0.00/0.00	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : appext
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : rpo6
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n069.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
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 08:18:08 CST 2018
3.01/3.17	% done 1022 iterations in 2.966s
3.01/3.17	% SZS status Theorem for 'stdin'
3.01/3.17	% SZS output start Refutation
3.01/3.17	tff(zf_stmt_177, conjecture,
3.01/3.17	  (app_encode_app(int,int,
3.01/3.17	                  app_encode_app(int,app_encode_fun(int,int),plus_plus(int),
3.01/3.17	                                 app_encode_app(int,int,
3.01/3.17	                                                app_encode_app(int,
3.01/3.17	                                                               app_encode_fun(
3.01/3.17	                                                               int,int),
3.01/3.17	                                                               times_times(
3.01/3.17	                                                               int),
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,int,
3.01/3.17	                                                               number_number_of(
3.01/3.17	                                                               int),
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,int,bit0,
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,int,bit0,
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,int,bit1,
3.01/3.17	                                                               pls))))),
3.01/3.17	                                                app_encode_app(nat,int,
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,
3.01/3.17	                                                               app_encode_fun(
3.01/3.17	                                                               nat,int),
3.01/3.17	                                                               power_power(
3.01/3.17	                                                               int),v),
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,nat,
3.01/3.17	                                                               number_number_of(
3.01/3.17	                                                               nat),
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,int,bit0,
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,int,bit1,
3.01/3.17	                                                               pls)))))),
3.01/3.17	                  app_encode_app(int,int,
3.01/3.17	                                 app_encode_app(int,app_encode_fun(int,int),
3.01/3.17	                                                times_times(int),
3.01/3.17	                                                app_encode_app(int,int,
3.01/3.17	                                                               number_number_of(
3.01/3.17	                                                               int),
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,int,bit0,
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,int,bit0,
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,int,bit1,
3.01/3.17	                                                               pls))))),
3.01/3.17	                                 app_encode_app(nat,int,
3.01/3.17	                                                app_encode_app(int,
3.01/3.17	                                                               app_encode_fun(
3.01/3.17	                                                               nat,int),
3.01/3.17	                                                               power_power(
3.01/3.17	                                                               int),w),
3.01/3.17	                                                app_encode_app(int,nat,
3.01/3.17	                                                               number_number_of(
3.01/3.17	                                                               nat),
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,int,bit0,
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,int,bit1,
3.01/3.17	                                                               pls)))))) =
3.01/3.17	   app_encode_app(int,int,
3.01/3.17	                  app_encode_app(int,app_encode_fun(int,int),plus_plus(int),
3.01/3.17	                                 app_encode_app(nat,int,
3.01/3.17	                                                app_encode_app(int,
3.01/3.17	                                                               app_encode_fun(
3.01/3.17	                                                               nat,int),
3.01/3.17	                                                               power_power(
3.01/3.17	                                                               int),
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,int,
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,
3.01/3.17	                                                               app_encode_fun(
3.01/3.17	                                                               int,int),
3.01/3.17	                                                               times_times(
3.01/3.17	                                                               int),
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,int,
3.01/3.17	                                                               number_number_of(
3.01/3.17	                                                               int),
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,int,bit0,
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,int,bit1,
3.01/3.17	                                                               pls)))),
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,int,
3.01/3.17	                                                               abs_abs(int),v))),
3.01/3.17	                                                app_encode_app(int,nat,
3.01/3.17	                                                               number_number_of(
3.01/3.17	                                                               nat),
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,int,bit0,
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,int,bit1,
3.01/3.17	                                                               pls))))),
3.01/3.17	                  app_encode_app(nat,int,
3.01/3.17	                                 app_encode_app(int,app_encode_fun(nat,int),
3.01/3.17	                                                power_power(int),
3.01/3.17	                                                app_encode_app(int,int,
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,
3.01/3.17	                                                               app_encode_fun(
3.01/3.17	                                                               int,int),
3.01/3.17	                                                               times_times(
3.01/3.17	                                                               int),
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,int,
3.01/3.17	                                                               number_number_of(
3.01/3.17	                                                               int),
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,int,bit0,
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,int,bit1,
3.01/3.17	                                                               pls)))),
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,int,
3.01/3.17	                                                               abs_abs(int),w))),
3.01/3.17	                                 app_encode_app(int,nat,
3.01/3.17	                                                number_number_of(nat),
3.01/3.17	                                                app_encode_app(int,int,bit0,
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,int,bit1,
3.01/3.17	                                                               pls))))))).
