app(int,app_encode_fun(int,int),
277.71/277.96	                                    times_times(int),
277.71/277.96	                                    app_encode_app(int,int,bit1,K)),
277.71/277.96	                     L1) =
277.71/277.96	      app_encode_app(int,int,
277.71/277.96	                     app_encode_app(int,app_encode_fun(int,int),
277.71/277.96	                                    plus_plus(int),
277.71/277.96	                                    app_encode_app(int,int,bit0,
277.71/277.96	                                                   app_encode_app(int,int,
277.71/277.96	                                                                  app_encode_app(
277.71/277.96	                                                                  int,
277.71/277.96	                                                                  app_encode_fun(
277.71/277.96	                                                                  int,int),
277.71/277.96	                                                                  times_times(
277.71/277.96	                                                                  int),K),L1))),
277.71/277.96	                     L1)))).
277.71/277.96	tff('5', plain,
277.71/277.96	    ![X11 : int, X12 : int]:
277.71/277.96	      app_encode_app(int, int, 
277.71/277.96	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
277.71/277.96	          app_encode_app(int, int, bit1, X11)), X12)
277.71/277.96	       = app_encode_app(int, int, 
277.71/277.96	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	             app_encode_app(int, int, bit0, 
277.71/277.96	               app_encode_app(int, int, 
277.71/277.96	                 app_encode_app(int, app_encode_fun(int, int), 
277.71/277.96	                   times_times(int), X11), X12))), X12),
277.71/277.96	    inference('cnf', [status(esa)], [zf_stmt_45])).
277.71/277.96	tff('6', plain,
277.71/277.96	    ![X0 : int]:
277.71/277.96	      app_encode_app(int, int, 
277.71/277.96	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
277.71/277.96	          app_encode_app(int, int, bit1, pls)), X0)
277.71/277.96	       = app_encode_app(int, int, 
277.71/277.96	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	             app_encode_app(int, int, bit0, pls)), X0),
277.71/277.96	    inference('sup+', [status(thm)], ['4', '5'])).
277.71/277.96	tff(zf_stmt_62, axiom, (app_encode_app(int,int,bit0,pls) = pls)).
277.71/277.96	tff('7', plain, app_encode_app(int, int, bit0, pls) = pls,
277.71/277.96	    inference('cnf', [status(esa)], [zf_stmt_62])).
277.71/277.96	tff('8', plain,
277.71/277.96	    ![X0 : int]:
277.71/277.96	      app_encode_app(int, int, 
277.71/277.96	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
277.71/277.96	          app_encode_app(int, int, bit1, pls)), X0)
277.71/277.96	       = app_encode_app(int, int, 
277.71/277.96	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
277.71/277.96	           X0),
277.71/277.96	    inference('demod', [status(thm)], ['6', '7'])).
277.71/277.96	tff(zf_stmt_139, axiom, (number_ring(int))).
277.71/277.96	tff('9', plain, number_ring(int),
277.71/277.96	    inference('cnf', [status(esa)], [zf_stmt_139])).
277.71/277.96	tff(zf_stmt_46, axiom,
277.71/277.96	  (![A:$tType]:
277.71/277.96	     (number_ring(A) =>
277.71/277.96	      (app_encode_app(int,A,number_number_of(A),
277.71/277.96	                      app_encode_app(int,int,bit1,pls)) =
277.71/277.96	       one_one(A))))).
277.71/277.96	tff('10', plain,
277.71/277.96	    ![X13 : $tType]:
277.71/277.96	      (app_encode_app(int, X13, number_number_of(X13), 
277.71/277.96	         app_encode_app(int, int, bit1, pls))
277.71/277.96	        = one_one(X13)
277.71/277.96	       | ~ number_ring(X13)),
277.71/277.96	    inference('cnf', [status(esa)], [zf_stmt_46])).
277.71/277.96	tff('11', plain,
277.71/277.96	    (~ $true
277.71/277.96	     | app_encode_app(int, int, number_number_of(int), 
277.71/277.96	         app_encode_app(int, int, bit1, pls))
277.71/277.96	        = one_one(int)),
277.71/277.96	    inference('sup-', [status(thm)], ['9', '10'])).
277.71/277.96	tff('12', plain,
277.71/277.96	    (~ $true | app_encode_app(int, int, bit1, pls) = one_one(int)),
277.71/277.96	    inference('demod', [status(thm)], ['11', '1'])).
277.71/277.96	tff('13', plain, app_encode_app(int, int, bit1, pls) = one_one(int),
277.71/277.96	    inference('simplify', [status(thm)], ['12'])).
277.71/277.96	tff(zf_stmt_93, axiom,
277.71/277.96	  (![L1:int,K:int]:
277.71/277.96	     (app_encode_app(int,int,
277.71/277.96	                     app_encode_app(int,app_encode_fun(int,int),
277.71/277.96	                                    plus_plus(int),
277.71/277.96	                                    app_encode_app(int,int,bit0,K)),
277.71/277.96	                     app_encode_app(int,int,bit1,L1)) =
277.71/277.96	      app_encode_app(int,int,bit1,
277.71/277.96	                     app_encode_app(int,int,
277.71/277.96	                                    app_encode_app(int,
277.71/277.96	                                                   app_encode_fun(int,int),
277.71/277.96	                                                   plus_plus(int),K),
277.71/277.96	                                    L1))))).
277.71/277.96	tff('14', plain,
277.71/277.96	    ![X120 : int, X121 : int]:
277.71/277.96	      app_encode_app(int, int, 
277.71/277.96	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	          app_encode_app(int, int, bit0, X120)), 
277.71/277.96	        app_encode_app(int, int, bit1, X121))
277.71/277.96	       = app_encode_app(int, int, bit1, 
277.71/277.96	           app_encode_app(int, int, 
277.71/277.96	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	               X120), X121)),
277.71/277.96	    inference('cnf', [status(esa)], [zf_stmt_93])).
277.71/277.96	tff(zf_stmt_71, axiom,
277.71/277.96	  (![L1:int,K:int]:
277.71/277.96	     (app_encode_app(int,int,
277.71/277.96	                     app_encode_app(int,app_encode_fun(int,int),
277.71/277.96	                                    plus_plus(int),
277.71/277.96	                                    app_encode_app(int,int,bit0,K)),
277.71/277.96	                     app_encode_app(int,int,bit0,L1)) =
277.71/277.96	      app_encode_app(int,int,bit0,
277.71/277.96	                     app_encode_app(int,int,
277.71/277.96	                                    app_encode_app(int,
277.71/277.96	                                                   app_encode_fun(int,int),
277.71/277.96	                                                   plus_plus(int),K),
277.71/277.96	                                    L1))))).
277.71/277.96	tff('15', plain,
277.71/277.96	    ![X57 : int, X58 : int]:
277.71/277.96	      app_encode_app(int, int, 
277.71/277.96	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	          app_encode_app(int, int, bit0, X57)), 
277.71/277.96	        app_encode_app(int, int, bit0, X58))
277.71/277.96	       = app_encode_app(int, int, bit0, 
277.71/277.96	           app_encode_app(int, int, 
277.71/277.96	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	               X57), X58)),
277.71/277.96	    inference('cnf', [status(esa)], [zf_stmt_71])).
277.71/277.96	tff('16', plain,
277.71/277.96	    ![X0 : int]:
277.71/277.96	      app_encode_app(int, int, 
277.71/277.96	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	          app_encode_app(int, int, bit0, X0)), pls)
277.71/277.96	       = app_encode_app(int, int, bit0, 
277.71/277.96	           app_encode_app(int, int, 
277.71/277.96	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	               X0), pls)),
277.71/277.96	    inference('sup+', [status(thm)], ['7', '15'])).
277.71/277.96	tff('17', plain,
277.71/277.96	    app_encode_app(int, $o, 
277.71/277.96	      app_encode_app(int, app_encode_fun(int, $o), ord_less(int), s), 
277.71/277.96	      app_encode_app(int, int, bit1, 
277.71/277.96	        app_encode_app(int, int, bit0, 
277.71/277.96	          app_encode_app(int, int, 
277.71/277.96	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	              app_encode_app(int, int, 
277.71/277.96	                app_encode_app(int, app_encode_fun(int, int), 
277.71/277.96	                  plus_plus(int), pls), m)), pls)))),
277.71/277.96	    inference('demod', [status(thm)], ['2', '3', '3', '8', '13', '14', '16'])).
277.71/277.96	tff(zf_stmt_140, axiom, (semiring(int))).
277.71/277.96	tff('18', plain, semiring(int),
277.71/277.96	    inference('cnf', [status(esa)], [zf_stmt_140])).
277.71/277.96	tff(zf_stmt_73, axiom,
277.71/277.96	  (![B:$tType]:
277.71/277.96	     ((number(B) & semiring(B)) =>
277.71/277.96	      (![V1:int,B1:B,A2:B]:
277.71/277.96	         (app_encode_app(B,B,
277.71/277.96	                         app_encode_app(B,app_encode_fun(B,B),times_times(B),
277.71/277.96	                                        app_encode_app(B,B,
277.71/277.96	                                                       app_encode_app(
277.71/277.96	                                                       B,app_encode_fun(B,B),
277.71/277.96	                                                       plus_plus(B),A2),B1)),
277.71/277.96	                         app_encode_app(int,B,number_number_of(B),V1)) =
277.71/277.96	          app_encode_app(B,B,
277.71/277.96	                         app_encode_app(B,app_encode_fun(B,B),plus_plus(B),
277.71/277.96	                                        app_encode_app(B,B,
277.71/277.96	                                                       app_encode_app(
277.71/277.96	                                                       B,app_encode_fun(B,B),
277.71/277.96	                                                       times_times(B),A2),
277.71/277.96	                                                       app_encode_app(
277.71/277.96	                                                       int,B,
277.71/277.96	                                                       number_number_of(B),V1))),
277.71/277.96	                         app_encode_app(B,B,
277.71/277.96	                                        app_encode_app(B,app_encode_fun(B,B),
277.71/277.96	                                                       times_times(B),B1),
277.71/277.96	                                        app_encode_app(int,B,
277.71/277.96	                                                       number_number_of(B),V1)))))))).
