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    : kbo
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n170.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 07:50:54 CST 2018
38.52/38.73	% done 6286 iterations in 38.537s
38.52/38.73	% SZS status Theorem for 'stdin'
38.52/38.73	% SZS output start Refutation
38.52/38.73	tff(zf_stmt_156, conjecture,
38.52/38.73	  (app_encode_app(int,int,
38.52/38.73	                  app_encode_app(int,app_encode_fun(int,int),
38.52/38.73	                                 minus_minus(int),
38.52/38.73	                                 app_encode_app(nat,int,
38.52/38.73	                                                app_encode_app(int,
38.52/38.73	                                                               app_encode_fun(
38.52/38.73	                                                               nat,int),
38.52/38.73	                                                               power_power(
38.52/38.73	                                                               int),s),
38.52/38.73	                                                app_encode_app(int,nat,
38.52/38.73	                                                               number_number_of(
38.52/38.73	                                                               nat),
38.52/38.73	                                                               app_encode_app(
38.52/38.73	                                                               int,int,bit0,
38.52/38.73	                                                               app_encode_app(
38.52/38.73	                                                               int,int,bit1,
38.52/38.73	                                                               pls))))),
38.52/38.73	                  app_encode_app(int,int,number_number_of(int),min)) =
38.52/38.73	   app_encode_app(int,int,
38.52/38.73	                  app_encode_app(int,app_encode_fun(int,int),plus_plus(int),
38.52/38.73	                                 app_encode_app(nat,int,
38.52/38.73	                                                app_encode_app(int,
38.52/38.73	                                                               app_encode_fun(
38.52/38.73	                                                               nat,int),
38.52/38.73	                                                               power_power(
38.52/38.73	                                                               int),s),
38.52/38.73	                                                app_encode_app(int,nat,
38.52/38.73	                                                               number_number_of(
38.52/38.73	                                                               nat),
38.52/38.73	                                                               app_encode_app(
38.52/38.73	                                                               int,int,bit0,
38.52/38.73	                                                               app_encode_app(
38.52/38.73	                                                               int,int,bit1,
38.52/38.73	                                                               pls))))),
38.52/38.73	                  one_one(int)))).
38.52/38.73	tff(zf_stmt_0, negated_conjecture,
38.52/38.73	  (app_encode_app(int,int,
38.52/38.73	                  app_encode_app(int,app_encode_fun(int,int),
38.52/38.73	                                 minus_minus(int),
38.52/38.73	                                 app_encode_app(nat,int,
38.52/38.73	                                                app_encode_app(int,
38.52/38.73	                                                               app_encode_fun(
38.52/38.73	                                                               nat,int),
38.52/38.73	                                                               power_power(
38.52/38.73	                                                               int),s),
38.52/38.73	                                                app_encode_app(int,nat,
38.52/38.73	                                                               number_number_of(
38.52/38.73	                                                               nat),
38.52/38.73	                                                               app_encode_app(
38.52/38.73	                                                               int,int,bit0,
38.52/38.73	                                                               app_encode_app(
38.52/38.73	                                                               int,int,bit1,
38.52/38.73	                                                               pls))))),
38.52/38.73	                  app_encode_app(int,int,number_number_of(int),min)) !=
38.52/38.73	   app_encode_app(int,int,
38.52/38.73	                  app_encode_app(int,app_encode_fun(int,int),plus_plus(int),
38.52/38.73	                                 app_encode_app(nat,int,
38.52/38.73	                                                app_encode_app(int,
38.52/38.73	                                                               app_encode_fun(
38.52/38.73	                                                               nat,int),
38.52/38.73	                                                               power_power(
38.52/38.73	                                                               int),s),
38.52/38.73	                                                app_encode_app(int,nat,
38.52/38.73	                                                               number_number_of(
38.52/38.73	                                                               nat),
38.52/38.73	                                                               app_encode_app(
38.52/38.73	                                                               int,int,bit0,
38.52/38.73	                                                               app_encode_app(
38.52/38.73	                                                               int,int,bit1,
38.52/38.73	                                                               pls))))),
38.52/38.73	                  one_one(int)))).
