0.00/0.00	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : app
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : rpo6
0.00/0.00	% Command    : 
0.00/0.01	#!/bin/sh
0.00/0.01	
0.00/0.01	./zipperposition.native ${1:+"$1"} \
0.00/0.01	  -i tptp \
0.00/0.01	  -o tptp \
0.00/0.01	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.01	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.01	  --no-ho \
0.00/0.01	  --no-avatar \
0.00/0.01	  --no-induction \
0.00/0.01	  --no-unif-pattern \
0.00/0.01	  --ord $2 \
0.00/0.01	  --simultaneous-sup false \
0.00/0.01	  --no-max-vars \
0.00/0.01	  --no-fool
0.00/0.20	% Computer   : n160.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 07:50:54 CST 2018
1.89/2.11	% done 1240 iterations in 1.902s
1.89/2.11	% SZS status Theorem for 'stdin'
1.89/2.11	% SZS output start Refutation
1.93/2.11	tff(zf_stmt_156, conjecture,
1.93/2.11	  (app_encode_app(int,int,
1.93/2.11	                  app_encode_app(int,app_encode_fun(int,int),
1.93/2.11	                                 minus_minus(int),
1.93/2.11	                                 app_encode_app(nat,int,
1.93/2.11	                                                app_encode_app(int,
1.93/2.11	                                                               app_encode_fun(
1.93/2.11	                                                               nat,int),
1.93/2.11	                                                               power_power(
1.93/2.11	                                                               int),s),
1.93/2.11	                                                app_encode_app(int,nat,
1.93/2.11	                                                               number_number_of(
1.93/2.11	                                                               nat),
1.93/2.11	                                                               app_encode_app(
1.93/2.11	                                                               int,int,bit0,
1.93/2.11	                                                               app_encode_app(
1.93/2.11	                                                               int,int,bit1,
1.93/2.11	                                                               pls))))),
1.93/2.11	                  app_encode_app(int,int,number_number_of(int),min)) =
1.93/2.11	   app_encode_app(int,int,
1.93/2.11	                  app_encode_app(int,app_encode_fun(int,int),plus_plus(int),
1.93/2.11	                                 app_encode_app(nat,int,
1.93/2.11	                                                app_encode_app(int,
1.93/2.11	                                                               app_encode_fun(
1.93/2.11	                                                               nat,int),
1.93/2.11	                                                               power_power(
1.93/2.11	                                                               int),s),
1.93/2.11	                                                app_encode_app(int,nat,
1.93/2.11	                                                               number_number_of(
1.93/2.11	                                                               nat),
1.93/2.11	                                                               app_encode_app(
1.93/2.11	                                                               int,int,bit0,
1.93/2.11	                                                               app_encode_app(
1.93/2.11	                                                               int,int,bit1,
1.93/2.11	                                                               pls))))),
1.93/2.11	                  one_one(int)))).
1.93/2.11	tff(zf_stmt_0, negated_conjecture,
1.93/2.11	  (app_encode_app(int,int,
1.93/2.11	                  app_encode_app(int,app_encode_fun(int,int),
1.93/2.11	                                 minus_minus(int),
1.93/2.11	                                 app_encode_app(nat,int,
1.93/2.11	                                                app_encode_app(int,
1.93/2.11	                                                               app_encode_fun(
1.93/2.11	                                                               nat,int),
1.93/2.11	                                                               power_power(
1.93/2.11	                                                               int),s),
1.93/2.11	                                                app_encode_app(int,nat,
1.93/2.11	                                                               number_number_of(
1.93/2.11	                                                               nat),
1.93/2.11	                                                               app_encode_app(
1.93/2.11	                                                               int,int,bit0,
1.93/2.11	                                                               app_encode_app(
1.93/2.11	                                                               int,int,bit1,
1.93/2.11	                                                               pls))))),
1.93/2.11	                  app_encode_app(int,int,number_number_of(int),min)) !=
1.93/2.11	   app_encode_app(int,int,
1.93/2.11	                  app_encode_app(int,app_encode_fun(int,int),plus_plus(int),
1.93/2.11	                                 app_encode_app(nat,int,
1.93/2.11	                                                app_encode_app(int,
1.93/2.11	                                                               app_encode_fun(
1.93/2.11	                                                               nat,int),
1.93/2.11	                                                               power_power(
1.93/2.11	                                                               int),s),
1.93/2.11	                                                app_encode_app(int,nat,
1.93/2.11	                                                               number_number_of(
1.93/2.11	                                                               nat),
1.93/2.11	                                                               app_encode_app(
1.93/2.11	                                                               int,int,bit0,
1.93/2.11	                                                               app_encode_app(
1.93/2.11	                                                               int,int,bit1,
1.93/2.11	                                                               pls))))),
1.93/2.11	                  one_one(int)))).
1.93/2.11	tff('0', plain,
1.93/2.11	    app_encode_app(int, int, 
1.93/2.11	      app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
1.93/2.11	        app_encode_app(nat, int, 
1.93/2.11	          app_encode_app(int, app_encode_fun(nat, int), power_power(int), s), 
1.93/2.11	          app_encode_app(int, nat, number_number_of(nat), 
1.93/2.11	            app_encode_app(int, int, bit0, 
1.93/2.11	              app_encode_app(int, int, bit1, pls))))), 
1.93/2.11	      app_encode_app(int, int, number_number_of(int), min))
1.93/2.11	     != app_encode_app(int, int, 
1.93/2.11	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.93/2.11	            app_encode_app(nat, int, 
1.93/2.11	              app_encode_app(int, app_encode_fun(nat, int), 
1.93/2.11	                power_power(int), s), 
1.93/2.11	              app_encode_app(int, nat, number_number_of(nat), 
1.93/2.11	                app_encode_app(int, int, bit0, 
1.93/2.11	                  app_encode_app(int, int, bit1, pls))))), one_one(int)),
1.93/2.11	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.93/2.11	tff(zf_stmt_132, axiom, (comm_monoid_mult(int))).
1.93/2.11	tff('1', plain, comm_monoid_mult(int),
1.93/2.11	    inference('cnf', [status(esa)], [zf_stmt_132])).
1.93/2.11	tff(zf_stmt_110, axiom,
1.93/2.11	  (![A:$tType]:
1.93/2.11	     (comm_monoid_mult(A) =>
1.93/2.11	      (![A1:A]:
1.93/2.11	         (app_encode_app(A,A,
1.93/2.11	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
1.93/2.11	                                        one_one(A)),
1.93/2.11	                         A1) =
1.93/2.11	          A1))))).
1.93/2.11	tff('2', plain,
1.93/2.11	    ![X147 : $tType, X148 : X147]:
1.93/2.11	      (app_encode_app(X147, X147, 
1.93/2.11	         app_encode_app(X147, app_encode_fun(X147, X147), times_times(X147), 
1.93/2.11	           one_one(X147)), X148)
1.93/2.11	        = X148
1.93/2.11	       | ~ comm_monoid_mult(X147)),
1.93/2.11	    inference('cnf', [status(esa)], [zf_stmt_110])).
1.93/2.11	tff('3', plain,
1.93/2.11	    ![X0 : int]:
1.93/2.11	      (~ $true
1.93/2.11	       | app_encode_app(int, int, 
1.93/2.11	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.93/2.11	             one_one(int)), X0)
1.93/2.11	          = X0),
1.93/2.11	    inference('sup-', [status(thm)], ['1', '2'])).
1.93/2.11	tff(zf_stmt_87, axiom,
1.93/2.11	  (one_one(int) =
1.93/2.11	   app_encode_app(int,int,number_number_of(int),
1.93/2.11	                  app_encode_app(int,int,bit1,pls)))).
1.93/2.11	tff('4', plain,
1.93/2.11	    one_one(int)
1.93/2.11	     = app_encode_app(int, int, number_number_of(int), 
1.93/2.11	         app_encode_app(int, int, bit1, pls)),
1.93/2.11	    inference('cnf', [status(esa)], [zf_stmt_87])).
1.93/2.11	tff(zf_stmt_71, axiom,
1.93/2.11	  (![K:int]: (app_encode_app(int,int,number_number_of(int),K) = K))).