277.71/277.96	tff('19', plain,
277.71/277.96	    ![X61 : $tType, X62 : X61, X63 : int, X64 : X61]:
277.71/277.96	      (app_encode_app(X61, X61, 
277.71/277.96	         app_encode_app(X61, app_encode_fun(X61, X61), times_times(X61), 
277.71/277.96	           app_encode_app(X61, X61, 
277.71/277.96	             app_encode_app(X61, app_encode_fun(X61, X61), plus_plus(X61), 
277.71/277.96	               X62), X64)), 
277.71/277.96	         app_encode_app(int, X61, number_number_of(X61), X63))
277.71/277.96	        = app_encode_app(X61, X61, 
277.71/277.96	            app_encode_app(X61, app_encode_fun(X61, X61), plus_plus(X61), 
277.71/277.96	              app_encode_app(X61, X61, 
277.71/277.96	                app_encode_app(X61, app_encode_fun(X61, X61), 
277.71/277.96	                  times_times(X61), X62), 
277.71/277.96	                app_encode_app(int, X61, number_number_of(X61), X63))), 
277.71/277.96	            app_encode_app(X61, X61, 
277.71/277.96	              app_encode_app(X61, app_encode_fun(X61, X61), 
277.71/277.96	                times_times(X61), X64), 
277.71/277.96	              app_encode_app(int, X61, number_number_of(X61), X63)))
277.71/277.96	       | ~ semiring(X61)
277.71/277.96	       | ~ number(X61)),
277.71/277.96	    inference('cnf', [status(esa)], [zf_stmt_73])).
277.71/277.96	tff('20', plain,
277.71/277.96	    ![X0 : int, X1 : int, X2 : int]:
277.71/277.96	      (~ $true
277.71/277.96	       | ~ number(int)
277.71/277.96	       | app_encode_app(int, int, 
277.71/277.96	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
277.71/277.96	             app_encode_app(int, int, 
277.71/277.96	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	                 X2), X1)), 
277.71/277.96	           app_encode_app(int, int, number_number_of(int), X0))
277.71/277.96	          = app_encode_app(int, int, 
277.71/277.96	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	                app_encode_app(int, int, 
277.71/277.96	                  app_encode_app(int, app_encode_fun(int, int), 
277.71/277.96	                    times_times(int), X2), 
277.71/277.96	                  app_encode_app(int, int, number_number_of(int), X0))), 
277.71/277.96	              app_encode_app(int, int, 
277.71/277.96	                app_encode_app(int, app_encode_fun(int, int), 
277.71/277.96	                  times_times(int), X1), 
277.71/277.96	                app_encode_app(int, int, number_number_of(int), X0)))),
277.71/277.96	    inference('sup-', [status(thm)], ['18', '19'])).
277.71/277.96	tff(zf_stmt_142, axiom, (number(int))).
277.71/277.96	tff('21', plain, number(int), inference('cnf', [status(esa)], [zf_stmt_142])).
277.71/277.96	tff('22', plain,
277.71/277.96	    ![X0 : int, X1 : int, X2 : int]:
277.71/277.96	      (~ $true
277.71/277.96	       | ~ $true
277.71/277.96	       | app_encode_app(int, int, 
277.71/277.96	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
277.71/277.96	             app_encode_app(int, int, 
277.71/277.96	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	                 X2), X1)), X0)
277.71/277.96	          = app_encode_app(int, int, 
277.71/277.96	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	                app_encode_app(int, int, 
277.71/277.96	                  app_encode_app(int, app_encode_fun(int, int), 
277.71/277.96	                    times_times(int), X2), X0)), 
277.71/277.96	              app_encode_app(int, int, 
277.71/277.96	                app_encode_app(int, app_encode_fun(int, int), 
277.71/277.96	                  times_times(int), X1), X0))),
277.71/277.96	    inference('demod', [status(thm)], ['20', '21', '1', '1', '1'])).
277.71/277.96	tff('23', plain,
277.71/277.96	    ![X0 : int, X1 : int, X2 : int]:
277.71/277.96	      app_encode_app(int, int, 
277.71/277.96	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
277.71/277.96	          app_encode_app(int, int, 
277.71/277.96	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X2), 
277.71/277.96	            X1)), X0)
277.71/277.96	       = app_encode_app(int, int, 
277.71/277.96	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	             app_encode_app(int, int, 
277.71/277.96	               app_encode_app(int, app_encode_fun(int, int), 
277.71/277.96	                 times_times(int), X2), X0)), 
277.71/277.96	           app_encode_app(int, int, 
277.71/277.96	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
277.71/277.96	               X1), X0)),
277.71/277.96	    inference('simplify', [status(thm)], ['22'])).
277.71/277.96	tff('24', plain,
277.71/277.96	    ![X0 : int, X1 : int]:
277.71/277.96	      app_encode_app(int, int, 
277.71/277.96	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
277.71/277.96	          app_encode_app(int, int, 
277.71/277.96	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X1), 
277.71/277.96	            pls)), X0)
277.71/277.96	       = app_encode_app(int, int, 
277.71/277.96	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	             app_encode_app(int, int, 
277.71/277.96	               app_encode_app(int, app_encode_fun(int, int), 
277.71/277.96	                 times_times(int), X1), X0)), pls),
277.71/277.96	    inference('sup+', [status(thm)], ['4', '23'])).
277.71/277.96	tff('25', plain,
277.71/277.96	    ![X0 : int]:
277.71/277.96	      app_encode_app(int, int, 
277.71/277.96	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
277.71/277.96	          app_encode_app(int, int, 
277.71/277.96	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	              app_encode_app(int, int, bit1, pls)), pls)), X0)
277.71/277.96	       = app_encode_app(int, int, 
277.71/277.96	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	             app_encode_app(int, int, 
277.71/277.96	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	                 pls), X0)), pls),
277.71/277.96	    inference('sup+', [status(thm)], ['8', '24'])).
277.71/277.96	tff(zf_stmt_92, axiom,
277.71/277.96	  (![L1:int,K:int]:
277.71/277.96	     (app_encode_app(int,int,
277.71/277.96	                     app_encode_app(int,app_encode_fun(int,int),
277.71/277.96	                                    plus_plus(int),
277.71/277.96	                                    app_encode_app(int,int,bit1,K)),
277.71/277.96	                     app_encode_app(int,int,bit0,L1)) =
277.71/277.96	      app_encode_app(int,int,bit1,
277.71/277.96	                     app_encode_app(int,int,
277.71/277.96	                                    app_encode_app(int,
277.71/277.96	                                                   app_encode_fun(int,int),
277.71/277.96	                                                   plus_plus(int),K),
277.71/277.96	                                    L1))))).
277.71/277.96	tff('26', plain,
277.71/277.96	    ![X118 : int, X119 : int]:
277.71/277.96	      app_encode_app(int, int, 
277.71/277.96	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	          app_encode_app(int, int, bit1, X118)), 
277.71/277.96	        app_encode_app(int, int, bit0, X119))
277.71/277.96	       = app_encode_app(int, int, bit1, 
277.71/277.96	           app_encode_app(int, int, 
277.71/277.96	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	               X118), X119)),
277.71/277.96	    inference('cnf', [status(esa)], [zf_stmt_92])).
277.71/277.96	tff('27', plain,
277.71/277.96	    ![X0 : int]:
277.71/277.96	      app_encode_app(int, int, 
277.71/277.96	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	          app_encode_app(int, int, bit1, X0)), pls)
277.71/277.96	       = app_encode_app(int, int, bit1, 
277.71/277.96	           app_encode_app(int, int, 
277.71/277.96	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	               X0), pls)),
277.71/277.96	    inference('sup+', [status(thm)], ['7', '26'])).
277.71/277.96	tff(zf_stmt_134, axiom, (linord219039673up_add(int))).
277.71/277.96	tff('28', plain, linord219039673up_add(int),
277.71/277.96	    inference('cnf', [status(esa)], [zf_stmt_134])).
277.71/277.96	tff(zf_stmt_55, axiom,
277.71/277.96	  (![A:$tType]:
277.71/277.96	     (linord219039673up_add(A) =>
277.71/277.96	      (![A1:A]:
277.71/277.96	         ((app_encode_app(A,A,
277.71/277.96	                          app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
277.71/277.96	                                         A1),
277.71/277.96	                          A1) =
277.71/277.96	           zero_zero(A)) <=>
277.71/277.96	          (A1 = zero_zero(A))))))).
277.71/277.96	tff('29', plain,
277.71/277.96	    ![X29 : $tType, X30 : X29]:
277.71/277.96	      (X30 != zero_zero(X29)
277.71/277.96	       | app_encode_app(X29, X29, 
277.71/277.96	           app_encode_app(X29, app_encode_fun(X29, X29), plus_plus(X29), X30), 
277.71/277.96	           X30)
277.71/277.96	          = zero_zero(X29)
277.71/277.96	       | ~ linord219039673up_add(X29)),
277.71/277.96	    inference('cnf', [status(esa)], [zf_stmt_55])).
277.71/277.96	tff('30', plain,
277.71/277.96	    ![X29 : $tType]:
277.71/277.96	      (~ linord219039673up_add(X29)
277.71/277.96	       | app_encode_app(X29, X29, 
277.71/277.96	           app_encode_app(X29, app_encode_fun(X29, X29), plus_plus(X29), 
277.71/277.96	             zero_zero(X29)), zero_zero(X29))
277.71/277.96	          = zero_zero(X29)),
277.71/277.96	    inference('simplify', [status(thm)], ['29'])).
277.71/277.96	tff('31', plain,
277.71/277.96	    (~ $true
277.71/277.96	     | app_encode_app(int, int, 
277.71/277.96	         app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	           zero_zero(int)), zero_zero(int))
277.71/277.96	        = zero_zero(int)),
277.71/277.96	    inference('sup-', [status(thm)], ['28', '30'])).
277.71/277.96	tff(zf_stmt_119, axiom, (pls = zero_zero(int))).
277.71/277.96	tff('32', plain, pls = zero_zero(int),
277.71/277.96	    inference('cnf', [status(esa)], [zf_stmt_119])).
277.71/277.96	tff('33', plain,
277.71/277.96	    (~ $true
277.71/277.96	     | app_encode_app(int, int, 
277.71/277.96	         app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
277.71/277.96	         pls)
277.71/277.96	        = pls),
277.71/277.96	    inference('demod', [status(thm)], ['31', '32', '32', '32'])).