3.01/3.17	tff(zf_stmt_0, negated_conjecture,
3.01/3.17	  (app_encode_app(int,int,
3.01/3.17	                  app_encode_app(int,app_encode_fun(int,int),plus_plus(int),
3.01/3.17	                                 app_encode_app(int,int,
3.01/3.17	                                                app_encode_app(int,
3.01/3.17	                                                               app_encode_fun(
3.01/3.17	                                                               int,int),
3.01/3.17	                                                               times_times(
3.01/3.17	                                                               int),
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,int,
3.01/3.17	                                                               number_number_of(
3.01/3.17	                                                               int),
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,int,bit0,
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,int,bit0,
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,int,bit1,
3.01/3.17	                                                               pls))))),
3.01/3.17	                                                app_encode_app(nat,int,
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,
3.01/3.17	                                                               app_encode_fun(
3.01/3.17	                                                               nat,int),
3.01/3.17	                                                               power_power(
3.01/3.17	                                                               int),v),
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,nat,
3.01/3.17	                                                               number_number_of(
3.01/3.17	                                                               nat),
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,int,bit0,
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,int,bit1,
3.01/3.17	                                                               pls)))))),
3.01/3.17	                  app_encode_app(int,int,
3.01/3.17	                                 app_encode_app(int,app_encode_fun(int,int),
3.01/3.17	                                                times_times(int),
3.01/3.17	                                                app_encode_app(int,int,
3.01/3.17	                                                               number_number_of(
3.01/3.17	                                                               int),
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,int,bit0,
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,int,bit0,
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,int,bit1,
3.01/3.17	                                                               pls))))),
3.01/3.17	                                 app_encode_app(nat,int,
3.01/3.17	                                                app_encode_app(int,
3.01/3.17	                                                               app_encode_fun(
3.01/3.17	                                                               nat,int),
3.01/3.17	                                                               power_power(
3.01/3.17	                                                               int),w),
3.01/3.17	                                                app_encode_app(int,nat,
3.01/3.17	                                                               number_number_of(
3.01/3.17	                                                               nat),
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,int,bit0,
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,int,bit1,
3.01/3.17	                                                               pls)))))) !=
3.01/3.17	   app_encode_app(int,int,
3.01/3.17	                  app_encode_app(int,app_encode_fun(int,int),plus_plus(int),
3.01/3.17	                                 app_encode_app(nat,int,
3.01/3.17	                                                app_encode_app(int,
3.01/3.17	                                                               app_encode_fun(
3.01/3.17	                                                               nat,int),
3.01/3.17	                                                               power_power(
3.01/3.17	                                                               int),
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,int,
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,
3.01/3.17	                                                               app_encode_fun(
3.01/3.17	                                                               int,int),
3.01/3.17	                                                               times_times(
3.01/3.17	                                                               int),
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,int,
3.01/3.17	                                                               number_number_of(
3.01/3.17	                                                               int),
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,int,bit0,
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,int,bit1,
3.01/3.17	                                                               pls)))),
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,int,
3.01/3.17	                                                               abs_abs(int),v))),
3.01/3.17	                                                app_encode_app(int,nat,
3.01/3.17	                                                               number_number_of(
3.01/3.17	                                                               nat),
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,int,bit0,
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,int,bit1,
3.01/3.17	                                                               pls))))),
3.01/3.17	                  app_encode_app(nat,int,
3.01/3.17	                                 app_encode_app(int,app_encode_fun(nat,int),
3.01/3.17	                                                power_power(int),
3.01/3.17	                                                app_encode_app(int,int,
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,
3.01/3.17	                                                               app_encode_fun(
3.01/3.17	                                                               int,int),
3.01/3.17	                                                               times_times(
3.01/3.17	                                                               int),
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,int,
3.01/3.17	                                                               number_number_of(
3.01/3.17	                                                               int),
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,int,bit0,
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,int,bit1,
3.01/3.17	                                                               pls)))),
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,int,
3.01/3.17	                                                               abs_abs(int),w))),
3.01/3.17	                                 app_encode_app(int,nat,
3.01/3.17	                                                number_number_of(nat),
3.01/3.17	                                                app_encode_app(int,int,bit0,
3.01/3.17	                                                               app_encode_app(
3.01/3.17	                                                               int,int,bit1,
3.01/3.17	                                                               pls))))))).
3.01/3.17	tff('0', plain,
3.01/3.17	    app_encode_app(int, int, 
3.01/3.17	      app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.01/3.17	        app_encode_app(int, int, 
3.01/3.17	          app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.01/3.17	            app_encode_app(int, int, number_number_of(int), 
3.01/3.17	              app_encode_app(int, int, bit0, 
3.01/3.17	                app_encode_app(int, int, bit0, 
3.01/3.17	                  app_encode_app(int, int, bit1, pls))))), 
3.01/3.17	          app_encode_app(nat, int, 
3.01/3.17	            app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
3.01/3.17	              v), 
3.01/3.17	            app_encode_app(int, nat, number_number_of(nat), 
3.01/3.17	              app_encode_app(int, int, bit0, 
3.01/3.17	                app_encode_app(int, int, bit1, pls)))))), 
3.01/3.17	      app_encode_app(int, int, 
3.01/3.17	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.01/3.17	          app_encode_app(int, int, number_number_of(int), 
3.01/3.17	            app_encode_app(int, int, bit0, 
3.01/3.17	              app_encode_app(int, int, bit0, 
3.01/3.17	                app_encode_app(int, int, bit1, pls))))), 
3.01/3.17	        app_encode_app(nat, int, 
3.01/3.17	          app_encode_app(int, app_encode_fun(nat, int), power_power(int), w), 
3.01/3.17	          app_encode_app(int, nat, number_number_of(nat), 
3.01/3.17	            app_encode_app(int, int, bit0, 
3.01/3.17	              app_encode_app(int, int, bit1, pls))))))
3.01/3.17	     != app_encode_app(int, int, 
3.01/3.17	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.01/3.17	            app_encode_app(nat, int, 
3.01/3.17	              app_encode_app(int, app_encode_fun(nat, int), 
3.01/3.17	                power_power(int), 
3.01/3.17	                app_encode_app(int, int, 
3.01/3.17	                  app_encode_app(int, app_encode_fun(int, int), 
3.01/3.17	                    times_times(int), 
3.01/3.17	                    app_encode_app(int, int, number_number_of(int), 
3.01/3.17	                      app_encode_app(int, int, bit0, 
3.01/3.17	                        app_encode_app(int, int, bit1, pls)))), 
3.01/3.17	                  app_encode_app(int, int, abs_abs(int), v))), 
3.01/3.17	              app_encode_app(int, nat, number_number_of(nat), 
3.01/3.17	                app_encode_app(int, int, bit0, 
3.01/3.17	                  app_encode_app(int, int, bit1, pls))))), 
3.01/3.17	          app_encode_app(nat, int, 
3.01/3.17	            app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
3.01/3.17	              app_encode_app(int, int, 
3.01/3.17	                app_encode_app(int, app_encode_fun(int, int), 
3.01/3.17	                  times_times(int), 
3.01/3.17	                  app_encode_app(int, int, number_number_of(int), 
3.01/3.17	                    app_encode_app(int, int, bit0, 
3.01/3.17	                      app_encode_app(int, int, bit1, pls)))), 
3.01/3.17	                app_encode_app(int, int, abs_abs(int), w))), 
3.01/3.17	            app_encode_app(int, nat, number_number_of(nat), 
3.01/3.17	              app_encode_app(int, int, bit0, 
3.01/3.17	                app_encode_app(int, int, bit1, pls))))),
3.01/3.17	    inference('cnf', [status(esa)], [zf_stmt_0])).
