0.00/0.00	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : appext
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : 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   : n090.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
43.51/43.74	% done 6779 iterations in 43.548s
43.51/43.74	% SZS status Theorem for 'stdin'
43.51/43.74	% SZS output start Refutation
43.51/43.74	tff(zf_stmt_157, conjecture,
43.51/43.74	  (app_encode_app(int,int,
43.51/43.74	                  app_encode_app(int,app_encode_fun(int,int),
43.51/43.74	                                 minus_minus(int),
43.51/43.74	                                 app_encode_app(nat,int,
43.51/43.74	                                                app_encode_app(int,
43.51/43.74	                                                               app_encode_fun(
43.51/43.74	                                                               nat,int),
43.51/43.74	                                                               power_power(
43.51/43.74	                                                               int),s),
43.51/43.74	                                                app_encode_app(int,nat,
43.51/43.74	                                                               number_number_of(
43.51/43.74	                                                               nat),
43.51/43.74	                                                               app_encode_app(
43.51/43.74	                                                               int,int,bit0,
43.51/43.74	                                                               app_encode_app(
43.51/43.74	                                                               int,int,bit1,
43.51/43.74	                                                               pls))))),
43.51/43.74	                  app_encode_app(int,int,number_number_of(int),min)) =
43.51/43.74	   app_encode_app(int,int,
43.51/43.74	                  app_encode_app(int,app_encode_fun(int,int),plus_plus(int),
43.51/43.74	                                 app_encode_app(nat,int,
43.51/43.74	                                                app_encode_app(int,
43.51/43.74	                                                               app_encode_fun(
43.51/43.74	                                                               nat,int),
43.51/43.74	                                                               power_power(
43.51/43.74	                                                               int),s),
43.51/43.74	                                                app_encode_app(int,nat,
43.51/43.74	                                                               number_number_of(
43.51/43.74	                                                               nat),
43.51/43.74	                                                               app_encode_app(
43.51/43.74	                                                               int,int,bit0,
43.51/43.74	                                                               app_encode_app(
43.51/43.74	                                                               int,int,bit1,
43.51/43.74	                                                               pls))))),
43.51/43.74	                  one_one(int)))).
43.51/43.74	tff(zf_stmt_0, negated_conjecture,
43.51/43.74	  (app_encode_app(int,int,
43.51/43.74	                  app_encode_app(int,app_encode_fun(int,int),
43.51/43.74	                                 minus_minus(int),
43.51/43.74	                                 app_encode_app(nat,int,
43.51/43.74	                                                app_encode_app(int,
43.51/43.74	                                                               app_encode_fun(
43.51/43.74	                                                               nat,int),
43.51/43.74	                                                               power_power(
43.51/43.74	                                                               int),s),
43.51/43.74	                                                app_encode_app(int,nat,
43.51/43.74	                                                               number_number_of(
43.51/43.74	                                                               nat),
43.51/43.74	                                                               app_encode_app(
43.51/43.74	                                                               int,int,bit0,
43.51/43.74	                                                               app_encode_app(
43.51/43.74	                                                               int,int,bit1,
43.51/43.74	                                                               pls))))),
43.51/43.74	                  app_encode_app(int,int,number_number_of(int),min)) !=
43.51/43.74	   app_encode_app(int,int,
43.51/43.74	                  app_encode_app(int,app_encode_fun(int,int),plus_plus(int),
43.51/43.74	                                 app_encode_app(nat,int,
43.51/43.74	                                                app_encode_app(int,
43.51/43.74	                                                               app_encode_fun(
43.51/43.74	                                                               nat,int),
43.51/43.74	                                                               power_power(
43.51/43.74	                                                               int),s),
43.51/43.74	                                                app_encode_app(int,nat,
43.51/43.74	                                                               number_number_of(
43.51/43.74	                                                               nat),
43.51/43.74	                                                               app_encode_app(
43.51/43.74	                                                               int,int,bit0,
43.51/43.74	                                                               app_encode_app(
43.51/43.74	                                                               int,int,bit1,
43.51/43.74	                                                               pls))))),
43.51/43.74	                  one_one(int)))).
