0.00/0.00	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : appext
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : kbo
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.20	% Computer   : n031.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 07:53:39 CST 2018
132.83/133.05	% done 11086 iterations in 132.848s
132.83/133.05	% SZS status Theorem for 'stdin'
132.83/133.05	% SZS output start Refutation
132.83/133.06	tff(zf_stmt_127, axiom,
132.83/133.06	  (![K:int]: (app_encode_app(int,int,number_number_of(int),K) = K))).
132.83/133.06	tff('0', plain,
132.83/133.06	    ![X200 : int]:
132.83/133.06	      app_encode_app(int, int, number_number_of(int), X200) = X200,
132.83/133.06	    inference('cnf', [status(esa)], [zf_stmt_127])).
132.83/133.06	tff(zf_stmt_47, axiom,
132.83/133.06	  (![A:$tType]:
132.83/133.06	     (number_ring(A) =>
132.83/133.06	      (app_encode_app(int,A,number_number_of(A),
132.83/133.06	                      app_encode_app(int,int,bit1,pls)) =
132.83/133.06	       one_one(A))))).
132.83/133.06	tff('1', plain,
132.83/133.06	    ![X17 : $tType]:
132.83/133.06	      (app_encode_app(int, X17, number_number_of(X17), 
132.83/133.06	         app_encode_app(int, int, bit1, pls))
132.83/133.06	        = one_one(X17)
132.83/133.06	       | ~ number_ring(X17)),
132.83/133.06	    inference('cnf', [status(esa)], [zf_stmt_47])).
132.83/133.06	tff('2', plain,
132.83/133.06	    (app_encode_app(int, int, bit1, pls) = one_one(int) | ~ number_ring(int)),
132.83/133.06	    inference('sup+', [status(thm)], ['0', '1'])).
132.83/133.06	tff(zf_stmt_140, axiom, (number_ring(int))).
132.83/133.06	tff('3', plain, number_ring(int),
132.83/133.06	    inference('cnf', [status(esa)], [zf_stmt_140])).
132.83/133.06	tff('4', plain,
132.83/133.06	    (app_encode_app(int, int, bit1, pls) = one_one(int) | ~ $true),
132.83/133.06	    inference('demod', [status(thm)], ['2', '3'])).
132.83/133.06	tff('5', plain, app_encode_app(int, int, bit1, pls) = one_one(int),
132.83/133.06	    inference('simplify', [status(thm)], ['4'])).
132.83/133.06	tff(zf_stmt_52, axiom,
132.83/133.06	  (![L1:int,K:int]:
132.83/133.06	     (app_encode_app(int,int,
132.83/133.06	                     app_encode_app(int,app_encode_fun(int,int),
132.83/133.06	                                    minus_minus(int),
132.83/133.06	                                    app_encode_app(int,int,bit1,K)),
132.83/133.06	                     app_encode_app(int,int,bit1,L1)) =
132.83/133.06	      app_encode_app(int,int,bit0,
132.83/133.06	                     app_encode_app(int,int,
132.83/133.06	                                    app_encode_app(int,
132.83/133.06	                                                   app_encode_fun(int,int),
132.83/133.06	                                                   minus_minus(int),K),
132.83/133.06	                                    L1))))).
132.83/133.06	tff('6', plain,
132.83/133.06	    ![X21 : int, X22 : int]:
132.83/133.06	      app_encode_app(int, int, 
132.83/133.06	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
132.83/133.06	          app_encode_app(int, int, bit1, X21)), 
132.83/133.06	        app_encode_app(int, int, bit1, X22))
132.83/133.06	       = app_encode_app(int, int, bit0, 
132.83/133.06	           app_encode_app(int, int, 
132.83/133.06	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
132.83/133.06	               X21), X22)),
132.83/133.06	    inference('cnf', [status(esa)], [zf_stmt_52])).
132.83/133.06	tff('7', plain,
132.83/133.06	    ![X0 : int]:
132.83/133.06	      app_encode_app(int, int, 
132.83/133.06	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
132.83/133.06	          app_encode_app(int, int, bit1, X0)), one_one(int))
132.83/133.06	       = app_encode_app(int, int, bit0, 
132.83/133.06	           app_encode_app(int, int, 
132.83/133.06	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
132.83/133.06	               X0), pls)),
132.83/133.06	    inference('sup+', [status(thm)], ['5', '6'])).
132.83/133.06	tff(zf_stmt_100, axiom,
132.83/133.06	  (![Z1:int,W1:int]:
132.83/133.06	     (app_encode_app(int,$o,
132.83/133.06	                     app_encode_app(int,app_encode_fun(int,$o),
132.83/133.06	                                    ord_less_eq(int),W1),
132.83/133.06	                     app_encode_app(int,int,
132.83/133.06	                                    app_encode_app(int,
132.83/133.06	                                                   app_encode_fun(int,int),
132.83/133.06	                                                   minus_minus(int),Z1),
132.83/133.06	                                    one_one(int))) <=>
132.83/133.06	      app_encode_app(int,$o,
132.83/133.06	                     app_encode_app(int,app_encode_fun(int,$o),ord_less(int),
132.83/133.06	                                    W1),
132.83/133.06	                     Z1)))).
132.83/133.06	tff('8', plain,
132.83/133.06	    ![X140 : int, X141 : int]:
132.83/133.06	      (app_encode_app(int, $o, 
132.83/133.06	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), X141), 
132.83/133.06	         app_encode_app(int, int, 
132.83/133.06	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
132.83/133.06	             X140), one_one(int)))
132.83/133.06	       | ~ app_encode_app(int, $o, 
132.83/133.06	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
132.83/133.06	               X141), X140)),
132.83/133.06	    inference('cnf', [status(esa)], [zf_stmt_100])).
132.83/133.06	tff('9', plain,
132.83/133.06	    ![X0 : int, X1 : int]:
132.83/133.06	      (app_encode_app(int, $o, 
132.83/133.06	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), X1), 
132.83/133.06	         app_encode_app(int, int, bit0, 
132.83/133.06	           app_encode_app(int, int, 
132.83/133.06	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
132.83/133.06	               X0), pls)))
132.83/133.06	       | ~ app_encode_app(int, $o, 
132.83/133.06	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X1), 
132.83/133.06	             app_encode_app(int, int, bit1, X0))),
132.83/133.06	    inference('sup+', [status(thm)], ['7', '8'])).
132.83/133.06	tff(zf_stmt_70, axiom,
132.83/133.06	  (![W:int]:
132.83/133.06	     (app_encode_app(int,int,
132.83/133.06	                     app_encode_app(int,app_encode_fun(int,int),
132.83/133.06	                                    times_times(int),pls),
132.83/133.06	                     W) =
132.83/133.06	      pls))).
132.83/133.06	tff('10', plain,
132.83/133.06	    ![X58 : int]:
132.83/133.06	      app_encode_app(int, int, 
132.83/133.06	        app_encode_app(int, app_encode_fun(int, int), times_times(int), pls), 
132.83/133.06	        X58)
132.83/133.06	       = pls,
132.83/133.06	    inference('cnf', [status(esa)], [zf_stmt_70])).
132.83/133.06	tff(zf_stmt_46, axiom,
132.83/133.06	  (![L1:int,K:int]:
132.83/133.06	     (app_encode_app(int,int,
132.83/133.06	                     app_encode_app(int,app_encode_fun(int,int),
132.83/133.06	                                    times_times(int),
132.83/133.06	                                    app_encode_app(int,int,bit1,K)),
132.83/133.06	                     L1) =
132.83/133.06	      app_encode_app(int,int,
132.83/133.06	                     app_encode_app(int,app_encode_fun(int,int),
132.83/133.06	                                    plus_plus(int),
132.83/133.06	                                    app_encode_app(int,int,bit0,
132.83/133.06	                                                   app_encode_app(int,int,
132.83/133.06	                                                                  app_encode_app(
132.83/133.06	                                                                  int,
132.83/133.06	                                                                  app_encode_fun(
132.83/133.06	                                                                  int,int),
132.83/133.06	                                                                  times_times(
132.83/133.06	                                                                  int),K),L1))),
132.83/133.06	                     L1)))).
132.83/133.06	tff('11', plain,
132.83/133.06	    ![X15 : int, X16 : int]:
132.83/133.06	      app_encode_app(int, int, 
132.83/133.06	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
132.83/133.06	          app_encode_app(int, int, bit1, X15)), X16)
132.83/133.06	       = app_encode_app(int, int, 
132.83/133.06	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.06	             app_encode_app(int, int, bit0, 
132.83/133.06	               app_encode_app(int, int, 
132.83/133.06	                 app_encode_app(int, app_encode_fun(int, int), 
132.83/133.06	                   times_times(int), X15), X16))), X16),
132.83/133.06	    inference('cnf', [status(esa)], [zf_stmt_46])).
132.83/133.06	tff('12', plain,
132.83/133.06	    ![X0 : int]:
132.83/133.06	      app_encode_app(int, int, 
132.83/133.06	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
132.83/133.06	          app_encode_app(int, int, bit1, pls)), X0)
132.83/133.06	       = app_encode_app(int, int, 
132.83/133.06	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.06	             app_encode_app(int, int, bit0, pls)), X0),
132.83/133.06	    inference('sup+', [status(thm)], ['10', '11'])).
132.83/133.06	tff(zf_stmt_63, axiom, (app_encode_app(int,int,bit0,pls) = pls)).
132.83/133.06	tff('13', plain, app_encode_app(int, int, bit0, pls) = pls,
132.83/133.06	    inference('cnf', [status(esa)], [zf_stmt_63])).
132.83/133.06	tff('14', plain,
132.83/133.06	    ![X0 : int]:
132.83/133.06	      app_encode_app(int, int, 
132.83/133.06	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
132.83/133.06	          one_one(int)), X0)
132.83/133.06	       = app_encode_app(int, int, 
132.83/133.06	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
132.83/133.06	           X0),
132.83/133.06	    inference('demod', [status(thm)], ['12', '5', '13'])).
132.83/133.06	tff(zf_stmt_77, axiom,
132.83/133.06	  (![B:$tType]:
132.83/133.06	     ((number(B) & ring(B)) =>
132.83/133.06	      (![V1:int,B1:B,A2:B]:
132.83/133.06	         (app_encode_app(B,B,
132.83/133.06	                         app_encode_app(B,app_encode_fun(B,B),times_times(B),
132.83/133.06	                                        app_encode_app(B,B,
132.83/133.06	                                                       app_encode_app(
132.83/133.06	                                                       B,app_encode_fun(B,B),
132.83/133.06	                                                       minus_minus(B),A2),B1)),
132.83/133.06	                         app_encode_app(int,B,number_number_of(B),V1)) =
132.83/133.06	          app_encode_app(B,B,
132.83/133.06	                         app_encode_app(B,app_encode_fun(B,B),minus_minus(B),
132.83/133.06	                                        app_encode_app(B,B,
132.83/133.06	                                                       app_encode_app(
132.83/133.06	                                                       B,app_encode_fun(B,B),
132.83/133.06	                                                       times_times(B),A2),
132.83/133.06	                                                       app_encode_app(
132.83/133.06	                                                       int,B,
132.83/133.06	                                                       number_number_of(B),V1))),
132.83/133.06	                         app_encode_app(B,B,
132.83/133.06	                                        app_encode_app(B,app_encode_fun(B,B),
132.83/133.06	                                                       times_times(B),B1),
132.83/133.06	                                        app_encode_app(int,B,
132.83/133.06	                                                       number_number_of(B),V1)))))))).