3.01/3.17	tff(zf_stmt_58, axiom,
3.01/3.17	  (![W:int]:
3.01/3.17	     (app_encode_app(int,int,
3.01/3.17	                     app_encode_app(int,app_encode_fun(int,int),
3.01/3.17	                                    times_times(int),pls),
3.01/3.17	                     W) =
3.01/3.17	      pls))).
3.01/3.17	tff('1', plain,
3.01/3.17	    ![X53 : int]:
3.01/3.17	      app_encode_app(int, int, 
3.01/3.17	        app_encode_app(int, app_encode_fun(int, int), times_times(int), pls), 
3.01/3.17	        X53)
3.01/3.17	       = pls,
3.01/3.17	    inference('cnf', [status(esa)], [zf_stmt_58])).
3.01/3.17	tff(zf_stmt_39, axiom,
3.01/3.17	  (![L:int,K:int]:
3.01/3.17	     (app_encode_app(int,int,
3.01/3.17	                     app_encode_app(int,app_encode_fun(int,int),
3.01/3.17	                                    times_times(int),
3.01/3.17	                                    app_encode_app(int,int,bit1,K)),
3.01/3.17	                     L) =
3.01/3.17	      app_encode_app(int,int,
3.01/3.17	                     app_encode_app(int,app_encode_fun(int,int),
3.01/3.17	                                    plus_plus(int),
3.01/3.17	                                    app_encode_app(int,int,bit0,
3.01/3.17	                                                   app_encode_app(int,int,
3.01/3.17	                                                                  app_encode_app(
3.01/3.17	                                                                  int,
3.01/3.17	                                                                  app_encode_fun(
3.01/3.17	                                                                  int,int),
3.01/3.17	                                                                  times_times(
3.01/3.17	                                                                  int),K),L))),
3.01/3.17	                     L)))).
3.01/3.17	tff('2', plain,
3.01/3.17	    ![X10 : int, X11 : int]:
3.01/3.17	      app_encode_app(int, int, 
3.01/3.17	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.01/3.17	          app_encode_app(int, int, bit1, X10)), X11)
3.01/3.17	       = app_encode_app(int, int, 
3.01/3.17	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.01/3.17	             app_encode_app(int, int, bit0, 
3.01/3.17	               app_encode_app(int, int, 
3.01/3.17	                 app_encode_app(int, app_encode_fun(int, int), 
3.01/3.17	                   times_times(int), X10), X11))), X11),
3.01/3.17	    inference('cnf', [status(esa)], [zf_stmt_39])).
3.01/3.17	tff('3', plain,
3.01/3.17	    ![X0 : int]:
3.01/3.17	      app_encode_app(int, int, 
3.01/3.17	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.01/3.17	          app_encode_app(int, int, bit1, pls)), X0)
3.01/3.17	       = app_encode_app(int, int, 
3.01/3.17	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.01/3.17	             app_encode_app(int, int, bit0, pls)), X0),
3.01/3.17	    inference('sup+', [status(thm)], ['1', '2'])).
3.01/3.17	tff(zf_stmt_57, axiom, (app_encode_app(int,int,bit0,pls) = pls)).
3.01/3.17	tff('4', plain, app_encode_app(int, int, bit0, pls) = pls,
3.01/3.17	    inference('cnf', [status(esa)], [zf_stmt_57])).
3.01/3.17	tff('5', plain,
3.01/3.17	    ![X0 : int]:
3.01/3.17	      app_encode_app(int, int, 
3.01/3.17	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.01/3.17	          app_encode_app(int, int, bit1, pls)), X0)
3.01/3.17	       = app_encode_app(int, int, 
3.01/3.17	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
3.01/3.17	           X0),
3.01/3.17	    inference('demod', [status(thm)], ['3', '4'])).
3.01/3.17	tff(zf_stmt_71, axiom,
3.01/3.17	  (![K:int]:
3.01/3.17	     (app_encode_app(int,int,
3.01/3.17	                     app_encode_app(int,app_encode_fun(int,int),
3.01/3.17	                                    plus_plus(int),pls),
3.01/3.17	                     K) =
3.01/3.17	      K))).
3.01/3.17	tff('6', plain,
3.01/3.17	    ![X84 : int]:
3.01/3.17	      app_encode_app(int, int, 
3.01/3.17	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
3.01/3.17	        X84)
3.01/3.17	       = X84,
3.01/3.17	    inference('cnf', [status(esa)], [zf_stmt_71])).
3.01/3.17	tff('7', plain,
3.01/3.17	    ![X0 : int]:
3.01/3.17	      app_encode_app(int, int, 
3.01/3.17	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.01/3.17	          app_encode_app(int, int, bit1, pls)), X0)
3.01/3.17	       = X0,
3.01/3.17	    inference('sup+', [status(thm)], ['5', '6'])).
3.01/3.17	tff(zf_stmt_72, axiom,
3.01/3.17	  (![K:int]:
3.01/3.17	     (app_encode_app(int,int,bit0,K) =
3.01/3.17	      app_encode_app(int,int,
3.01/3.17	                     app_encode_app(int,app_encode_fun(int,int),
3.01/3.17	                                    plus_plus(int),K),
3.01/3.17	                     K)))).
3.01/3.17	tff('8', plain,
3.01/3.17	    ![X85 : int]:
3.01/3.17	      app_encode_app(int, int, bit0, X85)
3.01/3.17	       = app_encode_app(int, int, 
3.01/3.17	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X85), 
3.01/3.17	           X85),
3.01/3.17	    inference('cnf', [status(esa)], [zf_stmt_72])).
3.01/3.17	tff(zf_stmt_59, axiom,
3.01/3.17	  (![L:int,K:int]:
3.01/3.17	     (app_encode_app(int,int,
3.01/3.17	                     app_encode_app(int,app_encode_fun(int,int),
3.01/3.17	                                    times_times(int),
3.01/3.17	                                    app_encode_app(int,int,bit0,K)),
3.01/3.17	                     L) =
3.01/3.17	      app_encode_app(int,int,bit0,
3.01/3.17	                     app_encode_app(int,int,
3.01/3.17	                                    app_encode_app(int,
3.01/3.17	                                                   app_encode_fun(int,int),
3.01/3.17	                                                   times_times(int),K),
3.01/3.17	                                    L))))).