43.51/43.74	tff('0', plain,
43.51/43.74	    app_encode_app(int, int, 
43.51/43.74	      app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
43.51/43.74	        app_encode_app(nat, int, 
43.51/43.74	          app_encode_app(int, app_encode_fun(nat, int), power_power(int), s), 
43.51/43.74	          app_encode_app(int, nat, number_number_of(nat), 
43.51/43.74	            app_encode_app(int, int, bit0, 
43.51/43.74	              app_encode_app(int, int, bit1, pls))))), 
43.51/43.74	      app_encode_app(int, int, number_number_of(int), min))
43.51/43.74	     != app_encode_app(int, int, 
43.51/43.74	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
43.51/43.74	            app_encode_app(nat, int, 
43.51/43.74	              app_encode_app(int, app_encode_fun(nat, int), 
43.51/43.74	                power_power(int), s), 
43.51/43.74	              app_encode_app(int, nat, number_number_of(nat), 
43.51/43.74	                app_encode_app(int, int, bit0, 
43.51/43.74	                  app_encode_app(int, int, bit1, pls))))), one_one(int)),
43.51/43.74	    inference('cnf', [status(esa)], [zf_stmt_0])).
43.51/43.74	tff(zf_stmt_88, axiom,
43.51/43.74	  (one_one(int) =
43.51/43.74	   app_encode_app(int,int,number_number_of(int),
43.51/43.74	                  app_encode_app(int,int,bit1,pls)))).
43.51/43.74	tff('1', plain,
43.51/43.74	    one_one(int)
43.51/43.74	     = app_encode_app(int, int, number_number_of(int), 
43.51/43.74	         app_encode_app(int, int, bit1, pls)),
43.51/43.74	    inference('cnf', [status(esa)], [zf_stmt_88])).
43.51/43.75	tff(zf_stmt_72, axiom,
43.51/43.75	  (![K:int]: (app_encode_app(int,int,number_number_of(int),K) = K))).
43.51/43.75	tff('2', plain,
43.51/43.75	    ![X64 : int]: app_encode_app(int, int, number_number_of(int), X64) = X64,
43.51/43.75	    inference('cnf', [status(esa)], [zf_stmt_72])).
43.51/43.75	tff('3', plain, one_one(int) = app_encode_app(int, int, bit1, pls),
43.51/43.75	    inference('demod', [status(thm)], ['1', '2'])).
43.51/43.75	tff(zf_stmt_97, axiom,
43.51/43.75	  (![B1:$tType]:
43.51/43.75	     ((monoid_mult(B1) & number(B1)) =>
43.51/43.75	      (![W:int]:
43.51/43.75	         (app_encode_app(nat,B1,
43.51/43.75	                         app_encode_app(B1,app_encode_fun(nat,B1),
43.51/43.75	                                        power_power(B1),
43.51/43.75	                                        app_encode_app(int,B1,
43.51/43.75	                                                       number_number_of(B1),W)),
43.51/43.75	                         app_encode_app(int,nat,number_number_of(nat),
43.51/43.75	                                        app_encode_app(int,int,bit0,
43.51/43.75	                                                       app_encode_app(
43.51/43.75	                                                       int,int,bit1,pls)))) =
43.51/43.75	          app_encode_app(B1,B1,
43.51/43.75	                         app_encode_app(B1,app_encode_fun(B1,B1),
43.51/43.75	                                        times_times(B1),
43.51/43.75	                                        app_encode_app(int,B1,
43.51/43.75	                                                       number_number_of(B1),W)),
43.51/43.75	                         app_encode_app(int,B1,number_number_of(B1),W))))))).