132.83/133.06	tff('15', plain,
132.83/133.06	    ![X74 : $tType, X75 : X74, X76 : int, X77 : X74]:
132.83/133.06	      (app_encode_app(X74, X74, 
132.83/133.06	         app_encode_app(X74, app_encode_fun(X74, X74), times_times(X74), 
132.83/133.06	           app_encode_app(X74, X74, 
132.83/133.06	             app_encode_app(X74, app_encode_fun(X74, X74), minus_minus(X74), 
132.83/133.06	               X75), X77)), 
132.83/133.06	         app_encode_app(int, X74, number_number_of(X74), X76))
132.83/133.06	        = app_encode_app(X74, X74, 
132.83/133.06	            app_encode_app(X74, app_encode_fun(X74, X74), minus_minus(X74), 
132.83/133.06	              app_encode_app(X74, X74, 
132.83/133.06	                app_encode_app(X74, app_encode_fun(X74, X74), 
132.83/133.06	                  times_times(X74), X75), 
132.83/133.06	                app_encode_app(int, X74, number_number_of(X74), X76))), 
132.83/133.06	            app_encode_app(X74, X74, 
132.83/133.06	              app_encode_app(X74, app_encode_fun(X74, X74), 
132.83/133.06	                times_times(X74), X77), 
132.83/133.06	              app_encode_app(int, X74, number_number_of(X74), X76)))
132.83/133.06	       | ~ ring(X74)
132.83/133.06	       | ~ number(X74)),
132.83/133.06	    inference('cnf', [status(esa)], [zf_stmt_77])).
132.83/133.06	tff('16', plain,
132.83/133.06	    ![X0 : int, X1 : int]:
132.83/133.06	      (app_encode_app(int, int, 
132.83/133.06	         app_encode_app(int, app_encode_fun(int, int), times_times(int), 
132.83/133.06	           app_encode_app(int, int, 
132.83/133.06	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
132.83/133.06	               X1), pls)), 
132.83/133.06	         app_encode_app(int, int, number_number_of(int), X0))
132.83/133.06	        = app_encode_app(int, int, 
132.83/133.06	            app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
132.83/133.06	              app_encode_app(int, int, 
132.83/133.06	                app_encode_app(int, app_encode_fun(int, int), 
132.83/133.06	                  times_times(int), X1), 
132.83/133.06	                app_encode_app(int, int, number_number_of(int), X0))), pls)
132.83/133.06	       | ~ number(int)
132.83/133.06	       | ~ ring(int)),
132.83/133.06	    inference('sup+', [status(thm)], ['10', '15'])).
132.83/133.06	tff(zf_stmt_143, axiom, (number(int))).
132.83/133.06	tff('17', plain, number(int), inference('cnf', [status(esa)], [zf_stmt_143])).
132.83/133.06	tff(zf_stmt_142, axiom, (ring(int))).
132.83/133.06	tff('18', plain, ring(int), inference('cnf', [status(esa)], [zf_stmt_142])).
132.83/133.06	tff('19', plain,
132.83/133.06	    ![X0 : int, X1 : int]:
132.83/133.06	      (app_encode_app(int, int, 
132.83/133.06	         app_encode_app(int, app_encode_fun(int, int), times_times(int), 
132.83/133.06	           app_encode_app(int, int, 
132.83/133.06	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
132.83/133.06	               X1), pls)), X0)
132.83/133.06	        = app_encode_app(int, int, 
132.83/133.06	            app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
132.83/133.06	              app_encode_app(int, int, 
132.83/133.06	                app_encode_app(int, app_encode_fun(int, int), 
132.83/133.06	                  times_times(int), X1), X0)), pls)
132.83/133.06	       | ~ $true
132.83/133.06	       | ~ $true),
132.83/133.06	    inference('demod', [status(thm)], ['16', '0', '0', '17', '18'])).
132.83/133.06	tff('20', plain,
132.83/133.06	    ![X0 : int, X1 : int]:
132.83/133.06	      app_encode_app(int, int, 
132.83/133.06	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
132.83/133.06	          app_encode_app(int, int, 
132.83/133.06	            app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
132.83/133.06	              X1), pls)), X0)
132.83/133.06	       = app_encode_app(int, int, 
132.83/133.06	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
132.83/133.06	             app_encode_app(int, int, 
132.83/133.06	               app_encode_app(int, app_encode_fun(int, int), 
132.83/133.06	                 times_times(int), X1), X0)), pls),
132.83/133.06	    inference('simplify', [status(thm)], ['19'])).
132.83/133.06	tff('21', plain,
132.83/133.06	    ![X0 : int]:
132.83/133.06	      app_encode_app(int, int, 
132.83/133.06	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
132.83/133.06	          app_encode_app(int, int, 
132.83/133.06	            app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
132.83/133.06	              one_one(int)), pls)), X0)
132.83/133.06	       = app_encode_app(int, int, 
132.83/133.06	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
132.83/133.06	             app_encode_app(int, int, 
132.83/133.06	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.06	                 pls), X0)), pls),
132.83/133.06	    inference('sup+', [status(thm)], ['14', '20'])).
132.83/133.06	tff(zf_stmt_51, axiom,
132.83/133.06	  (![L1:int,K:int]:
132.83/133.06	     (app_encode_app(int,int,
132.83/133.06	                     app_encode_app(int,app_encode_fun(int,int),
132.83/133.06	                                    minus_minus(int),
132.83/133.06	                                    app_encode_app(int,int,bit1,K)),
132.83/133.06	                     app_encode_app(int,int,bit0,L1)) =
132.83/133.06	      app_encode_app(int,int,bit1,
132.83/133.06	                     app_encode_app(int,int,
132.83/133.06	                                    app_encode_app(int,
132.83/133.06	                                                   app_encode_fun(int,int),
132.83/133.06	                                                   minus_minus(int),K),
132.83/133.06	                                    L1))))).
132.83/133.06	tff('22', plain,
132.83/133.06	    ![X19 : int, X20 : int]:
132.83/133.06	      app_encode_app(int, int, 
132.83/133.06	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
132.83/133.06	          app_encode_app(int, int, bit1, X19)), 
132.83/133.06	        app_encode_app(int, int, bit0, X20))
132.83/133.06	       = app_encode_app(int, int, bit1, 
132.83/133.06	           app_encode_app(int, int, 
132.83/133.06	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
132.83/133.06	               X19), X20)),
132.83/133.06	    inference('cnf', [status(esa)], [zf_stmt_51])).
132.83/133.06	tff('23', plain,
132.83/133.06	    ![X0 : int]:
132.83/133.06	      app_encode_app(int, int, 
132.83/133.06	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
132.83/133.06	          app_encode_app(int, int, bit1, X0)), pls)
132.83/133.06	       = app_encode_app(int, int, bit1, 
132.83/133.06	           app_encode_app(int, int, 
132.83/133.06	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
132.83/133.06	               X0), pls)),
132.83/133.06	    inference('sup+', [status(thm)], ['13', '22'])).
132.83/133.06	tff('24', plain,
132.83/133.06	    app_encode_app(int, int, 
132.83/133.06	      app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
132.83/133.06	        one_one(int)), pls)
132.83/133.06	     = app_encode_app(int, int, bit1, 
132.83/133.06	         app_encode_app(int, int, 
132.83/133.06	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
132.83/133.06	             pls), pls)),
132.83/133.06	    inference('sup+', [status(thm)], ['5', '23'])).
132.83/133.06	tff('25', plain,
132.83/133.06	    ![X0 : int, X1 : int, X2 : int]:
132.83/133.06	      (app_encode_app(int, int, 
132.83/133.06	         app_encode_app(int, app_encode_fun(int, int), times_times(int), 
132.83/133.06	           app_encode_app(int, int, 
132.83/133.06	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
132.83/133.06	               X2), X1)), 
132.83/133.06	         app_encode_app(int, int, number_number_of(int), X0))
132.83/133.06	        = app_encode_app(int, int, 
132.83/133.06	            app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
132.83/133.06	              app_encode_app(int, int, 
132.83/133.06	                app_encode_app(int, app_encode_fun(int, int), 
132.83/133.06	                  times_times(int), X2), X0)), 
132.83/133.06	            app_encode_app(int, int, 
132.83/133.06	              app_encode_app(int, app_encode_fun(int, int), 
132.83/133.06	                times_times(int), X1), 
132.83/133.06	              app_encode_app(int, int, number_number_of(int), X0)))
132.83/133.06	       | ~ number(int)
132.83/133.06	       | ~ ring(int)),
132.83/133.06	    inference('sup+', [status(thm)], ['0', '15'])).
132.83/133.06	tff('26', plain,
132.83/133.06	    ![X0 : int, X1 : int, X2 : int]:
132.83/133.06	      (app_encode_app(int, int, 
132.83/133.06	         app_encode_app(int, app_encode_fun(int, int), times_times(int), 
132.83/133.06	           app_encode_app(int, int, 
132.83/133.06	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
132.83/133.06	               X2), X1)), X0)
132.83/133.06	        = app_encode_app(int, int, 
132.83/133.06	            app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
132.83/133.06	              app_encode_app(int, int, 
132.83/133.06	                app_encode_app(int, app_encode_fun(int, int), 
132.83/133.06	                  times_times(int), X2), X0)), 
132.83/133.06	            app_encode_app(int, int, 
132.83/133.06	              app_encode_app(int, app_encode_fun(int, int), 
132.83/133.06	                times_times(int), X1), X0))
132.83/133.06	       | ~ $true
132.83/133.06	       | ~ $true),
132.83/133.06	    inference('demod', [status(thm)], ['25', '0', '0', '17', '18'])).
132.83/133.06	tff('27', plain,
132.83/133.06	    ![X0 : int, X1 : int, X2 : int]:
132.83/133.06	      app_encode_app(int, int, 
132.83/133.06	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
132.83/133.06	          app_encode_app(int, int, 
132.83/133.06	            app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
132.83/133.06	              X2), X1)), X0)
132.83/133.06	       = app_encode_app(int, int, 
132.83/133.06	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
132.83/133.06	             app_encode_app(int, int, 
132.83/133.06	               app_encode_app(int, app_encode_fun(int, int), 
132.83/133.06	                 times_times(int), X2), X0)), 
132.83/133.06	           app_encode_app(int, int, 
132.83/133.06	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
132.83/133.06	               X1), X0)),
132.83/133.06	    inference('simplify', [status(thm)], ['26'])).