3.01/3.17	tff('9', plain,
3.01/3.17	    ![X54 : int, X55 : int]:
3.01/3.17	      app_encode_app(int, int, 
3.01/3.17	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.01/3.17	          app_encode_app(int, int, bit0, X54)), X55)
3.01/3.17	       = app_encode_app(int, int, bit0, 
3.01/3.17	           app_encode_app(int, int, 
3.01/3.17	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.01/3.17	               X54), X55)),
3.01/3.17	    inference('cnf', [status(esa)], [zf_stmt_59])).
3.01/3.17	tff('10', plain,
3.01/3.17	    ![X0 : int, X1 : int]:
3.01/3.17	      app_encode_app(int, int, 
3.01/3.17	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.01/3.17	          app_encode_app(int, int, 
3.01/3.17	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
3.01/3.17	            X0)), X1)
3.01/3.17	       = app_encode_app(int, int, bit0, 
3.01/3.17	           app_encode_app(int, int, 
3.01/3.17	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.01/3.17	               X0), X1)),
3.01/3.17	    inference('sup+', [status(thm)], ['8', '9'])).
3.01/3.17	tff('11', plain,
3.01/3.17	    ![X0 : int]:
3.01/3.17	      app_encode_app(int, int, 
3.01/3.17	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.01/3.17	          app_encode_app(int, int, 
3.01/3.17	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.01/3.17	              app_encode_app(int, int, bit1, pls)), 
3.01/3.17	            app_encode_app(int, int, bit1, pls))), X0)
3.01/3.17	       = app_encode_app(int, int, bit0, X0),
3.01/3.17	    inference('sup+', [status(thm)], ['7', '10'])).
3.01/3.17	tff('12', plain,
3.01/3.17	    ![X85 : int]:
3.01/3.17	      app_encode_app(int, int, 
3.01/3.17	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.01/3.17	          app_encode_app(int, int, 
3.01/3.17	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.01/3.17	              app_encode_app(int, int, bit1, pls)), 
3.01/3.17	            app_encode_app(int, int, bit1, pls))), X85)
3.01/3.17	       = app_encode_app(int, int, 
3.01/3.17	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X85), 
3.01/3.17	           X85),
3.01/3.17	    inference('demod', [status(thm)], ['8', '11'])).
3.01/3.17	tff(zf_stmt_68, axiom,
3.01/3.17	  (![K:int]: (app_encode_app(int,int,number_number_of(int),K) = K))).
3.01/3.17	tff('13', plain,
3.01/3.17	    ![X79 : int]: app_encode_app(int, int, number_number_of(int), X79) = X79,
3.01/3.17	    inference('cnf', [status(esa)], [zf_stmt_68])).
3.01/3.17	tff(zf_stmt_141, axiom, (comm_semiring_1(int))).
3.01/3.17	tff('14', plain, comm_semiring_1(int),
3.01/3.17	    inference('cnf', [status(esa)], [zf_stmt_141])).
3.01/3.17	tff(zf_stmt_105, axiom,
3.01/3.17	  (![A:$tType]:
3.01/3.17	     (comm_semiring_1(A) =>
3.01/3.17	      (![B:A,A1:A]:
3.01/3.17	         (app_encode_app(A,A,
3.01/3.17	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
3.01/3.17	                                        A1),
3.01/3.17	                         B) =
3.01/3.17	          app_encode_app(A,A,
3.01/3.17	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
3.01/3.17	                                        B),
3.01/3.17	                         A1)))))).
3.01/3.17	tff('15', plain,
3.01/3.17	    ![X159 : $tType, X160 : X159, X161 : X159]:
3.01/3.17	      (app_encode_app(X159, X159, 
3.01/3.17	         app_encode_app(X159, app_encode_fun(X159, X159), times_times(X159), 
3.01/3.17	           X161), X160)
3.01/3.17	        = app_encode_app(X159, X159, 
3.01/3.17	            app_encode_app(X159, app_encode_fun(X159, X159), 
3.01/3.17	              times_times(X159), X160), X161)
3.01/3.17	       | ~ comm_semiring_1(X159)),
3.01/3.17	    inference('cnf', [status(esa)], [zf_stmt_105])).
3.01/3.17	tff('16', plain,
3.01/3.17	    ![X0 : int, X1 : int]:
3.01/3.17	      (~ $true
3.01/3.17	       | app_encode_app(int, int, 
3.01/3.17	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.01/3.17	             X1), X0)
3.01/3.17	          = app_encode_app(int, int, 
3.01/3.17	              app_encode_app(int, app_encode_fun(int, int), 
3.01/3.17	                times_times(int), X0), X1)),
3.01/3.17	    inference('sup-', [status(thm)], ['14', '15'])).
3.01/3.17	tff('17', plain,
3.01/3.17	    ![X0 : int, X1 : int]:
3.01/3.17	      app_encode_app(int, int, 
3.01/3.17	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X1), 
3.01/3.17	        X0)
3.01/3.17	       = app_encode_app(int, int, 
3.01/3.17	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.01/3.17	             X0), X1),
3.01/3.17	    inference('simplify', [status(thm)], ['16'])).
3.01/3.17	tff(zf_stmt_146, axiom, (number_ring(int))).
3.01/3.17	tff('18', plain, number_ring(int),
3.01/3.17	    inference('cnf', [status(esa)], [zf_stmt_146])).