43.51/43.75	tff('4', plain,
43.51/43.75	    ![X110 : $tType, X111 : int]:
43.51/43.75	      (app_encode_app(nat, X110, 
43.51/43.75	         app_encode_app(X110, app_encode_fun(nat, X110), power_power(X110), 
43.51/43.75	           app_encode_app(int, X110, number_number_of(X110), X111)), 
43.51/43.75	         app_encode_app(int, nat, number_number_of(nat), 
43.51/43.75	           app_encode_app(int, int, bit0, 
43.51/43.75	             app_encode_app(int, int, bit1, pls))))
43.51/43.75	        = app_encode_app(X110, X110, 
43.51/43.75	            app_encode_app(X110, app_encode_fun(X110, X110), 
43.51/43.75	              times_times(X110), 
43.51/43.75	              app_encode_app(int, X110, number_number_of(X110), X111)), 
43.51/43.75	            app_encode_app(int, X110, number_number_of(X110), X111))
43.51/43.75	       | ~ number(X110)
43.51/43.75	       | ~ monoid_mult(X110)),
43.51/43.75	    inference('cnf', [status(esa)], [zf_stmt_97])).
43.51/43.75	tff('5', plain,
43.51/43.75	    ![X110 : $tType, X111 : int]:
43.51/43.75	      (app_encode_app(nat, X110, 
43.51/43.75	         app_encode_app(X110, app_encode_fun(nat, X110), power_power(X110), 
43.51/43.75	           app_encode_app(int, X110, number_number_of(X110), X111)), 
43.51/43.75	         app_encode_app(int, nat, number_number_of(nat), 
43.51/43.75	           app_encode_app(int, int, bit0, one_one(int))))
43.51/43.75	        = app_encode_app(X110, X110, 
43.51/43.75	            app_encode_app(X110, app_encode_fun(X110, X110), 
43.51/43.75	              times_times(X110), 
43.51/43.75	              app_encode_app(int, X110, number_number_of(X110), X111)), 
43.51/43.75	            app_encode_app(int, X110, number_number_of(X110), X111))
43.51/43.75	       | ~ number(X110)
43.51/43.75	       | ~ monoid_mult(X110)),
43.51/43.75	    inference('demod', [status(thm)], ['4', '3'])).
43.51/43.75	tff('6', plain,
43.51/43.75	    ![X0 : int]:
43.51/43.75	      (app_encode_app(nat, int, 
43.51/43.75	         app_encode_app(int, app_encode_fun(nat, int), power_power(int), X0), 
43.51/43.75	         app_encode_app(int, nat, number_number_of(nat), 
43.51/43.75	           app_encode_app(int, int, bit0, one_one(int))))
43.51/43.75	        = app_encode_app(int, int, 
43.51/43.75	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
43.51/43.75	              app_encode_app(int, int, number_number_of(int), X0)), 
43.51/43.75	            app_encode_app(int, int, number_number_of(int), X0))
43.51/43.75	       | ~ monoid_mult(int)
43.51/43.75	       | ~ number(int)),
43.51/43.75	    inference('sup+', [status(thm)], ['2', '5'])).
43.51/43.75	tff(zf_stmt_136, axiom, (monoid_mult(int))).
43.51/43.75	tff('7', plain, monoid_mult(int),
43.51/43.75	    inference('cnf', [status(esa)], [zf_stmt_136])).
43.51/43.75	tff(zf_stmt_142, axiom, (number(int))).
43.51/43.75	tff('8', plain, number(int), inference('cnf', [status(esa)], [zf_stmt_142])).
43.51/43.75	tff('9', plain,
43.51/43.75	    ![X0 : int]:
43.51/43.75	      (app_encode_app(nat, int, 
43.51/43.75	         app_encode_app(int, app_encode_fun(nat, int), power_power(int), X0), 
43.51/43.75	         app_encode_app(int, nat, number_number_of(nat), 
43.51/43.75	           app_encode_app(int, int, bit0, one_one(int))))
43.51/43.75	        = app_encode_app(int, int, 
43.51/43.75	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
43.51/43.75	              X0), X0)
43.51/43.75	       | ~ $true
43.51/43.75	       | ~ $true),
43.51/43.75	    inference('demod', [status(thm)], ['6', '2', '2', '7', '8'])).
