0.00/0.00	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : appext
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : rpo6
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.20	% Computer   : n100.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 07:50:55 CST 2018
1.97/2.15	% done 1247 iterations in 1.949s
1.97/2.15	% SZS status Theorem for 'stdin'
1.97/2.15	% SZS output start Refutation
1.97/2.16	tff(zf_stmt_157, conjecture,
1.97/2.16	  (app_encode_app(int,int,
1.97/2.16	                  app_encode_app(int,app_encode_fun(int,int),
1.97/2.16	                                 minus_minus(int),
1.97/2.16	                                 app_encode_app(nat,int,
1.97/2.16	                                                app_encode_app(int,
1.97/2.16	                                                               app_encode_fun(
1.97/2.16	                                                               nat,int),
1.97/2.16	                                                               power_power(
1.97/2.16	                                                               int),s),
1.97/2.16	                                                app_encode_app(int,nat,
1.97/2.16	                                                               number_number_of(
1.97/2.16	                                                               nat),
1.97/2.16	                                                               app_encode_app(
1.97/2.16	                                                               int,int,bit0,
1.97/2.16	                                                               app_encode_app(
1.97/2.16	                                                               int,int,bit1,
1.97/2.16	                                                               pls))))),
1.97/2.16	                  app_encode_app(int,int,number_number_of(int),min)) =
1.97/2.16	   app_encode_app(int,int,
1.97/2.16	                  app_encode_app(int,app_encode_fun(int,int),plus_plus(int),
1.97/2.16	                                 app_encode_app(nat,int,
1.97/2.16	                                                app_encode_app(int,
1.97/2.16	                                                               app_encode_fun(
1.97/2.16	                                                               nat,int),
1.97/2.16	                                                               power_power(
1.97/2.16	                                                               int),s),
1.97/2.16	                                                app_encode_app(int,nat,
1.97/2.16	                                                               number_number_of(
1.97/2.16	                                                               nat),
1.97/2.16	                                                               app_encode_app(
1.97/2.16	                                                               int,int,bit0,
1.97/2.16	                                                               app_encode_app(
1.97/2.16	                                                               int,int,bit1,
1.97/2.16	                                                               pls))))),
1.97/2.16	                  one_one(int)))).
1.97/2.16	tff(zf_stmt_0, negated_conjecture,
1.97/2.16	  (app_encode_app(int,int,
1.97/2.16	                  app_encode_app(int,app_encode_fun(int,int),
1.97/2.16	                                 minus_minus(int),
1.97/2.16	                                 app_encode_app(nat,int,
1.97/2.16	                                                app_encode_app(int,
1.97/2.16	                                                               app_encode_fun(
1.97/2.16	                                                               nat,int),
1.97/2.16	                                                               power_power(
1.97/2.16	                                                               int),s),
1.97/2.16	                                                app_encode_app(int,nat,
1.97/2.16	                                                               number_number_of(
1.97/2.16	                                                               nat),
1.97/2.16	                                                               app_encode_app(
1.97/2.16	                                                               int,int,bit0,
1.97/2.16	                                                               app_encode_app(
1.97/2.16	                                                               int,int,bit1,
1.97/2.16	                                                               pls))))),
1.97/2.16	                  app_encode_app(int,int,number_number_of(int),min)) !=
1.97/2.16	   app_encode_app(int,int,
1.97/2.16	                  app_encode_app(int,app_encode_fun(int,int),plus_plus(int),
1.97/2.16	                                 app_encode_app(nat,int,
1.97/2.16	                                                app_encode_app(int,
1.97/2.16	                                                               app_encode_fun(
1.97/2.16	                                                               nat,int),
1.97/2.16	                                                               power_power(
1.97/2.16	                                                               int),s),
1.97/2.16	                                                app_encode_app(int,nat,
1.97/2.16	                                                               number_number_of(
1.97/2.16	                                                               nat),
1.97/2.16	                                                               app_encode_app(
1.97/2.16	                                                               int,int,bit0,
1.97/2.16	                                                               app_encode_app(
1.97/2.16	                                                               int,int,bit1,
1.97/2.16	                                                               pls))))),
1.97/2.16	                  one_one(int)))).
1.97/2.16	tff('0', plain,
1.97/2.16	    app_encode_app(int, int, 
1.97/2.16	      app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
1.97/2.16	        app_encode_app(nat, int, 
1.97/2.16	          app_encode_app(int, app_encode_fun(nat, int), power_power(int), s), 
1.97/2.16	          app_encode_app(int, nat, number_number_of(nat), 
1.97/2.16	            app_encode_app(int, int, bit0, 
1.97/2.16	              app_encode_app(int, int, bit1, pls))))), 
1.97/2.16	      app_encode_app(int, int, number_number_of(int), min))
1.97/2.16	     != app_encode_app(int, int, 
1.97/2.16	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.97/2.16	            app_encode_app(nat, int, 
1.97/2.16	              app_encode_app(int, app_encode_fun(nat, int), 
1.97/2.16	                power_power(int), s), 
1.97/2.16	              app_encode_app(int, nat, number_number_of(nat), 
1.97/2.16	                app_encode_app(int, int, bit0, 
1.97/2.16	                  app_encode_app(int, int, bit1, pls))))), one_one(int)),
1.97/2.16	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.97/2.16	tff(zf_stmt_133, axiom, (comm_monoid_mult(int))).
1.97/2.16	tff('1', plain, comm_monoid_mult(int),
1.97/2.16	    inference('cnf', [status(esa)], [zf_stmt_133])).
1.97/2.16	tff(zf_stmt_111, axiom,
1.97/2.16	  (![A:$tType]:
1.97/2.16	     (comm_monoid_mult(A) =>
1.97/2.16	      (![A1:A]:
1.97/2.16	         (app_encode_app(A,A,
1.97/2.16	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
1.97/2.16	                                        one_one(A)),
1.97/2.16	                         A1) =
1.97/2.16	          A1))))).
1.97/2.16	tff('2', plain,
1.97/2.16	    ![X151 : $tType, X152 : X151]:
1.97/2.16	      (app_encode_app(X151, X151, 
1.97/2.16	         app_encode_app(X151, app_encode_fun(X151, X151), times_times(X151), 
1.97/2.16	           one_one(X151)), X152)
1.97/2.16	        = X152
1.97/2.16	       | ~ comm_monoid_mult(X151)),
1.97/2.16	    inference('cnf', [status(esa)], [zf_stmt_111])).
1.97/2.16	tff('3', plain,
1.97/2.16	    ![X0 : int]:
1.97/2.16	      (~ $true
1.97/2.16	       | app_encode_app(int, int, 
1.97/2.16	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.97/2.16	             one_one(int)), X0)
1.97/2.16	          = X0),
1.97/2.16	    inference('sup-', [status(thm)], ['1', '2'])).
1.97/2.16	tff(zf_stmt_88, axiom,
1.97/2.16	  (one_one(int) =
1.97/2.16	   app_encode_app(int,int,number_number_of(int),
1.97/2.16	                  app_encode_app(int,int,bit1,pls)))).
1.97/2.16	tff('4', plain,
1.97/2.16	    one_one(int)
1.97/2.16	     = app_encode_app(int, int, number_number_of(int), 
1.97/2.16	         app_encode_app(int, int, bit1, pls)),
1.97/2.16	    inference('cnf', [status(esa)], [zf_stmt_88])).
1.97/2.16	tff(zf_stmt_72, axiom,
1.97/2.16	  (![K:int]: (app_encode_app(int,int,number_number_of(int),K) = K))).
1.97/2.16	tff('5', plain,
1.97/2.16	    ![X64 : int]: app_encode_app(int, int, number_number_of(int), X64) = X64,
1.97/2.16	    inference('cnf', [status(esa)], [zf_stmt_72])).
1.97/2.16	tff('6', plain, one_one(int) = app_encode_app(int, int, bit1, pls),
1.97/2.16	    inference('demod', [status(thm)], ['4', '5'])).