277.71/277.96	tff('34', plain,
277.71/277.96	    app_encode_app(int, int, 
277.71/277.96	      app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
277.71/277.96	      pls)
277.71/277.96	     = pls,
277.71/277.96	    inference('simplify', [status(thm)], ['33'])).
277.71/277.96	tff('35', plain,
277.71/277.96	    ![X0 : int]:
277.71/277.96	      app_encode_app(int, int, 
277.71/277.96	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
277.71/277.96	        X0)
277.71/277.96	       = app_encode_app(int, int, 
277.71/277.96	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	             app_encode_app(int, int, 
277.71/277.96	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	                 pls), X0)), pls),
277.71/277.96	    inference('demod', [status(thm)], ['25', '27', '34', '8'])).
277.71/277.96	tff('36', plain,
277.71/277.96	    app_encode_app(int, $o, 
277.71/277.96	      app_encode_app(int, app_encode_fun(int, $o), ord_less(int), s), 
277.71/277.96	      app_encode_app(int, int, bit1, 
277.71/277.96	        app_encode_app(int, int, bit0, 
277.71/277.96	          app_encode_app(int, int, 
277.71/277.96	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	              pls), m)))),
277.71/277.96	    inference('demod', [status(thm)], ['17', '35'])).
277.71/277.96	tff(zf_stmt_133, axiom,
277.71/277.96	  (![A:$tType]:
277.71/277.96	     (number_ring(A) =>
277.71/277.96	      (![W:int]:
277.71/277.96	         (app_encode_app(int,A,number_number_of(A),
277.71/277.96	                         app_encode_app(int,int,bit0,W)) =
277.71/277.96	          app_encode_app(A,A,
277.71/277.96	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
277.71/277.96	                                        app_encode_app(A,A,
277.71/277.96	                                                       app_encode_app(
277.71/277.96	                                                       A,app_encode_fun(A,A),
277.71/277.96	                                                       plus_plus(A),
277.71/277.96	                                                       zero_zero(A)),
277.71/277.96	                                                       app_encode_app(
277.71/277.96	                                                       int,A,
277.71/277.96	                                                       number_number_of(A),W))),
277.71/277.96	                         app_encode_app(int,A,number_number_of(A),W))))))).
277.71/277.96	tff('37', plain,
277.71/277.96	    ![X206 : $tType, X207 : int]:
277.71/277.96	      (app_encode_app(int, X206, number_number_of(X206), 
277.71/277.96	         app_encode_app(int, int, bit0, X207))
277.71/277.96	        = app_encode_app(X206, X206, 
277.71/277.96	            app_encode_app(X206, app_encode_fun(X206, X206), 
277.71/277.96	              plus_plus(X206), 
277.71/277.96	              app_encode_app(X206, X206, 
277.71/277.96	                app_encode_app(X206, app_encode_fun(X206, X206), 
277.71/277.96	                  plus_plus(X206), zero_zero(X206)), 
277.71/277.96	                app_encode_app(int, X206, number_number_of(X206), X207))), 
277.71/277.96	            app_encode_app(int, X206, number_number_of(X206), X207))
277.71/277.96	       | ~ number_ring(X206)),
277.71/277.96	    inference('cnf', [status(esa)], [zf_stmt_133])).
277.71/277.96	tff('38', plain,
277.71/277.96	    ![X0 : int]:
277.71/277.96	      (~ $true
277.71/277.96	       | app_encode_app(int, int, number_number_of(int), 
277.71/277.96	           app_encode_app(int, int, bit0, X0))
277.71/277.96	          = app_encode_app(int, int, 
277.71/277.96	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	                app_encode_app(int, int, 
277.71/277.96	                  app_encode_app(int, app_encode_fun(int, int), 
277.71/277.96	                    plus_plus(int), zero_zero(int)), 
277.71/277.96	                  app_encode_app(int, int, number_number_of(int), X0))), 
277.71/277.96	              app_encode_app(int, int, number_number_of(int), X0))),
277.71/277.96	    inference('sup-', [status(thm)], ['9', '37'])).
277.71/277.96	tff(zf_stmt_82, axiom,
277.71/277.96	  (![A:$tType]:
277.71/277.96	     (number_ring(A) =>
277.71/277.96	      (![Z:A,W:int,V1:int]:
277.71/277.96	         (app_encode_app(A,A,
277.71/277.96	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
277.71/277.96	                                        app_encode_app(int,A,
277.71/277.96	                                                       number_number_of(A),V1)),
277.71/277.96	                         app_encode_app(A,A,
277.71/277.96	                                        app_encode_app(A,app_encode_fun(A,A),
277.71/277.96	                                                       plus_plus(A),
277.71/277.96	                                                       app_encode_app(
277.71/277.96	                                                       int,A,
277.71/277.96	                                                       number_number_of(A),W)),
277.71/277.96	                                        Z)) =
277.71/277.96	          app_encode_app(A,A,
277.71/277.96	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
277.71/277.96	                                        app_encode_app(int,A,
277.71/277.96	                                                       number_number_of(A),
277.71/277.96	                                                       app_encode_app(
277.71/277.96	                                                       int,int,
277.71/277.96	                                                       app_encode_app(
277.71/277.96	                                                       int,
277.71/277.96	                                                       app_encode_fun(
277.71/277.96	                                                       int,int),
277.71/277.96	                                                       plus_plus(int),V1),W))),
277.71/277.96	                         Z)))))).
277.71/277.96	tff('39', plain,
277.71/277.96	    ![X93 : $tType, X94 : int, X95 : int, X96 : X93]:
277.71/277.96	      (app_encode_app(X93, X93, 
277.71/277.96	         app_encode_app(X93, app_encode_fun(X93, X93), plus_plus(X93), 
277.71/277.96	           app_encode_app(int, X93, number_number_of(X93), X94)), 
277.71/277.96	         app_encode_app(X93, X93, 
277.71/277.96	           app_encode_app(X93, app_encode_fun(X93, X93), plus_plus(X93), 
277.71/277.96	             app_encode_app(int, X93, number_number_of(X93), X95)), X96))
277.71/277.96	        = app_encode_app(X93, X93, 
277.71/277.96	            app_encode_app(X93, app_encode_fun(X93, X93), plus_plus(X93), 
277.71/277.96	              app_encode_app(int, X93, number_number_of(X93), 
277.71/277.96	                app_encode_app(int, int, 
277.71/277.96	                  app_encode_app(int, app_encode_fun(int, int), 
277.71/277.96	                    plus_plus(int), X94), X95))), X96)
277.71/277.96	       | ~ number_ring(X93)),
277.71/277.96	    inference('cnf', [status(esa)], [zf_stmt_82])).
277.71/277.96	tff('40', plain,
277.71/277.96	    ![X0 : int, X1 : int, X2 : int]:
277.71/277.96	      (~ $true
277.71/277.96	       | app_encode_app(int, int, 
277.71/277.96	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	             app_encode_app(int, int, number_number_of(int), X2)), 
277.71/277.96	           app_encode_app(int, int, 
277.71/277.96	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	               app_encode_app(int, int, number_number_of(int), X1)), X0))
277.71/277.96	          = app_encode_app(int, int, 
277.71/277.96	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	                app_encode_app(int, int, number_number_of(int), 
277.71/277.96	                  app_encode_app(int, int, 
277.71/277.96	                    app_encode_app(int, app_encode_fun(int, int), 
277.71/277.96	                      plus_plus(int), X2), X1))), X0)),
277.71/277.96	    inference('sup-', [status(thm)], ['9', '39'])).
277.71/277.96	tff('41', plain,
277.71/277.96	    ![X0 : int, X1 : int, X2 : int]:
277.71/277.96	      (~ $true
277.71/277.96	       | app_encode_app(int, int, 
277.71/277.96	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X2), 
277.71/277.96	           app_encode_app(int, int, 
277.71/277.96	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	               X1), X0))
277.71/277.96	          = app_encode_app(int, int, 
277.71/277.96	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	                app_encode_app(int, int, 
277.71/277.96	                  app_encode_app(int, app_encode_fun(int, int), 
277.71/277.96	                    plus_plus(int), X2), X1)), X0)),
277.71/277.96	    inference('demod', [status(thm)], ['40', '1', '1', '1'])).
277.71/277.96	tff('42', plain,
277.71/277.96	    ![X0 : int, X1 : int, X2 : int]:
277.71/277.96	      app_encode_app(int, int, 
277.71/277.96	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X2), 
277.71/277.96	        app_encode_app(int, int, 
277.71/277.96	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X1), 
277.71/277.96	          X0))
277.71/277.96	       = app_encode_app(int, int, 
277.71/277.96	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	             app_encode_app(int, int, 
277.71/277.96	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	                 X2), X1)), X0),
277.71/277.96	    inference('simplify', [status(thm)], ['41'])).
277.71/277.96	tff('43', plain,
277.71/277.96	    ![X0 : int]:
277.71/277.96	      (~ $true
277.71/277.96	       | app_encode_app(int, int, bit0, X0)
277.71/277.96	          = app_encode_app(int, int, 
277.71/277.96	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	                pls), 
277.71/277.96	              app_encode_app(int, int, 
277.71/277.96	                app_encode_app(int, app_encode_fun(int, int), 
277.71/277.96	                  plus_plus(int), X0), X0))),
277.71/277.96	    inference('demod', [status(thm)], ['38', '1', '32', '1', '1', '42'])).
277.71/277.96	tff('44', plain,
277.71/277.96	    ![X0 : int]:
277.71/277.96	      app_encode_app(int, int, bit0, X0)
277.71/277.96	       = app_encode_app(int, int, 
277.71/277.96	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
277.71/277.96	           app_encode_app(int, int, 
277.71/277.96	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	               X0), X0)),
277.71/277.96	    inference('simplify', [status(thm)], ['43'])).
277.71/277.96	tff('45', plain,
277.71/277.96	    ![X0 : int]:
277.71/277.96	      app_encode_app(int, int, 
277.71/277.96	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
277.71/277.96	        app_encode_app(int, int, bit1, X0))
277.71/277.96	       = app_encode_app(int, int, bit1, 
277.71/277.96	           app_encode_app(int, int, 
277.71/277.96	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	               pls), X0)),
277.71/277.96	    inference('sup+', [status(thm)], ['7', '14'])).