43.51/43.75	tff('10', plain,
43.51/43.75	    ![X0 : int]:
43.51/43.75	      app_encode_app(nat, int, 
43.51/43.75	        app_encode_app(int, app_encode_fun(nat, int), power_power(int), X0), 
43.51/43.75	        app_encode_app(int, nat, number_number_of(nat), 
43.51/43.75	          app_encode_app(int, int, bit0, one_one(int))))
43.51/43.75	       = app_encode_app(int, int, 
43.51/43.75	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
43.51/43.75	             X0), X0),
43.51/43.75	    inference('simplify', [status(thm)], ['9'])).
43.51/43.75	tff('11', plain,
43.51/43.75	    app_encode_app(int, int, 
43.51/43.75	      app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
43.51/43.75	        app_encode_app(int, int, 
43.51/43.75	          app_encode_app(int, app_encode_fun(int, int), times_times(int), s), 
43.51/43.75	          s)), min)
43.51/43.75	     != app_encode_app(int, int, 
43.51/43.75	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
43.51/43.75	            app_encode_app(int, int, 
43.51/43.75	              app_encode_app(int, app_encode_fun(int, int), 
43.51/43.75	                times_times(int), s), s)), one_one(int)),
43.51/43.75	    inference('demod', [status(thm)], ['0', '3', '10', '2', '3', '10'])).
43.51/43.75	tff(zf_stmt_60, axiom, (app_encode_app(int,int,bit1,min) = min)).
43.51/43.75	tff('12', plain, app_encode_app(int, int, bit1, min) = min,
43.51/43.75	    inference('cnf', [status(esa)], [zf_stmt_60])).
43.51/43.75	tff(zf_stmt_40, axiom,
43.51/43.75	  (![L:int]:
43.51/43.75	     (app_encode_app(int,int,
43.51/43.75	                     app_encode_app(int,app_encode_fun(int,int),
43.51/43.75	                                    minus_minus(int),pls),
43.51/43.75	                     app_encode_app(int,int,bit1,L)) =
43.51/43.75	      app_encode_app(int,int,bit1,
43.51/43.75	                     app_encode_app(int,int,
43.51/43.75	                                    app_encode_app(int,
43.51/43.75	                                                   app_encode_fun(int,int),
43.51/43.75	                                                   minus_minus(int),min),
43.51/43.75	                                    L))))).
43.51/43.75	tff('13', plain,
43.51/43.75	    ![X12 : int]:
43.51/43.75	      app_encode_app(int, int, 
43.51/43.75	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), pls), 
43.51/43.75	        app_encode_app(int, int, bit1, X12))
43.51/43.75	       = app_encode_app(int, int, bit1, 
43.51/43.75	           app_encode_app(int, int, 
43.51/43.75	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
43.51/43.75	               min), X12)),
43.51/43.75	    inference('cnf', [status(esa)], [zf_stmt_40])).
43.51/43.75	tff('14', plain,
43.51/43.75	    app_encode_app(int, int, 
43.51/43.75	      app_encode_app(int, app_encode_fun(int, int), minus_minus(int), pls), 
43.51/43.75	      min)
43.51/43.75	     = app_encode_app(int, int, bit1, 
43.51/43.75	         app_encode_app(int, int, 
43.51/43.75	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
43.51/43.75	             min), min)),
43.51/43.75	    inference('sup+', [status(thm)], ['12', '13'])).