132.83/133.06	tff(zf_stmt_76, axiom,
132.83/133.06	  (![A:$tType]:
132.83/133.06	     (number_ring(A) =>
132.83/133.06	      (app_encode_app(int,A,number_number_of(A),pls) = zero_zero(A))))).
132.83/133.06	tff('28', plain,
132.83/133.06	    ![X73 : $tType]:
132.83/133.06	      (app_encode_app(int, X73, number_number_of(X73), pls) = zero_zero(X73)
132.83/133.06	       | ~ number_ring(X73)),
132.83/133.06	    inference('cnf', [status(esa)], [zf_stmt_76])).
132.83/133.06	tff(zf_stmt_78, axiom,
132.83/133.06	  (![B:$tType]:
132.83/133.06	     ((number(B) & ring(B)) =>
132.83/133.06	      (![C:B,B1:B,V1:int]:
132.83/133.06	         (app_encode_app(B,B,
132.83/133.06	                         app_encode_app(B,app_encode_fun(B,B),times_times(B),
132.83/133.06	                                        app_encode_app(int,B,
132.83/133.06	                                                       number_number_of(B),V1)),
132.83/133.06	                         app_encode_app(B,B,
132.83/133.06	                                        app_encode_app(B,app_encode_fun(B,B),
132.83/133.06	                                                       minus_minus(B),B1),
132.83/133.06	                                        C)) =
132.83/133.06	          app_encode_app(B,B,
132.83/133.06	                         app_encode_app(B,app_encode_fun(B,B),minus_minus(B),
132.83/133.06	                                        app_encode_app(B,B,
132.83/133.06	                                                       app_encode_app(
132.83/133.06	                                                       B,app_encode_fun(B,B),
132.83/133.06	                                                       times_times(B),
132.83/133.06	                                                       app_encode_app(
132.83/133.06	                                                       int,B,
132.83/133.06	                                                       number_number_of(B),V1)),
132.83/133.06	                                                       B1)),
132.83/133.06	                         app_encode_app(B,B,
132.83/133.06	                                        app_encode_app(B,app_encode_fun(B,B),
132.83/133.06	                                                       times_times(B),
132.83/133.06	                                                       app_encode_app(
132.83/133.06	                                                       int,B,
132.83/133.06	                                                       number_number_of(B),V1)),
132.83/133.06	                                        C))))))).
132.83/133.06	tff('29', plain,
132.83/133.06	    ![X78 : $tType, X79 : int, X80 : X78, X81 : X78]:
132.83/133.06	      (app_encode_app(X78, X78, 
132.83/133.06	         app_encode_app(X78, app_encode_fun(X78, X78), times_times(X78), 
132.83/133.06	           app_encode_app(int, X78, number_number_of(X78), X79)), 
132.83/133.06	         app_encode_app(X78, X78, 
132.83/133.06	           app_encode_app(X78, app_encode_fun(X78, X78), minus_minus(X78), 
132.83/133.06	             X80), X81))
132.83/133.06	        = app_encode_app(X78, X78, 
132.83/133.06	            app_encode_app(X78, app_encode_fun(X78, X78), minus_minus(X78), 
132.83/133.06	              app_encode_app(X78, X78, 
132.83/133.06	                app_encode_app(X78, app_encode_fun(X78, X78), 
132.83/133.06	                  times_times(X78), 
132.83/133.06	                  app_encode_app(int, X78, number_number_of(X78), X79)), X80)), 
132.83/133.06	            app_encode_app(X78, X78, 
132.83/133.06	              app_encode_app(X78, app_encode_fun(X78, X78), 
132.83/133.06	                times_times(X78), 
132.83/133.06	                app_encode_app(int, X78, number_number_of(X78), X79)), X81))
132.83/133.06	       | ~ ring(X78)
132.83/133.06	       | ~ number(X78)),
132.83/133.06	    inference('cnf', [status(esa)], [zf_stmt_78])).
132.83/133.06	tff('30', plain,
132.83/133.06	    ![X0 : $tType, X1 : X0, X2 : X0]:
132.83/133.06	      (app_encode_app(X0, X0, 
132.83/133.06	         app_encode_app(X0, app_encode_fun(X0, X0), times_times(X0), 
132.83/133.06	           app_encode_app(int, X0, number_number_of(X0), pls)), 
132.83/133.06	         app_encode_app(X0, X0, 
132.83/133.06	           app_encode_app(X0, app_encode_fun(X0, X0), minus_minus(X0), X2), 
132.83/133.06	           X1))
132.83/133.06	        = app_encode_app(X0, X0, 
132.83/133.06	            app_encode_app(X0, app_encode_fun(X0, X0), minus_minus(X0), 
132.83/133.06	              app_encode_app(X0, X0, 
132.83/133.06	                app_encode_app(X0, app_encode_fun(X0, X0), times_times(X0), 
132.83/133.06	                  zero_zero(X0)), X2)), 
132.83/133.06	            app_encode_app(X0, X0, 
132.83/133.06	              app_encode_app(X0, app_encode_fun(X0, X0), times_times(X0), 
132.83/133.06	                app_encode_app(int, X0, number_number_of(X0), pls)), X1))
132.83/133.06	       | ~ number_ring(X0)
132.83/133.06	       | ~ number(X0)
132.83/133.06	       | ~ ring(X0)),
132.83/133.06	    inference('sup+', [status(thm)], ['28', '29'])).
132.83/133.06	tff('31', plain,
132.83/133.06	    ![X0 : int]:
132.83/133.06	      (app_encode_app(int, int, 
132.83/133.06	         app_encode_app(int, app_encode_fun(int, int), times_times(int), 
132.83/133.06	           app_encode_app(int, int, number_number_of(int), pls)), 
132.83/133.06	         app_encode_app(int, int, 
132.83/133.06	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
132.83/133.06	             X0), X0))
132.83/133.06	        = app_encode_app(int, int, 
132.83/133.06	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
132.83/133.06	              app_encode_app(int, int, 
132.83/133.06	                app_encode_app(int, app_encode_fun(int, int), 
132.83/133.06	                  minus_minus(int), zero_zero(int)), 
132.83/133.06	                app_encode_app(int, int, number_number_of(int), pls))), X0)
132.83/133.06	       | ~ ring(int)
132.83/133.06	       | ~ number(int)
132.83/133.06	       | ~ number_ring(int)),
132.83/133.06	    inference('sup+', [status(thm)], ['27', '30'])).
132.83/133.06	tff(zf_stmt_120, axiom, (pls = zero_zero(int))).
132.83/133.06	tff('32', plain, pls = zero_zero(int),
132.83/133.06	    inference('cnf', [status(esa)], [zf_stmt_120])).
132.83/133.06	tff('33', plain,
132.83/133.06	    ![X0 : int, X1 : int]:
132.83/133.06	      (app_encode_app(int, int, 
132.83/133.06	         app_encode_app(int, app_encode_fun(int, int), times_times(int), 
132.83/133.06	           app_encode_app(int, int, 
132.83/133.06	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
132.83/133.06	               pls), X1)), 
132.83/133.06	         app_encode_app(int, int, number_number_of(int), X0))
132.83/133.06	        = app_encode_app(int, int, 
132.83/133.06	            app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
132.83/133.06	              pls), 
132.83/133.06	            app_encode_app(int, int, 
132.83/133.06	              app_encode_app(int, app_encode_fun(int, int), 
132.83/133.06	                times_times(int), X1), 
132.83/133.06	              app_encode_app(int, int, number_number_of(int), X0)))
132.83/133.06	       | ~ number(int)
132.83/133.06	       | ~ ring(int)),
132.83/133.06	    inference('sup+', [status(thm)], ['10', '15'])).
132.83/133.06	tff('34', plain,
132.83/133.06	    ![X0 : int, X1 : int]:
132.83/133.06	      (app_encode_app(int, int, 
132.83/133.06	         app_encode_app(int, app_encode_fun(int, int), times_times(int), 
132.83/133.06	           app_encode_app(int, int, 
132.83/133.06	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
132.83/133.06	               pls), X1)), X0)
132.83/133.06	        = app_encode_app(int, int, 
132.83/133.06	            app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
132.83/133.06	              pls), 
132.83/133.06	            app_encode_app(int, int, 
132.83/133.06	              app_encode_app(int, app_encode_fun(int, int), 
132.83/133.06	                times_times(int), X1), X0))
132.83/133.06	       | ~ $true
132.83/133.06	       | ~ $true),
132.83/133.06	    inference('demod', [status(thm)], ['33', '0', '0', '17', '18'])).
132.83/133.06	tff('35', plain,
132.83/133.06	    ![X0 : int, X1 : int]:
132.83/133.06	      app_encode_app(int, int, 
132.83/133.06	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
132.83/133.06	          app_encode_app(int, int, 
132.83/133.06	            app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
132.83/133.06	              pls), X1)), X0)
132.83/133.06	       = app_encode_app(int, int, 
132.83/133.06	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
132.83/133.06	             pls), 
132.83/133.06	           app_encode_app(int, int, 
132.83/133.06	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
132.83/133.06	               X1), X0)),
132.83/133.06	    inference('simplify', [status(thm)], ['34'])).
132.83/133.06	tff('36', plain,
132.83/133.06	    (pls
132.83/133.06	      = app_encode_app(int, int, 
132.83/133.06	          app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
132.83/133.06	            pls), pls)
132.83/133.06	     | ~ $true
132.83/133.06	     | ~ $true
132.83/133.06	     | ~ $true),
132.83/133.06	    inference('demod', [status(thm)],
132.83/133.06	              ['31', '0', '10', '32', '0', '35', '10', '18', '17', '3'])).
132.83/133.06	tff('37', plain,
132.83/133.06	    pls
132.83/133.06	     = app_encode_app(int, int, 
132.83/133.06	         app_encode_app(int, app_encode_fun(int, int), minus_minus(int), pls), 
132.83/133.06	         pls),
132.83/133.06	    inference('simplify', [status(thm)], ['36'])).
132.83/133.06	tff('38', plain,
132.83/133.06	    app_encode_app(int, int, 
132.83/133.06	      app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
132.83/133.06	        one_one(int)), pls)
132.83/133.06	     = app_encode_app(int, int, bit1, pls),
132.83/133.06	    inference('demod', [status(thm)], ['24', '37'])).
132.83/133.06	tff('39', plain,
132.83/133.06	    app_encode_app(int, int, 
132.83/133.06	      app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
132.83/133.06	        one_one(int)), pls)
132.83/133.06	     = one_one(int),
132.83/133.06	    inference('demod', [status(thm)], ['38', '5'])).