1.93/2.11	tff('5', plain,
1.93/2.11	    ![X60 : int]: app_encode_app(int, int, number_number_of(int), X60) = X60,
1.93/2.11	    inference('cnf', [status(esa)], [zf_stmt_71])).
1.93/2.11	tff('6', plain, one_one(int) = app_encode_app(int, int, bit1, pls),
1.93/2.11	    inference('demod', [status(thm)], ['4', '5'])).
1.93/2.11	tff('7', plain,
1.93/2.11	    ![X0 : int]:
1.93/2.11	      (~ $true
1.93/2.11	       | app_encode_app(int, int, 
1.93/2.11	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.93/2.11	             app_encode_app(int, int, bit1, pls)), X0)
1.93/2.11	          = X0),
1.93/2.11	    inference('demod', [status(thm)], ['3', '6'])).
1.93/2.11	tff('8', plain,
1.93/2.11	    ![X0 : int]:
1.93/2.11	      app_encode_app(int, int, 
1.93/2.11	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.93/2.11	          app_encode_app(int, int, bit1, pls)), X0)
1.93/2.11	       = X0,
1.93/2.11	    inference('simplify', [status(thm)], ['7'])).
1.93/2.11	tff(zf_stmt_74, axiom,
1.93/2.11	  (![K:int]:
1.93/2.11	     (app_encode_app(int,int,bit0,K) =
1.93/2.11	      app_encode_app(int,int,
1.93/2.11	                     app_encode_app(int,app_encode_fun(int,int),
1.93/2.11	                                    plus_plus(int),K),
1.93/2.11	                     K)))).
1.93/2.11	tff('9', plain,
1.93/2.11	    ![X63 : int]:
1.93/2.11	      app_encode_app(int, int, bit0, X63)
1.93/2.11	       = app_encode_app(int, int, 
1.93/2.11	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X63), 
1.93/2.11	           X63),
1.93/2.11	    inference('cnf', [status(esa)], [zf_stmt_74])).
1.93/2.11	tff(zf_stmt_98, axiom,
1.93/2.11	  (![L:int,K:int]:
1.93/2.11	     (app_encode_app(int,int,
1.93/2.11	                     app_encode_app(int,app_encode_fun(int,int),
1.93/2.11	                                    times_times(int),
1.93/2.11	                                    app_encode_app(int,int,bit0,K)),
1.93/2.11	                     L) =
1.93/2.11	      app_encode_app(int,int,bit0,
1.93/2.11	                     app_encode_app(int,int,
1.93/2.11	                                    app_encode_app(int,
1.93/2.11	                                                   app_encode_fun(int,int),
1.93/2.11	                                                   times_times(int),K),
1.93/2.11	                                    L))))).
1.93/2.11	tff('10', plain,
1.93/2.11	    ![X109 : int, X110 : int]:
1.93/2.11	      app_encode_app(int, int, 
1.93/2.11	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.93/2.11	          app_encode_app(int, int, bit0, X109)), X110)
1.93/2.11	       = app_encode_app(int, int, bit0, 
1.93/2.11	           app_encode_app(int, int, 
1.93/2.11	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.93/2.11	               X109), X110)),
1.93/2.11	    inference('cnf', [status(esa)], [zf_stmt_98])).
1.93/2.11	tff('11', plain,
1.93/2.11	    ![X0 : int, X1 : int]:
1.93/2.11	      app_encode_app(int, int, 
1.93/2.11	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.93/2.11	          app_encode_app(int, int, 
1.93/2.11	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
1.93/2.11	            X0)), X1)
1.93/2.11	       = app_encode_app(int, int, bit0, 
1.93/2.11	           app_encode_app(int, int, 
1.93/2.11	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.93/2.11	               X0), X1)),
1.93/2.11	    inference('sup+', [status(thm)], ['9', '10'])).
1.93/2.11	tff('12', plain,
1.93/2.11	    ![X0 : int]:
1.93/2.11	      app_encode_app(int, int, 
1.93/2.11	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.93/2.11	          app_encode_app(int, int, 
1.93/2.11	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.93/2.11	              app_encode_app(int, int, bit1, pls)), 
1.93/2.11	            app_encode_app(int, int, bit1, pls))), X0)
1.93/2.11	       = app_encode_app(int, int, bit0, X0),
1.93/2.11	    inference('sup+', [status(thm)], ['8', '11'])).
1.93/2.11	tff('13', plain,
1.93/2.11	    ![X63 : int]:
1.93/2.11	      app_encode_app(int, int, 
1.93/2.11	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.93/2.11	          app_encode_app(int, int, 
1.93/2.11	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.93/2.11	              app_encode_app(int, int, bit1, pls)), 
1.93/2.11	            app_encode_app(int, int, bit1, pls))), X63)
1.93/2.11	       = app_encode_app(int, int, 
1.93/2.11	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X63), 
1.93/2.11	           X63),
1.93/2.11	    inference('demod', [status(thm)], ['9', '12'])).
1.93/2.11	tff(zf_stmt_141, axiom, (number(int))).
1.93/2.11	tff('14', plain, number(int), inference('cnf', [status(esa)], [zf_stmt_141])).
1.93/2.11	tff(zf_stmt_96, axiom,
1.93/2.11	  (![B1:$tType]:
1.93/2.11	     ((monoid_mult(B1) & number(B1)) =>
1.93/2.11	      (![W:int]:
1.93/2.11	         (app_encode_app(nat,B1,
1.93/2.11	                         app_encode_app(B1,app_encode_fun(nat,B1),
1.93/2.11	                                        power_power(B1),
1.93/2.11	                                        app_encode_app(int,B1,
1.93/2.11	                                                       number_number_of(B1),W)),
1.93/2.11	                         app_encode_app(int,nat,number_number_of(nat),
1.93/2.11	                                        app_encode_app(int,int,bit0,
1.93/2.11	                                                       app_encode_app(
1.93/2.11	                                                       int,int,bit1,pls)))) =
1.93/2.11	          app_encode_app(B1,B1,
1.93/2.11	                         app_encode_app(B1,app_encode_fun(B1,B1),
1.93/2.11	                                        times_times(B1),
1.93/2.11	                                        app_encode_app(int,B1,
1.93/2.11	                                                       number_number_of(B1),W)),
1.93/2.11	                         app_encode_app(int,B1,number_number_of(B1),W))))))).
1.93/2.11	tff('15', plain,
1.93/2.11	    ![X106 : $tType, X107 : int]:
1.93/2.11	      (app_encode_app(nat, X106, 
1.93/2.11	         app_encode_app(X106, app_encode_fun(nat, X106), power_power(X106), 
1.93/2.11	           app_encode_app(int, X106, number_number_of(X106), X107)), 
1.93/2.11	         app_encode_app(int, nat, number_number_of(nat), 
1.93/2.11	           app_encode_app(int, int, bit0, 
1.93/2.11	             app_encode_app(int, int, bit1, pls))))
1.93/2.11	        = app_encode_app(X106, X106, 
1.93/2.11	            app_encode_app(X106, app_encode_fun(X106, X106), 
1.93/2.11	              times_times(X106), 
1.93/2.11	              app_encode_app(int, X106, number_number_of(X106), X107)), 
1.93/2.11	            app_encode_app(int, X106, number_number_of(X106), X107))
1.93/2.11	       | ~ number(X106)
1.93/2.11	       | ~ monoid_mult(X106)),
1.93/2.11	    inference('cnf', [status(esa)], [zf_stmt_96])).