277.71/277.96	tff('46', plain,
277.71/277.96	    ![X0 : int, X1 : int]:
277.71/277.96	      app_encode_app(int, int, 
277.71/277.96	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	          app_encode_app(int, int, bit1, X0)), 
277.71/277.96	        app_encode_app(int, int, 
277.71/277.96	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
277.71/277.96	          X1))
277.71/277.96	       = app_encode_app(int, int, 
277.71/277.96	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	             app_encode_app(int, int, bit1, 
277.71/277.96	               app_encode_app(int, int, 
277.71/277.96	                 app_encode_app(int, app_encode_fun(int, int), 
277.71/277.96	                   plus_plus(int), X0), pls))), X1),
277.71/277.96	    inference('sup+', [status(thm)], ['27', '42'])).
277.71/277.96	tff('47', plain,
277.71/277.96	    ![X0 : int]:
277.71/277.96	      app_encode_app(int, int, 
277.71/277.96	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	          app_encode_app(int, int, bit1, pls)), 
277.71/277.96	        app_encode_app(int, int, 
277.71/277.96	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
277.71/277.96	          X0))
277.71/277.96	       = app_encode_app(int, int, 
277.71/277.96	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	             app_encode_app(int, int, bit1, pls)), X0),
277.71/277.96	    inference('sup+', [status(thm)], ['34', '46'])).
277.71/277.96	tff('48', plain,
277.71/277.96	    ![X0 : int]:
277.71/277.96	      app_encode_app(int, int, 
277.71/277.96	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	          app_encode_app(int, int, bit1, pls)), 
277.71/277.96	        app_encode_app(int, int, bit1, 
277.71/277.96	          app_encode_app(int, int, 
277.71/277.96	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	              pls), X0)))
277.71/277.96	       = app_encode_app(int, int, 
277.71/277.96	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	             app_encode_app(int, int, bit1, pls)), 
277.71/277.96	           app_encode_app(int, int, bit1, X0)),
277.71/277.96	    inference('sup+', [status(thm)], ['45', '47'])).
277.71/277.96	tff(zf_stmt_44, axiom,
277.71/277.96	  (![A:$tType]:
277.71/277.96	     (number_ring(A) =>
277.71/277.96	      (app_encode_app(A,A,
277.71/277.96	                      app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
277.71/277.96	                                     one_one(A)),
277.71/277.96	                      one_one(A)) =
277.71/277.96	       app_encode_app(int,A,number_number_of(A),
277.71/277.96	                      app_encode_app(int,int,bit0,
277.71/277.96	                                     app_encode_app(int,int,bit1,pls))))))).
277.71/277.96	tff('49', plain,
277.71/277.96	    ![X10 : $tType]:
277.71/277.96	      (app_encode_app(X10, X10, 
277.71/277.96	         app_encode_app(X10, app_encode_fun(X10, X10), plus_plus(X10), 
277.71/277.96	           one_one(X10)), one_one(X10))
277.71/277.96	        = app_encode_app(int, X10, number_number_of(X10), 
277.71/277.96	            app_encode_app(int, int, bit0, 
277.71/277.96	              app_encode_app(int, int, bit1, pls)))
277.71/277.96	       | ~ number_ring(X10)),
277.71/277.96	    inference('cnf', [status(esa)], [zf_stmt_44])).
277.71/277.96	tff('50', plain,
277.71/277.96	    (~ $true
277.71/277.96	     | app_encode_app(int, int, 
277.71/277.96	         app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	           one_one(int)), one_one(int))
277.71/277.96	        = app_encode_app(int, int, number_number_of(int), 
277.71/277.96	            app_encode_app(int, int, bit0, 
277.71/277.96	              app_encode_app(int, int, bit1, pls)))),
277.71/277.96	    inference('sup-', [status(thm)], ['9', '49'])).
277.71/277.96	tff('51', plain,
277.71/277.96	    (~ $true
277.71/277.96	     | app_encode_app(int, int, 
277.71/277.96	         app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	           app_encode_app(int, int, bit1, pls)), 
277.71/277.96	         app_encode_app(int, int, bit1, pls))
277.71/277.96	        = app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls))),
277.71/277.96	    inference('demod', [status(thm)], ['50', '13', '13', '1'])).
277.71/277.96	tff('52', plain,
277.71/277.96	    app_encode_app(int, int, 
277.71/277.96	      app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	        app_encode_app(int, int, bit1, pls)), 
277.71/277.96	      app_encode_app(int, int, bit1, pls))
277.71/277.96	     = app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls)),
277.71/277.96	    inference('simplify', [status(thm)], ['51'])).
277.71/277.96	tff('53', plain,
277.71/277.96	    ![X0 : int]:
277.71/277.96	      app_encode_app(int, int, 
277.71/277.96	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	          app_encode_app(int, int, bit1, pls)), 
277.71/277.96	        app_encode_app(int, int, 
277.71/277.96	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	            app_encode_app(int, int, bit1, pls)), X0))
277.71/277.96	       = app_encode_app(int, int, 
277.71/277.96	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	             app_encode_app(int, int, bit0, 
277.71/277.96	               app_encode_app(int, int, bit1, pls))), X0),
277.71/277.96	    inference('sup+', [status(thm)], ['52', '42'])).
277.71/277.96	tff('54', plain,
277.71/277.96	    ![X0 : int]:
277.71/277.96	      app_encode_app(int, int, 
277.71/277.96	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	          app_encode_app(int, int, bit1, pls)), 
277.71/277.96	        app_encode_app(int, int, 
277.71/277.96	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	            app_encode_app(int, int, bit1, pls)), 
277.71/277.96	          app_encode_app(int, int, bit0, X0)))
277.71/277.96	       = app_encode_app(int, int, bit0, 
277.71/277.96	           app_encode_app(int, int, 
277.71/277.96	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	               app_encode_app(int, int, bit1, pls)), X0)),
277.71/277.96	    inference('sup+', [status(thm)], ['15', '53'])).
277.71/277.96	tff('55', plain,
277.71/277.96	    ![X0 : int]:
277.71/277.96	      app_encode_app(int, int, 
277.71/277.96	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	          app_encode_app(int, int, bit1, pls)), 
277.71/277.96	        app_encode_app(int, int, bit1, 
277.71/277.96	          app_encode_app(int, int, 
277.71/277.96	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	              pls), X0)))
277.71/277.96	       = app_encode_app(int, int, bit0, 
277.71/277.96	           app_encode_app(int, int, 
277.71/277.96	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	               app_encode_app(int, int, bit1, pls)), X0)),
277.71/277.96	    inference('demod', [status(thm)], ['54', '26'])).
277.71/277.96	tff('56', plain,
277.71/277.96	    ![X0 : int]:
277.71/277.96	      app_encode_app(int, int, 
277.71/277.96	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	          app_encode_app(int, int, bit1, pls)), 
277.71/277.96	        app_encode_app(int, int, bit1, X0))
277.71/277.96	       = app_encode_app(int, int, bit0, 
277.71/277.96	           app_encode_app(int, int, 
277.71/277.96	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	               app_encode_app(int, int, bit1, pls)), X0)),
277.71/277.96	    inference('sup+', [status(thm)], ['48', '55'])).
277.71/277.96	tff(zf_stmt_74, axiom,
277.71/277.96	  (![B:$tType]:
277.71/277.96	     ((number(B) & semiring(B)) =>
277.71/277.96	      (![C:B,B1:B,V1:int]:
277.71/277.96	         (app_encode_app(B,B,
277.71/277.96	                         app_encode_app(B,app_encode_fun(B,B),times_times(B),
277.71/277.96	                                        app_encode_app(int,B,
277.71/277.96	                                                       number_number_of(B),V1)),
277.71/277.96	                         app_encode_app(B,B,
277.71/277.96	                                        app_encode_app(B,app_encode_fun(B,B),
277.71/277.96	                                                       plus_plus(B),B1),
277.71/277.96	                                        C)) =
277.71/277.96	          app_encode_app(B,B,
277.71/277.96	                         app_encode_app(B,app_encode_fun(B,B),plus_plus(B),
277.71/277.96	                                        app_encode_app(B,B,
277.71/277.96	                                                       app_encode_app(
277.71/277.96	                                                       B,app_encode_fun(B,B),
277.71/277.96	                                                       times_times(B),
277.71/277.96	                                                       app_encode_app(
277.71/277.96	                                                       int,B,
277.71/277.96	                                                       number_number_of(B),V1)),
277.71/277.96	                                                       B1)),
277.71/277.96	                         app_encode_app(B,B,
277.71/277.96	                                        app_encode_app(B,app_encode_fun(B,B),
277.71/277.96	                                                       times_times(B),
277.71/277.96	                                                       app_encode_app(
277.71/277.96	                                                       int,B,
277.71/277.96	                                                       number_number_of(B),V1)),
277.71/277.96	                                        C))))))).
277.71/277.96	tff('57', plain,
277.71/277.96	    ![X65 : $tType, X66 : int, X67 : X65, X68 : X65]:
277.71/277.96	      (app_encode_app(X65, X65, 
277.71/277.96	         app_encode_app(X65, app_encode_fun(X65, X65), times_times(X65), 
277.71/277.96	           app_encode_app(int, X65, number_number_of(X65), X66)), 
277.71/277.96	         app_encode_app(X65, X65, 
277.71/277.96	           app_encode_app(X65, app_encode_fun(X65, X65), plus_plus(X65), X67), 
277.71/277.96	           X68))
277.71/277.96	        = app_encode_app(X65, X65, 
277.71/277.96	            app_encode_app(X65, app_encode_fun(X65, X65), plus_plus(X65), 
277.71/277.96	              app_encode_app(X65, X65, 
277.71/277.96	                app_encode_app(X65, app_encode_fun(X65, X65), 
277.71/277.96	                  times_times(X65), 
277.71/277.96	                  app_encode_app(int, X65, number_number_of(X65), X66)), X67)), 
277.71/277.96	            app_encode_app(X65, X65, 
277.71/277.96	              app_encode_app(X65, app_encode_fun(X65, X65), 
277.71/277.96	                times_times(X65), 
277.71/277.96	                app_encode_app(int, X65, number_number_of(X65), X66)), X68))
277.71/277.96	       | ~ semiring(X65)
277.71/277.96	       | ~ number(X65)),
277.71/277.96	    inference('cnf', [status(esa)], [zf_stmt_74])).