132.83/133.06	tff(zf_stmt_2, axiom,
132.83/133.06	  (![X:app_encode_fun(Alpha,Beta),Y:app_encode_fun(Alpha,Beta)]:
132.83/133.06	     ((![Z:Alpha]:
132.83/133.06	         (app_encode_app(Alpha,Beta,X,Z) = app_encode_app(Alpha,Beta,Y,Z))) =>
132.83/133.06	      (X = Y)))).
132.83/133.06	tff('40', plain,
132.83/133.06	    ![X0 : $tType, X1 : $tType, X2 : app_encode_fun(X0, X1), 
132.83/133.06	      X3 : app_encode_fun(X0, X1)]:
132.83/133.06	      (X3 = X2
132.83/133.06	       | app_encode_app(X0, X1, X3, sk_Z(X1, X0, X2, X3))
132.83/133.06	          != app_encode_app(X0, X1, X2, sk_Z(X1, X0, X2, X3))),
132.83/133.06	    inference('cnf', [status(esa)], [zf_stmt_2])).
132.83/133.06	tff('41', plain,
132.83/133.06	    ![X0 : app_encode_fun(int, int)]:
132.83/133.06	      (app_encode_app(int, int, X0, 
132.83/133.06	         sk_Z(int, int, 
132.83/133.06	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
132.83/133.06	             one_one(int)), X0))
132.83/133.06	        != app_encode_app(int, int, 
132.83/133.06	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.06	               pls), 
132.83/133.06	             sk_Z(int, int, 
132.83/133.06	               app_encode_app(int, app_encode_fun(int, int), 
132.83/133.06	                 times_times(int), one_one(int)), X0))
132.83/133.06	       | X0
132.83/133.06	          = app_encode_app(int, app_encode_fun(int, int), times_times(int), 
132.83/133.06	              one_one(int))),
132.83/133.06	    inference('sup-', [status(thm)], ['14', '40'])).
132.83/133.06	tff('42', plain,
132.83/133.06	    app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls)
132.83/133.06	     = app_encode_app(int, app_encode_fun(int, int), times_times(int), 
132.83/133.06	         one_one(int)),
132.83/133.06	    inference('eq_res', [status(thm)], ['41'])).
132.83/133.06	tff('43', plain,
132.83/133.06	    ![X0 : int]:
132.83/133.06	      app_encode_app(int, int, 
132.83/133.06	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
132.83/133.06	        X0)
132.83/133.06	       = app_encode_app(int, int, 
132.83/133.06	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
132.83/133.06	             app_encode_app(int, int, 
132.83/133.06	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.06	                 pls), X0)), pls),
132.83/133.06	    inference('demod', [status(thm)], ['21', '39', '42'])).
132.83/133.06	tff(zf_stmt_83, axiom,
132.83/133.06	  (![A:$tType]:
132.83/133.06	     (number_ring(A) =>
132.83/133.06	      (![Z:A,W:int,V1:int]:
132.83/133.06	         (app_encode_app(A,A,
132.83/133.06	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
132.83/133.06	                                        app_encode_app(int,A,
132.83/133.06	                                                       number_number_of(A),V1)),
132.83/133.06	                         app_encode_app(A,A,
132.83/133.06	                                        app_encode_app(A,app_encode_fun(A,A),
132.83/133.06	                                                       plus_plus(A),
132.83/133.06	                                                       app_encode_app(
132.83/133.06	                                                       int,A,
132.83/133.06	                                                       number_number_of(A),W)),
132.83/133.06	                                        Z)) =
132.83/133.06	          app_encode_app(A,A,
132.83/133.06	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
132.83/133.06	                                        app_encode_app(int,A,
132.83/133.06	                                                       number_number_of(A),
132.83/133.06	                                                       app_encode_app(
132.83/133.06	                                                       int,int,
132.83/133.06	                                                       app_encode_app(
132.83/133.06	                                                       int,
132.83/133.06	                                                       app_encode_fun(
132.83/133.06	                                                       int,int),
132.83/133.06	                                                       plus_plus(int),V1),W))),
132.83/133.06	                         Z)))))).
132.83/133.06	tff('44', plain,
132.83/133.06	    ![X97 : $tType, X98 : int, X99 : int, X100 : X97]:
132.83/133.06	      (app_encode_app(X97, X97, 
132.83/133.06	         app_encode_app(X97, app_encode_fun(X97, X97), plus_plus(X97), 
132.83/133.06	           app_encode_app(int, X97, number_number_of(X97), X98)), 
132.83/133.06	         app_encode_app(X97, X97, 
132.83/133.06	           app_encode_app(X97, app_encode_fun(X97, X97), plus_plus(X97), 
132.83/133.06	             app_encode_app(int, X97, number_number_of(X97), X99)), X100))
132.83/133.06	        = app_encode_app(X97, X97, 
132.83/133.06	            app_encode_app(X97, app_encode_fun(X97, X97), plus_plus(X97), 
132.83/133.06	              app_encode_app(int, X97, number_number_of(X97), 
132.83/133.06	                app_encode_app(int, int, 
132.83/133.06	                  app_encode_app(int, app_encode_fun(int, int), 
132.83/133.06	                    plus_plus(int), X98), X99))), X100)
132.83/133.06	       | ~ number_ring(X97)),
132.83/133.06	    inference('cnf', [status(esa)], [zf_stmt_83])).
132.83/133.06	tff('45', plain,
132.83/133.06	    ![X0 : int, X1 : int, X2 : int]:
132.83/133.06	      (app_encode_app(int, int, 
132.83/133.06	         app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
132.83/133.06	         app_encode_app(int, int, 
132.83/133.06	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.06	             app_encode_app(int, int, number_number_of(int), X2)), X1))
132.83/133.06	        = app_encode_app(int, int, 
132.83/133.06	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.06	              app_encode_app(int, int, number_number_of(int), 
132.83/133.06	                app_encode_app(int, int, 
132.83/133.06	                  app_encode_app(int, app_encode_fun(int, int), 
132.83/133.06	                    plus_plus(int), X0), X2))), X1)
132.83/133.06	       | ~ number_ring(int)),
132.83/133.06	    inference('sup+', [status(thm)], ['0', '44'])).
132.83/133.06	tff('46', plain,
132.83/133.06	    ![X0 : int, X1 : int, X2 : int]:
132.83/133.06	      (app_encode_app(int, int, 
132.83/133.06	         app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
132.83/133.06	         app_encode_app(int, int, 
132.83/133.06	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X2), 
132.83/133.06	           X1))
132.83/133.06	        = app_encode_app(int, int, 
132.83/133.06	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.06	              app_encode_app(int, int, 
132.83/133.06	                app_encode_app(int, app_encode_fun(int, int), 
132.83/133.06	                  plus_plus(int), X0), X2)), X1)
132.83/133.06	       | ~ $true),
132.83/133.06	    inference('demod', [status(thm)], ['45', '0', '0', '3'])).
132.83/133.06	tff('47', plain,
132.83/133.06	    ![X0 : int, X1 : int, X2 : int]:
132.83/133.06	      app_encode_app(int, int, 
132.83/133.06	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
132.83/133.06	        app_encode_app(int, int, 
132.83/133.06	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X2), 
132.83/133.06	          X1))
132.83/133.06	       = app_encode_app(int, int, 
132.83/133.06	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.06	             app_encode_app(int, int, 
132.83/133.06	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.06	                 X0), X2)), X1),
132.83/133.06	    inference('simplify', [status(thm)], ['46'])).
132.83/133.06	tff(zf_stmt_134, axiom,
132.83/133.06	  (![A:$tType]:
132.83/133.06	     (number_ring(A) =>
132.83/133.06	      (![W:int]:
132.83/133.06	         (app_encode_app(int,A,number_number_of(A),
132.83/133.06	                         app_encode_app(int,int,bit0,W)) =
132.83/133.06	          app_encode_app(A,A,
132.83/133.06	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
132.83/133.06	                                        app_encode_app(A,A,
132.83/133.06	                                                       app_encode_app(
132.83/133.06	                                                       A,app_encode_fun(A,A),
132.83/133.06	                                                       plus_plus(A),
132.83/133.06	                                                       zero_zero(A)),
132.83/133.06	                                                       app_encode_app(
132.83/133.06	                                                       int,A,
132.83/133.06	                                                       number_number_of(A),W))),
132.83/133.06	                         app_encode_app(int,A,number_number_of(A),W))))))).
132.83/133.06	tff('48', plain,
132.83/133.06	    ![X210 : $tType, X211 : int]:
132.83/133.06	      (app_encode_app(int, X210, number_number_of(X210), 
132.83/133.06	         app_encode_app(int, int, bit0, X211))
132.83/133.06	        = app_encode_app(X210, X210, 
132.83/133.06	            app_encode_app(X210, app_encode_fun(X210, X210), 
132.83/133.06	              plus_plus(X210), 
132.83/133.06	              app_encode_app(X210, X210, 
132.83/133.06	                app_encode_app(X210, app_encode_fun(X210, X210), 
132.83/133.06	                  plus_plus(X210), zero_zero(X210)), 
132.83/133.06	                app_encode_app(int, X210, number_number_of(X210), X211))), 
132.83/133.06	            app_encode_app(int, X210, number_number_of(X210), X211))
132.83/133.06	       | ~ number_ring(X210)),
132.83/133.06	    inference('cnf', [status(esa)], [zf_stmt_134])).
132.83/133.06	tff('49', plain,
132.83/133.06	    ![X0 : int]:
132.83/133.06	      (app_encode_app(int, int, number_number_of(int), 
132.83/133.06	         app_encode_app(int, int, bit0, X0))
132.83/133.06	        = app_encode_app(int, int, 
132.83/133.06	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.06	              zero_zero(int)), 
132.83/133.06	            app_encode_app(int, int, 
132.83/133.06	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.06	                app_encode_app(int, int, number_number_of(int), X0)), 
132.83/133.06	              app_encode_app(int, int, number_number_of(int), X0)))
132.83/133.06	       | ~ number_ring(int)),
132.83/133.06	    inference('sup+', [status(thm)], ['47', '48'])).
132.83/133.06	tff('50', plain,
132.83/133.06	    ![X0 : int]:
132.83/133.06	      (app_encode_app(int, int, bit0, X0)
132.83/133.06	        = app_encode_app(int, int, 
132.83/133.06	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.06	              pls), 
132.83/133.06	            app_encode_app(int, int, 
132.83/133.06	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.06	                X0), X0))
132.83/133.06	       | ~ $true),
132.83/133.06	    inference('demod', [status(thm)], ['49', '0', '32', '0', '0', '3'])).