1.97/2.16	tff('7', plain,
1.97/2.16	    ![X0 : int]:
1.97/2.16	      (~ $true
1.97/2.16	       | app_encode_app(int, int, 
1.97/2.16	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.97/2.16	             app_encode_app(int, int, bit1, pls)), X0)
1.97/2.16	          = X0),
1.97/2.16	    inference('demod', [status(thm)], ['3', '6'])).
1.97/2.16	tff('8', plain,
1.97/2.16	    ![X0 : int]:
1.97/2.16	      app_encode_app(int, int, 
1.97/2.16	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.97/2.16	          app_encode_app(int, int, bit1, pls)), X0)
1.97/2.16	       = X0,
1.97/2.16	    inference('simplify', [status(thm)], ['7'])).
1.97/2.16	tff(zf_stmt_75, axiom,
1.97/2.16	  (![K:int]:
1.97/2.16	     (app_encode_app(int,int,bit0,K) =
1.97/2.16	      app_encode_app(int,int,
1.97/2.16	                     app_encode_app(int,app_encode_fun(int,int),
1.97/2.16	                                    plus_plus(int),K),
1.97/2.16	                     K)))).
1.97/2.16	tff('9', plain,
1.97/2.16	    ![X67 : int]:
1.97/2.16	      app_encode_app(int, int, bit0, X67)
1.97/2.16	       = app_encode_app(int, int, 
1.97/2.16	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X67), 
1.97/2.16	           X67),
1.97/2.16	    inference('cnf', [status(esa)], [zf_stmt_75])).
1.97/2.16	tff(zf_stmt_99, axiom,
1.97/2.16	  (![L:int,K:int]:
1.97/2.16	     (app_encode_app(int,int,
1.97/2.16	                     app_encode_app(int,app_encode_fun(int,int),
1.97/2.16	                                    times_times(int),
1.97/2.16	                                    app_encode_app(int,int,bit0,K)),
1.97/2.16	                     L) =
1.97/2.16	      app_encode_app(int,int,bit0,
1.97/2.16	                     app_encode_app(int,int,
1.97/2.16	                                    app_encode_app(int,
1.97/2.16	                                                   app_encode_fun(int,int),
1.97/2.16	                                                   times_times(int),K),
1.97/2.16	                                    L))))).
1.97/2.16	tff('10', plain,
1.97/2.16	    ![X113 : int, X114 : int]:
1.97/2.16	      app_encode_app(int, int, 
1.97/2.16	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.97/2.16	          app_encode_app(int, int, bit0, X113)), X114)
1.97/2.16	       = app_encode_app(int, int, bit0, 
1.97/2.16	           app_encode_app(int, int, 
1.97/2.16	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.97/2.16	               X113), X114)),
1.97/2.16	    inference('cnf', [status(esa)], [zf_stmt_99])).
1.97/2.16	tff('11', plain,
1.97/2.16	    ![X0 : int, X1 : int]:
1.97/2.16	      app_encode_app(int, int, 
1.97/2.16	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.97/2.16	          app_encode_app(int, int, 
1.97/2.16	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
1.97/2.16	            X0)), X1)
1.97/2.16	       = app_encode_app(int, int, bit0, 
1.97/2.16	           app_encode_app(int, int, 
1.97/2.16	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.97/2.16	               X0), X1)),
1.97/2.16	    inference('sup+', [status(thm)], ['9', '10'])).
1.97/2.16	tff('12', plain,
1.97/2.16	    ![X0 : int]:
1.97/2.16	      app_encode_app(int, int, 
1.97/2.16	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.97/2.16	          app_encode_app(int, int, 
1.97/2.16	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.97/2.16	              app_encode_app(int, int, bit1, pls)), 
1.97/2.16	            app_encode_app(int, int, bit1, pls))), X0)
1.97/2.16	       = app_encode_app(int, int, bit0, X0),
1.97/2.16	    inference('sup+', [status(thm)], ['8', '11'])).
1.97/2.16	tff('13', plain,
1.97/2.16	    ![X67 : int]:
1.97/2.16	      app_encode_app(int, int, 
1.97/2.16	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.97/2.16	          app_encode_app(int, int, 
1.97/2.16	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.97/2.16	              app_encode_app(int, int, bit1, pls)), 
1.97/2.16	            app_encode_app(int, int, bit1, pls))), X67)
1.97/2.16	       = app_encode_app(int, int, 
1.97/2.16	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X67), 
1.97/2.16	           X67),
1.97/2.16	    inference('demod', [status(thm)], ['9', '12'])).
1.97/2.16	tff(zf_stmt_142, axiom, (number(int))).
1.97/2.16	tff('14', plain, number(int), inference('cnf', [status(esa)], [zf_stmt_142])).
1.97/2.16	tff(zf_stmt_97, axiom,
1.97/2.16	  (![B1:$tType]:
1.97/2.16	     ((monoid_mult(B1) & number(B1)) =>
1.97/2.16	      (![W:int]:
1.97/2.16	         (app_encode_app(nat,B1,
1.97/2.16	                         app_encode_app(B1,app_encode_fun(nat,B1),
1.97/2.16	                                        power_power(B1),
1.97/2.16	                                        app_encode_app(int,B1,
1.97/2.16	                                                       number_number_of(B1),W)),
1.97/2.16	                         app_encode_app(int,nat,number_number_of(nat),
1.97/2.16	                                        app_encode_app(int,int,bit0,
1.97/2.16	                                                       app_encode_app(
1.97/2.16	                                                       int,int,bit1,pls)))) =
1.97/2.16	          app_encode_app(B1,B1,
1.97/2.16	                         app_encode_app(B1,app_encode_fun(B1,B1),
1.97/2.16	                                        times_times(B1),
1.97/2.16	                                        app_encode_app(int,B1,
1.97/2.16	                                                       number_number_of(B1),W)),
1.97/2.16	                         app_encode_app(int,B1,number_number_of(B1),W))))))).
1.97/2.16	tff('15', plain,
1.97/2.16	    ![X110 : $tType, X111 : int]:
1.97/2.16	      (app_encode_app(nat, X110, 
1.97/2.16	         app_encode_app(X110, app_encode_fun(nat, X110), power_power(X110), 
1.97/2.16	           app_encode_app(int, X110, number_number_of(X110), X111)), 
1.97/2.16	         app_encode_app(int, nat, number_number_of(nat), 
1.97/2.16	           app_encode_app(int, int, bit0, 
1.97/2.16	             app_encode_app(int, int, bit1, pls))))
1.97/2.16	        = app_encode_app(X110, X110, 
1.97/2.16	            app_encode_app(X110, app_encode_fun(X110, X110), 
1.97/2.16	              times_times(X110), 
1.97/2.16	              app_encode_app(int, X110, number_number_of(X110), X111)), 
1.97/2.16	            app_encode_app(int, X110, number_number_of(X110), X111))
1.97/2.16	       | ~ number(X110)
1.97/2.16	       | ~ monoid_mult(X110)),
1.97/2.16	    inference('cnf', [status(esa)], [zf_stmt_97])).
1.97/2.16	tff('16', plain,
1.97/2.16	    ![X110 : $tType, X111 : int]:
1.97/2.16	      (app_encode_app(nat, X110, 
1.97/2.16	         app_encode_app(X110, app_encode_fun(nat, X110), power_power(X110), 
1.97/2.16	           app_encode_app(int, X110, number_number_of(X110), X111)), 
1.97/2.16	         app_encode_app(int, nat, number_number_of(nat), 
1.97/2.16	           app_encode_app(int, int, 
1.97/2.16	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.97/2.16	               app_encode_app(int, int, bit1, pls)), 
1.97/2.16	             app_encode_app(int, int, bit1, pls))))
1.97/2.16	        = app_encode_app(X110, X110, 
1.97/2.16	            app_encode_app(X110, app_encode_fun(X110, X110), 
1.97/2.16	              times_times(X110), 
1.97/2.16	              app_encode_app(int, X110, number_number_of(X110), X111)), 
1.97/2.16	            app_encode_app(int, X110, number_number_of(X110), X111))
1.97/2.16	       | ~ number(X110)
1.97/2.16	       | ~ monoid_mult(X110)),
1.97/2.16	    inference('demod', [status(thm)], ['15', '12', '13'])).