3.01/3.17	tff(zf_stmt_63, axiom,
3.01/3.17	  (![A:$tType]:
3.01/3.17	     (number_ring(A) =>
3.01/3.17	      (![Z1:A,W:int,V:int]:
3.01/3.17	         (app_encode_app(A,A,
3.01/3.17	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
3.01/3.17	                                        app_encode_app(int,A,
3.01/3.17	                                                       number_number_of(A),V)),
3.01/3.17	                         app_encode_app(A,A,
3.01/3.17	                                        app_encode_app(A,app_encode_fun(A,A),
3.01/3.17	                                                       times_times(A),
3.01/3.17	                                                       app_encode_app(
3.01/3.17	                                                       int,A,
3.01/3.17	                                                       number_number_of(A),W)),
3.01/3.17	                                        Z1)) =
3.01/3.17	          app_encode_app(A,A,
3.01/3.17	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
3.01/3.17	                                        app_encode_app(int,A,
3.01/3.17	                                                       number_number_of(A),
3.01/3.17	                                                       app_encode_app(
3.01/3.17	                                                       int,int,
3.01/3.17	                                                       app_encode_app(
3.01/3.17	                                                       int,
3.01/3.17	                                                       app_encode_fun(
3.01/3.17	                                                       int,int),
3.01/3.17	                                                       times_times(int),V),W))),
3.01/3.17	                         Z1)))))).
3.01/3.17	tff('19', plain,
3.01/3.17	    ![X66 : $tType, X67 : int, X68 : int, X69 : X66]:
3.01/3.17	      (app_encode_app(X66, X66, 
3.01/3.17	         app_encode_app(X66, app_encode_fun(X66, X66), times_times(X66), 
3.01/3.17	           app_encode_app(int, X66, number_number_of(X66), X67)), 
3.01/3.17	         app_encode_app(X66, X66, 
3.01/3.17	           app_encode_app(X66, app_encode_fun(X66, X66), times_times(X66), 
3.01/3.17	             app_encode_app(int, X66, number_number_of(X66), X68)), X69))
3.01/3.17	        = app_encode_app(X66, X66, 
3.01/3.17	            app_encode_app(X66, app_encode_fun(X66, X66), times_times(X66), 
3.01/3.17	              app_encode_app(int, X66, number_number_of(X66), 
3.01/3.17	                app_encode_app(int, int, 
3.01/3.17	                  app_encode_app(int, app_encode_fun(int, int), 
3.01/3.17	                    times_times(int), X67), X68))), X69)
3.01/3.17	       | ~ number_ring(X66)),
3.01/3.17	    inference('cnf', [status(esa)], [zf_stmt_63])).
3.01/3.17	tff('20', plain,
3.01/3.17	    ![X0 : int, X1 : int, X2 : int]:
3.01/3.17	      (~ $true
3.01/3.17	       | app_encode_app(int, int, 
3.01/3.17	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.01/3.17	             app_encode_app(int, int, number_number_of(int), X2)), 
3.01/3.17	           app_encode_app(int, int, 
3.01/3.17	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.01/3.17	               app_encode_app(int, int, number_number_of(int), X1)), X0))
3.01/3.17	          = app_encode_app(int, int, 
3.01/3.17	              app_encode_app(int, app_encode_fun(int, int), 
3.01/3.17	                times_times(int), 
3.01/3.17	                app_encode_app(int, int, number_number_of(int), 
3.01/3.17	                  app_encode_app(int, int, 
3.01/3.17	                    app_encode_app(int, app_encode_fun(int, int), 
3.01/3.17	                      times_times(int), X2), X1))), X0)),
3.01/3.17	    inference('sup-', [status(thm)], ['18', '19'])).
3.01/3.17	tff('21', plain,
3.01/3.17	    ![X0 : int, X1 : int, X2 : int]:
3.01/3.17	      (~ $true
3.01/3.17	       | app_encode_app(int, int, 
3.01/3.17	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.01/3.17	             X2), 
3.01/3.17	           app_encode_app(int, int, 
3.01/3.17	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.01/3.17	               X1), X0))
3.01/3.17	          = app_encode_app(int, int, 
3.01/3.17	              app_encode_app(int, app_encode_fun(int, int), 
3.01/3.17	                times_times(int), 
3.01/3.17	                app_encode_app(int, int, 
3.01/3.17	                  app_encode_app(int, app_encode_fun(int, int), 
3.01/3.17	                    times_times(int), X2), X1)), X0)),
3.01/3.17	    inference('demod', [status(thm)], ['20', '13', '13', '13'])).
3.01/3.17	tff('22', plain,
3.01/3.17	    ![X0 : int, X1 : int, X2 : int]:
3.01/3.17	      app_encode_app(int, int, 
3.01/3.17	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X2), 
3.01/3.17	        app_encode_app(int, int, 
3.01/3.17	          app_encode_app(int, app_encode_fun(int, int), times_times(int), X1), 
3.01/3.17	          X0))
3.01/3.17	       = app_encode_app(int, int, 
3.01/3.17	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.01/3.17	             app_encode_app(int, int, 
3.01/3.17	               app_encode_app(int, app_encode_fun(int, int), 
3.01/3.17	                 times_times(int), X2), X1)), X0),
3.01/3.17	    inference('simplify', [status(thm)], ['21'])).
3.01/3.17	tff('23', plain,
3.01/3.17	    ![X0 : int, X1 : int, X2 : int]:
3.01/3.17	      app_encode_app(int, int, 
3.01/3.17	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X0), 
3.01/3.17	        app_encode_app(int, int, 
3.01/3.17	          app_encode_app(int, app_encode_fun(int, int), times_times(int), X1), 
3.01/3.17	          X2))
3.01/3.17	       = app_encode_app(int, int, 
3.01/3.17	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.01/3.17	             app_encode_app(int, int, 
3.01/3.17	               app_encode_app(int, app_encode_fun(int, int), 
3.01/3.17	                 times_times(int), X1), X0)), X2),
3.01/3.17	    inference('sup+', [status(thm)], ['17', '22'])).