132.83/133.06	tff('51', plain,
132.83/133.06	    ![X0 : int]:
132.83/133.06	      app_encode_app(int, int, bit0, X0)
132.83/133.06	       = app_encode_app(int, int, 
132.83/133.06	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
132.83/133.06	           app_encode_app(int, int, 
132.83/133.06	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.06	               X0), X0)),
132.83/133.06	    inference('simplify', [status(thm)], ['50'])).
132.83/133.06	tff(zf_stmt_94, axiom,
132.83/133.06	  (![L1:int,K:int]:
132.83/133.06	     (app_encode_app(int,int,
132.83/133.06	                     app_encode_app(int,app_encode_fun(int,int),
132.83/133.06	                                    plus_plus(int),
132.83/133.06	                                    app_encode_app(int,int,bit0,K)),
132.83/133.06	                     app_encode_app(int,int,bit1,L1)) =
132.83/133.06	      app_encode_app(int,int,bit1,
132.83/133.06	                     app_encode_app(int,int,
132.83/133.06	                                    app_encode_app(int,
132.83/133.06	                                                   app_encode_fun(int,int),
132.83/133.06	                                                   plus_plus(int),K),
132.83/133.06	                                    L1))))).
132.83/133.06	tff('52', plain,
132.83/133.06	    ![X124 : int, X125 : int]:
132.83/133.06	      app_encode_app(int, int, 
132.83/133.06	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.06	          app_encode_app(int, int, bit0, X124)), 
132.83/133.06	        app_encode_app(int, int, bit1, X125))
132.83/133.06	       = app_encode_app(int, int, bit1, 
132.83/133.06	           app_encode_app(int, int, 
132.83/133.06	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.06	               X124), X125)),
132.83/133.06	    inference('cnf', [status(esa)], [zf_stmt_94])).
132.83/133.06	tff('53', plain,
132.83/133.06	    ![X0 : int]:
132.83/133.06	      app_encode_app(int, int, 
132.83/133.06	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
132.83/133.06	        app_encode_app(int, int, bit1, X0))
132.83/133.06	       = app_encode_app(int, int, bit1, 
132.83/133.06	           app_encode_app(int, int, 
132.83/133.06	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.06	               pls), X0)),
132.83/133.06	    inference('sup+', [status(thm)], ['13', '52'])).
132.83/133.06	tff('54', plain,
132.83/133.06	    app_encode_app(int, int, 
132.83/133.06	      app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
132.83/133.06	      one_one(int))
132.83/133.06	     = app_encode_app(int, int, bit1, 
132.83/133.06	         app_encode_app(int, int, 
132.83/133.06	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
132.83/133.06	           pls)),
132.83/133.06	    inference('sup+', [status(thm)], ['5', '53'])).
132.83/133.06	tff(zf_stmt_56, axiom,
132.83/133.06	  (![A:$tType]:
132.83/133.06	     (linord219039673up_add(A) =>
132.83/133.06	      (![A1:A]:
132.83/133.06	         ((app_encode_app(A,A,
132.83/133.06	                          app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
132.83/133.06	                                         A1),
132.83/133.06	                          A1) =
132.83/133.06	           zero_zero(A)) <=>
132.83/133.06	          (A1 = zero_zero(A))))))).
132.83/133.06	tff('55', plain,
132.83/133.06	    ![X33 : $tType, X34 : X33]:
132.83/133.06	      (X34 != zero_zero(X33)
132.83/133.06	       | app_encode_app(X33, X33, 
132.83/133.06	           app_encode_app(X33, app_encode_fun(X33, X33), plus_plus(X33), X34), 
132.83/133.06	           X34)
132.83/133.06	          = zero_zero(X33)
132.83/133.06	       | ~ linord219039673up_add(X33)),
132.83/133.06	    inference('cnf', [status(esa)], [zf_stmt_56])).
132.83/133.06	tff('56', plain,
132.83/133.06	    ![X33 : $tType]:
132.83/133.06	      (~ linord219039673up_add(X33)
132.83/133.06	       | app_encode_app(X33, X33, 
132.83/133.06	           app_encode_app(X33, app_encode_fun(X33, X33), plus_plus(X33), 
132.83/133.06	             zero_zero(X33)), zero_zero(X33))
132.83/133.06	          = zero_zero(X33)),
132.83/133.06	    inference('simplify', [status(thm)], ['55'])).
132.83/133.06	tff('57', plain,
132.83/133.06	    (app_encode_app(int, int, 
132.83/133.06	       app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
132.83/133.06	       zero_zero(int))
132.83/133.06	      = zero_zero(int)
132.83/133.06	     | ~ linord219039673up_add(int)),
132.83/133.06	    inference('sup+', [status(thm)], ['32', '56'])).
132.83/133.06	tff(zf_stmt_135, axiom, (linord219039673up_add(int))).
132.83/133.06	tff('58', plain, linord219039673up_add(int),
132.83/133.06	    inference('cnf', [status(esa)], [zf_stmt_135])).
132.83/133.06	tff('59', plain,
132.83/133.06	    (app_encode_app(int, int, 
132.83/133.06	       app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
132.83/133.06	       pls)
132.83/133.06	      = pls
132.83/133.06	     | ~ $true),
132.83/133.06	    inference('demod', [status(thm)], ['57', '32', '32', '58'])).
132.83/133.06	tff('60', plain,
132.83/133.06	    app_encode_app(int, int, 
132.83/133.06	      app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
132.83/133.06	      pls)
132.83/133.06	     = pls,
132.83/133.06	    inference('simplify', [status(thm)], ['59'])).
132.83/133.06	tff('61', plain,
132.83/133.06	    app_encode_app(int, int, 
132.83/133.06	      app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
132.83/133.06	      one_one(int))
132.83/133.06	     = app_encode_app(int, int, bit1, pls),
132.83/133.06	    inference('demod', [status(thm)], ['54', '60'])).
132.83/133.06	tff('62', plain,
132.83/133.06	    app_encode_app(int, int, 
132.83/133.06	      app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
132.83/133.06	      one_one(int))
132.83/133.06	     = one_one(int),
132.83/133.06	    inference('demod', [status(thm)], ['61', '5'])).
132.83/133.06	tff(zf_stmt_74, axiom,
132.83/133.06	  (![B:$tType]:
132.83/133.06	     ((number(B) & semiring(B)) =>
132.83/133.06	      (![V1:int,B1:B,A2:B]:
132.83/133.06	         (app_encode_app(B,B,
132.83/133.06	                         app_encode_app(B,app_encode_fun(B,B),times_times(B),
132.83/133.06	                                        app_encode_app(B,B,
132.83/133.06	                                                       app_encode_app(
132.83/133.06	                                                       B,app_encode_fun(B,B),
132.83/133.06	                                                       plus_plus(B),A2),B1)),
132.83/133.06	                         app_encode_app(int,B,number_number_of(B),V1)) =
132.83/133.06	          app_encode_app(B,B,
132.83/133.06	                         app_encode_app(B,app_encode_fun(B,B),plus_plus(B),
132.83/133.06	                                        app_encode_app(B,B,
132.83/133.06	                                                       app_encode_app(
132.83/133.06	                                                       B,app_encode_fun(B,B),
132.83/133.06	                                                       times_times(B),A2),
132.83/133.06	                                                       app_encode_app(
132.83/133.06	                                                       int,B,
132.83/133.06	                                                       number_number_of(B),V1))),
132.83/133.06	                         app_encode_app(B,B,
132.83/133.06	                                        app_encode_app(B,app_encode_fun(B,B),
132.83/133.06	                                                       times_times(B),B1),
132.83/133.06	                                        app_encode_app(int,B,
132.83/133.06	                                                       number_number_of(B),V1)))))))).
132.83/133.06	tff('63', plain,
132.83/133.06	    ![X65 : $tType, X66 : X65, X67 : int, X68 : X65]:
132.83/133.06	      (app_encode_app(X65, X65, 
132.83/133.06	         app_encode_app(X65, app_encode_fun(X65, X65), times_times(X65), 
132.83/133.06	           app_encode_app(X65, X65, 
132.83/133.06	             app_encode_app(X65, app_encode_fun(X65, X65), plus_plus(X65), 
132.83/133.06	               X66), X68)), 
132.83/133.06	         app_encode_app(int, X65, number_number_of(X65), X67))
132.83/133.06	        = app_encode_app(X65, X65, 
132.83/133.06	            app_encode_app(X65, app_encode_fun(X65, X65), plus_plus(X65), 
132.83/133.06	              app_encode_app(X65, X65, 
132.83/133.06	                app_encode_app(X65, app_encode_fun(X65, X65), 
132.83/133.06	                  times_times(X65), X66), 
132.83/133.06	                app_encode_app(int, X65, number_number_of(X65), X67))), 
132.83/133.06	            app_encode_app(X65, X65, 
132.83/133.06	              app_encode_app(X65, app_encode_fun(X65, X65), 
132.83/133.06	                times_times(X65), X68), 
132.83/133.06	              app_encode_app(int, X65, number_number_of(X65), X67)))
132.83/133.06	       | ~ semiring(X65)
132.83/133.06	       | ~ number(X65)),
132.83/133.06	    inference('cnf', [status(esa)], [zf_stmt_74])).
132.83/133.06	tff('64', plain,
132.83/133.06	    ![X0 : int, X1 : int]:
132.83/133.06	      (app_encode_app(int, int, 
132.83/133.06	         app_encode_app(int, app_encode_fun(int, int), times_times(int), 
132.83/133.06	           app_encode_app(int, int, 
132.83/133.06	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.06	               pls), X1)), 
132.83/133.06	         app_encode_app(int, int, number_number_of(int), X0))
132.83/133.06	        = app_encode_app(int, int, 
132.83/133.06	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.06	              pls), 
132.83/133.06	            app_encode_app(int, int, 
132.83/133.06	              app_encode_app(int, app_encode_fun(int, int), 
132.83/133.06	                times_times(int), X1), 
132.83/133.06	              app_encode_app(int, int, number_number_of(int), X0)))
132.83/133.06	       | ~ number(int)
132.83/133.06	       | ~ semiring(int)),
132.83/133.06	    inference('sup+', [status(thm)], ['10', '63'])).
132.83/133.06	tff(zf_stmt_141, axiom, (semiring(int))).
132.83/133.06	tff('65', plain, semiring(int),
132.83/133.06	    inference('cnf', [status(esa)], [zf_stmt_141])).
132.83/133.06	tff('66', plain,
132.83/133.06	    ![X0 : int, X1 : int]:
132.83/133.06	      (app_encode_app(int, int, 
132.83/133.06	         app_encode_app(int, app_encode_fun(int, int), times_times(int), 
132.83/133.06	           app_encode_app(int, int, 
132.83/133.06	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.06	               pls), X1)), X0)
132.83/133.06	        = app_encode_app(int, int, 
132.83/133.06	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.06	              pls), 
132.83/133.06	            app_encode_app(int, int, 
132.83/133.06	              app_encode_app(int, app_encode_fun(int, int), 
132.83/133.06	                times_times(int), X1), X0))
132.83/133.06	       | ~ $true
132.83/133.06	       | ~ $true),
132.83/133.06	    inference('demod', [status(thm)], ['64', '0', '0', '17', '65'])).