1.97/2.16	tff('17', plain,
1.97/2.16	    ![X0 : int]:
1.97/2.16	      (~ $true
1.97/2.16	       | ~ monoid_mult(int)
1.97/2.16	       | app_encode_app(nat, int, 
1.97/2.16	           app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
1.97/2.16	             app_encode_app(int, int, number_number_of(int), X0)), 
1.97/2.16	           app_encode_app(int, nat, number_number_of(nat), 
1.97/2.16	             app_encode_app(int, int, 
1.97/2.16	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.97/2.16	                 app_encode_app(int, int, bit1, pls)), 
1.97/2.16	               app_encode_app(int, int, bit1, pls))))
1.97/2.16	          = app_encode_app(int, int, 
1.97/2.16	              app_encode_app(int, app_encode_fun(int, int), 
1.97/2.16	                times_times(int), 
1.97/2.16	                app_encode_app(int, int, number_number_of(int), X0)), 
1.97/2.16	              app_encode_app(int, int, number_number_of(int), X0))),
1.97/2.16	    inference('sup-', [status(thm)], ['14', '16'])).
1.97/2.16	tff(zf_stmt_136, axiom, (monoid_mult(int))).
1.97/2.16	tff('18', plain, monoid_mult(int),
1.97/2.16	    inference('cnf', [status(esa)], [zf_stmt_136])).
1.97/2.16	tff('19', plain,
1.97/2.16	    ![X0 : int]:
1.97/2.16	      (~ $true
1.97/2.16	       | ~ $true
1.97/2.16	       | app_encode_app(nat, int, 
1.97/2.16	           app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
1.97/2.16	             X0), 
1.97/2.16	           app_encode_app(int, nat, number_number_of(nat), 
1.97/2.16	             app_encode_app(int, int, 
1.97/2.16	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.97/2.16	                 app_encode_app(int, int, bit1, pls)), 
1.97/2.16	               app_encode_app(int, int, bit1, pls))))
1.97/2.16	          = app_encode_app(int, int, 
1.97/2.16	              app_encode_app(int, app_encode_fun(int, int), 
1.97/2.16	                times_times(int), X0), X0)),
1.97/2.16	    inference('demod', [status(thm)], ['17', '18', '5', '5', '5'])).
1.97/2.16	tff('20', plain,
1.97/2.16	    ![X0 : int]:
1.97/2.16	      app_encode_app(nat, int, 
1.97/2.16	        app_encode_app(int, app_encode_fun(nat, int), power_power(int), X0), 
1.97/2.16	        app_encode_app(int, nat, number_number_of(nat), 
1.97/2.16	          app_encode_app(int, int, 
1.97/2.16	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.97/2.16	              app_encode_app(int, int, bit1, pls)), 
1.97/2.16	            app_encode_app(int, int, bit1, pls))))
1.97/2.16	       = app_encode_app(int, int, 
1.97/2.16	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.97/2.16	             X0), X0),
1.97/2.16	    inference('simplify', [status(thm)], ['19'])).
1.97/2.16	tff(zf_stmt_73, axiom,
1.97/2.16	  (![K:int]:
1.97/2.16	     (app_encode_app(int,int,
1.97/2.16	                     app_encode_app(int,app_encode_fun(int,int),
1.97/2.16	                                    plus_plus(int),K),
1.97/2.16	                     pls) =
1.97/2.16	      K))).
1.97/2.16	tff('21', plain,
1.97/2.16	    ![X65 : int]:
1.97/2.16	      app_encode_app(int, int, 
1.97/2.16	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X65), 
1.97/2.16	        pls)
1.97/2.16	       = X65,
1.97/2.16	    inference('cnf', [status(esa)], [zf_stmt_73])).
1.97/2.16	tff(zf_stmt_139, axiom, (number_ring(int))).
1.97/2.16	tff('22', plain, number_ring(int),
1.97/2.16	    inference('cnf', [status(esa)], [zf_stmt_139])).
1.97/2.16	tff(zf_stmt_87, axiom,
1.97/2.16	  (![A:$tType]:
1.97/2.16	     (number_ring(A) =>
1.97/2.16	      (![C:A,W:int,V:int]:
1.97/2.16	         (app_encode_app(A,A,
1.97/2.16	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
1.97/2.16	                                        app_encode_app(int,A,
1.97/2.16	                                                       number_number_of(A),V)),
1.97/2.16	                         app_encode_app(A,A,
1.97/2.16	                                        app_encode_app(A,app_encode_fun(A,A),
1.97/2.16	                                                       minus_minus(A),
1.97/2.16	                                                       app_encode_app(
1.97/2.16	                                                       int,A,
1.97/2.16	                                                       number_number_of(A),W)),
1.97/2.16	                                        C)) =
1.97/2.16	          app_encode_app(A,A,
1.97/2.16	                         app_encode_app(A,app_encode_fun(A,A),minus_minus(A),
1.97/2.16	                                        app_encode_app(int,A,
1.97/2.16	                                                       number_number_of(A),
1.97/2.16	                                                       app_encode_app(
1.97/2.16	                                                       int,int,
1.97/2.16	                                                       app_encode_app(
1.97/2.16	                                                       int,
1.97/2.16	                                                       app_encode_fun(
1.97/2.16	                                                       int,int),
1.97/2.16	                                                       plus_plus(int),V),W))),
1.97/2.16	                         C)))))).
1.97/2.16	tff('23', plain,
1.97/2.16	    ![X86 : $tType, X87 : int, X88 : int, X89 : X86]:
1.97/2.16	      (app_encode_app(X86, X86, 
1.97/2.16	         app_encode_app(X86, app_encode_fun(X86, X86), plus_plus(X86), 
1.97/2.16	           app_encode_app(int, X86, number_number_of(X86), X87)), 
1.97/2.16	         app_encode_app(X86, X86, 
1.97/2.16	           app_encode_app(X86, app_encode_fun(X86, X86), minus_minus(X86), 
1.97/2.16	             app_encode_app(int, X86, number_number_of(X86), X88)), X89))
1.97/2.16	        = app_encode_app(X86, X86, 
1.97/2.16	            app_encode_app(X86, app_encode_fun(X86, X86), minus_minus(X86), 
1.97/2.16	              app_encode_app(int, X86, number_number_of(X86), 
1.97/2.16	                app_encode_app(int, int, 
1.97/2.16	                  app_encode_app(int, app_encode_fun(int, int), 
1.97/2.16	                    plus_plus(int), X87), X88))), X89)
1.97/2.16	       | ~ number_ring(X86)),
1.97/2.16	    inference('cnf', [status(esa)], [zf_stmt_87])).
1.97/2.16	tff('24', plain,
1.97/2.16	    ![X0 : int, X1 : int, X2 : int]:
1.97/2.16	      (~ $true
1.97/2.16	       | app_encode_app(int, int, 
1.97/2.16	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.97/2.16	             app_encode_app(int, int, number_number_of(int), X2)), 
1.97/2.16	           app_encode_app(int, int, 
1.97/2.16	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
1.97/2.16	               app_encode_app(int, int, number_number_of(int), X1)), X0))
1.97/2.16	          = app_encode_app(int, int, 
1.97/2.16	              app_encode_app(int, app_encode_fun(int, int), 
1.97/2.16	                minus_minus(int), 
1.97/2.16	                app_encode_app(int, int, number_number_of(int), 
1.97/2.16	                  app_encode_app(int, int, 
1.97/2.16	                    app_encode_app(int, app_encode_fun(int, int), 
1.97/2.16	                      plus_plus(int), X2), X1))), X0)),
1.97/2.16	    inference('sup-', [status(thm)], ['22', '23'])).