277.71/277.96	tff('58', plain,
277.71/277.96	    ![X0 : int, X1 : int, X2 : int]:
277.71/277.96	      (~ $true
277.71/277.96	       | ~ number(int)
277.71/277.96	       | app_encode_app(int, int, 
277.71/277.96	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
277.71/277.96	             app_encode_app(int, int, number_number_of(int), X2)), 
277.71/277.96	           app_encode_app(int, int, 
277.71/277.96	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	               X1), X0))
277.71/277.96	          = app_encode_app(int, int, 
277.71/277.96	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	                app_encode_app(int, int, 
277.71/277.96	                  app_encode_app(int, app_encode_fun(int, int), 
277.71/277.96	                    times_times(int), 
277.71/277.96	                    app_encode_app(int, int, number_number_of(int), X2)), X1)), 
277.71/277.96	              app_encode_app(int, int, 
277.71/277.96	                app_encode_app(int, app_encode_fun(int, int), 
277.71/277.96	                  times_times(int), 
277.71/277.96	                  app_encode_app(int, int, number_number_of(int), X2)), X0))),
277.71/277.96	    inference('sup-', [status(thm)], ['18', '57'])).
277.71/277.96	tff('59', plain,
277.71/277.96	    ![X0 : int, X1 : int, X2 : int]:
277.71/277.96	      (~ $true
277.71/277.96	       | ~ $true
277.71/277.96	       | app_encode_app(int, int, 
277.71/277.96	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
277.71/277.96	             X2), 
277.71/277.96	           app_encode_app(int, int, 
277.71/277.96	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	               X1), X0))
277.71/277.96	          = app_encode_app(int, int, 
277.71/277.96	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	                app_encode_app(int, int, 
277.71/277.96	                  app_encode_app(int, app_encode_fun(int, int), 
277.71/277.96	                    times_times(int), X2), X1)), 
277.71/277.96	              app_encode_app(int, int, 
277.71/277.96	                app_encode_app(int, app_encode_fun(int, int), 
277.71/277.96	                  times_times(int), X2), X0))),
277.71/277.96	    inference('demod', [status(thm)], ['58', '21', '1', '1', '1'])).
277.71/277.96	tff('60', plain,
277.71/277.96	    ![X0 : int, X1 : int, X2 : int]:
277.71/277.96	      app_encode_app(int, int, 
277.71/277.96	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X2), 
277.71/277.96	        app_encode_app(int, int, 
277.71/277.96	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X1), 
277.71/277.96	          X0))
277.71/277.96	       = app_encode_app(int, int, 
277.71/277.96	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	             app_encode_app(int, int, 
277.71/277.96	               app_encode_app(int, app_encode_fun(int, int), 
277.71/277.96	                 times_times(int), X2), X1)), 
277.71/277.96	           app_encode_app(int, int, 
277.71/277.96	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
277.71/277.96	               X2), X0)),
277.71/277.96	    inference('simplify', [status(thm)], ['59'])).
277.71/277.96	tff('61', plain,
277.71/277.96	    ![X0 : int, X1 : int]:
277.71/277.96	      app_encode_app(int, int, 
277.71/277.96	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
277.71/277.96	          app_encode_app(int, int, 
277.71/277.96	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X1), 
277.71/277.96	            X1)), X0)
277.71/277.96	       = app_encode_app(int, int, 
277.71/277.96	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
277.71/277.96	             X1), 
277.71/277.96	           app_encode_app(int, int, 
277.71/277.96	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	               X0), X0)),
277.71/277.96	    inference('sup+', [status(thm)], ['60', '23'])).
277.71/277.96	tff('62', plain,
277.71/277.96	    ![X0 : int]:
277.71/277.96	      app_encode_app(int, int, 
277.71/277.96	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
277.71/277.96	          app_encode_app(int, int, bit0, 
277.71/277.96	            app_encode_app(int, int, 
277.71/277.96	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	                app_encode_app(int, int, bit1, pls)), pls))), X0)
277.71/277.96	       = app_encode_app(int, int, 
277.71/277.96	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
277.71/277.96	             app_encode_app(int, int, bit1, pls)), 
277.71/277.96	           app_encode_app(int, int, 
277.71/277.96	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	               X0), X0)),
277.71/277.96	    inference('sup+', [status(thm)], ['56', '61'])).
277.71/277.96	tff('63', plain,
277.71/277.96	    ![X0 : int]:
277.71/277.96	      app_encode_app(int, int, bit0, 
277.71/277.96	        app_encode_app(int, int, 
277.71/277.96	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
277.71/277.96	          X0))
277.71/277.96	       = app_encode_app(int, int, 
277.71/277.96	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
277.71/277.96	           app_encode_app(int, int, 
277.71/277.96	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	               X0), X0)),
277.71/277.96	    inference('demod', [status(thm)], ['62', '27', '34', '3', '8', '8'])).
277.71/277.96	tff('64', plain,
277.71/277.96	    ![X0 : int]:
277.71/277.96	      app_encode_app(int, int, bit0, 
277.71/277.96	        app_encode_app(int, int, 
277.71/277.96	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
277.71/277.96	          X0))
277.71/277.96	       = app_encode_app(int, int, bit0, X0),
277.71/277.96	    inference('sup+', [status(thm)], ['44', '63'])).
277.71/277.96	tff('65', plain,
277.71/277.96	    app_encode_app(int, $o, 
277.71/277.96	      app_encode_app(int, app_encode_fun(int, $o), ord_less(int), s), 
277.71/277.96	      app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m))),
277.71/277.96	    inference('demod', [status(thm)], ['36', '64'])).
277.71/277.96	tff(zf_stmt_51, axiom,
277.71/277.96	  (![L1:int,K:int]:
277.71/277.96	     (app_encode_app(int,int,
277.71/277.96	                     app_encode_app(int,app_encode_fun(int,int),
277.71/277.96	                                    minus_minus(int),
277.71/277.96	                                    app_encode_app(int,int,bit1,K)),
277.71/277.96	                     app_encode_app(int,int,bit1,L1)) =
277.71/277.96	      app_encode_app(int,int,bit0,
277.71/277.96	                     app_encode_app(int,int,
277.71/277.96	                                    app_encode_app(int,
277.71/277.96	                                                   app_encode_fun(int,int),
277.71/277.96	                                                   minus_minus(int),K),
277.71/277.96	                                    L1))))).
277.71/277.96	tff('66', plain,
277.71/277.96	    ![X17 : int, X18 : int]:
277.71/277.96	      app_encode_app(int, int, 
277.71/277.96	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
277.71/277.96	          app_encode_app(int, int, bit1, X17)), 
277.71/277.96	        app_encode_app(int, int, bit1, X18))
277.71/277.96	       = app_encode_app(int, int, bit0, 
277.71/277.96	           app_encode_app(int, int, 
277.71/277.96	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
277.71/277.96	               X17), X18)),
277.71/277.96	    inference('cnf', [status(esa)], [zf_stmt_51])).
277.71/277.96	tff(zf_stmt_99, axiom,
277.71/277.96	  (![Z1:int,W1:int]:
277.71/277.96	     (app_encode_app(int,$o,
277.71/277.96	                     app_encode_app(int,app_encode_fun(int,$o),
277.71/277.96	                                    ord_less_eq(int),W1),
277.71/277.96	                     app_encode_app(int,int,
277.71/277.96	                                    app_encode_app(int,
277.71/277.96	                                                   app_encode_fun(int,int),
277.71/277.96	                                                   minus_minus(int),Z1),
277.71/277.96	                                    one_one(int))) <=>
277.71/277.96	      app_encode_app(int,$o,
277.71/277.96	                     app_encode_app(int,app_encode_fun(int,$o),ord_less(int),
277.71/277.96	                                    W1),
277.71/277.96	                     Z1)))).
277.71/277.96	tff('67', plain,
277.71/277.96	    ![X136 : int, X137 : int]:
277.71/277.96	      (app_encode_app(int, $o, 
277.71/277.96	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), X137), 
277.71/277.96	         app_encode_app(int, int, 
277.71/277.96	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
277.71/277.96	             X136), one_one(int)))
277.71/277.96	       | ~ app_encode_app(int, $o, 
277.71/277.96	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
277.71/277.96	               X137), X136)),
277.71/277.96	    inference('cnf', [status(esa)], [zf_stmt_99])).
277.71/277.96	tff('68', plain,
277.71/277.96	    ![X136 : int, X137 : int]:
277.71/277.96	      (app_encode_app(int, $o, 
277.71/277.96	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), X137), 
277.71/277.96	         app_encode_app(int, int, 
277.71/277.96	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
277.71/277.96	             X136), app_encode_app(int, int, bit1, pls)))
277.71/277.96	       | ~ app_encode_app(int, $o, 
277.71/277.96	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
277.71/277.96	               X137), X136)),
277.71/277.96	    inference('demod', [status(thm)], ['67', '13'])).
277.71/277.96	tff('69', plain,
277.71/277.96	    ![X0 : int, X1 : int]:
277.71/277.96	      (app_encode_app(int, $o, 
277.71/277.96	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), X1), 
277.71/277.96	         app_encode_app(int, int, bit0, 
277.71/277.96	           app_encode_app(int, int, 
277.71/277.96	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
277.71/277.96	               X0), pls)))
277.71/277.96	       | ~ app_encode_app(int, $o, 
277.71/277.96	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X1), 
277.71/277.96	             app_encode_app(int, int, bit1, X0))),
277.71/277.96	    inference('sup+', [status(thm)], ['66', '68'])).
277.71/277.96	tff(zf_stmt_141, axiom, (ring(int))).
277.71/277.96	tff('70', plain, ring(int), inference('cnf', [status(esa)], [zf_stmt_141])).