38.52/38.73	tff('0', plain,
38.52/38.73	    app_encode_app(int, int, 
38.52/38.73	      app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
38.52/38.73	        app_encode_app(nat, int, 
38.52/38.73	          app_encode_app(int, app_encode_fun(nat, int), power_power(int), s), 
38.52/38.73	          app_encode_app(int, nat, number_number_of(nat), 
38.52/38.73	            app_encode_app(int, int, bit0, 
38.52/38.73	              app_encode_app(int, int, bit1, pls))))), 
38.52/38.73	      app_encode_app(int, int, number_number_of(int), min))
38.52/38.73	     != app_encode_app(int, int, 
38.52/38.73	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
38.52/38.73	            app_encode_app(nat, int, 
38.52/38.73	              app_encode_app(int, app_encode_fun(nat, int), 
38.52/38.73	                power_power(int), s), 
38.52/38.73	              app_encode_app(int, nat, number_number_of(nat), 
38.52/38.73	                app_encode_app(int, int, bit0, 
38.52/38.73	                  app_encode_app(int, int, bit1, pls))))), one_one(int)),
38.52/38.73	    inference('cnf', [status(esa)], [zf_stmt_0])).
38.52/38.73	tff(zf_stmt_87, axiom,
38.52/38.73	  (one_one(int) =
38.52/38.73	   app_encode_app(int,int,number_number_of(int),
38.52/38.73	                  app_encode_app(int,int,bit1,pls)))).
38.52/38.73	tff('1', plain,
38.52/38.73	    one_one(int)
38.52/38.73	     = app_encode_app(int, int, number_number_of(int), 
38.52/38.73	         app_encode_app(int, int, bit1, pls)),
38.52/38.73	    inference('cnf', [status(esa)], [zf_stmt_87])).
38.52/38.73	tff(zf_stmt_71, axiom,
38.52/38.73	  (![K:int]: (app_encode_app(int,int,number_number_of(int),K) = K))).
38.52/38.73	tff('2', plain,
38.52/38.73	    ![X60 : int]: app_encode_app(int, int, number_number_of(int), X60) = X60,
38.52/38.73	    inference('cnf', [status(esa)], [zf_stmt_71])).
38.52/38.73	tff('3', plain, one_one(int) = app_encode_app(int, int, bit1, pls),
38.52/38.73	    inference('demod', [status(thm)], ['1', '2'])).
38.52/38.73	tff(zf_stmt_96, axiom,
38.52/38.73	  (![B1:$tType]:
38.52/38.73	     ((monoid_mult(B1) & number(B1)) =>
38.52/38.73	      (![W:int]:
38.52/38.73	         (app_encode_app(nat,B1,
38.52/38.73	                         app_encode_app(B1,app_encode_fun(nat,B1),
38.52/38.73	                                        power_power(B1),
38.52/38.73	                                        app_encode_app(int,B1,
38.52/38.73	                                                       number_number_of(B1),W)),
38.52/38.73	                         app_encode_app(int,nat,number_number_of(nat),
38.52/38.73	                                        app_encode_app(int,int,bit0,
38.52/38.73	                                                       app_encode_app(
38.52/38.73	                                                       int,int,bit1,pls)))) =
38.52/38.73	          app_encode_app(B1,B1,
38.52/38.73	                         app_encode_app(B1,app_encode_fun(B1,B1),
38.52/38.73	                                        times_times(B1),
38.52/38.73	                                        app_encode_app(int,B1,
38.52/38.73	                                                       number_number_of(B1),W)),
38.52/38.73	                         app_encode_app(int,B1,number_number_of(B1),W))))))).