1.97/2.16	tff('25', plain,
1.97/2.16	    ![X0 : int, X1 : int, X2 : int]:
1.97/2.16	      (~ $true
1.97/2.16	       | app_encode_app(int, int, 
1.97/2.16	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X2), 
1.97/2.16	           app_encode_app(int, int, 
1.97/2.16	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
1.97/2.16	               X1), X0))
1.97/2.16	          = app_encode_app(int, int, 
1.97/2.16	              app_encode_app(int, app_encode_fun(int, int), 
1.97/2.16	                minus_minus(int), 
1.97/2.16	                app_encode_app(int, int, 
1.97/2.16	                  app_encode_app(int, app_encode_fun(int, int), 
1.97/2.16	                    plus_plus(int), X2), X1)), X0)),
1.97/2.16	    inference('demod', [status(thm)], ['24', '5', '5', '5'])).
1.97/2.16	tff('26', plain,
1.97/2.16	    ![X0 : int, X1 : int, X2 : int]:
1.97/2.16	      app_encode_app(int, int, 
1.97/2.16	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X2), 
1.97/2.16	        app_encode_app(int, int, 
1.97/2.16	          app_encode_app(int, app_encode_fun(int, int), minus_minus(int), X1), 
1.97/2.16	          X0))
1.97/2.16	       = app_encode_app(int, int, 
1.97/2.16	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
1.97/2.16	             app_encode_app(int, int, 
1.97/2.16	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.97/2.16	                 X2), X1)), X0),
1.97/2.16	    inference('simplify', [status(thm)], ['25'])).
1.97/2.16	tff('27', plain,
1.97/2.16	    ![X0 : int, X1 : int]:
1.97/2.16	      app_encode_app(int, int, 
1.97/2.16	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
1.97/2.16	        app_encode_app(int, int, 
1.97/2.16	          app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
1.97/2.16	            pls), X1))
1.97/2.16	       = app_encode_app(int, int, 
1.97/2.16	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
1.97/2.16	             X0), X1),
1.97/2.16	    inference('sup+', [status(thm)], ['21', '26'])).
1.97/2.16	tff('28', plain,
1.97/2.16	    app_encode_app(int, int, 
1.97/2.16	      app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.97/2.16	        app_encode_app(int, int, 
1.97/2.16	          app_encode_app(int, app_encode_fun(int, int), times_times(int), s), 
1.97/2.16	          s)), 
1.97/2.16	      app_encode_app(int, int, 
1.97/2.16	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), pls), 
1.97/2.16	        min))
1.97/2.16	     != app_encode_app(int, int, 
1.97/2.16	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.97/2.16	            app_encode_app(int, int, 
1.97/2.16	              app_encode_app(int, app_encode_fun(int, int), 
1.97/2.16	                times_times(int), s), s)), 
1.97/2.16	          app_encode_app(int, int, bit1, pls)),
1.97/2.16	    inference('demod', [status(thm)],
1.97/2.16	              ['0', '12', '13', '20', '5', '27', '12', '13', '20', '6'])).
1.97/2.16	tff(zf_stmt_60, axiom, (app_encode_app(int,int,bit1,min) = min)).
1.97/2.16	tff('29', plain, app_encode_app(int, int, bit1, min) = min,
1.97/2.16	    inference('cnf', [status(esa)], [zf_stmt_60])).
1.97/2.16	tff(zf_stmt_40, axiom,
1.97/2.16	  (![L:int]:
1.97/2.16	     (app_encode_app(int,int,
1.97/2.16	                     app_encode_app(int,app_encode_fun(int,int),
1.97/2.16	                                    minus_minus(int),pls),
1.97/2.16	                     app_encode_app(int,int,bit1,L)) =
1.97/2.16	      app_encode_app(int,int,bit1,
1.97/2.16	                     app_encode_app(int,int,
1.97/2.16	                                    app_encode_app(int,
1.97/2.16	                                                   app_encode_fun(int,int),
1.97/2.16	                                                   minus_minus(int),min),
1.97/2.16	                                    L))))).
1.97/2.16	tff('30', plain,
1.97/2.16	    ![X12 : int]:
1.97/2.16	      app_encode_app(int, int, 
1.97/2.16	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), pls), 
1.97/2.16	        app_encode_app(int, int, bit1, X12))
1.97/2.16	       = app_encode_app(int, int, bit1, 
1.97/2.16	           app_encode_app(int, int, 
1.97/2.16	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
1.97/2.16	               min), X12)),
1.97/2.16	    inference('cnf', [status(esa)], [zf_stmt_40])).
1.97/2.16	tff('31', plain,
1.97/2.16	    ![X12 : int]:
1.97/2.16	      app_encode_app(int, int, 
1.97/2.16	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), pls), 
1.97/2.16	        app_encode_app(int, int, bit1, X12))
1.97/2.16	       = app_encode_app(int, int, bit1, 
1.97/2.16	           app_encode_app(int, int, 
1.97/2.16	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.97/2.16	               min), 
1.97/2.16	             app_encode_app(int, int, 
1.97/2.16	               app_encode_app(int, app_encode_fun(int, int), 
1.97/2.16	                 minus_minus(int), pls), X12))),
1.97/2.16	    inference('demod', [status(thm)], ['30', '27'])).
1.97/2.16	tff('32', plain,
1.97/2.16	    app_encode_app(int, int, 
1.97/2.16	      app_encode_app(int, app_encode_fun(int, int), minus_minus(int), pls), 
1.97/2.16	      min)
1.97/2.16	     = app_encode_app(int, int, bit1, 
1.97/2.16	         app_encode_app(int, int, 
1.97/2.16	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), min), 
1.97/2.16	           app_encode_app(int, int, 
1.97/2.16	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
1.97/2.16	               pls), min))),
1.97/2.16	    inference('sup+', [status(thm)], ['29', '31'])).
1.97/2.16	tff(zf_stmt_119, axiom,
1.97/2.16	  (![W:int,Z2:int,Z1:int]:
1.97/2.16	     (app_encode_app(int,int,
1.97/2.16	                     app_encode_app(int,app_encode_fun(int,int),
1.97/2.16	                                    times_times(int),
1.97/2.16	                                    app_encode_app(int,int,
1.97/2.16	                                                   app_encode_app(int,
1.97/2.16	                                                                  app_encode_fun(
1.97/2.16	                                                                  int,int),
1.97/2.16	                                                                  plus_plus(
1.97/2.16	                                                                  int),Z1),
1.97/2.16	                                                   Z2)),
1.97/2.16	                     W) =
1.97/2.16	      app_encode_app(int,int,
1.97/2.16	                     app_encode_app(int,app_encode_fun(int,int),
1.97/2.16	                                    plus_plus(int),
1.97/2.16	                                    app_encode_app(int,int,
1.97/2.16	                                                   app_encode_app(int,
1.97/2.16	                                                                  app_encode_fun(
1.97/2.16	                                                                  int,int),
1.97/2.16	                                                                  times_times(
1.97/2.16	                                                                  int),Z1),
1.97/2.16	                                                   W)),
1.97/2.16	                     app_encode_app(int,int,
1.97/2.16	                                    app_encode_app(int,
1.97/2.16	                                                   app_encode_fun(int,int),
1.97/2.16	                                                   times_times(int),Z2),
1.97/2.16	                                    W))))).
1.97/2.16	tff('33', plain,
1.97/2.16	    ![X175 : int, X176 : int, X177 : int]:
1.97/2.16	      app_encode_app(int, int, 
1.97/2.16	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.97/2.16	          app_encode_app(int, int, 
1.97/2.16	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.97/2.16	              X175), X177)), X176)
1.97/2.16	       = app_encode_app(int, int, 
1.97/2.16	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.97/2.16	             app_encode_app(int, int, 
1.97/2.16	               app_encode_app(int, app_encode_fun(int, int), 
1.97/2.16	                 times_times(int), X175), X176)), 
1.97/2.16	           app_encode_app(int, int, 
1.97/2.16	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.97/2.16	               X177), X176)),
1.97/2.16	    inference('cnf', [status(esa)], [zf_stmt_119])).