1.93/2.11	tff('16', plain,
1.93/2.11	    ![X106 : $tType, X107 : int]:
1.93/2.11	      (app_encode_app(nat, X106, 
1.93/2.11	         app_encode_app(X106, app_encode_fun(nat, X106), power_power(X106), 
1.93/2.11	           app_encode_app(int, X106, number_number_of(X106), X107)), 
1.93/2.11	         app_encode_app(int, nat, number_number_of(nat), 
1.93/2.11	           app_encode_app(int, int, 
1.93/2.11	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.93/2.11	               app_encode_app(int, int, bit1, pls)), 
1.93/2.11	             app_encode_app(int, int, bit1, pls))))
1.93/2.11	        = app_encode_app(X106, X106, 
1.93/2.11	            app_encode_app(X106, app_encode_fun(X106, X106), 
1.93/2.11	              times_times(X106), 
1.93/2.11	              app_encode_app(int, X106, number_number_of(X106), X107)), 
1.93/2.11	            app_encode_app(int, X106, number_number_of(X106), X107))
1.93/2.11	       | ~ number(X106)
1.93/2.11	       | ~ monoid_mult(X106)),
1.93/2.11	    inference('demod', [status(thm)], ['15', '12', '13'])).
1.93/2.11	tff('17', plain,
1.93/2.11	    ![X0 : int]:
1.93/2.11	      (~ $true
1.93/2.11	       | ~ monoid_mult(int)
1.93/2.11	       | app_encode_app(nat, int, 
1.93/2.11	           app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
1.93/2.11	             app_encode_app(int, int, number_number_of(int), X0)), 
1.93/2.11	           app_encode_app(int, nat, number_number_of(nat), 
1.93/2.11	             app_encode_app(int, int, 
1.93/2.11	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.93/2.11	                 app_encode_app(int, int, bit1, pls)), 
1.93/2.11	               app_encode_app(int, int, bit1, pls))))
1.93/2.11	          = app_encode_app(int, int, 
1.93/2.11	              app_encode_app(int, app_encode_fun(int, int), 
1.93/2.11	                times_times(int), 
1.93/2.11	                app_encode_app(int, int, number_number_of(int), X0)), 
1.93/2.11	              app_encode_app(int, int, number_number_of(int), X0))),
1.93/2.11	    inference('sup-', [status(thm)], ['14', '16'])).
1.93/2.11	tff(zf_stmt_135, axiom, (monoid_mult(int))).
1.93/2.11	tff('18', plain, monoid_mult(int),
1.93/2.11	    inference('cnf', [status(esa)], [zf_stmt_135])).
1.93/2.11	tff('19', plain,
1.93/2.11	    ![X0 : int]:
1.93/2.11	      (~ $true
1.93/2.11	       | ~ $true
1.93/2.11	       | app_encode_app(nat, int, 
1.93/2.11	           app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
1.93/2.11	             X0), 
1.93/2.11	           app_encode_app(int, nat, number_number_of(nat), 
1.93/2.11	             app_encode_app(int, int, 
1.93/2.11	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.93/2.11	                 app_encode_app(int, int, bit1, pls)), 
1.93/2.11	               app_encode_app(int, int, bit1, pls))))
1.93/2.11	          = app_encode_app(int, int, 
1.93/2.11	              app_encode_app(int, app_encode_fun(int, int), 
1.93/2.11	                times_times(int), X0), X0)),
1.93/2.11	    inference('demod', [status(thm)], ['17', '18', '5', '5', '5'])).
1.93/2.11	tff('20', plain,
1.93/2.11	    ![X0 : int]:
1.93/2.11	      app_encode_app(nat, int, 
1.93/2.11	        app_encode_app(int, app_encode_fun(nat, int), power_power(int), X0), 
1.93/2.11	        app_encode_app(int, nat, number_number_of(nat), 
1.93/2.11	          app_encode_app(int, int, 
1.93/2.11	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.93/2.11	              app_encode_app(int, int, bit1, pls)), 
1.93/2.11	            app_encode_app(int, int, bit1, pls))))
1.93/2.11	       = app_encode_app(int, int, 
1.93/2.11	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.93/2.11	             X0), X0),
1.93/2.11	    inference('simplify', [status(thm)], ['19'])).
1.93/2.11	tff(zf_stmt_72, axiom,
1.93/2.11	  (![K:int]:
1.93/2.11	     (app_encode_app(int,int,
1.93/2.11	                     app_encode_app(int,app_encode_fun(int,int),
1.93/2.11	                                    plus_plus(int),K),
1.93/2.11	                     pls) =
1.93/2.11	      K))).
1.93/2.11	tff('21', plain,
1.93/2.11	    ![X61 : int]:
1.93/2.11	      app_encode_app(int, int, 
1.93/2.11	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X61), 
1.93/2.11	        pls)
1.93/2.11	       = X61,
1.93/2.11	    inference('cnf', [status(esa)], [zf_stmt_72])).
1.93/2.11	tff(zf_stmt_138, axiom, (number_ring(int))).
1.93/2.11	tff('22', plain, number_ring(int),
1.93/2.11	    inference('cnf', [status(esa)], [zf_stmt_138])).
1.93/2.11	tff(zf_stmt_86, axiom,
1.93/2.11	  (![A:$tType]:
1.93/2.11	     (number_ring(A) =>
1.93/2.11	      (![C:A,W:int,V:int]:
1.93/2.11	         (app_encode_app(A,A,
1.93/2.11	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
1.93/2.11	                                        app_encode_app(int,A,
1.93/2.11	                                                       number_number_of(A),V)),
1.93/2.11	                         app_encode_app(A,A,
1.93/2.11	                                        app_encode_app(A,app_encode_fun(A,A),
1.93/2.11	                                                       minus_minus(A),
1.93/2.11	                                                       app_encode_app(
1.93/2.11	                                                       int,A,
1.93/2.11	                                                       number_number_of(A),W)),
1.93/2.11	                                        C)) =
1.93/2.11	          app_encode_app(A,A,
1.93/2.11	                         app_encode_app(A,app_encode_fun(A,A),minus_minus(A),
1.93/2.11	                                        app_encode_app(int,A,
1.93/2.11	                                                       number_number_of(A),
1.93/2.11	                                                       app_encode_app(
1.93/2.11	                                                       int,int,
1.93/2.11	                                                       app_encode_app(
1.93/2.11	                                                       int,
1.93/2.11	                                                       app_encode_fun(
1.93/2.11	                                                       int,int),
1.93/2.11	                                                       plus_plus(int),V),W))),
1.93/2.11	                         C)))))).
1.93/2.11	tff('23', plain,
1.93/2.11	    ![X82 : $tType, X83 : int, X84 : int, X85 : X82]:
1.93/2.11	      (app_encode_app(X82, X82, 
1.93/2.11	         app_encode_app(X82, app_encode_fun(X82, X82), plus_plus(X82), 
1.93/2.11	           app_encode_app(int, X82, number_number_of(X82), X83)), 
1.93/2.11	         app_encode_app(X82, X82, 
1.93/2.11	           app_encode_app(X82, app_encode_fun(X82, X82), minus_minus(X82), 
1.93/2.11	             app_encode_app(int, X82, number_number_of(X82), X84)), X85))
1.93/2.11	        = app_encode_app(X82, X82, 
1.93/2.11	            app_encode_app(X82, app_encode_fun(X82, X82), minus_minus(X82), 
1.93/2.11	              app_encode_app(int, X82, number_number_of(X82), 
1.93/2.11	                app_encode_app(int, int, 
1.93/2.11	                  app_encode_app(int, app_encode_fun(int, int), 
1.93/2.11	                    plus_plus(int), X83), X84))), X85)
1.93/2.11	       | ~ number_ring(X82)),
1.93/2.11	    inference('cnf', [status(esa)], [zf_stmt_86])).
1.93/2.11	tff('24', plain,
1.93/2.11	    ![X0 : int, X1 : int, X2 : int]:
1.93/2.11	      (~ $true
1.93/2.11	       | app_encode_app(int, int, 
1.93/2.11	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.93/2.11	             app_encode_app(int, int, number_number_of(int), X2)), 
1.93/2.11	           app_encode_app(int, int, 
1.93/2.11	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
1.93/2.11	               app_encode_app(int, int, number_number_of(int), X1)), X0))
1.93/2.11	          = app_encode_app(int, int, 
1.93/2.11	              app_encode_app(int, app_encode_fun(int, int), 
1.93/2.11	                minus_minus(int), 
1.93/2.11	                app_encode_app(int, int, number_number_of(int), 
1.93/2.11	                  app_encode_app(int, int, 
1.93/2.11	                    app_encode_app(int, app_encode_fun(int, int), 
1.93/2.11	                      plus_plus(int), X2), X1))), X0)),
1.93/2.11	    inference('sup-', [status(thm)], ['22', '23'])).