277.71/277.96	tff(zf_stmt_76, axiom,
277.71/277.96	  (![B:$tType]:
277.71/277.96	     ((number(B) & ring(B)) =>
277.71/277.96	      (![V1:int,B1:B,A2:B]:
277.71/277.96	         (app_encode_app(B,B,
277.71/277.96	                         app_encode_app(B,app_encode_fun(B,B),times_times(B),
277.71/277.96	                                        app_encode_app(B,B,
277.71/277.96	                                                       app_encode_app(
277.71/277.96	                                                       B,app_encode_fun(B,B),
277.71/277.96	                                                       minus_minus(B),A2),B1)),
277.71/277.96	                         app_encode_app(int,B,number_number_of(B),V1)) =
277.71/277.96	          app_encode_app(B,B,
277.71/277.96	                         app_encode_app(B,app_encode_fun(B,B),minus_minus(B),
277.71/277.96	                                        app_encode_app(B,B,
277.71/277.96	                                                       app_encode_app(
277.71/277.96	                                                       B,app_encode_fun(B,B),
277.71/277.96	                                                       times_times(B),A2),
277.71/277.96	                                                       app_encode_app(
277.71/277.96	                                                       int,B,
277.71/277.96	                                                       number_number_of(B),V1))),
277.71/277.96	                         app_encode_app(B,B,
277.71/277.96	                                        app_encode_app(B,app_encode_fun(B,B),
277.71/277.96	                                                       times_times(B),B1),
277.71/277.96	                                        app_encode_app(int,B,
277.71/277.96	                                                       number_number_of(B),V1)))))))).
277.71/277.96	tff('71', plain,
277.71/277.96	    ![X70 : $tType, X71 : X70, X72 : int, X73 : X70]:
277.71/277.96	      (app_encode_app(X70, X70, 
277.71/277.96	         app_encode_app(X70, app_encode_fun(X70, X70), times_times(X70), 
277.71/277.96	           app_encode_app(X70, X70, 
277.71/277.96	             app_encode_app(X70, app_encode_fun(X70, X70), minus_minus(X70), 
277.71/277.96	               X71), X73)), 
277.71/277.96	         app_encode_app(int, X70, number_number_of(X70), X72))
277.71/277.96	        = app_encode_app(X70, X70, 
277.71/277.96	            app_encode_app(X70, app_encode_fun(X70, X70), minus_minus(X70), 
277.71/277.96	              app_encode_app(X70, X70, 
277.71/277.96	                app_encode_app(X70, app_encode_fun(X70, X70), 
277.71/277.96	                  times_times(X70), X71), 
277.71/277.96	                app_encode_app(int, X70, number_number_of(X70), X72))), 
277.71/277.96	            app_encode_app(X70, X70, 
277.71/277.96	              app_encode_app(X70, app_encode_fun(X70, X70), 
277.71/277.96	                times_times(X70), X73), 
277.71/277.96	              app_encode_app(int, X70, number_number_of(X70), X72)))
277.71/277.96	       | ~ ring(X70)
277.71/277.96	       | ~ number(X70)),
277.71/277.96	    inference('cnf', [status(esa)], [zf_stmt_76])).
277.71/277.96	tff('72', plain,
277.71/277.96	    ![X0 : int, X1 : int, X2 : int]:
277.71/277.96	      (~ $true
277.71/277.96	       | ~ number(int)
277.71/277.96	       | app_encode_app(int, int, 
277.71/277.96	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
277.71/277.96	             app_encode_app(int, int, 
277.71/277.96	               app_encode_app(int, app_encode_fun(int, int), 
277.71/277.96	                 minus_minus(int), X2), X1)), 
277.71/277.96	           app_encode_app(int, int, number_number_of(int), X0))
277.71/277.96	          = app_encode_app(int, int, 
277.71/277.96	              app_encode_app(int, app_encode_fun(int, int), 
277.71/277.96	                minus_minus(int), 
277.71/277.96	                app_encode_app(int, int, 
277.71/277.96	                  app_encode_app(int, app_encode_fun(int, int), 
277.71/277.96	                    times_times(int), X2), 
277.71/277.96	                  app_encode_app(int, int, number_number_of(int), X0))), 
277.71/277.96	              app_encode_app(int, int, 
277.71/277.96	                app_encode_app(int, app_encode_fun(int, int), 
277.71/277.96	                  times_times(int), X1), 
277.71/277.96	                app_encode_app(int, int, number_number_of(int), X0)))),
277.71/277.96	    inference('sup-', [status(thm)], ['70', '71'])).
277.71/277.96	tff('73', plain,
277.71/277.96	    ![X0 : int, X1 : int, X2 : int]:
277.71/277.96	      (~ $true
277.71/277.96	       | ~ $true
277.71/277.96	       | app_encode_app(int, int, 
277.71/277.96	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
277.71/277.96	             app_encode_app(int, int, 
277.71/277.96	               app_encode_app(int, app_encode_fun(int, int), 
277.71/277.96	                 minus_minus(int), X2), X1)), X0)
277.71/277.96	          = app_encode_app(int, int, 
277.71/277.96	              app_encode_app(int, app_encode_fun(int, int), 
277.71/277.96	                minus_minus(int), 
277.71/277.96	                app_encode_app(int, int, 
277.71/277.96	                  app_encode_app(int, app_encode_fun(int, int), 
277.71/277.96	                    times_times(int), X2), X0)), 
277.71/277.96	              app_encode_app(int, int, 
277.71/277.96	                app_encode_app(int, app_encode_fun(int, int), 
277.71/277.96	                  times_times(int), X1), X0))),
277.71/277.96	    inference('demod', [status(thm)], ['72', '21', '1', '1', '1'])).
277.71/277.96	tff('74', plain,
277.71/277.96	    ![X0 : int, X1 : int, X2 : int]:
277.71/277.96	      app_encode_app(int, int, 
277.71/277.96	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
277.71/277.96	          app_encode_app(int, int, 
277.71/277.96	            app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
277.71/277.96	              X2), X1)), X0)
277.71/277.96	       = app_encode_app(int, int, 
277.71/277.96	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
277.71/277.96	             app_encode_app(int, int, 
277.71/277.96	               app_encode_app(int, app_encode_fun(int, int), 
277.71/277.96	                 times_times(int), X2), X0)), 
277.71/277.96	           app_encode_app(int, int, 
277.71/277.96	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
277.71/277.96	               X1), X0)),
277.71/277.96	    inference('simplify', [status(thm)], ['73'])).
277.71/277.96	tff('75', plain,
277.71/277.96	    ![X0 : int, X1 : int]:
277.71/277.96	      app_encode_app(int, int, 
277.71/277.96	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
277.71/277.96	          app_encode_app(int, int, 
277.71/277.96	            app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
277.71/277.96	              X1), pls)), X0)
277.71/277.96	       = app_encode_app(int, int, 
277.71/277.96	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
277.71/277.96	             app_encode_app(int, int, 
277.71/277.96	               app_encode_app(int, app_encode_fun(int, int), 
277.71/277.96	                 times_times(int), X1), X0)), pls),
277.71/277.96	    inference('sup+', [status(thm)], ['4', '74'])).
277.71/277.96	tff('76', plain,
277.71/277.96	    ![X0 : int]:
277.71/277.96	      app_encode_app(int, int, 
277.71/277.96	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
277.71/277.96	          app_encode_app(int, int, 
277.71/277.96	            app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
277.71/277.96	              app_encode_app(int, int, bit1, pls)), pls)), X0)
277.71/277.96	       = app_encode_app(int, int, 
277.71/277.96	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
277.71/277.96	             app_encode_app(int, int, 
277.71/277.96	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.96	                 pls), X0)), pls),
277.71/277.96	    inference('sup+', [status(thm)], ['8', '75'])).
277.71/277.96	tff(zf_stmt_50, axiom,
277.71/277.96	  (![L1:int,K:int]:
277.71/277.96	     (app_encode_app(int,int,
277.71/277.96	                     app_encode_app(int,app_encode_fun(int,int),
277.71/277.96	                                    minus_minus(int),
277.71/277.96	                                    app_encode_app(int,int,bit1,K)),
277.71/277.96	                     app_encode_app(int,int,bit0,L1)) =
277.71/277.96	      app_encode_app(int,int,bit1,
277.71/277.96	                     app_encode_app(int,int,
277.71/277.96	                                    app_encode_app(int,
277.71/277.96	                                                   app_encode_fun(int,int),
277.71/277.96	                                                   minus_minus(int),K),
277.71/277.96	                                    L1))))).
277.71/277.96	tff('77', plain,
277.71/277.96	    ![X15 : int, X16 : int]:
277.71/277.96	      app_encode_app(int, int, 
277.71/277.96	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
277.71/277.97	          app_encode_app(int, int, bit1, X15)), 
277.71/277.97	        app_encode_app(int, int, bit0, X16))
277.71/277.97	       = app_encode_app(int, int, bit1, 
277.71/277.97	           app_encode_app(int, int, 
277.71/277.97	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
277.71/277.97	               X15), X16)),
277.71/277.97	    inference('cnf', [status(esa)], [zf_stmt_50])).
277.71/277.97	tff('78', plain,
277.71/277.97	    ![X0 : int]:
277.71/277.97	      app_encode_app(int, int, 
277.71/277.97	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
277.71/277.97	          app_encode_app(int, int, bit1, X0)), pls)
277.71/277.97	       = app_encode_app(int, int, bit1, 
277.71/277.97	           app_encode_app(int, int, 
277.71/277.97	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
277.71/277.97	               X0), pls)),
277.71/277.97	    inference('sup+', [status(thm)], ['7', '77'])).
277.71/277.97	tff(zf_stmt_77, axiom,
277.71/277.97	  (![B:$tType]:
277.71/277.97	     ((number(B) & ring(B)) =>
277.71/277.97	      (![C:B,B1:B,V1:int]:
277.71/277.97	         (app_encode_app(B,B,
277.71/277.97	                         app_encode_app(B,app_encode_fun(B,B),times_times(B),
277.71/277.97	                                        app_encode_app(int,B,
277.71/277.97	                                                       number_number_of(B),V1)),
277.71/277.97	                         app_encode_app(B,B,
277.71/277.97	                                        app_encode_app(B,app_encode_fun(B,B),
277.71/277.97	                                                       minus_minus(B),B1),
277.71/277.97	                                        C)) =
277.71/277.97	          app_encode_app(B,B,
277.71/277.97	                         app_encode_app(B,app_encode_fun(B,B),minus_minus(B),
277.71/277.97	                                        app_encode_app(B,B,
277.71/277.97	                                                       app_encode_app(
277.71/277.97	                                                       B,app_encode_fun(B,B),
277.71/277.97	                                                       times_times(B),
277.71/277.97	                                                       app_encode_app(
277.71/277.97	                                                       int,B,
277.71/277.97	                                                       number_number_of(B),V1)),
277.71/277.97	                                                       B1)),
277.71/277.97	                         app_encode_app(B,B,
277.71/277.97	                                        app_encode_app(B,app_encode_fun(B,B),
277.71/277.97	                                                       times_times(B),
277.71/277.97	                                                       app_encode_app(
277.71/277.97	                                                       int,B,
277.71/277.97	                                                       number_number_of(B),V1)),
277.71/277.97	                                        C))))))).