1.97/2.16	tff(zf_stmt_118, axiom,
1.97/2.16	  (![Z2:int,Z1:int,W:int]:
1.97/2.16	     (app_encode_app(int,int,
1.97/2.16	                     app_encode_app(int,app_encode_fun(int,int),
1.97/2.16	                                    times_times(int),W),
1.97/2.16	                     app_encode_app(int,int,
1.97/2.16	                                    app_encode_app(int,
1.97/2.16	                                                   app_encode_fun(int,int),
1.97/2.16	                                                   plus_plus(int),Z1),
1.97/2.16	                                    Z2)) =
1.97/2.16	      app_encode_app(int,int,
1.97/2.16	                     app_encode_app(int,app_encode_fun(int,int),
1.97/2.16	                                    plus_plus(int),
1.97/2.16	                                    app_encode_app(int,int,
1.97/2.16	                                                   app_encode_app(int,
1.97/2.16	                                                                  app_encode_fun(
1.97/2.16	                                                                  int,int),
1.97/2.16	                                                                  times_times(
1.97/2.16	                                                                  int),W),
1.97/2.16	                                                   Z1)),
1.97/2.16	                     app_encode_app(int,int,
1.97/2.16	                                    app_encode_app(int,
1.97/2.16	                                                   app_encode_fun(int,int),
1.97/2.16	                                                   times_times(int),W),
1.97/2.16	                                    Z2))))).
1.97/2.16	tff('34', plain,
1.97/2.16	    ![X172 : int, X173 : int, X174 : int]:
1.97/2.16	      app_encode_app(int, int, 
1.97/2.16	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X172), 
1.97/2.16	        app_encode_app(int, int, 
1.97/2.16	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X173), 
1.97/2.16	          X174))
1.97/2.16	       = app_encode_app(int, int, 
1.97/2.16	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.97/2.16	             app_encode_app(int, int, 
1.97/2.16	               app_encode_app(int, app_encode_fun(int, int), 
1.97/2.16	                 times_times(int), X172), X173)), 
1.97/2.16	           app_encode_app(int, int, 
1.97/2.16	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.97/2.16	               X172), X174)),
1.97/2.16	    inference('cnf', [status(esa)], [zf_stmt_118])).
1.97/2.16	tff('35', plain,
1.97/2.16	    ![X0 : int, X1 : int]:
1.97/2.16	      app_encode_app(int, int, 
1.97/2.16	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X1), 
1.97/2.16	        app_encode_app(int, int, 
1.97/2.16	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
1.97/2.16	          X0))
1.97/2.16	       = app_encode_app(int, int, 
1.97/2.16	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.97/2.16	             app_encode_app(int, int, 
1.97/2.16	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.97/2.16	                 X1), X1)), X0),
1.97/2.16	    inference('sup+', [status(thm)], ['33', '34'])).
1.97/2.16	tff(zf_stmt_109, axiom,
1.97/2.16	  (![A:$tType]:
1.97/2.16	     (comm_monoid_mult(A) =>
1.97/2.16	      (![A1:A]:
1.97/2.16	         (app_encode_app(A,A,
1.97/2.16	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
1.97/2.16	                                        A1),
1.97/2.16	                         one_one(A)) =
1.97/2.16	          A1))))).
1.97/2.16	tff('36', plain,
1.97/2.16	    ![X147 : $tType, X148 : X147]:
1.97/2.16	      (app_encode_app(X147, X147, 
1.97/2.16	         app_encode_app(X147, app_encode_fun(X147, X147), times_times(X147), 
1.97/2.16	           X148), one_one(X147))
1.97/2.16	        = X148
1.97/2.16	       | ~ comm_monoid_mult(X147)),
1.97/2.16	    inference('cnf', [status(esa)], [zf_stmt_109])).
1.97/2.16	tff('37', plain,
1.97/2.16	    ![X0 : int]:
1.97/2.16	      (~ $true
1.97/2.16	       | app_encode_app(int, int, 
1.97/2.16	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.97/2.16	             X0), one_one(int))
1.97/2.16	          = X0),
1.97/2.16	    inference('sup-', [status(thm)], ['1', '36'])).
1.97/2.16	tff('38', plain,
1.97/2.16	    ![X0 : int]:
1.97/2.16	      (~ $true
1.97/2.16	       | app_encode_app(int, int, 
1.97/2.16	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.97/2.16	             X0), app_encode_app(int, int, bit1, pls))
1.97/2.16	          = X0),
1.97/2.16	    inference('demod', [status(thm)], ['37', '6'])).
1.97/2.16	tff('39', plain,
1.97/2.16	    ![X0 : int]:
1.97/2.16	      app_encode_app(int, int, 
1.97/2.16	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X0), 
1.97/2.16	        app_encode_app(int, int, bit1, pls))
1.97/2.16	       = X0,
1.97/2.16	    inference('simplify', [status(thm)], ['38'])).
1.97/2.16	tff('40', plain,
1.97/2.16	    ![X0 : int]:
1.97/2.16	      app_encode_app(int, int, 
1.97/2.16	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X0), 
1.97/2.16	        app_encode_app(int, int, 
1.97/2.16	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.97/2.16	            app_encode_app(int, int, bit1, pls)), 
1.97/2.16	          app_encode_app(int, int, bit1, pls)))
1.97/2.16	       = app_encode_app(int, int, 
1.97/2.16	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
1.97/2.16	           X0),
1.97/2.16	    inference('sup+', [status(thm)], ['35', '39'])).
1.97/2.16	tff(zf_stmt_120, axiom,
1.97/2.16	  (![Z2:int,Z1:int,W:int]:
1.97/2.16	     (app_encode_app(int,int,
1.97/2.16	                     app_encode_app(int,app_encode_fun(int,int),
1.97/2.16	                                    times_times(int),W),
1.97/2.16	                     app_encode_app(int,int,
1.97/2.16	                                    app_encode_app(int,
1.97/2.16	                                                   app_encode_fun(int,int),
1.97/2.16	                                                   minus_minus(int),Z1),
1.97/2.16	                                    Z2)) =
1.97/2.16	      app_encode_app(int,int,
1.97/2.16	                     app_encode_app(int,app_encode_fun(int,int),
1.97/2.16	                                    minus_minus(int),
1.97/2.16	                                    app_encode_app(int,int,
1.97/2.16	                                                   app_encode_app(int,
1.97/2.16	                                                                  app_encode_fun(
1.97/2.16	                                                                  int,int),
1.97/2.16	                                                                  times_times(
1.97/2.16	                                                                  int),W),
1.97/2.16	                                                   Z1)),
1.97/2.16	                     app_encode_app(int,int,
1.97/2.16	                                    app_encode_app(int,
1.97/2.16	                                                   app_encode_fun(int,int),
1.97/2.16	                                                   times_times(int),W),
1.97/2.16	                                    Z2))))).
1.97/2.16	tff('41', plain,
1.97/2.16	    ![X178 : int, X179 : int, X180 : int]:
1.97/2.16	      app_encode_app(int, int, 
1.97/2.16	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X178), 
1.97/2.16	        app_encode_app(int, int, 
1.97/2.16	          app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
1.97/2.16	            X179), X180))
1.97/2.16	       = app_encode_app(int, int, 
1.97/2.16	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
1.97/2.16	             app_encode_app(int, int, 
1.97/2.16	               app_encode_app(int, app_encode_fun(int, int), 
1.97/2.16	                 times_times(int), X178), X179)), 
1.97/2.16	           app_encode_app(int, int, 
1.97/2.16	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.97/2.16	               X178), X180)),
1.97/2.16	    inference('cnf', [status(esa)], [zf_stmt_120])).
1.97/2.16	tff('42', plain,
1.97/2.16	    ![X0 : int, X1 : int]:
1.97/2.16	      app_encode_app(int, int, 
1.97/2.16	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X0), 
1.97/2.16	        app_encode_app(int, int, 
1.97/2.16	          app_encode_app(int, app_encode_fun(int, int), minus_minus(int), X1), 
1.97/2.16	          app_encode_app(int, int, bit1, pls)))
1.97/2.16	       = app_encode_app(int, int, 
1.97/2.16	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
1.97/2.16	             app_encode_app(int, int, 
1.97/2.16	               app_encode_app(int, app_encode_fun(int, int), 
1.97/2.16	                 times_times(int), X0), X1)), X0),
1.97/2.16	    inference('sup+', [status(thm)], ['39', '41'])).