132.83/133.06	tff('67', plain,
132.83/133.06	    ![X0 : int, X1 : int]:
132.83/133.06	      app_encode_app(int, int, 
132.83/133.06	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
132.83/133.06	          app_encode_app(int, int, 
132.83/133.06	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.06	              pls), X1)), X0)
132.83/133.06	       = app_encode_app(int, int, 
132.83/133.06	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
132.83/133.06	           app_encode_app(int, int, 
132.83/133.06	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
132.83/133.06	               X1), X0)),
132.83/133.06	    inference('simplify', [status(thm)], ['66'])).
132.83/133.06	tff('68', plain,
132.83/133.06	    ![X0 : int]:
132.83/133.06	      app_encode_app(int, int, 
132.83/133.06	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
132.83/133.06	          one_one(int)), X0)
132.83/133.06	       = app_encode_app(int, int, 
132.83/133.06	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
132.83/133.06	           app_encode_app(int, int, 
132.83/133.06	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
132.83/133.06	               one_one(int)), X0)),
132.83/133.06	    inference('sup+', [status(thm)], ['62', '67'])).
132.83/133.06	tff('69', plain,
132.83/133.06	    ![X0 : int]:
132.83/133.06	      app_encode_app(int, int, 
132.83/133.06	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
132.83/133.06	        X0)
132.83/133.06	       = app_encode_app(int, int, 
132.83/133.06	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
132.83/133.06	           app_encode_app(int, int, 
132.83/133.06	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.06	               pls), X0)),
132.83/133.06	    inference('demod', [status(thm)], ['68', '14', '14'])).
132.83/133.06	tff('70', plain,
132.83/133.06	    ![X0 : int]:
132.83/133.06	      app_encode_app(int, int, 
132.83/133.06	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
132.83/133.06	        app_encode_app(int, int, 
132.83/133.06	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
132.83/133.06	          X0))
132.83/133.06	       = app_encode_app(int, int, 
132.83/133.06	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
132.83/133.06	           app_encode_app(int, int, bit0, X0)),
132.83/133.06	    inference('sup+', [status(thm)], ['51', '69'])).
132.83/133.06	tff(zf_stmt_72, axiom,
132.83/133.06	  (![L1:int,K:int]:
132.83/133.06	     (app_encode_app(int,int,
132.83/133.06	                     app_encode_app(int,app_encode_fun(int,int),
132.83/133.06	                                    plus_plus(int),
132.83/133.06	                                    app_encode_app(int,int,bit0,K)),
132.83/133.06	                     app_encode_app(int,int,bit0,L1)) =
132.83/133.06	      app_encode_app(int,int,bit0,
132.83/133.06	                     app_encode_app(int,int,
132.83/133.06	                                    app_encode_app(int,
132.83/133.06	                                                   app_encode_fun(int,int),
132.83/133.06	                                                   plus_plus(int),K),
132.83/133.06	                                    L1))))).
132.83/133.06	tff('71', plain,
132.83/133.06	    ![X61 : int, X62 : int]:
132.83/133.06	      app_encode_app(int, int, 
132.83/133.06	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.06	          app_encode_app(int, int, bit0, X61)), 
132.83/133.06	        app_encode_app(int, int, bit0, X62))
132.83/133.06	       = app_encode_app(int, int, bit0, 
132.83/133.06	           app_encode_app(int, int, 
132.83/133.06	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.06	               X61), X62)),
132.83/133.06	    inference('cnf', [status(esa)], [zf_stmt_72])).
132.83/133.06	tff('72', plain,
132.83/133.06	    ![X0 : int]:
132.83/133.06	      app_encode_app(int, int, 
132.83/133.06	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
132.83/133.06	        app_encode_app(int, int, bit0, X0))
132.83/133.06	       = app_encode_app(int, int, bit0, 
132.83/133.06	           app_encode_app(int, int, 
132.83/133.06	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.06	               pls), X0)),
132.83/133.06	    inference('sup+', [status(thm)], ['13', '71'])).
132.83/133.06	tff('73', plain,
132.83/133.06	    ![X0 : int]:
132.83/133.06	      app_encode_app(int, int, 
132.83/133.06	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
132.83/133.06	        app_encode_app(int, int, 
132.83/133.06	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
132.83/133.06	          X0))
132.83/133.06	       = app_encode_app(int, int, bit0, 
132.83/133.06	           app_encode_app(int, int, 
132.83/133.06	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.06	               pls), X0)),
132.83/133.06	    inference('demod', [status(thm)], ['70', '72'])).
132.83/133.06	tff('74', plain,
132.83/133.06	    ![X0 : int]:
132.83/133.06	      app_encode_app(int, int, bit0, X0)
132.83/133.06	       = app_encode_app(int, int, bit0, 
132.83/133.06	           app_encode_app(int, int, 
132.83/133.06	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.06	               pls), X0)),
132.83/133.06	    inference('sup+', [status(thm)], ['73', '51'])).
132.83/133.06	tff(zf_stmt_73, axiom,
132.83/133.06	  (![L1:int,K:int]:
132.83/133.06	     (app_encode_app(int,int,
132.83/133.06	                     app_encode_app(int,app_encode_fun(int,int),
132.83/133.06	                                    minus_minus(int),
132.83/133.06	                                    app_encode_app(int,int,bit0,K)),
132.83/133.06	                     app_encode_app(int,int,bit0,L1)) =
132.83/133.06	      app_encode_app(int,int,bit0,
132.83/133.06	                     app_encode_app(int,int,
132.83/133.06	                                    app_encode_app(int,
132.83/133.06	                                                   app_encode_fun(int,int),
132.83/133.06	                                                   minus_minus(int),K),
132.83/133.06	                                    L1))))).
132.83/133.06	tff('75', plain,
132.83/133.06	    ![X63 : int, X64 : int]:
132.83/133.06	      app_encode_app(int, int, 
132.83/133.06	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
132.83/133.06	          app_encode_app(int, int, bit0, X63)), 
132.83/133.06	        app_encode_app(int, int, bit0, X64))
132.83/133.06	       = app_encode_app(int, int, bit0, 
132.83/133.06	           app_encode_app(int, int, 
132.83/133.06	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
132.83/133.06	               X63), X64)),
132.83/133.06	    inference('cnf', [status(esa)], [zf_stmt_73])).
132.83/133.06	tff('76', plain,
132.83/133.06	    ![X0 : int, X1 : int]:
132.83/133.06	      app_encode_app(int, int, 
132.83/133.06	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
132.83/133.06	          app_encode_app(int, int, bit0, X0)), 
132.83/133.06	        app_encode_app(int, int, bit0, X1))
132.83/133.06	       = app_encode_app(int, int, bit0, 
132.83/133.06	           app_encode_app(int, int, 
132.83/133.06	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
132.83/133.06	               app_encode_app(int, int, 
132.83/133.06	                 app_encode_app(int, app_encode_fun(int, int), 
132.83/133.06	                   plus_plus(int), pls), X0)), X1)),
132.83/133.06	    inference('sup+', [status(thm)], ['74', '75'])).
132.83/133.06	tff('77', plain,
132.83/133.06	    ![X0 : int, X1 : int]:
132.83/133.06	      app_encode_app(int, int, bit0, 
132.83/133.06	        app_encode_app(int, int, 
132.83/133.06	          app_encode_app(int, app_encode_fun(int, int), minus_minus(int), X0), 
132.83/133.06	          X1))
132.83/133.06	       = app_encode_app(int, int, bit0, 
132.83/133.06	           app_encode_app(int, int, 
132.83/133.06	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
132.83/133.06	               app_encode_app(int, int, 
132.83/133.06	                 app_encode_app(int, app_encode_fun(int, int), 
132.83/133.06	                   plus_plus(int), pls), X0)), X1)),
132.83/133.06	    inference('demod', [status(thm)], ['76', '75'])).
132.83/133.06	tff('78', plain,
132.83/133.06	    ![X0 : int]:
132.83/133.06	      app_encode_app(int, int, bit0, 
132.83/133.06	        app_encode_app(int, int, 
132.83/133.06	          app_encode_app(int, app_encode_fun(int, int), minus_minus(int), X0), 
132.83/133.06	          pls))
132.83/133.06	       = app_encode_app(int, int, bit0, 
132.83/133.06	           app_encode_app(int, int, 
132.83/133.06	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.06	               pls), X0)),
132.83/133.06	    inference('sup+', [status(thm)], ['43', '77'])).
132.83/133.06	tff('79', plain,
132.83/133.06	    ![X0 : int]:
132.83/133.06	      app_encode_app(int, int, bit0, 
132.83/133.06	        app_encode_app(int, int, 
132.83/133.06	          app_encode_app(int, app_encode_fun(int, int), minus_minus(int), X0), 
132.83/133.06	          pls))
132.83/133.06	       = app_encode_app(int, int, bit0, X0),
132.83/133.06	    inference('demod', [status(thm)], ['78', '74'])).
132.83/133.06	tff('80', plain,
132.83/133.06	    ![X0 : int, X1 : int]:
132.83/133.06	      (app_encode_app(int, $o, 
132.83/133.06	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), X1), 
132.83/133.06	         app_encode_app(int, int, bit0, X0))
132.83/133.06	       | ~ app_encode_app(int, $o, 
132.83/133.06	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X1), 
132.83/133.06	             app_encode_app(int, int, bit1, X0))),
132.83/133.06	    inference('demod', [status(thm)], ['9', '79'])).
132.83/133.06	tff(zf_stmt_151, conjecture,
132.83/133.06	  (app_encode_app(int,$o,
132.83/133.06	                  app_encode_app(int,app_encode_fun(int,$o),ord_less_eq(int),
132.83/133.06	                                 s),
132.83/133.06	                  app_encode_app(int,int,
132.83/133.06	                                 app_encode_app(int,app_encode_fun(int,int),
132.83/133.06	                                                minus_minus(int),
132.83/133.06	                                                app_encode_app(int,int,
132.83/133.06	                                                               app_encode_app(
132.83/133.06	                                                               int,
132.83/133.06	                                                               app_encode_fun(
132.83/133.06	                                                               int,int),
132.83/133.06	                                                               plus_plus(int),
132.83/133.06	                                                               app_encode_app(
132.83/133.06	                                                               int,int,
132.83/133.06	                                                               app_encode_app(
132.83/133.06	                                                               int,
132.83/133.06	                                                               app_encode_fun(
132.83/133.06	                                                               int,int),
132.83/133.06	                                                               times_times(
132.83/133.06	                                                               int),
132.83/133.06	                                                               app_encode_app(
132.83/133.06	                                                               int,int,
132.83/133.06	                                                               number_number_of(
132.83/133.06	                                                               int),
132.83/133.06	                                                               app_encode_app(
132.83/133.06	                                                               int,int,bit0,
132.83/133.06	                                                               app_encode_app(
132.83/133.06	                                                               int,int,bit0,
132.83/133.06	                                                               app_encode_app(
132.83/133.06	                                                               int,int,bit1,
132.83/133.06	                                                               pls))))),m)),
132.83/133.06	                                                               one_one(int))),
132.83/133.06	                                 one_one(int))))).