1.93/2.11	tff('25', plain,
1.93/2.11	    ![X0 : int, X1 : int, X2 : int]:
1.93/2.11	      (~ $true
1.93/2.11	       | app_encode_app(int, int, 
1.93/2.11	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X2), 
1.93/2.11	           app_encode_app(int, int, 
1.93/2.11	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
1.93/2.11	               X1), X0))
1.93/2.11	          = app_encode_app(int, int, 
1.93/2.11	              app_encode_app(int, app_encode_fun(int, int), 
1.93/2.11	                minus_minus(int), 
1.93/2.11	                app_encode_app(int, int, 
1.93/2.11	                  app_encode_app(int, app_encode_fun(int, int), 
1.93/2.11	                    plus_plus(int), X2), X1)), X0)),
1.93/2.11	    inference('demod', [status(thm)], ['24', '5', '5', '5'])).
1.93/2.11	tff('26', plain,
1.93/2.11	    ![X0 : int, X1 : int, X2 : int]:
1.93/2.11	      app_encode_app(int, int, 
1.93/2.11	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X2), 
1.93/2.11	        app_encode_app(int, int, 
1.93/2.11	          app_encode_app(int, app_encode_fun(int, int), minus_minus(int), X1), 
1.93/2.11	          X0))
1.93/2.11	       = app_encode_app(int, int, 
1.93/2.11	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
1.93/2.11	             app_encode_app(int, int, 
1.93/2.11	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.93/2.11	                 X2), X1)), X0),
1.93/2.11	    inference('simplify', [status(thm)], ['25'])).
1.93/2.11	tff('27', plain,
1.93/2.11	    ![X0 : int, X1 : int]:
1.93/2.11	      app_encode_app(int, int, 
1.93/2.11	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
1.93/2.11	        app_encode_app(int, int, 
1.93/2.11	          app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
1.93/2.11	            pls), X1))
1.93/2.11	       = app_encode_app(int, int, 
1.93/2.11	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
1.93/2.11	             X0), X1),
1.93/2.11	    inference('sup+', [status(thm)], ['21', '26'])).
1.93/2.11	tff('28', plain,
1.93/2.11	    app_encode_app(int, int, 
1.93/2.11	      app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.93/2.11	        app_encode_app(int, int, 
1.93/2.11	          app_encode_app(int, app_encode_fun(int, int), times_times(int), s), 
1.93/2.11	          s)), 
1.93/2.11	      app_encode_app(int, int, 
1.93/2.11	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), pls), 
1.93/2.11	        min))
1.93/2.11	     != app_encode_app(int, int, 
1.93/2.11	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.93/2.11	            app_encode_app(int, int, 
1.93/2.11	              app_encode_app(int, app_encode_fun(int, int), 
1.93/2.11	                times_times(int), s), s)), 
1.93/2.11	          app_encode_app(int, int, bit1, pls)),
1.93/2.11	    inference('demod', [status(thm)],
1.93/2.11	              ['0', '12', '13', '20', '5', '27', '12', '13', '20', '6'])).
1.93/2.11	tff(zf_stmt_59, axiom, (app_encode_app(int,int,bit1,min) = min)).
1.93/2.11	tff('29', plain, app_encode_app(int, int, bit1, min) = min,
1.93/2.11	    inference('cnf', [status(esa)], [zf_stmt_59])).
1.93/2.11	tff(zf_stmt_39, axiom,
1.93/2.11	  (![L:int]:
1.93/2.11	     (app_encode_app(int,int,
1.93/2.11	                     app_encode_app(int,app_encode_fun(int,int),
1.93/2.11	                                    minus_minus(int),pls),
1.93/2.11	                     app_encode_app(int,int,bit1,L)) =
1.93/2.11	      app_encode_app(int,int,bit1,
1.93/2.11	                     app_encode_app(int,int,
1.93/2.11	                                    app_encode_app(int,
1.93/2.11	                                                   app_encode_fun(int,int),
1.93/2.11	                                                   minus_minus(int),min),
1.93/2.11	                                    L))))).
1.93/2.11	tff('30', plain,
1.93/2.11	    ![X8 : int]:
1.93/2.11	      app_encode_app(int, int, 
1.93/2.11	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), pls), 
1.93/2.11	        app_encode_app(int, int, bit1, X8))
1.93/2.11	       = app_encode_app(int, int, bit1, 
1.93/2.11	           app_encode_app(int, int, 
1.93/2.11	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
1.93/2.11	               min), X8)),
1.93/2.11	    inference('cnf', [status(esa)], [zf_stmt_39])).
1.93/2.11	tff('31', plain,
1.93/2.11	    ![X8 : int]:
1.93/2.11	      app_encode_app(int, int, 
1.93/2.11	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), pls), 
1.93/2.11	        app_encode_app(int, int, bit1, X8))
1.93/2.11	       = app_encode_app(int, int, bit1, 
1.93/2.11	           app_encode_app(int, int, 
1.93/2.11	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.93/2.11	               min), 
1.93/2.11	             app_encode_app(int, int, 
1.93/2.11	               app_encode_app(int, app_encode_fun(int, int), 
1.93/2.11	                 minus_minus(int), pls), X8))),
1.93/2.11	    inference('demod', [status(thm)], ['30', '27'])).
1.93/2.11	tff('32', plain,
1.93/2.11	    app_encode_app(int, int, 
1.93/2.11	      app_encode_app(int, app_encode_fun(int, int), minus_minus(int), pls), 
1.93/2.11	      min)
1.93/2.11	     = app_encode_app(int, int, bit1, 
1.93/2.11	         app_encode_app(int, int, 
1.93/2.11	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), min), 
1.93/2.11	           app_encode_app(int, int, 
1.93/2.11	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
1.93/2.11	               pls), min))),
1.93/2.11	    inference('sup+', [status(thm)], ['29', '31'])).
1.93/2.11	tff(zf_stmt_118, axiom,
1.93/2.11	  (![W:int,Z2:int,Z1:int]:
1.93/2.11	     (app_encode_app(int,int,
1.93/2.11	                     app_encode_app(int,app_encode_fun(int,int),
1.93/2.11	                                    times_times(int),
1.93/2.11	                                    app_encode_app(int,int,
1.93/2.11	                                                   app_encode_app(int,
1.93/2.11	                                                                  app_encode_fun(
1.93/2.11	                                                                  int,int),
1.93/2.11	                                                                  plus_plus(
1.93/2.11	                                                                  int),Z1),
1.93/2.11	                                                   Z2)),
1.93/2.11	                     W) =
1.93/2.11	      app_encode_app(int,int,
1.93/2.11	                     app_encode_app(int,app_encode_fun(int,int),
1.93/2.11	                                    plus_plus(int),
1.93/2.11	                                    app_encode_app(int,int,
1.93/2.11	                                                   app_encode_app(int,
1.93/2.11	                                                                  app_encode_fun(
1.93/2.11	                                                                  int,int),
1.93/2.11	                                                                  times_times(
1.93/2.11	                                                                  int),Z1),
1.93/2.11	                                                   W)),
1.93/2.11	                     app_encode_app(int,int,
1.93/2.11	                                    app_encode_app(int,
1.93/2.11	                                                   app_encode_fun(int,int),
1.93/2.11	                                                   times_times(int),Z2),
1.93/2.11	                                    W))))).
1.93/2.11	tff('33', plain,
1.93/2.11	    ![X171 : int, X172 : int, X173 : int]:
1.93/2.11	      app_encode_app(int, int, 
1.93/2.11	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.93/2.11	          app_encode_app(int, int, 
1.93/2.11	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.93/2.11	              X171), X173)), X172)
1.93/2.11	       = app_encode_app(int, int, 
1.93/2.11	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.93/2.11	             app_encode_app(int, int, 
1.93/2.11	               app_encode_app(int, app_encode_fun(int, int), 
1.93/2.11	                 times_times(int), X171), X172)), 
1.93/2.11	           app_encode_app(int, int, 
1.93/2.11	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.93/2.11	               X173), X172)),
1.93/2.11	    inference('cnf', [status(esa)], [zf_stmt_118])).