1.97/2.16	tff(zf_stmt_76, axiom,
1.97/2.16	  (![K:int]:
1.97/2.16	     (app_encode_app(int,int,
1.97/2.16	                     app_encode_app(int,app_encode_fun(int,int),
1.97/2.16	                                    minus_minus(int),K),
1.97/2.16	                     pls) =
1.97/2.16	      K))).
1.97/2.16	tff('43', plain,
1.97/2.16	    ![X68 : int]:
1.97/2.16	      app_encode_app(int, int, 
1.97/2.16	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), X68), 
1.97/2.16	        pls)
1.97/2.16	       = X68,
1.97/2.16	    inference('cnf', [status(esa)], [zf_stmt_76])).
1.97/2.16	tff('44', plain,
1.97/2.16	    app_encode_app(int, int, 
1.97/2.16	      app_encode_app(int, app_encode_fun(int, int), minus_minus(int), pls), 
1.97/2.16	      app_encode_app(int, int, bit1, pls))
1.97/2.16	     = app_encode_app(int, int, bit1, min),
1.97/2.16	    inference('sup+', [status(thm)], ['43', '30'])).
1.97/2.16	tff('45', plain,
1.97/2.16	    app_encode_app(int, int, 
1.97/2.16	      app_encode_app(int, app_encode_fun(int, int), minus_minus(int), pls), 
1.97/2.16	      app_encode_app(int, int, bit1, pls))
1.97/2.16	     = min,
1.97/2.16	    inference('demod', [status(thm)], ['44', '29'])).
1.97/2.16	tff('46', plain,
1.97/2.16	    ![X0 : int]:
1.97/2.16	      app_encode_app(int, int, 
1.97/2.16	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
1.97/2.16	        min)
1.97/2.16	       = app_encode_app(int, int, 
1.97/2.16	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
1.97/2.16	             X0), app_encode_app(int, int, bit1, pls)),
1.97/2.16	    inference('sup+', [status(thm)], ['45', '27'])).
1.97/2.16	tff('47', plain,
1.97/2.16	    ![X0 : int, X1 : int]:
1.97/2.16	      app_encode_app(int, int, 
1.97/2.16	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X0), 
1.97/2.16	        app_encode_app(int, int, 
1.97/2.16	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X1), 
1.97/2.16	          min))
1.97/2.16	       = app_encode_app(int, int, 
1.97/2.16	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
1.97/2.16	             app_encode_app(int, int, 
1.97/2.16	               app_encode_app(int, app_encode_fun(int, int), 
1.97/2.16	                 times_times(int), X0), X1)), X0),
1.97/2.16	    inference('demod', [status(thm)], ['42', '46'])).
1.97/2.16	tff('48', plain,
1.97/2.16	    ![X0 : int]:
1.97/2.16	      app_encode_app(int, int, 
1.97/2.16	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X0), 
1.97/2.16	        app_encode_app(int, int, 
1.97/2.16	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.97/2.16	            app_encode_app(int, int, 
1.97/2.16	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.97/2.16	                app_encode_app(int, int, bit1, pls)), 
1.97/2.16	              app_encode_app(int, int, bit1, pls))), min))
1.97/2.16	       = app_encode_app(int, int, 
1.97/2.16	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
1.97/2.16	             app_encode_app(int, int, 
1.97/2.16	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.97/2.16	                 X0), X0)), X0),
1.97/2.16	    inference('sup+', [status(thm)], ['40', '47'])).
1.97/2.16	tff(zf_stmt_65, axiom,
1.97/2.16	  (![A:$tType]:
1.97/2.16	     (number_ring(A) =>
1.97/2.16	      (![Z:A,W:int,V:int]:
1.97/2.16	         (app_encode_app(A,A,
1.97/2.16	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
1.97/2.16	                                        app_encode_app(int,A,
1.97/2.16	                                                       number_number_of(A),V)),
1.97/2.16	                         app_encode_app(A,A,
1.97/2.16	                                        app_encode_app(A,app_encode_fun(A,A),
1.97/2.16	                                                       plus_plus(A),
1.97/2.16	                                                       app_encode_app(
1.97/2.16	                                                       int,A,
1.97/2.16	                                                       number_number_of(A),W)),
1.97/2.16	                                        Z)) =
1.97/2.16	          app_encode_app(A,A,
1.97/2.16	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
1.97/2.16	                                        app_encode_app(int,A,
1.97/2.16	                                                       number_number_of(A),
1.97/2.16	                                                       app_encode_app(
1.97/2.16	                                                       int,int,
1.97/2.16	                                                       app_encode_app(
1.97/2.16	                                                       int,
1.97/2.16	                                                       app_encode_fun(
1.97/2.16	                                                       int,int),
1.97/2.16	                                                       plus_plus(int),V),W))),
1.97/2.16	                         Z)))))).
1.97/2.16	tff('49', plain,
1.97/2.16	    ![X51 : $tType, X52 : int, X53 : int, X54 : X51]:
1.97/2.16	      (app_encode_app(X51, X51, 
1.97/2.16	         app_encode_app(X51, app_encode_fun(X51, X51), plus_plus(X51), 
1.97/2.16	           app_encode_app(int, X51, number_number_of(X51), X52)), 
1.97/2.16	         app_encode_app(X51, X51, 
1.97/2.16	           app_encode_app(X51, app_encode_fun(X51, X51), plus_plus(X51), 
1.97/2.16	             app_encode_app(int, X51, number_number_of(X51), X53)), X54))
1.97/2.16	        = app_encode_app(X51, X51, 
1.97/2.16	            app_encode_app(X51, app_encode_fun(X51, X51), plus_plus(X51), 
1.97/2.16	              app_encode_app(int, X51, number_number_of(X51), 
1.97/2.16	                app_encode_app(int, int, 
1.97/2.16	                  app_encode_app(int, app_encode_fun(int, int), 
1.97/2.16	                    plus_plus(int), X52), X53))), X54)
1.97/2.16	       | ~ number_ring(X51)),
1.97/2.16	    inference('cnf', [status(esa)], [zf_stmt_65])).
1.97/2.16	tff('50', plain,
1.97/2.16	    ![X0 : int, X1 : int, X2 : int]:
1.97/2.16	      (~ $true
1.97/2.16	       | app_encode_app(int, int, 
1.97/2.16	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.97/2.16	             app_encode_app(int, int, number_number_of(int), X2)), 
1.97/2.16	           app_encode_app(int, int, 
1.97/2.16	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.97/2.16	               app_encode_app(int, int, number_number_of(int), X1)), X0))
1.97/2.16	          = app_encode_app(int, int, 
1.97/2.16	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.97/2.16	                app_encode_app(int, int, number_number_of(int), 
1.97/2.16	                  app_encode_app(int, int, 
1.97/2.16	                    app_encode_app(int, app_encode_fun(int, int), 
1.97/2.16	                      plus_plus(int), X2), X1))), X0)),
1.97/2.16	    inference('sup-', [status(thm)], ['22', '49'])).
1.97/2.16	tff('51', plain,
1.97/2.16	    ![X0 : int, X1 : int, X2 : int]:
1.97/2.16	      (~ $true
1.97/2.16	       | app_encode_app(int, int, 
1.97/2.16	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X2), 
1.97/2.16	           app_encode_app(int, int, 
1.97/2.16	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.97/2.16	               X1), X0))
1.97/2.16	          = app_encode_app(int, int, 
1.97/2.16	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.97/2.16	                app_encode_app(int, int, 
1.97/2.16	                  app_encode_app(int, app_encode_fun(int, int), 
1.97/2.16	                    plus_plus(int), X2), X1)), X0)),
1.97/2.16	    inference('demod', [status(thm)], ['50', '5', '5', '5'])).