38.52/38.73	tff('4', plain,
38.52/38.73	    ![X106 : $tType, X107 : int]:
38.52/38.73	      (app_encode_app(nat, X106, 
38.52/38.73	         app_encode_app(X106, app_encode_fun(nat, X106), power_power(X106), 
38.52/38.73	           app_encode_app(int, X106, number_number_of(X106), X107)), 
38.52/38.73	         app_encode_app(int, nat, number_number_of(nat), 
38.52/38.73	           app_encode_app(int, int, bit0, 
38.52/38.73	             app_encode_app(int, int, bit1, pls))))
38.52/38.73	        = app_encode_app(X106, X106, 
38.52/38.73	            app_encode_app(X106, app_encode_fun(X106, X106), 
38.52/38.73	              times_times(X106), 
38.52/38.73	              app_encode_app(int, X106, number_number_of(X106), X107)), 
38.52/38.73	            app_encode_app(int, X106, number_number_of(X106), X107))
38.52/38.73	       | ~ number(X106)
38.52/38.73	       | ~ monoid_mult(X106)),
38.52/38.73	    inference('cnf', [status(esa)], [zf_stmt_96])).
38.52/38.73	tff('5', plain,
38.52/38.73	    ![X106 : $tType, X107 : int]:
38.52/38.73	      (app_encode_app(nat, X106, 
38.52/38.73	         app_encode_app(X106, app_encode_fun(nat, X106), power_power(X106), 
38.52/38.73	           app_encode_app(int, X106, number_number_of(X106), X107)), 
38.52/38.73	         app_encode_app(int, nat, number_number_of(nat), 
38.52/38.73	           app_encode_app(int, int, bit0, one_one(int))))
38.52/38.73	        = app_encode_app(X106, X106, 
38.52/38.73	            app_encode_app(X106, app_encode_fun(X106, X106), 
38.52/38.73	              times_times(X106), 
38.52/38.73	              app_encode_app(int, X106, number_number_of(X106), X107)), 
38.52/38.73	            app_encode_app(int, X106, number_number_of(X106), X107))
38.52/38.73	       | ~ number(X106)
38.52/38.73	       | ~ monoid_mult(X106)),
38.52/38.73	    inference('demod', [status(thm)], ['4', '3'])).
38.52/38.73	tff('6', plain,
38.52/38.73	    ![X0 : int]:
38.52/38.73	      (app_encode_app(nat, int, 
38.52/38.73	         app_encode_app(int, app_encode_fun(nat, int), power_power(int), X0), 
38.52/38.73	         app_encode_app(int, nat, number_number_of(nat), 
38.52/38.73	           app_encode_app(int, int, bit0, one_one(int))))
38.52/38.73	        = app_encode_app(int, int, 
38.52/38.73	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
38.52/38.73	              app_encode_app(int, int, number_number_of(int), X0)), 
38.52/38.73	            app_encode_app(int, int, number_number_of(int), X0))
38.52/38.73	       | ~ monoid_mult(int)
38.52/38.73	       | ~ number(int)),
38.52/38.73	    inference('sup+', [status(thm)], ['2', '5'])).
38.52/38.73	tff(zf_stmt_135, axiom, (monoid_mult(int))).
38.52/38.73	tff('7', plain, monoid_mult(int),
38.52/38.73	    inference('cnf', [status(esa)], [zf_stmt_135])).
38.52/38.73	tff(zf_stmt_141, axiom, (number(int))).
38.52/38.73	tff('8', plain, number(int), inference('cnf', [status(esa)], [zf_stmt_141])).
38.52/38.73	tff('9', plain,
38.52/38.73	    ![X0 : int]:
38.52/38.73	      (app_encode_app(nat, int, 
38.52/38.73	         app_encode_app(int, app_encode_fun(nat, int), power_power(int), X0), 
38.52/38.73	         app_encode_app(int, nat, number_number_of(nat), 
38.52/38.73	           app_encode_app(int, int, bit0, one_one(int))))
38.52/38.73	        = app_encode_app(int, int, 
38.52/38.73	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
38.52/38.73	              X0), X0)
38.52/38.73	       | ~ $true
38.52/38.73	       | ~ $true),
38.52/38.73	    inference('demod', [status(thm)], ['6', '2', '2', '7', '8'])).