132.83/133.06	tff(zf_stmt_0, negated_conjecture,
132.83/133.06	  (~
132.83/133.06	    app_encode_app(int,$o,
132.83/133.06	                   app_encode_app(int,app_encode_fun(int,$o),
132.83/133.06	                                  ord_less_eq(int),s),
132.83/133.06	                   app_encode_app(int,int,
132.83/133.06	                                  app_encode_app(int,app_encode_fun(int,int),
132.83/133.06	                                                 minus_minus(int),
132.83/133.06	                                                 app_encode_app(int,int,
132.83/133.06	                                                                app_encode_app(
132.83/133.06	                                                                int,
132.83/133.06	                                                                app_encode_fun(
132.83/133.06	                                                                int,int),
132.83/133.06	                                                                plus_plus(
132.83/133.06	                                                                int),
132.83/133.06	                                                                app_encode_app(
132.83/133.06	                                                                int,int,
132.83/133.06	                                                                app_encode_app(
132.83/133.06	                                                                int,
132.83/133.06	                                                                app_encode_fun(
132.83/133.06	                                                                int,int),
132.83/133.06	                                                                times_times(
132.83/133.06	                                                                int),
132.83/133.06	                                                                app_encode_app(
132.83/133.06	                                                                int,int,
132.83/133.06	                                                                number_number_of(
132.83/133.06	                                                                int),
132.83/133.06	                                                                app_encode_app(
132.83/133.06	                                                                int,int,bit0,
132.83/133.06	                                                                app_encode_app(
132.83/133.06	                                                                int,int,bit0,
132.83/133.06	                                                                app_encode_app(
132.83/133.06	                                                                int,int,bit1,
132.83/133.06	                                                                pls))))),m)),
132.83/133.06	                                                                one_one(int))),
132.83/133.06	                                  one_one(int))))).
132.83/133.06	tff('81', plain,
132.83/133.06	    ~ app_encode_app(int, $o, 
132.83/133.06	        app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), s), 
132.83/133.06	        app_encode_app(int, int, 
132.83/133.06	          app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
132.83/133.06	            app_encode_app(int, int, 
132.83/133.06	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.06	                app_encode_app(int, int, 
132.83/133.06	                  app_encode_app(int, app_encode_fun(int, int), 
132.83/133.06	                    times_times(int), 
132.83/133.06	                    app_encode_app(int, int, number_number_of(int), 
132.83/133.06	                      app_encode_app(int, int, bit0, 
132.83/133.06	                        app_encode_app(int, int, bit0, 
132.83/133.06	                          app_encode_app(int, int, bit1, pls))))), m)), 
132.83/133.06	              one_one(int))), one_one(int))),
132.83/133.06	    inference('cnf', [status(esa)], [zf_stmt_0])).
132.83/133.06	tff(zf_stmt_71, axiom,
132.83/133.06	  (![L1:int,K:int]:
132.83/133.06	     (app_encode_app(int,int,
132.83/133.06	                     app_encode_app(int,app_encode_fun(int,int),
132.83/133.06	                                    times_times(int),
132.83/133.06	                                    app_encode_app(int,int,bit0,K)),
132.83/133.06	                     L1) =
132.83/133.06	      app_encode_app(int,int,bit0,
132.83/133.06	                     app_encode_app(int,int,
132.83/133.06	                                    app_encode_app(int,
132.83/133.06	                                                   app_encode_fun(int,int),
132.83/133.06	                                                   times_times(int),K),
132.83/133.06	                                    L1))))).
132.83/133.06	tff('82', plain,
132.83/133.06	    ![X59 : int, X60 : int]:
132.83/133.06	      app_encode_app(int, int, 
132.83/133.06	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
132.83/133.06	          app_encode_app(int, int, bit0, X59)), X60)
132.83/133.06	       = app_encode_app(int, int, bit0, 
132.83/133.06	           app_encode_app(int, int, 
132.83/133.06	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
132.83/133.06	               X59), X60)),
132.83/133.06	    inference('cnf', [status(esa)], [zf_stmt_71])).
132.83/133.06	tff('83', plain,
132.83/133.06	    ![X0 : int]:
132.83/133.06	      app_encode_app(int, int, 
132.83/133.06	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.06	          app_encode_app(int, int, bit0, X0)), one_one(int))
132.83/133.06	       = app_encode_app(int, int, bit1, 
132.83/133.06	           app_encode_app(int, int, 
132.83/133.06	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.06	               X0), pls)),
132.83/133.06	    inference('sup+', [status(thm)], ['5', '52'])).
132.83/133.06	tff('84', plain,
132.83/133.06	    ![X0 : int]:
132.83/133.06	      app_encode_app(int, int, 
132.83/133.06	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.06	          app_encode_app(int, int, bit0, X0)), pls)
132.83/133.07	       = app_encode_app(int, int, bit0, 
132.83/133.07	           app_encode_app(int, int, 
132.83/133.07	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.07	               X0), pls)),
132.83/133.07	    inference('sup+', [status(thm)], ['13', '71'])).
132.83/133.07	tff(zf_stmt_93, axiom,
132.83/133.07	  (![L1:int,K:int]:
132.83/133.07	     (app_encode_app(int,int,
132.83/133.07	                     app_encode_app(int,app_encode_fun(int,int),
132.83/133.07	                                    plus_plus(int),
132.83/133.07	                                    app_encode_app(int,int,bit1,K)),
132.83/133.07	                     app_encode_app(int,int,bit0,L1)) =
132.83/133.07	      app_encode_app(int,int,bit1,
132.83/133.07	                     app_encode_app(int,int,
132.83/133.07	                                    app_encode_app(int,
132.83/133.07	                                                   app_encode_fun(int,int),
132.83/133.07	                                                   plus_plus(int),K),
132.83/133.07	                                    L1))))).
132.83/133.07	tff('85', plain,
132.83/133.07	    ![X122 : int, X123 : int]:
132.83/133.07	      app_encode_app(int, int, 
132.83/133.07	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.07	          app_encode_app(int, int, bit1, X122)), 
132.83/133.07	        app_encode_app(int, int, bit0, X123))
132.83/133.07	       = app_encode_app(int, int, bit1, 
132.83/133.07	           app_encode_app(int, int, 
132.83/133.07	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.07	               X122), X123)),
132.83/133.07	    inference('cnf', [status(esa)], [zf_stmt_93])).
132.83/133.07	tff('86', plain,
132.83/133.07	    ![X0 : int]:
132.83/133.07	      app_encode_app(int, int, 
132.83/133.07	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.07	          app_encode_app(int, int, bit1, X0)), pls)
132.83/133.07	       = app_encode_app(int, int, bit1, 
132.83/133.07	           app_encode_app(int, int, 
132.83/133.07	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.07	               X0), pls)),
132.83/133.07	    inference('sup+', [status(thm)], ['13', '85'])).
132.83/133.07	tff('87', plain,
132.83/133.07	    app_encode_app(int, int, 
132.83/133.07	      app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.07	        one_one(int)), pls)
132.83/133.07	     = app_encode_app(int, int, bit1, 
132.83/133.07	         app_encode_app(int, int, 
132.83/133.07	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
132.83/133.07	           pls)),
132.83/133.07	    inference('sup+', [status(thm)], ['5', '86'])).
132.83/133.07	tff('88', plain,
132.83/133.07	    app_encode_app(int, int, 
132.83/133.07	      app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.07	        one_one(int)), pls)
132.83/133.07	     = app_encode_app(int, int, 
132.83/133.07	         app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
132.83/133.07	         one_one(int)),
132.83/133.07	    inference('sup+', [status(thm)], ['54', '87'])).
132.83/133.07	tff('89', plain,
132.83/133.07	    app_encode_app(int, int, 
132.83/133.07	      app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.07	        one_one(int)), pls)
132.83/133.07	     = one_one(int),
132.83/133.07	    inference('demod', [status(thm)], ['88', '62'])).
132.83/133.07	tff('90', plain,
132.83/133.07	    ![X0 : int, X1 : int]:
132.83/133.07	      (app_encode_app(int, int, 
132.83/133.07	         app_encode_app(int, app_encode_fun(int, int), times_times(int), 
132.83/133.07	           app_encode_app(int, int, 
132.83/133.07	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.07	               X1), pls)), 
132.83/133.07	         app_encode_app(int, int, number_number_of(int), X0))
132.83/133.07	        = app_encode_app(int, int, 
132.83/133.07	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.07	              app_encode_app(int, int, 
132.83/133.07	                app_encode_app(int, app_encode_fun(int, int), 
132.83/133.07	                  times_times(int), X1), 
132.83/133.07	                app_encode_app(int, int, number_number_of(int), X0))), pls)
132.83/133.07	       | ~ number(int)
132.83/133.07	       | ~ semiring(int)),
132.83/133.07	    inference('sup+', [status(thm)], ['10', '63'])).
132.83/133.07	tff('91', plain,
132.83/133.07	    ![X0 : int, X1 : int]:
132.83/133.07	      (app_encode_app(int, int, 
132.83/133.07	         app_encode_app(int, app_encode_fun(int, int), times_times(int), 
132.83/133.07	           app_encode_app(int, int, 
132.83/133.07	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.07	               X1), pls)), X0)
132.83/133.07	        = app_encode_app(int, int, 
132.83/133.07	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.07	              app_encode_app(int, int, 
132.83/133.07	                app_encode_app(int, app_encode_fun(int, int), 
132.83/133.07	                  times_times(int), X1), X0)), pls)
132.83/133.07	       | ~ $true
132.83/133.07	       | ~ $true),
132.83/133.07	    inference('demod', [status(thm)], ['90', '0', '0', '17', '65'])).
132.83/133.07	tff('92', plain,
132.83/133.07	    ![X0 : int, X1 : int]:
132.83/133.07	      app_encode_app(int, int, 
132.83/133.07	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
132.83/133.07	          app_encode_app(int, int, 
132.83/133.07	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X1), 
132.83/133.07	            pls)), X0)
132.83/133.07	       = app_encode_app(int, int, 
132.83/133.07	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.07	             app_encode_app(int, int, 
132.83/133.07	               app_encode_app(int, app_encode_fun(int, int), 
132.83/133.07	                 times_times(int), X1), X0)), pls),
132.83/133.07	    inference('simplify', [status(thm)], ['91'])).