3.01/3.17	tff(zf_stmt_75, axiom,
3.01/3.17	  (![Z2:int,Z11:int,W:int]:
3.01/3.17	     (app_encode_app(int,int,
3.01/3.17	                     app_encode_app(int,app_encode_fun(int,int),
3.01/3.17	                                    times_times(int),W),
3.01/3.17	                     app_encode_app(int,int,
3.01/3.17	                                    app_encode_app(int,
3.01/3.17	                                                   app_encode_fun(int,int),
3.01/3.17	                                                   plus_plus(int),Z11),
3.01/3.17	                                    Z2)) =
3.01/3.17	      app_encode_app(int,int,
3.01/3.17	                     app_encode_app(int,app_encode_fun(int,int),
3.01/3.17	                                    plus_plus(int),
3.01/3.17	                                    app_encode_app(int,int,
3.01/3.17	                                                   app_encode_app(int,
3.01/3.17	                                                                  app_encode_fun(
3.01/3.17	                                                                  int,int),
3.01/3.17	                                                                  times_times(
3.01/3.17	                                                                  int),W),
3.01/3.17	                                                   Z11)),
3.01/3.17	                     app_encode_app(int,int,
3.01/3.17	                                    app_encode_app(int,
3.01/3.17	                                                   app_encode_fun(int,int),
3.01/3.17	                                                   times_times(int),W),
3.01/3.17	                                    Z2))))).
3.01/3.17	tff('24', plain,
3.01/3.17	    ![X91 : int, X92 : int, X93 : int]:
3.01/3.17	      app_encode_app(int, int, 
3.01/3.17	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X91), 
3.01/3.17	        app_encode_app(int, int, 
3.01/3.17	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X92), 
3.01/3.17	          X93))
3.01/3.17	       = app_encode_app(int, int, 
3.01/3.17	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.01/3.17	             app_encode_app(int, int, 
3.01/3.17	               app_encode_app(int, app_encode_fun(int, int), 
3.01/3.17	                 times_times(int), X91), X92)), 
3.01/3.17	           app_encode_app(int, int, 
3.01/3.17	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.01/3.17	               X91), X93)),
3.01/3.17	    inference('cnf', [status(esa)], [zf_stmt_75])).
3.01/3.17	tff('25', plain,
3.01/3.17	    app_encode_app(int, int, 
3.01/3.17	      app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.01/3.17	        app_encode_app(int, int, 
3.01/3.17	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.01/3.17	            app_encode_app(int, int, bit1, pls)), 
3.01/3.17	          app_encode_app(int, int, bit1, pls))), 
3.01/3.17	      app_encode_app(int, int, 
3.01/3.17	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.01/3.17	          app_encode_app(int, int, 
3.01/3.17	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.01/3.17	              app_encode_app(int, int, bit1, pls)), 
3.01/3.17	            app_encode_app(int, int, bit1, pls))), 
3.01/3.17	        app_encode_app(int, int, 
3.01/3.17	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.01/3.17	            app_encode_app(nat, int, 
3.01/3.17	              app_encode_app(int, app_encode_fun(nat, int), 
3.01/3.17	                power_power(int), v), 
3.01/3.17	              app_encode_app(int, nat, number_number_of(nat), 
3.01/3.17	                app_encode_app(int, int, 
3.01/3.17	                  app_encode_app(int, app_encode_fun(int, int), 
3.01/3.17	                    plus_plus(int), app_encode_app(int, int, bit1, pls)), 
3.01/3.17	                  app_encode_app(int, int, bit1, pls))))), 
3.01/3.17	          app_encode_app(nat, int, 
3.01/3.17	            app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
3.01/3.17	              w), 
3.01/3.17	            app_encode_app(int, nat, number_number_of(nat), 
3.01/3.17	              app_encode_app(int, int, 
3.01/3.17	                app_encode_app(int, app_encode_fun(int, int), 
3.01/3.17	                  plus_plus(int), app_encode_app(int, int, bit1, pls)), 
3.01/3.17	                app_encode_app(int, int, bit1, pls)))))))
3.01/3.17	     != app_encode_app(int, int, 
3.01/3.17	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.01/3.17	            app_encode_app(nat, int, 
3.01/3.17	              app_encode_app(int, app_encode_fun(nat, int), 
3.01/3.17	                power_power(int), 
3.01/3.17	                app_encode_app(int, int, 
3.01/3.17	                  app_encode_app(int, app_encode_fun(int, int), 
3.01/3.17	                    times_times(int), 
3.01/3.17	                    app_encode_app(int, int, 
3.01/3.17	                      app_encode_app(int, app_encode_fun(int, int), 
3.01/3.17	                        plus_plus(int), app_encode_app(int, int, bit1, pls)), 
3.01/3.17	                      app_encode_app(int, int, bit1, pls))), 
3.01/3.17	                  app_encode_app(int, int, abs_abs(int), v))), 
3.01/3.17	              app_encode_app(int, nat, number_number_of(nat), 
3.01/3.17	                app_encode_app(int, int, 
3.01/3.17	                  app_encode_app(int, app_encode_fun(int, int), 
3.01/3.17	                    plus_plus(int), app_encode_app(int, int, bit1, pls)), 
3.01/3.17	                  app_encode_app(int, int, bit1, pls))))), 
3.01/3.17	          app_encode_app(nat, int, 
3.01/3.17	            app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
3.01/3.17	              app_encode_app(int, int, 
3.01/3.17	                app_encode_app(int, app_encode_fun(int, int), 
3.01/3.17	                  times_times(int), 
3.01/3.17	                  app_encode_app(int, int, 
3.01/3.17	                    app_encode_app(int, app_encode_fun(int, int), 
3.01/3.17	                      plus_plus(int), app_encode_app(int, int, bit1, pls)), 
3.01/3.17	                    app_encode_app(int, int, bit1, pls))), 
3.01/3.17	                app_encode_app(int, int, abs_abs(int), w))), 
3.01/3.17	            app_encode_app(int, nat, number_number_of(nat), 
3.01/3.17	              app_encode_app(int, int, 
3.01/3.17	                app_encode_app(int, app_encode_fun(int, int), 
3.01/3.17	                  plus_plus(int), app_encode_app(int, int, bit1, pls)), 
3.01/3.17	                app_encode_app(int, int, bit1, pls))))),
3.01/3.17	    inference('demod', [status(thm)],
3.01/3.17	              ['0', '11', '12', '11', '13', '11', '12', '23', '11', '12', 
3.01/3.17	               '11', '13', '11', '12', '23', '24', '24', '11', '12', '13', 
3.01/3.17	               '11', '12', '11', '12', '13', '11', '12'])).