1.97/2.16	tff('52', plain,
1.97/2.16	    ![X0 : int, X1 : int, X2 : int]:
1.97/2.16	      app_encode_app(int, int, 
1.97/2.16	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X2), 
1.97/2.16	        app_encode_app(int, int, 
1.97/2.16	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X1), 
1.97/2.16	          X0))
1.97/2.16	       = app_encode_app(int, int, 
1.97/2.16	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.97/2.16	             app_encode_app(int, int, 
1.97/2.16	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.97/2.16	                 X2), X1)), X0),
1.97/2.16	    inference('simplify', [status(thm)], ['51'])).
1.97/2.16	tff(zf_stmt_45, axiom,
1.97/2.16	  (![L:int,K:int]:
1.97/2.16	     (app_encode_app(int,int,
1.97/2.16	                     app_encode_app(int,app_encode_fun(int,int),
1.97/2.16	                                    plus_plus(int),
1.97/2.16	                                    app_encode_app(int,int,bit0,K)),
1.97/2.16	                     app_encode_app(int,int,bit1,L)) =
1.97/2.16	      app_encode_app(int,int,bit1,
1.97/2.16	                     app_encode_app(int,int,
1.97/2.16	                                    app_encode_app(int,
1.97/2.16	                                                   app_encode_fun(int,int),
1.97/2.16	                                                   plus_plus(int),K),
1.97/2.16	                                    L))))).
1.97/2.16	tff('53', plain,
1.97/2.16	    ![X19 : int, X20 : int]:
1.97/2.16	      app_encode_app(int, int, 
1.97/2.16	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.97/2.16	          app_encode_app(int, int, bit0, X19)), 
1.97/2.16	        app_encode_app(int, int, bit1, X20))
1.97/2.16	       = app_encode_app(int, int, bit1, 
1.97/2.16	           app_encode_app(int, int, 
1.97/2.16	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.97/2.16	               X19), X20)),
1.97/2.16	    inference('cnf', [status(esa)], [zf_stmt_45])).
1.97/2.16	tff('54', plain,
1.97/2.16	    ![X0 : int]:
1.97/2.16	      app_encode_app(int, int, 
1.97/2.16	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.97/2.16	          app_encode_app(int, int, bit0, X0)), min)
1.97/2.16	       = app_encode_app(int, int, bit1, 
1.97/2.16	           app_encode_app(int, int, 
1.97/2.16	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.97/2.16	               X0), min)),
1.97/2.16	    inference('sup+', [status(thm)], ['29', '53'])).
1.97/2.16	tff('55', plain,
1.97/2.16	    ![X0 : int]:
1.97/2.16	      app_encode_app(int, int, 
1.97/2.16	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.97/2.16	          app_encode_app(int, int, 
1.97/2.16	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
1.97/2.16	            X0)), min)
1.97/2.16	       = app_encode_app(int, int, bit1, 
1.97/2.16	           app_encode_app(int, int, 
1.97/2.16	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.97/2.16	               X0), min)),
1.97/2.16	    inference('sup+', [status(thm)], ['9', '54'])).
1.97/2.16	tff('56', plain,
1.97/2.16	    ![X0 : int]:
1.97/2.16	      app_encode_app(int, int, 
1.97/2.16	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
1.97/2.16	        app_encode_app(int, int, 
1.97/2.16	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
1.97/2.16	          min))
1.97/2.16	       = app_encode_app(int, int, bit1, 
1.97/2.16	           app_encode_app(int, int, 
1.97/2.16	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.97/2.16	               X0), min)),
1.97/2.16	    inference('demod', [status(thm)], ['55', '52'])).
1.97/2.16	tff(zf_stmt_125, axiom,
1.97/2.16	  (![N1:int,Ma:int]:
1.97/2.16	     ((app_encode_app(int,int,
1.97/2.16	                      app_encode_app(int,app_encode_fun(int,int),
1.97/2.16	                                     times_times(int),Ma),
1.97/2.16	                      N1) =
1.97/2.16	       one_one(int)) <=>
1.97/2.16	      (((Ma = one_one(int)) & (N1 = one_one(int))) | 
1.97/2.16	       ((Ma = app_encode_app(int,int,number_number_of(int),min)) & 
1.97/2.16	        (N1 = app_encode_app(int,int,number_number_of(int),min))))))).
1.97/2.16	tff('57', plain,
1.97/2.16	    ![X192 : int, X193 : int]:
1.97/2.16	      (app_encode_app(int, int, 
1.97/2.16	         app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.97/2.16	           X193), X192)
1.97/2.16	        = one_one(int)
1.97/2.16	       | X193 != app_encode_app(int, int, number_number_of(int), min)
1.97/2.16	       | X192 != app_encode_app(int, int, number_number_of(int), min)),
1.97/2.16	    inference('cnf', [status(esa)], [zf_stmt_125])).
1.97/2.16	tff('58', plain,
1.97/2.16	    app_encode_app(int, int, 
1.97/2.16	      app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.97/2.16	        app_encode_app(int, int, number_number_of(int), min)), 
1.97/2.16	      app_encode_app(int, int, number_number_of(int), min))
1.97/2.16	     = one_one(int),
1.97/2.16	    inference('simplify', [status(thm)], ['57'])).
1.97/2.16	tff('59', plain,
1.97/2.16	    app_encode_app(int, int, 
1.97/2.16	      app_encode_app(int, app_encode_fun(int, int), times_times(int), min), 
1.97/2.16	      min)
1.97/2.16	     = app_encode_app(int, int, bit1, pls),
1.97/2.16	    inference('demod', [status(thm)], ['58', '5', '5', '6'])).
1.97/2.16	tff(zf_stmt_106, axiom,
1.97/2.16	  (![L:int,K:int]:
1.97/2.16	     (app_encode_app(int,int,
1.97/2.16	                     app_encode_app(int,app_encode_fun(int,int),
1.97/2.16	                                    times_times(int),
1.97/2.16	                                    app_encode_app(int,int,bit1,K)),
1.97/2.16	                     L) =
1.97/2.16	      app_encode_app(int,int,
1.97/2.16	                     app_encode_app(int,app_encode_fun(int,int),
1.97/2.16	                                    plus_plus(int),
1.97/2.16	                                    app_encode_app(int,int,bit0,
1.97/2.16	                                                   app_encode_app(int,int,
1.97/2.16	                                                                  app_encode_app(
1.97/2.16	                                                                  int,
1.97/2.16	                                                                  app_encode_fun(
1.97/2.16	                                                                  int,int),
1.97/2.16	                                                                  times_times(
1.97/2.16	                                                                  int),K),L))),
1.97/2.16	                     L)))).
1.97/2.16	tff('60', plain,
1.97/2.16	    ![X138 : int, X139 : int]:
1.97/2.16	      app_encode_app(int, int, 
1.97/2.16	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.97/2.16	          app_encode_app(int, int, bit1, X138)), X139)
1.97/2.16	       = app_encode_app(int, int, 
1.97/2.16	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.97/2.16	             app_encode_app(int, int, bit0, 
1.97/2.16	               app_encode_app(int, int, 
1.97/2.16	                 app_encode_app(int, app_encode_fun(int, int), 
1.97/2.16	                   times_times(int), X138), X139))), X139),
1.97/2.16	    inference('cnf', [status(esa)], [zf_stmt_106])).
1.97/2.16	tff('61', plain,
1.97/2.16	    ![X138 : int, X139 : int]:
1.97/2.16	      app_encode_app(int, int, 
1.97/2.16	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.97/2.16	          app_encode_app(int, int, bit1, X138)), X139)
1.97/2.16	       = app_encode_app(int, int, 
1.97/2.16	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.97/2.16	             app_encode_app(int, int, 
1.97/2.16	               app_encode_app(int, app_encode_fun(int, int), 
1.97/2.16	                 times_times(int), 
1.97/2.16	                 app_encode_app(int, int, 
1.97/2.16	                   app_encode_app(int, app_encode_fun(int, int), 
1.97/2.16	                     plus_plus(int), app_encode_app(int, int, bit1, pls)), 
1.97/2.16	                   app_encode_app(int, int, bit1, pls))), 
1.97/2.16	               app_encode_app(int, int, 
1.97/2.16	                 app_encode_app(int, app_encode_fun(int, int), 
1.97/2.16	                   times_times(int), X138), X139))), X139),
1.97/2.16	    inference('demod', [status(thm)], ['60', '12'])).