277.71/277.97	tff('79', plain,
277.71/277.97	    ![X74 : $tType, X75 : int, X76 : X74, X77 : X74]:
277.71/277.97	      (app_encode_app(X74, X74, 
277.71/277.97	         app_encode_app(X74, app_encode_fun(X74, X74), times_times(X74), 
277.71/277.97	           app_encode_app(int, X74, number_number_of(X74), X75)), 
277.71/277.97	         app_encode_app(X74, X74, 
277.71/277.97	           app_encode_app(X74, app_encode_fun(X74, X74), minus_minus(X74), 
277.71/277.97	             X76), X77))
277.71/277.97	        = app_encode_app(X74, X74, 
277.71/277.97	            app_encode_app(X74, app_encode_fun(X74, X74), minus_minus(X74), 
277.71/277.97	              app_encode_app(X74, X74, 
277.71/277.97	                app_encode_app(X74, app_encode_fun(X74, X74), 
277.71/277.97	                  times_times(X74), 
277.71/277.97	                  app_encode_app(int, X74, number_number_of(X74), X75)), X76)), 
277.71/277.97	            app_encode_app(X74, X74, 
277.71/277.97	              app_encode_app(X74, app_encode_fun(X74, X74), 
277.71/277.97	                times_times(X74), 
277.71/277.97	                app_encode_app(int, X74, number_number_of(X74), X75)), X77))
277.71/277.97	       | ~ ring(X74)
277.71/277.97	       | ~ number(X74)),
277.71/277.97	    inference('cnf', [status(esa)], [zf_stmt_77])).
277.71/277.97	tff('80', plain,
277.71/277.97	    ![X0 : int, X1 : int, X2 : int]:
277.71/277.97	      (~ $true
277.71/277.97	       | ~ number(int)
277.71/277.97	       | app_encode_app(int, int, 
277.71/277.97	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
277.71/277.97	             app_encode_app(int, int, number_number_of(int), X2)), 
277.71/277.97	           app_encode_app(int, int, 
277.71/277.97	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
277.71/277.97	               X1), X0))
277.71/277.97	          = app_encode_app(int, int, 
277.71/277.97	              app_encode_app(int, app_encode_fun(int, int), 
277.71/277.97	                minus_minus(int), 
277.71/277.97	                app_encode_app(int, int, 
277.71/277.97	                  app_encode_app(int, app_encode_fun(int, int), 
277.71/277.97	                    times_times(int), 
277.71/277.97	                    app_encode_app(int, int, number_number_of(int), X2)), X1)), 
277.71/277.97	              app_encode_app(int, int, 
277.71/277.97	                app_encode_app(int, app_encode_fun(int, int), 
277.71/277.97	                  times_times(int), 
277.71/277.97	                  app_encode_app(int, int, number_number_of(int), X2)), X0))),
277.71/277.97	    inference('sup-', [status(thm)], ['70', '79'])).
277.71/277.97	tff('81', plain,
277.71/277.97	    ![X0 : int, X1 : int, X2 : int]:
277.71/277.97	      (~ $true
277.71/277.97	       | ~ $true
277.71/277.97	       | app_encode_app(int, int, 
277.71/277.97	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
277.71/277.97	             X2), 
277.71/277.97	           app_encode_app(int, int, 
277.71/277.97	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
277.71/277.97	               X1), X0))
277.71/277.97	          = app_encode_app(int, int, 
277.71/277.97	              app_encode_app(int, app_encode_fun(int, int), 
277.71/277.97	                minus_minus(int), 
277.71/277.97	                app_encode_app(int, int, 
277.71/277.97	                  app_encode_app(int, app_encode_fun(int, int), 
277.71/277.97	                    times_times(int), X2), X1)), 
277.71/277.97	              app_encode_app(int, int, 
277.71/277.97	                app_encode_app(int, app_encode_fun(int, int), 
277.71/277.97	                  times_times(int), X2), X0))),
277.71/277.97	    inference('demod', [status(thm)], ['80', '21', '1', '1', '1'])).
277.71/277.97	tff('82', plain,
277.71/277.97	    ![X0 : int, X1 : int, X2 : int]:
277.71/277.97	      app_encode_app(int, int, 
277.71/277.97	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X2), 
277.71/277.97	        app_encode_app(int, int, 
277.71/277.97	          app_encode_app(int, app_encode_fun(int, int), minus_minus(int), X1), 
277.71/277.97	          X0))
277.71/277.97	       = app_encode_app(int, int, 
277.71/277.97	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
277.71/277.97	             app_encode_app(int, int, 
277.71/277.97	               app_encode_app(int, app_encode_fun(int, int), 
277.71/277.97	                 times_times(int), X2), X1)), 
277.71/277.97	           app_encode_app(int, int, 
277.71/277.97	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
277.71/277.97	               X2), X0)),
277.71/277.97	    inference('simplify', [status(thm)], ['81'])).
277.71/277.97	tff('83', plain,
277.71/277.97	    ![X0 : int, X1 : int]:
277.71/277.97	      app_encode_app(int, int, 
277.71/277.97	        app_encode_app(int, app_encode_fun(int, int), times_times(int), pls), 
277.71/277.97	        app_encode_app(int, int, 
277.71/277.97	          app_encode_app(int, app_encode_fun(int, int), minus_minus(int), X1), 
277.71/277.97	          X0))
277.71/277.97	       = app_encode_app(int, int, 
277.71/277.97	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
277.71/277.97	             pls), 
277.71/277.97	           app_encode_app(int, int, 
277.71/277.97	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
277.71/277.97	               pls), X0)),
277.71/277.97	    inference('sup+', [status(thm)], ['4', '82'])).
277.71/277.97	tff('84', plain,
277.71/277.97	    pls
277.71/277.97	     = app_encode_app(int, int, 
277.71/277.97	         app_encode_app(int, app_encode_fun(int, int), minus_minus(int), pls), 
277.71/277.97	         pls),
277.71/277.97	    inference('demod', [status(thm)], ['83', '4', '4'])).
277.71/277.97	tff('85', plain,
277.71/277.97	    ![X0 : int]:
277.71/277.97	      app_encode_app(int, int, 
277.71/277.97	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
277.71/277.97	        X0)
277.71/277.97	       = app_encode_app(int, int, 
277.71/277.97	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
277.71/277.97	             app_encode_app(int, int, 
277.71/277.97	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.97	                 pls), X0)), pls),
277.71/277.97	    inference('demod', [status(thm)], ['76', '78', '84', '8'])).
277.71/277.97	tff(zf_stmt_72, axiom,
277.71/277.97	  (![L1:int,K:int]:
277.71/277.97	     (app_encode_app(int,int,
277.71/277.97	                     app_encode_app(int,app_encode_fun(int,int),
277.71/277.97	                                    minus_minus(int),
277.71/277.97	                                    app_encode_app(int,int,bit0,K)),
277.71/277.97	                     app_encode_app(int,int,bit0,L1)) =
277.71/277.97	      app_encode_app(int,int,bit0,
277.71/277.97	                     app_encode_app(int,int,
277.71/277.97	                                    app_encode_app(int,
277.71/277.97	                                                   app_encode_fun(int,int),
277.71/277.97	                                                   minus_minus(int),K),
277.71/277.97	                                    L1))))).
277.71/277.97	tff('86', plain,
277.71/277.97	    ![X59 : int, X60 : int]:
277.71/277.97	      app_encode_app(int, int, 
277.71/277.97	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
277.71/277.97	          app_encode_app(int, int, bit0, X59)), 
277.71/277.97	        app_encode_app(int, int, bit0, X60))
277.71/277.97	       = app_encode_app(int, int, bit0, 
277.71/277.97	           app_encode_app(int, int, 
277.71/277.97	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
277.71/277.97	               X59), X60)),
277.71/277.97	    inference('cnf', [status(esa)], [zf_stmt_72])).
277.71/277.97	tff('87', plain,
277.71/277.97	    ![X0 : int, X1 : int]:
277.71/277.97	      app_encode_app(int, int, 
277.71/277.97	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
277.71/277.97	          app_encode_app(int, int, bit0, X0)), 
277.71/277.97	        app_encode_app(int, int, bit0, X1))
277.71/277.97	       = app_encode_app(int, int, bit0, 
277.71/277.97	           app_encode_app(int, int, 
277.71/277.97	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
277.71/277.97	               app_encode_app(int, int, 
277.71/277.97	                 app_encode_app(int, app_encode_fun(int, int), 
277.71/277.97	                   plus_plus(int), pls), X0)), X1)),
277.71/277.97	    inference('sup+', [status(thm)], ['64', '86'])).
277.71/277.97	tff('88', plain,
277.71/277.97	    ![X0 : int, X1 : int]:
277.71/277.97	      app_encode_app(int, int, bit0, 
277.71/277.97	        app_encode_app(int, int, 
277.71/277.97	          app_encode_app(int, app_encode_fun(int, int), minus_minus(int), X0), 
277.71/277.97	          X1))
277.71/277.97	       = app_encode_app(int, int, bit0, 
277.71/277.97	           app_encode_app(int, int, 
277.71/277.97	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
277.71/277.97	               app_encode_app(int, int, 
277.71/277.97	                 app_encode_app(int, app_encode_fun(int, int), 
277.71/277.97	                   plus_plus(int), pls), X0)), X1)),
277.71/277.97	    inference('demod', [status(thm)], ['87', '86'])).