1.93/2.11	tff(zf_stmt_117, axiom,
1.93/2.11	  (![Z2:int,Z1:int,W:int]:
1.93/2.11	     (app_encode_app(int,int,
1.93/2.11	                     app_encode_app(int,app_encode_fun(int,int),
1.93/2.11	                                    times_times(int),W),
1.93/2.11	                     app_encode_app(int,int,
1.93/2.11	                                    app_encode_app(int,
1.93/2.11	                                                   app_encode_fun(int,int),
1.93/2.11	                                                   plus_plus(int),Z1),
1.93/2.11	                                    Z2)) =
1.93/2.11	      app_encode_app(int,int,
1.93/2.11	                     app_encode_app(int,app_encode_fun(int,int),
1.93/2.11	                                    plus_plus(int),
1.93/2.11	                                    app_encode_app(int,int,
1.93/2.11	                                                   app_encode_app(int,
1.93/2.11	                                                                  app_encode_fun(
1.93/2.11	                                                                  int,int),
1.93/2.11	                                                                  times_times(
1.93/2.11	                                                                  int),W),
1.93/2.11	                                                   Z1)),
1.93/2.11	                     app_encode_app(int,int,
1.93/2.11	                                    app_encode_app(int,
1.93/2.11	                                                   app_encode_fun(int,int),
1.93/2.11	                                                   times_times(int),W),
1.93/2.11	                                    Z2))))).
1.93/2.11	tff('34', plain,
1.93/2.11	    ![X168 : int, X169 : int, X170 : int]:
1.93/2.11	      app_encode_app(int, int, 
1.93/2.11	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X168), 
1.93/2.11	        app_encode_app(int, int, 
1.93/2.11	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X169), 
1.93/2.11	          X170))
1.93/2.11	       = app_encode_app(int, int, 
1.93/2.11	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.93/2.11	             app_encode_app(int, int, 
1.93/2.11	               app_encode_app(int, app_encode_fun(int, int), 
1.93/2.11	                 times_times(int), X168), X169)), 
1.93/2.11	           app_encode_app(int, int, 
1.93/2.11	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.93/2.11	               X168), X170)),
1.93/2.11	    inference('cnf', [status(esa)], [zf_stmt_117])).
1.93/2.11	tff('35', plain,
1.93/2.11	    ![X0 : int, X1 : int]:
1.93/2.11	      app_encode_app(int, int, 
1.93/2.11	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X1), 
1.93/2.11	        app_encode_app(int, int, 
1.93/2.11	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
1.93/2.11	          X0))
1.93/2.11	       = app_encode_app(int, int, 
1.93/2.11	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.93/2.11	             app_encode_app(int, int, 
1.93/2.11	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.93/2.11	                 X1), X1)), X0),
1.93/2.11	    inference('sup+', [status(thm)], ['33', '34'])).
1.93/2.11	tff(zf_stmt_108, axiom,
1.93/2.11	  (![A:$tType]:
1.93/2.11	     (comm_monoid_mult(A) =>
1.93/2.11	      (![A1:A]:
1.93/2.11	         (app_encode_app(A,A,
1.93/2.11	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
1.93/2.11	                                        A1),
1.93/2.11	                         one_one(A)) =
1.93/2.11	          A1))))).
1.93/2.11	tff('36', plain,
1.93/2.11	    ![X143 : $tType, X144 : X143]:
1.93/2.11	      (app_encode_app(X143, X143, 
1.93/2.11	         app_encode_app(X143, app_encode_fun(X143, X143), times_times(X143), 
1.93/2.11	           X144), one_one(X143))
1.93/2.11	        = X144
1.93/2.11	       | ~ comm_monoid_mult(X143)),
1.93/2.11	    inference('cnf', [status(esa)], [zf_stmt_108])).
1.93/2.11	tff('37', plain,
1.93/2.11	    ![X0 : int]:
1.93/2.11	      (~ $true
1.93/2.11	       | app_encode_app(int, int, 
1.93/2.11	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.93/2.11	             X0), one_one(int))
1.93/2.11	          = X0),
1.93/2.11	    inference('sup-', [status(thm)], ['1', '36'])).
1.93/2.11	tff('38', plain,
1.93/2.11	    ![X0 : int]:
1.93/2.11	      (~ $true
1.93/2.11	       | app_encode_app(int, int, 
1.93/2.11	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.93/2.11	             X0), app_encode_app(int, int, bit1, pls))
1.93/2.11	          = X0),
1.93/2.11	    inference('demod', [status(thm)], ['37', '6'])).
1.93/2.11	tff('39', plain,
1.93/2.11	    ![X0 : int]:
1.93/2.11	      app_encode_app(int, int, 
1.93/2.11	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X0), 
1.93/2.11	        app_encode_app(int, int, bit1, pls))
1.93/2.11	       = X0,
1.93/2.11	    inference('simplify', [status(thm)], ['38'])).
1.93/2.11	tff('40', plain,
1.93/2.11	    ![X0 : int]:
1.93/2.11	      app_encode_app(int, int, 
1.93/2.11	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X0), 
1.93/2.11	        app_encode_app(int, int, 
1.93/2.11	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.93/2.11	            app_encode_app(int, int, bit1, pls)), 
1.93/2.11	          app_encode_app(int, int, bit1, pls)))
1.93/2.11	       = app_encode_app(int, int, 
1.93/2.11	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
1.93/2.11	           X0),
1.93/2.11	    inference('sup+', [status(thm)], ['35', '39'])).
1.93/2.11	tff(zf_stmt_119, axiom,
1.93/2.11	  (![Z2:int,Z1:int,W:int]:
1.93/2.11	     (app_encode_app(int,int,
1.93/2.11	                     app_encode_app(int,app_encode_fun(int,int),
1.93/2.11	                                    times_times(int),W),
1.93/2.11	                     app_encode_app(int,int,
1.93/2.11	                                    app_encode_app(int,
1.93/2.11	                                                   app_encode_fun(int,int),
1.93/2.11	                                                   minus_minus(int),Z1),
1.93/2.11	                                    Z2)) =
1.93/2.11	      app_encode_app(int,int,
1.93/2.11	                     app_encode_app(int,app_encode_fun(int,int),
1.93/2.11	                                    minus_minus(int),
1.93/2.11	                                    app_encode_app(int,int,
1.93/2.11	                                                   app_encode_app(int,
1.93/2.11	                                                                  app_encode_fun(
1.93/2.11	                                                                  int,int),
1.93/2.11	                                                                  times_times(
1.93/2.11	                                                                  int),W),
1.93/2.11	                                                   Z1)),
1.93/2.11	                     app_encode_app(int,int,
1.93/2.11	                                    app_encode_app(int,
1.93/2.11	                                                   app_encode_fun(int,int),
1.93/2.11	                                                   times_times(int),W),
1.93/2.11	                                    Z2))))).
1.93/2.11	tff('41', plain,
1.93/2.11	    ![X174 : int, X175 : int, X176 : int]:
1.93/2.11	      app_encode_app(int, int, 
1.93/2.11	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X174), 
1.93/2.11	        app_encode_app(int, int, 
1.93/2.11	          app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
1.93/2.11	            X175), X176))
1.93/2.11	       = app_encode_app(int, int, 
1.93/2.11	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
1.93/2.11	             app_encode_app(int, int, 
1.93/2.11	               app_encode_app(int, app_encode_fun(int, int), 
1.93/2.11	                 times_times(int), X174), X175)), 
1.93/2.11	           app_encode_app(int, int, 
1.93/2.11	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.93/2.11	               X174), X176)),
1.93/2.11	    inference('cnf', [status(esa)], [zf_stmt_119])).