38.52/38.73	tff('10', plain,
38.52/38.73	    ![X0 : int]:
38.52/38.73	      app_encode_app(nat, int, 
38.52/38.73	        app_encode_app(int, app_encode_fun(nat, int), power_power(int), X0), 
38.52/38.73	        app_encode_app(int, nat, number_number_of(nat), 
38.52/38.73	          app_encode_app(int, int, bit0, one_one(int))))
38.52/38.73	       = app_encode_app(int, int, 
38.52/38.73	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
38.52/38.73	             X0), X0),
38.52/38.73	    inference('simplify', [status(thm)], ['9'])).
38.52/38.73	tff('11', plain,
38.52/38.73	    app_encode_app(int, int, 
38.52/38.73	      app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
38.52/38.73	        app_encode_app(int, int, 
38.52/38.73	          app_encode_app(int, app_encode_fun(int, int), times_times(int), s), 
38.52/38.73	          s)), min)
38.52/38.73	     != app_encode_app(int, int, 
38.52/38.73	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
38.52/38.73	            app_encode_app(int, int, 
38.52/38.73	              app_encode_app(int, app_encode_fun(int, int), 
38.52/38.73	                times_times(int), s), s)), one_one(int)),
38.52/38.73	    inference('demod', [status(thm)], ['0', '3', '10', '2', '3', '10'])).
38.52/38.73	tff(zf_stmt_59, axiom, (app_encode_app(int,int,bit1,min) = min)).
38.52/38.73	tff('12', plain, app_encode_app(int, int, bit1, min) = min,
38.52/38.73	    inference('cnf', [status(esa)], [zf_stmt_59])).
38.52/38.73	tff(zf_stmt_39, axiom,
38.52/38.73	  (![L:int]:
38.52/38.73	     (app_encode_app(int,int,
38.52/38.73	                     app_encode_app(int,app_encode_fun(int,int),
38.52/38.73	                                    minus_minus(int),pls),
38.52/38.73	                     app_encode_app(int,int,bit1,L)) =
38.52/38.73	      app_encode_app(int,int,bit1,
38.52/38.73	                     app_encode_app(int,int,
38.52/38.73	                                    app_encode_app(int,
38.52/38.73	                                                   app_encode_fun(int,int),
38.52/38.73	                                                   minus_minus(int),min),
38.52/38.73	                                    L))))).
38.52/38.73	tff('13', plain,
38.52/38.73	    ![X8 : int]:
38.52/38.73	      app_encode_app(int, int, 
38.52/38.73	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), pls), 
38.52/38.73	        app_encode_app(int, int, bit1, X8))
38.52/38.73	       = app_encode_app(int, int, bit1, 
38.52/38.73	           app_encode_app(int, int, 
38.52/38.73	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
38.52/38.73	               min), X8)),
38.52/38.73	    inference('cnf', [status(esa)], [zf_stmt_39])).
38.52/38.73	tff('14', plain,
38.52/38.73	    app_encode_app(int, int, 
38.52/38.73	      app_encode_app(int, app_encode_fun(int, int), minus_minus(int), pls), 
38.52/38.73	      min)
38.52/38.73	     = app_encode_app(int, int, bit1, 
38.52/38.73	         app_encode_app(int, int, 
38.52/38.73	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
38.52/38.73	             min), min)),
38.52/38.73	    inference('sup+', [status(thm)], ['12', '13'])).