43.51/43.75	tff(zf_stmt_39, axiom,
43.51/43.75	  (![L:int]:
43.51/43.75	     (app_encode_app(int,int,
43.51/43.75	                     app_encode_app(int,app_encode_fun(int,int),
43.51/43.75	                                    minus_minus(int),min),
43.51/43.75	                     app_encode_app(int,int,bit1,L)) =
43.51/43.75	      app_encode_app(int,int,bit0,
43.51/43.75	                     app_encode_app(int,int,
43.51/43.75	                                    app_encode_app(int,
43.51/43.75	                                                   app_encode_fun(int,int),
43.51/43.75	                                                   minus_minus(int),min),
43.51/43.75	                                    L))))).
43.51/43.75	tff('15', plain,
43.51/43.75	    ![X11 : int]:
43.51/43.75	      app_encode_app(int, int, 
43.51/43.75	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), min), 
43.51/43.75	        app_encode_app(int, int, bit1, X11))
43.51/43.75	       = app_encode_app(int, int, bit0, 
43.51/43.75	           app_encode_app(int, int, 
43.51/43.75	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
43.51/43.75	               min), X11)),
43.51/43.75	    inference('cnf', [status(esa)], [zf_stmt_39])).
43.51/43.75	tff('16', plain,
43.51/43.75	    app_encode_app(int, int, 
43.51/43.75	      app_encode_app(int, app_encode_fun(int, int), minus_minus(int), min), 
43.51/43.75	      min)
43.51/43.75	     = app_encode_app(int, int, bit0, 
43.51/43.75	         app_encode_app(int, int, 
43.51/43.75	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
43.51/43.75	             min), min)),
43.51/43.75	    inference('sup+', [status(thm)], ['12', '15'])).
43.51/43.75	tff(zf_stmt_75, axiom,
43.51/43.75	  (![K:int]:
43.51/43.75	     (app_encode_app(int,int,bit0,K) =
43.51/43.75	      app_encode_app(int,int,
43.51/43.75	                     app_encode_app(int,app_encode_fun(int,int),
43.51/43.75	                                    plus_plus(int),K),
43.51/43.75	                     K)))).
43.51/43.75	tff('17', plain,
43.51/43.75	    ![X67 : int]:
43.51/43.75	      app_encode_app(int, int, bit0, X67)
43.51/43.75	       = app_encode_app(int, int, 
43.51/43.75	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X67), 
43.51/43.75	           X67),
43.51/43.75	    inference('cnf', [status(esa)], [zf_stmt_75])).
43.51/43.75	tff(zf_stmt_74, axiom,
43.51/43.75	  (![K:int]:
43.51/43.75	     (app_encode_app(int,int,
43.51/43.75	                     app_encode_app(int,app_encode_fun(int,int),
43.51/43.75	                                    plus_plus(int),pls),
43.51/43.75	                     K) =
43.51/43.75	      K))).
43.51/43.75	tff('18', plain,
43.51/43.75	    ![X66 : int]:
43.51/43.75	      app_encode_app(int, int, 
43.51/43.75	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
43.51/43.75	        X66)
43.51/43.75	       = X66,
43.51/43.75	    inference('cnf', [status(esa)], [zf_stmt_74])).
43.51/43.75	tff(zf_stmt_93, axiom,
43.51/43.75	  (![A:$tType]:
43.51/43.75	     (cancel_semigroup_add(A) =>
43.51/43.75	      (![C1:A,A2:A,B2:A]:
43.51/43.75	         ((app_encode_app(A,A,
43.51/43.75	                          app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
43.51/43.75	                                         B2),
43.51/43.75	                          A2) =
43.51/43.75	           app_encode_app(A,A,
43.51/43.75	                          app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
43.51/43.75	                                         C1),
43.51/43.75	                          A2)) <=>
43.51/43.75	          (B2 = C1)))))).