1.93/2.11	tff('42', plain,
1.93/2.11	    ![X0 : int, X1 : int]:
1.93/2.11	      app_encode_app(int, int, 
1.93/2.11	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X0), 
1.93/2.11	        app_encode_app(int, int, 
1.93/2.11	          app_encode_app(int, app_encode_fun(int, int), minus_minus(int), X1), 
1.93/2.11	          app_encode_app(int, int, bit1, pls)))
1.93/2.11	       = app_encode_app(int, int, 
1.93/2.11	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
1.93/2.11	             app_encode_app(int, int, 
1.93/2.11	               app_encode_app(int, app_encode_fun(int, int), 
1.93/2.11	                 times_times(int), X0), X1)), X0),
1.93/2.11	    inference('sup+', [status(thm)], ['39', '41'])).
1.93/2.11	tff(zf_stmt_75, axiom,
1.93/2.11	  (![K:int]:
1.93/2.11	     (app_encode_app(int,int,
1.93/2.11	                     app_encode_app(int,app_encode_fun(int,int),
1.93/2.11	                                    minus_minus(int),K),
1.93/2.11	                     pls) =
1.93/2.11	      K))).
1.93/2.11	tff('43', plain,
1.93/2.11	    ![X64 : int]:
1.93/2.11	      app_encode_app(int, int, 
1.93/2.11	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), X64), 
1.93/2.11	        pls)
1.93/2.11	       = X64,
1.93/2.11	    inference('cnf', [status(esa)], [zf_stmt_75])).
1.93/2.11	tff('44', plain,
1.93/2.11	    app_encode_app(int, int, 
1.93/2.11	      app_encode_app(int, app_encode_fun(int, int), minus_minus(int), pls), 
1.93/2.11	      app_encode_app(int, int, bit1, pls))
1.93/2.11	     = app_encode_app(int, int, bit1, min),
1.93/2.11	    inference('sup+', [status(thm)], ['43', '30'])).
1.93/2.11	tff('45', plain,
1.93/2.11	    app_encode_app(int, int, 
1.93/2.11	      app_encode_app(int, app_encode_fun(int, int), minus_minus(int), pls), 
1.93/2.11	      app_encode_app(int, int, bit1, pls))
1.93/2.11	     = min,
1.93/2.11	    inference('demod', [status(thm)], ['44', '29'])).
1.93/2.11	tff('46', plain,
1.93/2.11	    ![X0 : int]:
1.93/2.11	      app_encode_app(int, int, 
1.93/2.11	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
1.93/2.11	        min)
1.93/2.11	       = app_encode_app(int, int, 
1.93/2.11	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
1.93/2.11	             X0), app_encode_app(int, int, bit1, pls)),
1.93/2.11	    inference('sup+', [status(thm)], ['45', '27'])).
1.93/2.11	tff('47', plain,
1.93/2.11	    ![X0 : int, X1 : int]:
1.93/2.11	      app_encode_app(int, int, 
1.93/2.11	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X0), 
1.93/2.11	        app_encode_app(int, int, 
1.93/2.11	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X1), 
1.93/2.11	          min))
1.93/2.11	       = app_encode_app(int, int, 
1.93/2.11	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
1.93/2.11	             app_encode_app(int, int, 
1.93/2.11	               app_encode_app(int, app_encode_fun(int, int), 
1.93/2.11	                 times_times(int), X0), X1)), X0),
1.93/2.11	    inference('demod', [status(thm)], ['42', '46'])).
1.93/2.11	tff('48', plain,
1.93/2.11	    ![X0 : int]:
1.93/2.11	      app_encode_app(int, int, 
1.93/2.11	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X0), 
1.93/2.11	        app_encode_app(int, int, 
1.93/2.11	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.93/2.11	            app_encode_app(int, int, 
1.93/2.11	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.93/2.11	                app_encode_app(int, int, bit1, pls)), 
1.93/2.11	              app_encode_app(int, int, bit1, pls))), min))
1.93/2.11	       = app_encode_app(int, int, 
1.93/2.11	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
1.93/2.11	             app_encode_app(int, int, 
1.93/2.11	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.93/2.11	                 X0), X0)), X0),
1.93/2.11	    inference('sup+', [status(thm)], ['40', '47'])).
1.93/2.11	tff(zf_stmt_64, axiom,
1.93/2.11	  (![A:$tType]:
1.93/2.11	     (number_ring(A) =>
1.93/2.11	      (![Z:A,W:int,V:int]:
1.93/2.11	         (app_encode_app(A,A,
1.93/2.11	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
1.93/2.11	                                        app_encode_app(int,A,
1.93/2.11	                                                       number_number_of(A),V)),
1.93/2.11	                         app_encode_app(A,A,
1.93/2.11	                                        app_encode_app(A,app_encode_fun(A,A),
1.93/2.11	                                                       plus_plus(A),
1.93/2.11	                                                       app_encode_app(
1.93/2.11	                                                       int,A,
1.93/2.11	                                                       number_number_of(A),W)),
1.93/2.11	                                        Z)) =
1.93/2.11	          app_encode_app(A,A,
1.93/2.11	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
1.93/2.11	                                        app_encode_app(int,A,
1.93/2.11	                                                       number_number_of(A),
1.93/2.11	                                                       app_encode_app(
1.93/2.11	                                                       int,int,
1.93/2.11	                                                       app_encode_app(
1.93/2.11	                                                       int,
1.93/2.11	                                                       app_encode_fun(
1.93/2.11	                                                       int,int),
1.93/2.11	                                                       plus_plus(int),V),W))),
1.93/2.11	                         Z)))))).
1.93/2.11	tff('49', plain,
1.93/2.11	    ![X47 : $tType, X48 : int, X49 : int, X50 : X47]:
1.93/2.11	      (app_encode_app(X47, X47, 
1.93/2.11	         app_encode_app(X47, app_encode_fun(X47, X47), plus_plus(X47), 
1.93/2.11	           app_encode_app(int, X47, number_number_of(X47), X48)), 
1.93/2.11	         app_encode_app(X47, X47, 
1.93/2.11	           app_encode_app(X47, app_encode_fun(X47, X47), plus_plus(X47), 
1.93/2.11	             app_encode_app(int, X47, number_number_of(X47), X49)), X50))
1.93/2.11	        = app_encode_app(X47, X47, 
1.93/2.11	            app_encode_app(X47, app_encode_fun(X47, X47), plus_plus(X47), 
1.93/2.11	              app_encode_app(int, X47, number_number_of(X47), 
1.93/2.11	                app_encode_app(int, int, 
1.93/2.11	                  app_encode_app(int, app_encode_fun(int, int), 
1.93/2.11	                    plus_plus(int), X48), X49))), X50)
1.93/2.11	       | ~ number_ring(X47)),
1.93/2.11	    inference('cnf', [status(esa)], [zf_stmt_64])).
1.93/2.11	tff('50', plain,
1.93/2.11	    ![X0 : int, X1 : int, X2 : int]:
1.93/2.11	      (~ $true
1.93/2.11	       | app_encode_app(int, int, 
1.93/2.11	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.93/2.11	             app_encode_app(int, int, number_number_of(int), X2)), 
1.93/2.11	           app_encode_app(int, int, 
1.93/2.11	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.93/2.11	               app_encode_app(int, int, number_number_of(int), X1)), X0))
1.93/2.11	          = app_encode_app(int, int, 
1.93/2.11	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.93/2.11	                app_encode_app(int, int, number_number_of(int), 
1.93/2.11	                  app_encode_app(int, int, 
1.93/2.11	                    app_encode_app(int, app_encode_fun(int, int), 
1.93/2.11	                      plus_plus(int), X2), X1))), X0)),
1.93/2.11	    inference('sup-', [status(thm)], ['22', '49'])).
1.93/2.11	tff('51', plain,
1.93/2.11	    ![X0 : int, X1 : int, X2 : int]:
1.93/2.11	      (~ $true
1.93/2.11	       | app_encode_app(int, int, 
1.93/2.11	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X2), 
1.93/2.11	           app_encode_app(int, int, 
1.93/2.11	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.93/2.11	               X1), X0))
1.93/2.11	          = app_encode_app(int, int, 
1.93/2.11	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.93/2.11	                app_encode_app(int, int, 
1.93/2.11	                  app_encode_app(int, app_encode_fun(int, int), 
1.93/2.11	                    plus_plus(int), X2), X1)), X0)),
1.93/2.11	    inference('demod', [status(thm)], ['50', '5', '5', '5'])).