38.52/38.73	tff(zf_stmt_38, axiom,
38.52/38.73	  (![L:int]:
38.52/38.73	     (app_encode_app(int,int,
38.52/38.73	                     app_encode_app(int,app_encode_fun(int,int),
38.52/38.73	                                    minus_minus(int),min),
38.52/38.73	                     app_encode_app(int,int,bit1,L)) =
38.52/38.73	      app_encode_app(int,int,bit0,
38.52/38.73	                     app_encode_app(int,int,
38.52/38.73	                                    app_encode_app(int,
38.52/38.73	                                                   app_encode_fun(int,int),
38.52/38.73	                                                   minus_minus(int),min),
38.52/38.73	                                    L))))).
38.52/38.73	tff('15', plain,
38.52/38.73	    ![X7 : int]:
38.52/38.73	      app_encode_app(int, int, 
38.52/38.73	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), min), 
38.52/38.73	        app_encode_app(int, int, bit1, X7))
38.52/38.73	       = app_encode_app(int, int, bit0, 
38.52/38.73	           app_encode_app(int, int, 
38.52/38.73	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
38.52/38.73	               min), X7)),
38.52/38.73	    inference('cnf', [status(esa)], [zf_stmt_38])).
38.52/38.73	tff('16', plain,
38.52/38.73	    app_encode_app(int, int, 
38.52/38.73	      app_encode_app(int, app_encode_fun(int, int), minus_minus(int), min), 
38.52/38.73	      min)
38.52/38.73	     = app_encode_app(int, int, bit0, 
38.52/38.73	         app_encode_app(int, int, 
38.52/38.73	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
38.52/38.73	             min), min)),
38.52/38.73	    inference('sup+', [status(thm)], ['12', '15'])).
38.52/38.73	tff(zf_stmt_74, axiom,
38.52/38.73	  (![K:int]:
38.52/38.73	     (app_encode_app(int,int,bit0,K) =
38.52/38.73	      app_encode_app(int,int,
38.52/38.73	                     app_encode_app(int,app_encode_fun(int,int),
38.52/38.73	                                    plus_plus(int),K),
38.52/38.73	                     K)))).
38.52/38.73	tff('17', plain,
38.52/38.73	    ![X63 : int]:
38.52/38.73	      app_encode_app(int, int, bit0, X63)
38.52/38.73	       = app_encode_app(int, int, 
38.52/38.73	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X63), 
38.52/38.73	           X63),
38.52/38.73	    inference('cnf', [status(esa)], [zf_stmt_74])).
38.52/38.73	tff(zf_stmt_73, axiom,
38.52/38.73	  (![K:int]:
38.52/38.73	     (app_encode_app(int,int,
38.52/38.73	                     app_encode_app(int,app_encode_fun(int,int),
38.52/38.73	                                    plus_plus(int),pls),
38.52/38.73	                     K) =
38.52/38.73	      K))).
38.52/38.73	tff('18', plain,
38.52/38.73	    ![X62 : int]:
38.52/38.73	      app_encode_app(int, int, 
38.52/38.73	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
38.52/38.73	        X62)
38.52/38.73	       = X62,
38.52/38.73	    inference('cnf', [status(esa)], [zf_stmt_73])).
38.52/38.73	tff(zf_stmt_92, axiom,
38.52/38.73	  (![A:$tType]:
38.52/38.73	     (cancel_semigroup_add(A) =>
38.52/38.73	      (![C1:A,A2:A,B2:A]:
38.52/38.73	         ((app_encode_app(A,A,
38.52/38.73	                          app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
38.52/38.73	                                         B2),
38.52/38.73	                          A2) =
38.52/38.73	           app_encode_app(A,A,
38.52/38.73	                          app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
38.52/38.73	                                         C1),
38.52/38.73	                          A2)) <=>
38.52/38.73	          (B2 = C1)))))).