132.83/133.07	tff('93', plain,
132.83/133.07	    ![X0 : int]:
132.83/133.07	      app_encode_app(int, int, 
132.83/133.07	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
132.83/133.07	          one_one(int)), X0)
132.83/133.07	       = app_encode_app(int, int, 
132.83/133.07	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.07	             app_encode_app(int, int, 
132.83/133.07	               app_encode_app(int, app_encode_fun(int, int), 
132.83/133.07	                 times_times(int), one_one(int)), X0)), pls),
132.83/133.07	    inference('sup+', [status(thm)], ['89', '92'])).
132.83/133.07	tff('94', plain,
132.83/133.07	    ![X0 : int]:
132.83/133.07	      app_encode_app(int, int, 
132.83/133.07	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
132.83/133.07	        X0)
132.83/133.07	       = app_encode_app(int, int, 
132.83/133.07	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.07	             app_encode_app(int, int, 
132.83/133.07	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.07	                 pls), X0)), pls),
132.83/133.07	    inference('demod', [status(thm)], ['93', '14', '14'])).
132.83/133.07	tff('95', plain,
132.83/133.07	    ![X0 : int]:
132.83/133.07	      app_encode_app(int, int, 
132.83/133.07	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
132.83/133.07	        X0)
132.83/133.07	       = app_encode_app(int, int, 
132.83/133.07	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
132.83/133.07	           app_encode_app(int, int, 
132.83/133.07	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.07	               X0), pls)),
132.83/133.07	    inference('demod', [status(thm)], ['94', '47'])).
132.83/133.07	tff('96', plain,
132.83/133.07	    ![X0 : int]:
132.83/133.07	      app_encode_app(int, int, 
132.83/133.07	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
132.83/133.07	          app_encode_app(int, int, bit0, X0)), pls)
132.83/133.07	       = app_encode_app(int, int, bit0, 
132.83/133.07	           app_encode_app(int, int, 
132.83/133.07	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
132.83/133.07	               X0), pls)),
132.83/133.07	    inference('sup+', [status(thm)], ['13', '75'])).
132.83/133.07	tff('97', plain,
132.83/133.07	    ~ app_encode_app(int, $o, 
132.83/133.07	        app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), s), 
132.83/133.07	        app_encode_app(int, int, bit0, 
132.83/133.07	          app_encode_app(int, int, bit0, 
132.83/133.07	            app_encode_app(int, int, 
132.83/133.07	              app_encode_app(int, app_encode_fun(int, int), 
132.83/133.07	                minus_minus(int), 
132.83/133.07	                app_encode_app(int, int, 
132.83/133.07	                  app_encode_app(int, app_encode_fun(int, int), 
132.83/133.07	                    plus_plus(int), pls), m)), pls)))),
132.83/133.07	    inference('demod', [status(thm)],
132.83/133.07	              ['81', '5', '0', '82', '82', '14', '83', '84', '47', '95', 
132.83/133.07	               '7', '96'])).
132.83/133.07	tff('98', plain,
132.83/133.07	    ~ app_encode_app(int, $o, 
132.83/133.07	        app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), s), 
132.83/133.07	        app_encode_app(int, int, bit0, 
132.83/133.07	          app_encode_app(int, int, bit0, 
132.83/133.07	            app_encode_app(int, int, 
132.83/133.07	              app_encode_app(int, app_encode_fun(int, int), 
132.83/133.07	                minus_minus(int), m), pls)))),
132.83/133.07	    inference('demod', [status(thm)], ['97', '77'])).
132.83/133.07	tff('99', plain,
132.83/133.07	    ~ app_encode_app(int, $o, 
132.83/133.07	        app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), s), 
132.83/133.07	        app_encode_app(int, int, bit0, app_encode_app(int, int, bit0, m))),
132.83/133.07	    inference('demod', [status(thm)], ['98', '79'])).
132.83/133.07	tff('100', plain,
132.83/133.07	    (~ $true
132.83/133.07	     | ~ app_encode_app(int, $o, 
132.83/133.07	           app_encode_app(int, app_encode_fun(int, $o), ord_less(int), s), 
132.83/133.07	           app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m)))),
132.83/133.07	    inference('sup-', [status(thm)], ['80', '99'])).
132.83/133.07	tff(zf_stmt_37, axiom,
132.83/133.07	  (app_encode_app(int,$o,
132.83/133.07	                  app_encode_app(int,app_encode_fun(int,$o),ord_less_eq(int),
132.83/133.07	                                 zero_zero(int)),
132.83/133.07	                  s) & 
132.83/133.07	   app_encode_app(int,$o,
132.83/133.07	                  app_encode_app(int,app_encode_fun(int,$o),ord_less(int),s),
132.83/133.07	                  app_encode_app(int,int,
132.83/133.07	                                 app_encode_app(int,app_encode_fun(int,int),
132.83/133.07	                                                plus_plus(int),
132.83/133.07	                                                app_encode_app(int,int,
132.83/133.07	                                                               app_encode_app(
132.83/133.07	                                                               int,
132.83/133.07	                                                               app_encode_fun(
132.83/133.07	                                                               int,int),
132.83/133.07	                                                               times_times(
132.83/133.07	                                                               int),
132.83/133.07	                                                               app_encode_app(
132.83/133.07	                                                               int,int,
132.83/133.07	                                                               number_number_of(
132.83/133.07	                                                               int),
132.83/133.07	                                                               app_encode_app(
132.83/133.07	                                                               int,int,bit0,
132.83/133.07	                                                               app_encode_app(
132.83/133.07	                                                               int,int,bit0,
132.83/133.07	                                                               app_encode_app(
132.83/133.07	                                                               int,int,bit1,
132.83/133.07	                                                               pls))))),m)),
132.83/133.07	                                 one_one(int))) & 
132.83/133.07	   app_encode_app(int,$o,
132.83/133.07	                  app_encode_app(int,app_encode_fun(int,$o),
132.83/133.07	                                 app_encode_app(int,
132.83/133.07	                                                app_encode_fun(int,
132.83/133.07	                                                               app_encode_fun(
132.83/133.07	                                                               int,$o)),
132.83/133.07	                                                zcong,s1),
132.83/133.07	                                 s),
132.83/133.07	                  app_encode_app(int,int,
132.83/133.07	                                 app_encode_app(int,app_encode_fun(int,int),
132.83/133.07	                                                plus_plus(int),
132.83/133.07	                                                app_encode_app(int,int,
132.83/133.07	                                                               app_encode_app(
132.83/133.07	                                                               int,
132.83/133.07	                                                               app_encode_fun(
132.83/133.07	                                                               int,int),
132.83/133.07	                                                               times_times(
132.83/133.07	                                                               int),
132.83/133.07	                                                               app_encode_app(
132.83/133.07	                                                               int,int,
132.83/133.07	                                                               number_number_of(
132.83/133.07	                                                               int),
132.83/133.07	                                                               app_encode_app(
132.83/133.07	                                                               int,int,bit0,
132.83/133.07	                                                               app_encode_app(
132.83/133.07	                                                               int,int,bit0,
132.83/133.07	                                                               app_encode_app(
132.83/133.07	                                                               int,int,bit1,
132.83/133.07	                                                               pls))))),m)),
132.83/133.07	                                 one_one(int))))).
132.83/133.07	tff('101', plain,
132.83/133.07	    app_encode_app(int, $o, 
132.83/133.07	      app_encode_app(int, app_encode_fun(int, $o), ord_less(int), s), 
132.83/133.07	      app_encode_app(int, int, 
132.83/133.07	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.07	          app_encode_app(int, int, 
132.83/133.07	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
132.83/133.07	              app_encode_app(int, int, number_number_of(int), 
132.83/133.07	                app_encode_app(int, int, bit0, 
132.83/133.07	                  app_encode_app(int, int, bit0, 
132.83/133.07	                    app_encode_app(int, int, bit1, pls))))), m)), 
132.83/133.07	        one_one(int))),
132.83/133.07	    inference('cnf', [status(esa)], [zf_stmt_37])).
132.83/133.07	tff('102', plain,
132.83/133.07	    app_encode_app(int, $o, 
132.83/133.07	      app_encode_app(int, app_encode_fun(int, $o), ord_less(int), s), 
132.83/133.07	      app_encode_app(int, int, 
132.83/133.07	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.07	          app_encode_app(int, int, 
132.83/133.07	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
132.83/133.07	              app_encode_app(int, int, bit0, 
132.83/133.07	                app_encode_app(int, int, bit0, 
132.83/133.07	                  app_encode_app(int, int, bit1, pls)))), m)), one_one(int))),
132.83/133.07	    inference('demod', [status(thm)], ['101', '0'])).
132.83/133.07	tff('103', plain,
132.83/133.07	    app_encode_app(int, $o, 
132.83/133.07	      app_encode_app(int, app_encode_fun(int, $o), ord_less(int), s), 
132.83/133.07	      app_encode_app(int, int, bit1, 
132.83/133.07	        app_encode_app(int, int, bit0, 
132.83/133.07	          app_encode_app(int, int, 
132.83/133.07	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.07	              app_encode_app(int, int, 
132.83/133.07	                app_encode_app(int, app_encode_fun(int, int), 
132.83/133.07	                  plus_plus(int), pls), m)), pls)))),
132.83/133.07	    inference('demod', [status(thm)],
132.83/133.07	              ['102', '5', '82', '82', '14', '83', '84'])).
132.83/133.07	tff('104', plain,
132.83/133.07	    app_encode_app(int, $o, 
132.83/133.07	      app_encode_app(int, app_encode_fun(int, $o), ord_less(int), s), 
132.83/133.07	      app_encode_app(int, int, bit1, 
132.83/133.07	        app_encode_app(int, int, bit0, 
132.83/133.07	          app_encode_app(int, int, 
132.83/133.07	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
132.83/133.07	              pls), m)))),
132.83/133.07	    inference('demod', [status(thm)], ['103', '94'])).
132.83/133.07	tff('105', plain,
132.83/133.07	    app_encode_app(int, $o, 
132.83/133.07	      app_encode_app(int, app_encode_fun(int, $o), ord_less(int), s), 
132.83/133.07	      app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m))),
132.83/133.07	    inference('demod', [status(thm)], ['104', '74'])).
132.83/133.07	tff('106', plain, (~ $true | ~ $true),
132.83/133.07	    inference('demod', [status(thm)], ['100', '105'])).
132.83/133.07	tff('107', plain, $false, inference('simplify', [status(thm)], ['106'])).
132.83/133.07	
132.83/133.07	% SZS output end Refutation
132.83/133.07	EOF