1.93/2.11	tff('52', plain,
1.93/2.11	    ![X0 : int, X1 : int, X2 : int]:
1.93/2.11	      app_encode_app(int, int, 
1.93/2.11	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X2), 
1.93/2.11	        app_encode_app(int, int, 
1.93/2.11	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X1), 
1.93/2.11	          X0))
1.93/2.11	       = app_encode_app(int, int, 
1.93/2.11	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.93/2.11	             app_encode_app(int, int, 
1.93/2.11	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.93/2.11	                 X2), X1)), X0),
1.93/2.11	    inference('simplify', [status(thm)], ['51'])).
1.93/2.11	tff(zf_stmt_44, axiom,
1.93/2.11	  (![L:int,K:int]:
1.93/2.11	     (app_encode_app(int,int,
1.93/2.11	                     app_encode_app(int,app_encode_fun(int,int),
1.93/2.11	                                    plus_plus(int),
1.93/2.11	                                    app_encode_app(int,int,bit0,K)),
1.93/2.11	                     app_encode_app(int,int,bit1,L)) =
1.93/2.11	      app_encode_app(int,int,bit1,
1.93/2.11	                     app_encode_app(int,int,
1.93/2.11	                                    app_encode_app(int,
1.93/2.11	                                                   app_encode_fun(int,int),
1.93/2.11	                                                   plus_plus(int),K),
1.93/2.11	                                    L))))).
1.93/2.11	tff('53', plain,
1.93/2.11	    ![X15 : int, X16 : int]:
1.93/2.11	      app_encode_app(int, int, 
1.93/2.11	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.93/2.11	          app_encode_app(int, int, bit0, X15)), 
1.93/2.11	        app_encode_app(int, int, bit1, X16))
1.93/2.11	       = app_encode_app(int, int, bit1, 
1.93/2.11	           app_encode_app(int, int, 
1.93/2.11	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.93/2.11	               X15), X16)),
1.93/2.11	    inference('cnf', [status(esa)], [zf_stmt_44])).
1.93/2.11	tff('54', plain,
1.93/2.11	    ![X0 : int]:
1.93/2.11	      app_encode_app(int, int, 
1.93/2.11	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.93/2.11	          app_encode_app(int, int, bit0, X0)), min)
1.93/2.11	       = app_encode_app(int, int, bit1, 
1.93/2.11	           app_encode_app(int, int, 
1.93/2.11	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.93/2.11	               X0), min)),
1.93/2.11	    inference('sup+', [status(thm)], ['29', '53'])).
1.93/2.11	tff('55', plain,
1.93/2.11	    ![X0 : int]:
1.93/2.11	      app_encode_app(int, int, 
1.93/2.11	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.93/2.11	          app_encode_app(int, int, 
1.93/2.11	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
1.93/2.11	            X0)), min)
1.93/2.11	       = app_encode_app(int, int, bit1, 
1.93/2.11	           app_encode_app(int, int, 
1.93/2.11	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.93/2.11	               X0), min)),
1.93/2.11	    inference('sup+', [status(thm)], ['9', '54'])).
1.93/2.11	tff('56', plain,
1.93/2.11	    ![X0 : int]:
1.93/2.11	      app_encode_app(int, int, 
1.93/2.11	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
1.93/2.11	        app_encode_app(int, int, 
1.93/2.11	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
1.93/2.11	          min))
1.93/2.11	       = app_encode_app(int, int, bit1, 
1.93/2.11	           app_encode_app(int, int, 
1.93/2.11	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.93/2.11	               X0), min)),
1.93/2.11	    inference('demod', [status(thm)], ['55', '52'])).
1.93/2.11	tff(zf_stmt_124, axiom,
1.93/2.11	  (![N1:int,Ma:int]:
1.93/2.11	     ((app_encode_app(int,int,
1.93/2.11	                      app_encode_app(int,app_encode_fun(int,int),
1.93/2.11	                                     times_times(int),Ma),
1.93/2.11	                      N1) =
1.93/2.11	       one_one(int)) <=>
1.93/2.11	      (((Ma = one_one(int)) & (N1 = one_one(int))) | 
1.93/2.11	       ((Ma = app_encode_app(int,int,number_number_of(int),min)) & 
1.93/2.11	        (N1 = app_encode_app(int,int,number_number_of(int),min))))))).
1.93/2.11	tff('57', plain,
1.93/2.11	    ![X188 : int, X189 : int]:
1.93/2.11	      (app_encode_app(int, int, 
1.93/2.11	         app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.93/2.11	           X189), X188)
1.93/2.11	        = one_one(int)
1.93/2.11	       | X189 != app_encode_app(int, int, number_number_of(int), min)
1.93/2.11	       | X188 != app_encode_app(int, int, number_number_of(int), min)),
1.93/2.11	    inference('cnf', [status(esa)], [zf_stmt_124])).
1.93/2.11	tff('58', plain,
1.93/2.11	    app_encode_app(int, int, 
1.93/2.11	      app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.93/2.11	        app_encode_app(int, int, number_number_of(int), min)), 
1.93/2.11	      app_encode_app(int, int, number_number_of(int), min))
1.93/2.11	     = one_one(int),
1.93/2.11	    inference('simplify', [status(thm)], ['57'])).
1.93/2.11	tff('59', plain,
1.93/2.11	    app_encode_app(int, int, 
1.93/2.11	      app_encode_app(int, app_encode_fun(int, int), times_times(int), min), 
1.93/2.11	      min)
1.93/2.11	     = app_encode_app(int, int, bit1, pls),
1.93/2.11	    inference('demod', [status(thm)], ['58', '5', '5', '6'])).
1.93/2.11	tff(zf_stmt_105, axiom,
1.93/2.11	  (![L:int,K:int]:
1.93/2.11	     (app_encode_app(int,int,
1.93/2.11	                     app_encode_app(int,app_encode_fun(int,int),
1.93/2.11	                                    times_times(int),
1.93/2.11	                                    app_encode_app(int,int,bit1,K)),
1.93/2.11	                     L) =
1.93/2.11	      app_encode_app(int,int,
1.93/2.11	                     app_encode_app(int,app_encode_fun(int,int),
1.93/2.11	                                    plus_plus(int),
1.93/2.11	                                    app_encode_app(int,int,bit0,
1.93/2.11	                                                   app_encode_app(int,int,
1.93/2.11	                                                                  app_encode_app(
1.93/2.11	                                                                  int,
1.93/2.11	                                                                  app_encode_fun(
1.93/2.11	                                                                  int,int),
1.93/2.11	                                                                  times_times(
1.93/2.11	                                                                  int),K),L))),
1.93/2.11	                     L)))).
1.93/2.11	tff('60', plain,
1.93/2.11	    ![X134 : int, X135 : int]:
1.93/2.11	      app_encode_app(int, int, 
1.93/2.11	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.93/2.11	          app_encode_app(int, int, bit1, X134)), X135)
1.93/2.11	       = app_encode_app(int, int, 
1.93/2.11	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.93/2.11	             app_encode_app(int, int, bit0, 
1.93/2.11	               app_encode_app(int, int, 
1.93/2.11	                 app_encode_app(int, app_encode_fun(int, int), 
1.93/2.11	                   times_times(int), X134), X135))), X135),
1.93/2.11	    inference('cnf', [status(esa)], [zf_stmt_105])).
1.93/2.11	tff('61', plain,
1.93/2.11	    ![X134 : int, X135 : int]:
1.93/2.11	      app_encode_app(int, int, 
1.93/2.11	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.93/2.11	          app_encode_app(int, int, bit1, X134)), X135)
1.93/2.11	       = app_encode_app(int, int, 
1.93/2.11	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.93/2.11	             app_encode_app(int, int, 
1.93/2.11	               app_encode_app(int, app_encode_fun(int, int), 
1.93/2.11	                 times_times(int), 
1.93/2.11	                 app_encode_app(int, int, 
1.93/2.11	                   app_encode_app(int, app_encode_fun(int, int), 
1.93/2.11	                     plus_plus(int), app_encode_app(int, int, bit1, pls)), 
1.93/2.11	                   app_encode_app(int, int, bit1, pls))), 
1.93/2.11	               app_encode_app(int, int, 
1.93/2.11	                 app_encode_app(int, app_encode_fun(int, int), 
1.93/2.11	                   times_times(int), X134), X135))), X135),
1.93/2.11	    inference('demod', [status(thm)], ['60', '12'])).