38.52/38.73	tff('19', plain,
38.52/38.73	    ![X91 : $tType, X92 : X91, X94 : X91, X95 : X91]:
38.52/38.73	      (app_encode_app(X91, X91, 
38.52/38.73	         app_encode_app(X91, app_encode_fun(X91, X91), plus_plus(X91), X95), 
38.52/38.73	         X94)
38.52/38.73	        != app_encode_app(X91, X91, 
38.52/38.73	             app_encode_app(X91, app_encode_fun(X91, X91), plus_plus(X91), 
38.52/38.73	               X92), X94)
38.52/38.73	       | X95 = X92
38.52/38.73	       | ~ cancel_semigroup_add(X91)),
38.52/38.73	    inference('cnf', [status(esa)], [zf_stmt_92])).
38.52/38.73	tff('20', plain,
38.52/38.73	    ![X0 : int, X1 : int]:
38.52/38.73	      (X0
38.52/38.73	        != app_encode_app(int, int, 
38.52/38.73	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
38.52/38.74	               X1), X0)
38.52/38.74	       | ~ cancel_semigroup_add(int)
38.52/38.74	       | pls = X1),
38.52/38.74	    inference('sup-', [status(thm)], ['18', '19'])).
38.52/38.74	tff(zf_stmt_130, axiom, (cancel_semigroup_add(int))).
38.52/38.74	tff('21', plain, cancel_semigroup_add(int),
38.52/38.74	    inference('cnf', [status(esa)], [zf_stmt_130])).
38.52/38.74	tff('22', plain,
38.52/38.74	    ![X0 : int, X1 : int]:
38.52/38.74	      (X0
38.52/38.74	        != app_encode_app(int, int, 
38.52/38.74	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
38.52/38.74	               X1), X0)
38.52/38.74	       | ~ $true
38.52/38.74	       | pls = X1),
38.52/38.74	    inference('demod', [status(thm)], ['20', '21'])).
38.52/38.74	tff('23', plain,
38.52/38.74	    ![X0 : int, X1 : int]:
38.52/38.74	      (pls = X1
38.52/38.74	       | X0
38.52/38.74	          != app_encode_app(int, int, 
38.52/38.74	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
38.52/38.74	                 X1), X0)),
38.52/38.74	    inference('simplify', [status(thm)], ['22'])).
38.52/38.74	tff('24', plain,
38.52/38.74	    ![X0 : int]: (X0 != app_encode_app(int, int, bit0, X0) | pls = X0),
38.52/38.74	    inference('sup-', [status(thm)], ['17', '23'])).
38.52/38.74	tff('25', plain,
38.52/38.74	    (app_encode_app(int, int, 
38.52/38.74	       app_encode_app(int, app_encode_fun(int, int), minus_minus(int), min), 
38.52/38.74	       min)
38.52/38.74	      != app_encode_app(int, int, 
38.52/38.74	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
38.52/38.74	             min), min)
38.52/38.74	     | pls
38.52/38.74	        = app_encode_app(int, int, 
38.52/38.74	            app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
38.52/38.74	              min), min)),
38.52/38.74	    inference('sup-', [status(thm)], ['16', '24'])).
38.52/38.74	tff('26', plain,
38.52/38.74	    pls
38.52/38.74	     = app_encode_app(int, int, 
38.52/38.74	         app_encode_app(int, app_encode_fun(int, int), minus_minus(int), min), 
38.52/38.74	         min),
38.52/38.74	    inference('simplify', [status(thm)], ['25'])).
38.52/38.74	tff('27', plain,
38.52/38.74	    app_encode_app(int, int, 
38.52/38.74	      app_encode_app(int, app_encode_fun(int, int), minus_minus(int), pls), 
38.52/38.74	      min)
38.52/38.74	     = app_encode_app(int, int, bit1, pls),
38.52/38.74	    inference('demod', [status(thm)], ['14', '26'])).
38.52/38.74	tff('28', plain,
38.52/38.74	    app_encode_app(int, int, 
38.52/38.74	      app_encode_app(int, app_encode_fun(int, int), minus_minus(int), pls), 
38.52/38.74	      min)
38.52/38.74	     = one_one(int),
38.52/38.74	    inference('demod', [status(thm)], ['27', '3'])).