277.71/277.97	tff('89', plain,
277.71/277.97	    ![X0 : int]:
277.71/277.97	      app_encode_app(int, int, bit0, 
277.71/277.97	        app_encode_app(int, int, 
277.71/277.97	          app_encode_app(int, app_encode_fun(int, int), minus_minus(int), X0), 
277.71/277.97	          pls))
277.71/277.97	       = app_encode_app(int, int, bit0, 
277.71/277.97	           app_encode_app(int, int, 
277.71/277.97	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.97	               pls), X0)),
277.71/277.97	    inference('sup+', [status(thm)], ['85', '88'])).
277.71/277.97	tff('90', plain,
277.71/277.97	    ![X0 : int]:
277.71/277.97	      app_encode_app(int, int, bit0, 
277.71/277.97	        app_encode_app(int, int, 
277.71/277.97	          app_encode_app(int, app_encode_fun(int, int), minus_minus(int), X0), 
277.71/277.97	          pls))
277.71/277.97	       = app_encode_app(int, int, bit0, X0),
277.71/277.97	    inference('demod', [status(thm)], ['89', '64'])).
277.71/277.97	tff('91', plain,
277.71/277.97	    ![X0 : int, X1 : int]:
277.71/277.97	      (app_encode_app(int, $o, 
277.71/277.97	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), X1), 
277.71/277.97	         app_encode_app(int, int, bit0, X0))
277.71/277.97	       | ~ app_encode_app(int, $o, 
277.71/277.97	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X1), 
277.71/277.97	             app_encode_app(int, int, bit1, X0))),
277.71/277.97	    inference('demod', [status(thm)], ['69', '90'])).
277.71/277.97	tff('92', plain,
277.71/277.97	    (~ $true
277.71/277.97	     | app_encode_app(int, $o, 
277.71/277.97	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), s), 
277.71/277.97	         app_encode_app(int, int, bit0, app_encode_app(int, int, bit0, m)))),
277.71/277.97	    inference('sup-', [status(thm)], ['65', '91'])).
277.71/277.97	tff('93', plain,
277.71/277.97	    app_encode_app(int, $o, 
277.71/277.97	      app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), s), 
277.71/277.97	      app_encode_app(int, int, bit0, app_encode_app(int, int, bit0, m))),
277.71/277.97	    inference('simplify', [status(thm)], ['92'])).
277.71/277.97	tff(zf_stmt_150, conjecture,
277.71/277.97	  (app_encode_app(int,$o,
277.71/277.97	                  app_encode_app(int,app_encode_fun(int,$o),ord_less_eq(int),
277.71/277.97	                                 s),
277.71/277.97	                  app_encode_app(int,int,
277.71/277.97	                                 app_encode_app(int,app_encode_fun(int,int),
277.71/277.97	                                                minus_minus(int),
277.71/277.97	                                                app_encode_app(int,int,
277.71/277.97	                                                               app_encode_app(
277.71/277.97	                                                               int,
277.71/277.97	                                                               app_encode_fun(
277.71/277.97	                                                               int,int),
277.71/277.97	                                                               plus_plus(int),
277.71/277.97	                                                               app_encode_app(
277.71/277.97	                                                               int,int,
277.71/277.97	                                                               app_encode_app(
277.71/277.97	                                                               int,
277.71/277.97	                                                               app_encode_fun(
277.71/277.97	                                                               int,int),
277.71/277.97	                                                               times_times(
277.71/277.97	                                                               int),
277.71/277.97	                                                               app_encode_app(
277.71/277.97	                                                               int,int,
277.71/277.97	                                                               number_number_of(
277.71/277.97	                                                               int),
277.71/277.97	                                                               app_encode_app(
277.71/277.97	                                                               int,int,bit0,
277.71/277.97	                                                               app_encode_app(
277.71/277.97	                                                               int,int,bit0,
277.71/277.97	                                                               app_encode_app(
277.71/277.97	                                                               int,int,bit1,
277.71/277.97	                                                               pls))))),m)),
277.71/277.97	                                                               one_one(int))),
277.71/277.97	                                 one_one(int))))).
277.71/277.97	tff(zf_stmt_0, negated_conjecture,
277.71/277.97	  (~
277.71/277.97	    app_encode_app(int,$o,
277.71/277.97	                   app_encode_app(int,app_encode_fun(int,$o),
277.71/277.97	                                  ord_less_eq(int),s),
277.71/277.97	                   app_encode_app(int,int,
277.71/277.97	                                  app_encode_app(int,app_encode_fun(int,int),
277.71/277.97	                                                 minus_minus(int),
277.71/277.97	                                                 app_encode_app(int,int,
277.71/277.97	                                                                app_encode_app(
277.71/277.97	                                                                int,
277.71/277.97	                                                                app_encode_fun(
277.71/277.97	                                                                int,int),
277.71/277.97	                                                                plus_plus(
277.71/277.97	                                                                int),
277.71/277.97	                                                                app_encode_app(
277.71/277.97	                                                                int,int,
277.71/277.97	                                                                app_encode_app(
277.71/277.97	                                                                int,
277.71/277.97	                                                                app_encode_fun(
277.71/277.97	                                                                int,int),
277.71/277.97	                                                                times_times(
277.71/277.97	                                                                int),
277.71/277.97	                                                                app_encode_app(
277.71/277.97	                                                                int,int,
277.71/277.97	                                                                number_number_of(
277.71/277.97	                                                                int),
277.71/277.97	                                                                app_encode_app(
277.71/277.97	                                                                int,int,bit0,
277.71/277.97	                                                                app_encode_app(
277.71/277.97	                                                                int,int,bit0,
277.71/277.97	                                                                app_encode_app(
277.71/277.97	                                                                int,int,bit1,
277.71/277.97	                                                                pls))))),m)),
277.71/277.97	                                                                one_one(int))),
277.71/277.97	                                  one_one(int))))).
277.71/277.97	tff('94', plain,
277.71/277.97	    ~ app_encode_app(int, $o, 
277.71/277.97	        app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), s), 
277.71/277.97	        app_encode_app(int, int, 
277.71/277.97	          app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
277.71/277.97	            app_encode_app(int, int, 
277.71/277.97	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.97	                app_encode_app(int, int, 
277.71/277.97	                  app_encode_app(int, app_encode_fun(int, int), 
277.71/277.97	                    times_times(int), 
277.71/277.97	                    app_encode_app(int, int, number_number_of(int), 
277.71/277.97	                      app_encode_app(int, int, bit0, 
277.71/277.97	                        app_encode_app(int, int, bit0, 
277.71/277.97	                          app_encode_app(int, int, bit1, pls))))), m)), 
277.71/277.97	              one_one(int))), one_one(int))),
277.71/277.97	    inference('cnf', [status(esa)], [zf_stmt_0])).
277.71/277.97	tff('95', plain,
277.71/277.97	    ![X0 : int]:
277.71/277.97	      app_encode_app(int, int, 
277.71/277.97	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
277.71/277.97	        X0)
277.71/277.97	       = app_encode_app(int, int, 
277.71/277.97	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
277.71/277.97	           app_encode_app(int, int, 
277.71/277.97	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.97	               X0), pls)),
277.71/277.97	    inference('demod', [status(thm)], ['35', '42'])).
277.71/277.97	tff('96', plain,
277.71/277.97	    ![X0 : int]:
277.71/277.97	      app_encode_app(int, int, bit0, 
277.71/277.97	        app_encode_app(int, int, 
277.71/277.97	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
277.71/277.97	          X0))
277.71/277.97	       = app_encode_app(int, int, bit0, 
277.71/277.97	           app_encode_app(int, int, 
277.71/277.97	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.97	               X0), pls)),
277.71/277.97	    inference('sup+', [status(thm)], ['95', '64'])).
277.71/277.97	tff('97', plain,
277.71/277.97	    ![X0 : int]:
277.71/277.97	      app_encode_app(int, int, bit0, X0)
277.71/277.97	       = app_encode_app(int, int, bit0, 
277.71/277.97	           app_encode_app(int, int, 
277.71/277.97	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.97	               X0), pls)),
277.71/277.97	    inference('demod', [status(thm)], ['96', '64'])).
277.71/277.97	tff('98', plain,
277.71/277.97	    ![X0 : int]:
277.71/277.97	      app_encode_app(int, int, 
277.71/277.97	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
277.71/277.97	          app_encode_app(int, int, bit0, X0)), pls)
277.71/277.97	       = app_encode_app(int, int, bit0, X0),
277.71/277.97	    inference('demod', [status(thm)], ['16', '97'])).
277.71/277.97	tff('99', plain,
277.71/277.97	    ![X0 : int]:
277.71/277.97	      app_encode_app(int, int, 
277.71/277.97	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
277.71/277.97	          app_encode_app(int, int, bit0, X0)), pls)
277.71/277.97	       = app_encode_app(int, int, bit0, 
277.71/277.97	           app_encode_app(int, int, 
277.71/277.97	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
277.71/277.97	               X0), pls)),
277.71/277.97	    inference('sup+', [status(thm)], ['7', '86'])).
277.71/277.97	tff('100', plain,
277.71/277.97	    ~ app_encode_app(int, $o, 
277.71/277.97	        app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), s), 
277.71/277.97	        app_encode_app(int, int, bit0, 
277.71/277.97	          app_encode_app(int, int, bit0, 
277.71/277.97	            app_encode_app(int, int, 
277.71/277.97	              app_encode_app(int, app_encode_fun(int, int), 
277.71/277.97	                minus_minus(int), m), pls)))),
277.71/277.97	    inference('demod', [status(thm)],
277.71/277.97	              ['94', '1', '3', '3', '8', '64', '13', '14', '98', '13', '66', 
277.71/277.97	               '99'])).
277.71/277.97	tff('101', plain,
277.71/277.97	    ~ app_encode_app(int, $o, 
277.71/277.97	        app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), s), 
277.71/277.97	        app_encode_app(int, int, bit0, app_encode_app(int, int, bit0, m))),
277.71/277.97	    inference('demod', [status(thm)], ['100', '90'])).
277.71/277.97	tff('102', plain, ~ $true, inference('sup-', [status(thm)], ['93', '101'])).
277.71/277.97	tff('103', plain, $false, inference('simplify', [status(thm)], ['102'])).
277.71/277.97	
277.71/277.97	% SZS output end Refutation
277.71/277.97	EOF