3.01/3.17	tff(zf_stmt_144, axiom, (monoid_mult(int))).
3.01/3.17	tff('26', plain, monoid_mult(int),
3.01/3.17	    inference('cnf', [status(esa)], [zf_stmt_144])).
3.01/3.17	tff(zf_stmt_36, axiom,
3.01/3.17	  (![B2:$tType]:
3.01/3.17	     ((monoid_mult(B2) & number(B2)) =>
3.01/3.17	      (![W:int]:
3.01/3.17	         (app_encode_app(nat,B2,
3.01/3.17	                         app_encode_app(B2,app_encode_fun(nat,B2),
3.01/3.17	                                        power_power(B2),
3.01/3.17	                                        app_encode_app(int,B2,
3.01/3.17	                                                       number_number_of(B2),W)),
3.01/3.17	                         app_encode_app(int,nat,number_number_of(nat),
3.01/3.17	                                        app_encode_app(int,int,bit0,
3.01/3.17	                                                       app_encode_app(
3.01/3.17	                                                       int,int,bit1,pls)))) =
3.01/3.17	          app_encode_app(B2,B2,
3.01/3.17	                         app_encode_app(B2,app_encode_fun(B2,B2),
3.01/3.17	                                        times_times(B2),
3.01/3.17	                                        app_encode_app(int,B2,
3.01/3.17	                                                       number_number_of(B2),W)),
3.01/3.17	                         app_encode_app(int,B2,number_number_of(B2),W))))))).
3.01/3.17	tff('27', plain,
3.01/3.17	    ![X4 : $tType, X5 : int]:
3.01/3.17	      (app_encode_app(nat, X4, 
3.01/3.17	         app_encode_app(X4, app_encode_fun(nat, X4), power_power(X4), 
3.01/3.17	           app_encode_app(int, X4, number_number_of(X4), X5)), 
3.01/3.17	         app_encode_app(int, nat, number_number_of(nat), 
3.01/3.17	           app_encode_app(int, int, bit0, 
3.01/3.17	             app_encode_app(int, int, bit1, pls))))
3.01/3.17	        = app_encode_app(X4, X4, 
3.01/3.17	            app_encode_app(X4, app_encode_fun(X4, X4), times_times(X4), 
3.01/3.17	              app_encode_app(int, X4, number_number_of(X4), X5)), 
3.01/3.17	            app_encode_app(int, X4, number_number_of(X4), X5))
3.01/3.17	       | ~ number(X4)
3.01/3.17	       | ~ monoid_mult(X4)),
3.01/3.17	    inference('cnf', [status(esa)], [zf_stmt_36])).
3.01/3.17	tff('28', plain,
3.01/3.17	    ![X0 : int]:
3.01/3.17	      (~ $true
3.01/3.17	       | ~ number(int)
3.01/3.17	       | app_encode_app(nat, int, 
3.01/3.17	           app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
3.01/3.17	             app_encode_app(int, int, number_number_of(int), X0)), 
3.01/3.17	           app_encode_app(int, nat, number_number_of(nat), 
3.01/3.17	             app_encode_app(int, int, bit0, 
3.01/3.17	               app_encode_app(int, int, bit1, pls))))
3.01/3.17	          = app_encode_app(int, int, 
3.01/3.17	              app_encode_app(int, app_encode_fun(int, int), 
3.01/3.17	                times_times(int), 
3.01/3.17	                app_encode_app(int, int, number_number_of(int), X0)), 
3.01/3.17	              app_encode_app(int, int, number_number_of(int), X0))),
3.01/3.17	    inference('sup-', [status(thm)], ['26', '27'])).
3.01/3.17	tff('29', plain,
3.01/3.17	    ![X0 : int]:
3.01/3.17	      (app_encode_app(nat, int, 
3.01/3.17	         app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
3.01/3.17	           app_encode_app(int, int, number_number_of(int), X0)), 
3.01/3.17	         app_encode_app(int, nat, number_number_of(nat), 
3.01/3.17	           app_encode_app(int, int, bit0, 
3.01/3.17	             app_encode_app(int, int, bit1, pls))))
3.01/3.17	        = app_encode_app(int, int, 
3.01/3.17	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.01/3.17	              app_encode_app(int, int, number_number_of(int), X0)), 
3.01/3.17	            app_encode_app(int, int, number_number_of(int), X0))
3.01/3.17	       | ~ number(int)),
3.01/3.17	    inference('simplify', [status(thm)], ['28'])).
3.01/3.17	tff(zf_stmt_148, axiom, (number(int))).
3.01/3.17	tff('30', plain, number(int), inference('cnf', [status(esa)], [zf_stmt_148])).
3.01/3.17	tff('31', plain,
3.01/3.17	    ![X0 : int]:
3.01/3.17	      (app_encode_app(nat, int, 
3.01/3.17	         app_encode_app(int, app_encode_fun(nat, int), power_power(int), X0), 
3.01/3.17	         app_encode_app(int, nat, number_number_of(nat), 
3.01/3.17	           app_encode_app(int, int, 
3.01/3.17	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.01/3.17	               app_encode_app(int, int, bit1, pls)), 
3.01/3.17	             app_encode_app(int, int, bit1, pls))))
3.01/3.17	        = app_encode_app(int, int, 
3.01/3.17	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.01/3.17	              X0), X0)
3.01/3.17	       | ~ $true),
3.01/3.17	    inference('demod', [status(thm)],
3.01/3.17	              ['29', '13', '11', '12', '13', '13', '30'])).
3.01/3.17	tff('32', plain,
3.01/3.17	    ![X0 : int]:
3.01/3.17	      app_encode_app(nat, int, 
3.01/3.17	        app_encode_app(int, app_encode_fun(nat, int), power_power(int), X0), 
3.01/3.17	        app_encode_app(int, nat, number_number_of(nat), 
3.01/3.17	          app_encode_app(int, int, 
3.01/3.17	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.01/3.17	              app_encode_app(int, int, bit1, pls)), 
3.01/3.17	            app_encode_app(int, int, bit1, pls))))
3.01/3.17	       = app_encode_app(int, int, 
3.01/3.17	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.01/3.17	             X0), X0),
3.01/3.17	    inference('simplify', [status(thm)], ['31'])).