38.52/38.74	tff(zf_stmt_72, axiom,
38.52/38.74	  (![K:int]:
38.52/38.74	     (app_encode_app(int,int,
38.52/38.74	                     app_encode_app(int,app_encode_fun(int,int),
38.52/38.74	                                    plus_plus(int),K),
38.52/38.74	                     pls) =
38.52/38.74	      K))).
38.52/38.74	tff('29', plain,
38.52/38.74	    ![X61 : int]:
38.52/38.74	      app_encode_app(int, int, 
38.52/38.74	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X61), 
38.52/38.74	        pls)
38.52/38.74	       = X61,
38.52/38.74	    inference('cnf', [status(esa)], [zf_stmt_72])).
38.52/38.74	tff(zf_stmt_86, axiom,
38.52/38.74	  (![A:$tType]:
38.52/38.74	     (number_ring(A) =>
38.52/38.74	      (![C:A,W:int,V:int]:
38.52/38.74	         (app_encode_app(A,A,
38.52/38.74	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
38.52/38.74	                                        app_encode_app(int,A,
38.52/38.74	                                                       number_number_of(A),V)),
38.52/38.74	                         app_encode_app(A,A,
38.52/38.74	                                        app_encode_app(A,app_encode_fun(A,A),
38.52/38.74	                                                       minus_minus(A),
38.52/38.74	                                                       app_encode_app(
38.52/38.74	                                                       int,A,
38.52/38.74	                                                       number_number_of(A),W)),
38.52/38.74	                                        C)) =
38.52/38.74	          app_encode_app(A,A,
38.52/38.74	                         app_encode_app(A,app_encode_fun(A,A),minus_minus(A),
38.52/38.74	                                        app_encode_app(int,A,
38.52/38.74	                                                       number_number_of(A),
38.52/38.74	                                                       app_encode_app(
38.52/38.74	                                                       int,int,
38.52/38.74	                                                       app_encode_app(
38.52/38.74	                                                       int,
38.52/38.74	                                                       app_encode_fun(
38.52/38.74	                                                       int,int),
38.52/38.74	                                                       plus_plus(int),V),W))),
38.52/38.74	                         C)))))).
38.52/38.74	tff('30', plain,
38.52/38.74	    ![X82 : $tType, X83 : int, X84 : int, X85 : X82]:
38.52/38.74	      (app_encode_app(X82, X82, 
38.52/38.74	         app_encode_app(X82, app_encode_fun(X82, X82), plus_plus(X82), 
38.52/38.74	           app_encode_app(int, X82, number_number_of(X82), X83)), 
38.52/38.74	         app_encode_app(X82, X82, 
38.52/38.74	           app_encode_app(X82, app_encode_fun(X82, X82), minus_minus(X82), 
38.52/38.74	             app_encode_app(int, X82, number_number_of(X82), X84)), X85))
38.52/38.74	        = app_encode_app(X82, X82, 
38.52/38.74	            app_encode_app(X82, app_encode_fun(X82, X82), minus_minus(X82), 
38.52/38.74	              app_encode_app(int, X82, number_number_of(X82), 
38.52/38.74	                app_encode_app(int, int, 
38.52/38.74	                  app_encode_app(int, app_encode_fun(int, int), 
38.52/38.74	                    plus_plus(int), X83), X84))), X85)
38.52/38.74	       | ~ number_ring(X82)),
38.52/38.74	    inference('cnf', [status(esa)], [zf_stmt_86])).
38.52/38.74	tff('31', plain,
38.52/38.74	    ![X0 : int, X1 : int, X2 : int]:
38.52/38.74	      (app_encode_app(int, int, 
38.52/38.74	         app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
38.52/38.74	         app_encode_app(int, int, 
38.52/38.74	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
38.52/38.74	             app_encode_app(int, int, number_number_of(int), X2)), X1))
38.52/38.74	        = app_encode_app(int, int, 
38.52/38.74	            app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
38.52/38.74	              app_encode_app(int, int, number_number_of(int), 
38.52/38.74	                app_encode_app(int, int, 
38.52/38.74	                  app_encode_app(int, app_encode_fun(int, int), 
38.52/38.74	                    plus_plus(int), X0), X2))), X1)
38.52/38.74	       | ~ number_ring(int)),
38.52/38.74	    inference('sup+', [status(thm)], ['2', '30'])).