43.51/43.75	tff('19', plain,
43.51/43.75	    ![X95 : $tType, X96 : X95, X98 : X95, X99 : X95]:
43.51/43.75	      (app_encode_app(X95, X95, 
43.51/43.75	         app_encode_app(X95, app_encode_fun(X95, X95), plus_plus(X95), X99), 
43.51/43.75	         X98)
43.51/43.75	        != app_encode_app(X95, X95, 
43.51/43.75	             app_encode_app(X95, app_encode_fun(X95, X95), plus_plus(X95), 
43.51/43.75	               X96), X98)
43.51/43.75	       | X99 = X96
43.51/43.75	       | ~ cancel_semigroup_add(X95)),
43.51/43.75	    inference('cnf', [status(esa)], [zf_stmt_93])).
43.51/43.75	tff('20', plain,
43.51/43.75	    ![X0 : int, X1 : int]:
43.51/43.75	      (X0
43.51/43.75	        != app_encode_app(int, int, 
43.51/43.75	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
43.51/43.75	               X1), X0)
43.51/43.75	       | ~ cancel_semigroup_add(int)
43.51/43.75	       | pls = X1),
43.51/43.75	    inference('sup-', [status(thm)], ['18', '19'])).
43.51/43.75	tff(zf_stmt_131, axiom, (cancel_semigroup_add(int))).
43.51/43.75	tff('21', plain, cancel_semigroup_add(int),
43.51/43.75	    inference('cnf', [status(esa)], [zf_stmt_131])).
43.51/43.75	tff('22', plain,
43.51/43.75	    ![X0 : int, X1 : int]:
43.51/43.75	      (X0
43.51/43.75	        != app_encode_app(int, int, 
43.51/43.75	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
43.51/43.75	               X1), X0)
43.51/43.75	       | ~ $true
43.51/43.75	       | pls = X1),
43.51/43.75	    inference('demod', [status(thm)], ['20', '21'])).
43.51/43.75	tff('23', plain,
43.51/43.75	    ![X0 : int, X1 : int]:
43.51/43.75	      (pls = X1
43.51/43.75	       | X0
43.51/43.75	          != app_encode_app(int, int, 
43.51/43.75	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
43.51/43.75	                 X1), X0)),
43.51/43.75	    inference('simplify', [status(thm)], ['22'])).
43.51/43.75	tff('24', plain,
43.51/43.75	    ![X0 : int]: (X0 != app_encode_app(int, int, bit0, X0) | pls = X0),
43.51/43.75	    inference('sup-', [status(thm)], ['17', '23'])).
43.51/43.75	tff('25', plain,
43.51/43.75	    (app_encode_app(int, int, 
43.51/43.75	       app_encode_app(int, app_encode_fun(int, int), minus_minus(int), min), 
43.51/43.75	       min)
43.51/43.75	      != app_encode_app(int, int, 
43.51/43.75	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
43.51/43.75	             min), min)
43.51/43.75	     | pls
43.51/43.75	        = app_encode_app(int, int, 
43.51/43.75	            app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
43.51/43.75	              min), min)),
43.51/43.75	    inference('sup-', [status(thm)], ['16', '24'])).
43.51/43.75	tff('26', plain,
43.51/43.75	    pls
43.51/43.75	     = app_encode_app(int, int, 
43.51/43.75	         app_encode_app(int, app_encode_fun(int, int), minus_minus(int), min), 
43.51/43.75	         min),
43.51/43.75	    inference('simplify', [status(thm)], ['25'])).
43.51/43.75	tff('27', plain,
43.51/43.75	    app_encode_app(int, int, 
43.51/43.75	      app_encode_app(int, app_encode_fun(int, int), minus_minus(int), pls), 
43.51/43.75	      min)
43.51/43.75	     = app_encode_app(int, int, bit1, pls),
43.51/43.75	    inference('demod', [status(thm)], ['14', '26'])).
43.51/43.75	tff('28', plain,
43.51/43.75	    app_encode_app(int, int, 
43.51/43.75	      app_encode_app(int, app_encode_fun(int, int), minus_minus(int), pls), 
43.51/43.75	      min)
43.51/43.75	     = one_one(int),
43.51/43.75	    inference('demod', [status(thm)], ['27', '3'])).