1.97/2.16	tff('62', plain,
1.97/2.16	    app_encode_app(int, int, 
1.97/2.16	      app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.97/2.16	        app_encode_app(int, int, bit1, min)), min)
1.97/2.16	     = app_encode_app(int, int, 
1.97/2.16	         app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.97/2.16	           app_encode_app(int, int, 
1.97/2.16	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.97/2.16	               app_encode_app(int, int, 
1.97/2.16	                 app_encode_app(int, app_encode_fun(int, int), 
1.97/2.16	                   plus_plus(int), app_encode_app(int, int, bit1, pls)), 
1.97/2.16	                 app_encode_app(int, int, bit1, pls))), 
1.97/2.16	             app_encode_app(int, int, bit1, pls))), min),
1.97/2.16	    inference('sup+', [status(thm)], ['59', '61'])).
1.97/2.16	tff('63', plain,
1.97/2.16	    app_encode_app(int, int, 
1.97/2.16	      app_encode_app(int, app_encode_fun(int, int), times_times(int), min), 
1.97/2.16	      min)
1.97/2.16	     = app_encode_app(int, int, bit1, 
1.97/2.16	         app_encode_app(int, int, 
1.97/2.16	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.97/2.16	             app_encode_app(int, int, bit1, pls)), min)),
1.97/2.16	    inference('demod', [status(thm)], ['62', '29', '13', '52', '56'])).
1.97/2.16	tff('64', plain,
1.97/2.16	    app_encode_app(int, int, bit1, 
1.97/2.16	      app_encode_app(int, int, 
1.97/2.16	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.97/2.16	          app_encode_app(int, int, bit1, pls)), min))
1.97/2.16	     = app_encode_app(int, int, bit1, pls),
1.97/2.16	    inference('sup+', [status(thm)], ['63', '59'])).
1.97/2.16	tff('65', plain,
1.97/2.16	    ![X0 : int]:
1.97/2.16	      X0
1.97/2.16	       = app_encode_app(int, int, 
1.97/2.16	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
1.97/2.16	           app_encode_app(int, int, 
1.97/2.16	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
1.97/2.16	               X0), X0)),
1.97/2.16	    inference('demod', [status(thm)], ['48', '52', '56', '64', '39', '26'])).
1.97/2.16	tff(zf_stmt_94, axiom,
1.97/2.16	  (![A:$tType]:
1.97/2.16	     (cancel_semigroup_add(A) =>
1.97/2.16	      (![C1:A,B2:A,A2:A]:
1.97/2.16	         ((app_encode_app(A,A,
1.97/2.16	                          app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
1.97/2.16	                                         A2),
1.97/2.16	                          B2) =
1.97/2.16	           app_encode_app(A,A,
1.97/2.16	                          app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
1.97/2.16	                                         A2),
1.97/2.16	                          C1)) <=>
1.97/2.16	          (B2 = C1)))))).
1.97/2.16	tff('66', plain,
1.97/2.16	    ![X100 : $tType, X101 : X100, X102 : X100, X104 : X100]:
1.97/2.16	      (app_encode_app(X100, X100, 
1.97/2.16	         app_encode_app(X100, app_encode_fun(X100, X100), plus_plus(X100), 
1.97/2.16	           X104), X102)
1.97/2.16	        != app_encode_app(X100, X100, 
1.97/2.16	             app_encode_app(X100, app_encode_fun(X100, X100), 
1.97/2.16	               plus_plus(X100), X104), X101)
1.97/2.16	       | X102 = X101
1.97/2.16	       | ~ cancel_semigroup_add(X100)),
1.97/2.16	    inference('cnf', [status(esa)], [zf_stmt_94])).
1.97/2.16	tff('67', plain,
1.97/2.16	    ![X0 : int, X1 : int]:
1.97/2.16	      (X0
1.97/2.16	        != app_encode_app(int, int, 
1.97/2.16	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.97/2.16	               X0), X1)
1.97/2.16	       | ~ cancel_semigroup_add(int)
1.97/2.16	       | pls = X1),
1.97/2.16	    inference('sup-', [status(thm)], ['21', '66'])).
1.97/2.16	tff(zf_stmt_131, axiom, (cancel_semigroup_add(int))).
1.97/2.16	tff('68', plain, cancel_semigroup_add(int),
1.97/2.16	    inference('cnf', [status(esa)], [zf_stmt_131])).
1.97/2.16	tff('69', plain,
1.97/2.16	    ![X0 : int, X1 : int]:
1.97/2.16	      (X0
1.97/2.16	        != app_encode_app(int, int, 
1.97/2.16	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.97/2.16	               X0), X1)
1.97/2.16	       | ~ $true
1.97/2.16	       | pls = X1),
1.97/2.16	    inference('demod', [status(thm)], ['67', '68'])).
1.97/2.16	tff('70', plain,
1.97/2.16	    ![X0 : int, X1 : int]:
1.97/2.16	      (pls = X1
1.97/2.16	       | X0
1.97/2.16	          != app_encode_app(int, int, 
1.97/2.16	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.97/2.16	                 X0), X1)),
1.97/2.16	    inference('simplify', [status(thm)], ['69'])).
1.97/2.16	tff('71', plain,
1.97/2.16	    ![X0 : int]:
1.97/2.16	      (X0 != X0
1.97/2.16	       | pls
1.97/2.16	          = app_encode_app(int, int, 
1.97/2.16	              app_encode_app(int, app_encode_fun(int, int), 
1.97/2.16	                minus_minus(int), X0), X0)),
1.97/2.16	    inference('sup-', [status(thm)], ['65', '70'])).
1.97/2.16	tff('72', plain,
1.97/2.16	    ![X0 : int]:
1.97/2.16	      pls
1.97/2.16	       = app_encode_app(int, int, 
1.97/2.16	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
1.97/2.16	             X0), X0),
1.97/2.16	    inference('simplify', [status(thm)], ['71'])).
1.97/2.16	tff('73', plain,
1.97/2.16	    ![X0 : int]:
1.97/2.16	      app_encode_app(int, int, 
1.97/2.16	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
1.97/2.16	        app_encode_app(int, int, 
1.97/2.16	          app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
1.97/2.16	            pls), X0))
1.97/2.16	       = pls,
1.97/2.16	    inference('sup+', [status(thm)], ['72', '27'])).
1.97/2.16	tff('74', plain,
1.97/2.16	    app_encode_app(int, int, 
1.97/2.16	      app_encode_app(int, app_encode_fun(int, int), minus_minus(int), pls), 
1.97/2.16	      min)
1.97/2.16	     = app_encode_app(int, int, bit1, pls),
1.97/2.16	    inference('demod', [status(thm)], ['32', '73'])).
1.97/2.16	tff('75', plain,
1.97/2.16	    app_encode_app(int, int, 
1.97/2.16	      app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.97/2.16	        app_encode_app(int, int, 
1.97/2.16	          app_encode_app(int, app_encode_fun(int, int), times_times(int), s), 
1.97/2.16	          s)), app_encode_app(int, int, bit1, pls))
1.97/2.16	     != app_encode_app(int, int, 
1.97/2.16	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.97/2.16	            app_encode_app(int, int, 
1.97/2.16	              app_encode_app(int, app_encode_fun(int, int), 
1.97/2.16	                times_times(int), s), s)), 
1.97/2.16	          app_encode_app(int, int, bit1, pls)),
1.97/2.16	    inference('demod', [status(thm)], ['28', '74'])).
1.97/2.16	tff('76', plain, $false, inference('simplify', [status(thm)], ['75'])).
1.97/2.16	
1.97/2.16	% SZS output end Refutation
1.97/2.16	EOF