38.52/38.74	tff(zf_stmt_138, axiom, (number_ring(int))).
38.52/38.74	tff('32', plain, number_ring(int),
38.52/38.74	    inference('cnf', [status(esa)], [zf_stmt_138])).
38.52/38.74	tff('33', plain,
38.52/38.74	    ![X0 : int, X1 : int, X2 : int]:
38.52/38.74	      (app_encode_app(int, int, 
38.52/38.74	         app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
38.52/38.74	         app_encode_app(int, int, 
38.52/38.74	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
38.52/38.74	             X2), X1))
38.52/38.74	        = app_encode_app(int, int, 
38.52/38.74	            app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
38.52/38.74	              app_encode_app(int, int, 
38.52/38.74	                app_encode_app(int, app_encode_fun(int, int), 
38.52/38.74	                  plus_plus(int), X0), X2)), X1)
38.52/38.74	       | ~ $true),
38.52/38.74	    inference('demod', [status(thm)], ['31', '2', '2', '32'])).
38.52/38.74	tff('34', plain,
38.52/38.74	    ![X0 : int, X1 : int, X2 : int]:
38.52/38.74	      app_encode_app(int, int, 
38.52/38.74	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
38.52/38.74	        app_encode_app(int, int, 
38.52/38.74	          app_encode_app(int, app_encode_fun(int, int), minus_minus(int), X2), 
38.52/38.74	          X1))
38.52/38.74	       = app_encode_app(int, int, 
38.52/38.74	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
38.52/38.74	             app_encode_app(int, int, 
38.52/38.74	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
38.52/38.74	                 X0), X2)), X1),
38.52/38.74	    inference('simplify', [status(thm)], ['33'])).
38.52/38.74	tff('35', plain,
38.52/38.74	    ![X0 : int, X1 : int]:
38.52/38.74	      app_encode_app(int, int, 
38.52/38.74	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
38.52/38.74	        app_encode_app(int, int, 
38.52/38.74	          app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
38.52/38.74	            pls), X1))
38.52/38.74	       = app_encode_app(int, int, 
38.52/38.74	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
38.52/38.74	             X0), X1),
38.52/38.74	    inference('sup+', [status(thm)], ['29', '34'])).
38.52/38.74	tff('36', plain,
38.52/38.74	    ![X0 : int]:
38.52/38.74	      app_encode_app(int, int, 
38.52/38.74	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
38.52/38.74	        one_one(int))
38.52/38.74	       = app_encode_app(int, int, 
38.52/38.74	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
38.52/38.74	             X0), min),
38.52/38.74	    inference('sup+', [status(thm)], ['28', '35'])).
38.52/38.74	tff('37', plain,
38.52/38.74	    app_encode_app(int, int, 
38.52/38.74	      app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
38.52/38.74	        app_encode_app(int, int, 
38.52/38.74	          app_encode_app(int, app_encode_fun(int, int), times_times(int), s), 
38.52/38.74	          s)), min)
38.52/38.74	     != app_encode_app(int, int, 
38.52/38.74	          app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
38.52/38.74	            app_encode_app(int, int, 
38.52/38.74	              app_encode_app(int, app_encode_fun(int, int), 
38.52/38.74	                times_times(int), s), s)), min),
38.52/38.74	    inference('demod', [status(thm)], ['11', '36'])).
38.52/38.74	tff('38', plain, $false, inference('simplify', [status(thm)], ['37'])).
38.52/38.74	
38.52/38.74	% SZS output end Refutation
38.52/38.74	EOF