43.51/43.75	tff(zf_stmt_73, axiom,
43.51/43.75	  (![K:int]:
43.51/43.75	     (app_encode_app(int,int,
43.51/43.75	                     app_encode_app(int,app_encode_fun(int,int),
43.51/43.75	                                    plus_plus(int),K),
43.51/43.75	                     pls) =
43.51/43.75	      K))).
43.51/43.75	tff('29', plain,
43.51/43.75	    ![X65 : int]:
43.51/43.75	      app_encode_app(int, int, 
43.51/43.75	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X65), 
43.51/43.75	        pls)
43.51/43.75	       = X65,
43.51/43.75	    inference('cnf', [status(esa)], [zf_stmt_73])).
43.51/43.75	tff(zf_stmt_87, axiom,
43.51/43.75	  (![A:$tType]:
43.51/43.75	     (number_ring(A) =>
43.51/43.75	      (![C:A,W:int,V:int]:
43.51/43.75	         (app_encode_app(A,A,
43.51/43.75	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
43.51/43.75	                                        app_encode_app(int,A,
43.51/43.75	                                                       number_number_of(A),V)),
43.51/43.75	                         app_encode_app(A,A,
43.51/43.75	                                        app_encode_app(A,app_encode_fun(A,A),
43.51/43.75	                                                       minus_minus(A),
43.51/43.75	                                                       app_encode_app(
43.51/43.75	                                                       int,A,
43.51/43.75	                                                       number_number_of(A),W)),
43.51/43.75	                                        C)) =
43.51/43.75	          app_encode_app(A,A,
43.51/43.75	                         app_encode_app(A,app_encode_fun(A,A),minus_minus(A),
43.51/43.75	                                        app_encode_app(int,A,
43.51/43.75	                                                       number_number_of(A),
43.51/43.75	                                                       app_encode_app(
43.51/43.75	                                                       int,int,
43.51/43.75	                                                       app_encode_app(
43.51/43.75	                                                       int,
43.51/43.75	                                                       app_encode_fun(
43.51/43.75	                                                       int,int),
43.51/43.75	                                                       plus_plus(int),V),W))),
43.51/43.75	                         C)))))).
43.51/43.75	tff('30', plain,
43.51/43.75	    ![X86 : $tType, X87 : int, X88 : int, X89 : X86]:
43.51/43.75	      (app_encode_app(X86, X86, 
43.51/43.75	         app_encode_app(X86, app_encode_fun(X86, X86), plus_plus(X86), 
43.51/43.75	           app_encode_app(int, X86, number_number_of(X86), X87)), 
43.51/43.75	         app_encode_app(X86, X86, 
43.51/43.75	           app_encode_app(X86, app_encode_fun(X86, X86), minus_minus(X86), 
43.51/43.75	             app_encode_app(int, X86, number_number_of(X86), X88)), X89))
43.51/43.75	        = app_encode_app(X86, X86, 
43.51/43.75	            app_encode_app(X86, app_encode_fun(X86, X86), minus_minus(X86), 
43.51/43.75	              app_encode_app(int, X86, number_number_of(X86), 
43.51/43.75	                app_encode_app(int, int, 
43.51/43.75	                  app_encode_app(int, app_encode_fun(int, int), 
43.51/43.75	                    plus_plus(int), X87), X88))), X89)
43.51/43.75	       | ~ number_ring(X86)),
43.51/43.75	    inference('cnf', [status(esa)], [zf_stmt_87])).
43.51/43.75	tff('31', plain,
43.51/43.75	    ![X0 : int, X1 : int, X2 : int]:
43.51/43.75	      (app_encode_app(int, int, 
43.51/43.75	         app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
43.51/43.75	         app_encode_app(int, int, 
43.51/43.75	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
43.51/43.75	             app_encode_app(int, int, number_number_of(int), X2)), X1))
43.51/43.75	        = app_encode_app(int, int, 
43.51/43.75	            app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
43.51/43.75	              app_encode_app(int, int, number_number_of(int), 
43.51/43.75	                app_encode_app(int, int, 
43.51/43.75	                  app_encode_app(int, app_encode_fun(int, int), 
43.51/43.75	                    plus_plus(int), X0), X2))), X1)
43.51/43.75	       | ~ number_ring(int)),
43.51/43.75	    inference('sup+', [status(thm)], ['2', '30'])).