1.93/2.11	tff('62', plain,
1.93/2.11	    app_encode_app(int, int, 
1.93/2.11	      app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.93/2.11	        app_encode_app(int, int, bit1, min)), min)
1.93/2.11	     = app_encode_app(int, int, 
1.93/2.11	         app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.93/2.11	           app_encode_app(int, int, 
1.93/2.11	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
1.93/2.11	               app_encode_app(int, int, 
1.93/2.11	                 app_encode_app(int, app_encode_fun(int, int), 
1.93/2.11	                   plus_plus(int), app_encode_app(int, int, bit1, pls)), 
1.93/2.11	                 app_encode_app(int, int, bit1, pls))), 
1.93/2.11	             app_encode_app(int, int, bit1, pls))), min),
1.93/2.11	    inference('sup+', [status(thm)], ['59', '61'])).
1.93/2.11	tff('63', plain,
1.93/2.11	    app_encode_app(int, int, 
1.93/2.11	      app_encode_app(int, app_encode_fun(int, int), times_times(int), min), 
1.93/2.11	      min)
1.93/2.11	     = app_encode_app(int, int, bit1, 
1.93/2.11	         app_encode_app(int, int, 
1.93/2.11	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.93/2.11	             app_encode_app(int, int, bit1, pls)), min)),
1.93/2.11	    inference('demod', [status(thm)], ['62', '29', '13', '52', '56'])).
1.93/2.11	tff('64', plain,
1.93/2.11	    app_encode_app(int, int, bit1, 
1.93/2.11	      app_encode_app(int, int, 
1.93/2.11	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.93/2.11	          app_encode_app(int, int, bit1, pls)), min))
1.93/2.11	     = app_encode_app(int, int, bit1, pls),
1.93/2.11	    inference('sup+', [status(thm)], ['63', '59'])).
1.93/2.11	tff('65', plain,
1.93/2.11	    ![X0 : int]:
1.93/2.11	      X0
1.93/2.11	       = app_encode_app(int, int, 
1.93/2.11	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
1.93/2.11	           app_encode_app(int, int, 
1.93/2.11	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
1.93/2.11	               X0), X0)),
1.93/2.11	    inference('demod', [status(thm)], ['48', '52', '56', '64', '39', '26'])).
1.93/2.11	tff(zf_stmt_93, axiom,
1.93/2.11	  (![A:$tType]:
1.93/2.11	     (cancel_semigroup_add(A) =>
1.93/2.11	      (![C1:A,B2:A,A2:A]:
1.93/2.11	         ((app_encode_app(A,A,
1.93/2.11	                          app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
1.93/2.11	                                         A2),
1.93/2.11	                          B2) =
1.93/2.11	           app_encode_app(A,A,
1.93/2.11	                          app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
1.93/2.11	                                         A2),
1.93/2.11	                          C1)) <=>
1.93/2.11	          (B2 = C1)))))).
1.93/2.11	tff('66', plain,
1.93/2.11	    ![X96 : $tType, X97 : X96, X98 : X96, X100 : X96]:
1.93/2.11	      (app_encode_app(X96, X96, 
1.93/2.11	         app_encode_app(X96, app_encode_fun(X96, X96), plus_plus(X96), X100), 
1.93/2.11	         X98)
1.93/2.11	        != app_encode_app(X96, X96, 
1.93/2.11	             app_encode_app(X96, app_encode_fun(X96, X96), plus_plus(X96), 
1.93/2.11	               X100), X97)
1.93/2.11	       | X98 = X97
1.93/2.11	       | ~ cancel_semigroup_add(X96)),
1.93/2.11	    inference('cnf', [status(esa)], [zf_stmt_93])).
1.93/2.11	tff('67', plain,
1.93/2.11	    ![X0 : int, X1 : int]:
1.93/2.11	      (X0
1.93/2.11	        != app_encode_app(int, int, 
1.93/2.11	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.93/2.11	               X0), X1)
1.93/2.11	       | ~ cancel_semigroup_add(int)
1.93/2.11	       | pls = X1),
1.93/2.11	    inference('sup-', [status(thm)], ['21', '66'])).
1.93/2.11	tff(zf_stmt_130, axiom, (cancel_semigroup_add(int))).
1.93/2.11	tff('68', plain, cancel_semigroup_add(int),
1.93/2.11	    inference('cnf', [status(esa)], [zf_stmt_130])).
1.93/2.11	tff('69', plain,
1.93/2.11	    ![X0 : int, X1 : int]:
1.93/2.11	      (X0
1.93/2.11	        != app_encode_app(int, int, 
1.93/2.11	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.93/2.11	               X0), X1)
1.93/2.11	       | ~ $true
1.93/2.11	       | pls = X1),
1.93/2.11	    inference('demod', [status(thm)], ['67', '68'])).
1.93/2.11	tff('70', plain,
1.93/2.11	    ![X0 : int, X1 : int]:
1.93/2.11	      (pls = X1
1.93/2.11	       | X0
1.93/2.11	          != app_encode_app(int, int, 
1.93/2.11	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.93/2.11	                 X0), X1)),
1.93/2.11	    inference('simplify', [status(thm)], ['69'])).
1.93/2.11	tff('71', plain,
1.93/2.11	    ![X0 : int]:
1.93/2.11	      (X0 != X0
1.93/2.11	       | pls
1.93/2.11	          = app_encode_app(int, int, 
1.93/2.11	              app_encode_app(int, app_encode_fun(int, int), 
1.93/2.11	                minus_minus(int), X0), X0)),
1.93/2.11	    inference('sup-', [status(thm)], ['65', '70'])).
1.93/2.11	tff('72', plain,
1.93/2.11	    ![X0 : int]:
1.93/2.11	      pls
1.93/2.11	       = app_encode_app(int, int, 
1.93/2.11	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
1.93/2.11	             X0), X0),
1.93/2.11	    inference('simplify', [status(thm)], ['71'])).
1.93/2.11	tff('73', plain,
1.93/2.11	    ![X0 : int]:
1.93/2.11	      app_encode_app(int, int, 
1.93/2.11	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
1.93/2.11	        app_encode_app(int, int, 
1.93/2.11	          app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
1.93/2.11	            pls), X0))
1.93/2.11	       = pls,
1.93/2.11	    inference('sup+', [status(thm)], ['72', '27'])).
1.93/2.11	tff('74', plain,
1.93/2.11	    app_encode_app(int, int, 
1.93/2.11	      app_encode_app(int, app_encode_fun(int, int), minus_minus(int), pls), 
1.93/2.11	      min)
1.93/2.11	     = app_encode_app(int, int, bit1, pls),
1.93/2.11	    inference('demod', [status(thm)], ['32', '73'])).
1.93/2.11	tff('75', plain,
1.93/2.11	    app_encode_app(int, int, 
1.93/2.11	      app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.93/2.11	        app_encode_app(int, int, 
1.93/2.11	          app_encode_app(int, app_encode_fun(int, int), times_times(int), s), 
1.93/2.11	          s)), app_encode_app(int, int, bit1, pls))
1.93/2.11	     != app_encode_app(int, int, 
1.93/2.11	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.93/2.11	            app_encode_app(int, int, 
1.93/2.11	              app_encode_app(int, app_encode_fun(int, int), 
1.93/2.11	                times_times(int), s), s)), 
1.93/2.11	          app_encode_app(int, int, bit1, pls)),
1.93/2.11	    inference('demod', [status(thm)], ['28', '74'])).
1.93/2.11	tff('76', plain, $false, inference('simplify', [status(thm)], ['75'])).
1.93/2.11	
1.93/2.11	% SZS output end Refutation
1.93/2.11	EOF