43.51/43.75	tff(zf_stmt_139, axiom, (number_ring(int))).
43.51/43.75	tff('32', plain, number_ring(int),
43.51/43.75	    inference('cnf', [status(esa)], [zf_stmt_139])).
43.51/43.75	tff('33', plain,
43.51/43.75	    ![X0 : int, X1 : int, X2 : int]:
43.51/43.75	      (app_encode_app(int, int, 
43.51/43.75	         app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
43.51/43.75	         app_encode_app(int, int, 
43.51/43.75	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
43.51/43.75	             X2), X1))
43.51/43.75	        = app_encode_app(int, int, 
43.51/43.75	            app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
43.51/43.75	              app_encode_app(int, int, 
43.51/43.75	                app_encode_app(int, app_encode_fun(int, int), 
43.51/43.75	                  plus_plus(int), X0), X2)), X1)
43.51/43.75	       | ~ $true),
43.51/43.75	    inference('demod', [status(thm)], ['31', '2', '2', '32'])).
43.51/43.75	tff('34', plain,
43.51/43.75	    ![X0 : int, X1 : int, X2 : int]:
43.51/43.75	      app_encode_app(int, int, 
43.51/43.75	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
43.51/43.75	        app_encode_app(int, int, 
43.51/43.75	          app_encode_app(int, app_encode_fun(int, int), minus_minus(int), X2), 
43.51/43.75	          X1))
43.51/43.75	       = app_encode_app(int, int, 
43.51/43.75	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
43.51/43.75	             app_encode_app(int, int, 
43.51/43.75	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
43.51/43.75	                 X0), X2)), X1),
43.51/43.75	    inference('simplify', [status(thm)], ['33'])).
43.51/43.75	tff('35', plain,
43.51/43.75	    ![X0 : int, X1 : int]:
43.51/43.75	      app_encode_app(int, int, 
43.51/43.75	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
43.51/43.75	        app_encode_app(int, int, 
43.51/43.75	          app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
43.51/43.75	            pls), X1))
43.51/43.75	       = app_encode_app(int, int, 
43.51/43.75	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
43.51/43.75	             X0), X1),
43.51/43.75	    inference('sup+', [status(thm)], ['29', '34'])).
43.51/43.75	tff('36', plain,
43.51/43.75	    ![X0 : int]:
43.51/43.75	      app_encode_app(int, int, 
43.51/43.75	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
43.51/43.75	        one_one(int))
43.51/43.75	       = app_encode_app(int, int, 
43.51/43.75	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
43.51/43.75	             X0), min),
43.51/43.75	    inference('sup+', [status(thm)], ['28', '35'])).
43.51/43.75	tff('37', plain,
43.51/43.75	    app_encode_app(int, int, 
43.51/43.75	      app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
43.51/43.75	        app_encode_app(int, int, 
43.51/43.75	          app_encode_app(int, app_encode_fun(int, int), times_times(int), s), 
43.51/43.75	          s)), min)
43.51/43.75	     != app_encode_app(int, int, 
43.51/43.75	          app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
43.51/43.75	            app_encode_app(int, int, 
43.51/43.75	              app_encode_app(int, app_encode_fun(int, int), 
43.51/43.75	                times_times(int), s), s)), min),
43.51/43.75	    inference('demod', [status(thm)], ['11', '36'])).
43.51/43.75	tff('38', plain, $false, inference('simplify', [status(thm)], ['37'])).
43.51/43.75	
43.51/43.75	% SZS output end Refutation
43.51/43.75	EOF