3.01/3.17	tff(zf_stmt_106, axiom,
3.01/3.17	  (![A:$tType]:
3.01/3.17	     (comm_semiring_1(A) =>
3.01/3.17	      (![Ry:A,Rx:A,Lx:A]:
3.01/3.17	         (app_encode_app(A,A,
3.01/3.17	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
3.01/3.17	                                        Lx),
3.01/3.17	                         app_encode_app(A,A,
3.01/3.17	                                        app_encode_app(A,app_encode_fun(A,A),
3.01/3.17	                                                       times_times(A),Rx),
3.01/3.17	                                        Ry)) =
3.01/3.17	          app_encode_app(A,A,
3.01/3.17	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
3.01/3.17	                                        Rx),
3.01/3.17	                         app_encode_app(A,A,
3.01/3.17	                                        app_encode_app(A,app_encode_fun(A,A),
3.01/3.17	                                                       times_times(A),Lx),
3.01/3.17	                                        Ry))))))).
3.01/3.17	tff('33', plain,
3.01/3.17	    ![X162 : $tType, X163 : X162, X164 : X162, X165 : X162]:
3.01/3.17	      (app_encode_app(X162, X162, 
3.01/3.17	         app_encode_app(X162, app_encode_fun(X162, X162), times_times(X162), 
3.01/3.17	           X164), 
3.01/3.17	         app_encode_app(X162, X162, 
3.01/3.17	           app_encode_app(X162, app_encode_fun(X162, X162), 
3.01/3.17	             times_times(X162), X163), X165))
3.01/3.17	        = app_encode_app(X162, X162, 
3.01/3.17	            app_encode_app(X162, app_encode_fun(X162, X162), 
3.01/3.17	              times_times(X162), X163), 
3.01/3.17	            app_encode_app(X162, X162, 
3.01/3.17	              app_encode_app(X162, app_encode_fun(X162, X162), 
3.01/3.17	                times_times(X162), X164), X165))
3.01/3.17	       | ~ comm_semiring_1(X162)),
3.01/3.17	    inference('cnf', [status(esa)], [zf_stmt_106])).
3.01/3.17	tff('34', plain,
3.01/3.17	    ![X0 : int, X1 : int, X2 : int]:
3.01/3.17	      (~ $true
3.01/3.17	       | app_encode_app(int, int, 
3.01/3.17	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.01/3.17	             X2), 
3.01/3.17	           app_encode_app(int, int, 
3.01/3.17	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.01/3.17	               X1), X0))
3.01/3.17	          = app_encode_app(int, int, 
3.01/3.17	              app_encode_app(int, app_encode_fun(int, int), 
3.01/3.17	                times_times(int), X1), 
3.01/3.17	              app_encode_app(int, int, 
3.01/3.17	                app_encode_app(int, app_encode_fun(int, int), 
3.01/3.17	                  times_times(int), X2), X0))),
3.01/3.17	    inference('sup-', [status(thm)], ['14', '33'])).
3.01/3.17	tff('35', plain,
3.01/3.17	    ![X0 : int, X1 : int, X2 : int]:
3.01/3.17	      app_encode_app(int, int, 
3.01/3.17	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X2), 
3.01/3.17	        app_encode_app(int, int, 
3.01/3.17	          app_encode_app(int, app_encode_fun(int, int), times_times(int), X1), 
3.01/3.17	          X0))
3.01/3.17	       = app_encode_app(int, int, 
3.01/3.17	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.01/3.17	             X1), 
3.01/3.17	           app_encode_app(int, int, 
3.01/3.17	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.01/3.17	               X2), X0)),
3.01/3.17	    inference('simplify', [status(thm)], ['34'])).
3.01/3.18	tff(zf_stmt_140, axiom, (linordered_idom(int))).
3.01/3.18	tff('36', plain, linordered_idom(int),
3.01/3.18	    inference('cnf', [status(esa)], [zf_stmt_140])).
3.01/3.18	tff(zf_stmt_97, axiom,
3.01/3.18	  (![A:$tType]:
3.01/3.18	     (linordered_idom(A) =>
3.01/3.18	      (![A1:A]:
3.01/3.18	         (app_encode_app(A,A,
3.01/3.18	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
3.01/3.18	                                        app_encode_app(A,A,abs_abs(A),A1)),
3.01/3.18	                         app_encode_app(A,A,abs_abs(A),A1)) =
3.01/3.18	          app_encode_app(A,A,
3.01/3.18	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
3.01/3.18	                                        A1),
3.01/3.18	                         A1)))))).
3.01/3.18	tff('37', plain,
3.01/3.18	    ![X137 : $tType, X138 : X137]:
3.01/3.18	      (app_encode_app(X137, X137, 
3.01/3.18	         app_encode_app(X137, app_encode_fun(X137, X137), times_times(X137), 
3.01/3.18	           app_encode_app(X137, X137, abs_abs(X137), X138)), 
3.01/3.18	         app_encode_app(X137, X137, abs_abs(X137), X138))
3.01/3.18	        = app_encode_app(X137, X137, 
3.01/3.18	            app_encode_app(X137, app_encode_fun(X137, X137), 
3.01/3.18	              times_times(X137), X138), X138)
3.01/3.18	       | ~ linordered_idom(X137)),
3.01/3.18	    inference('cnf', [status(esa)], [zf_stmt_97])).
3.01/3.18	tff('38', plain,
3.01/3.18	    ![X0 : int]:
3.01/3.18	      (~ $true
3.01/3.18	       | app_encode_app(int, int, 
3.01/3.18	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.01/3.18	             app_encode_app(int, int, abs_abs(int), X0)), 
3.01/3.18	           app_encode_app(int, int, abs_abs(int), X0))
3.01/3.18	          = app_encode_app(int, int, 
3.01/3.18	              app_encode_app(int, app_encode_fun(int, int), 
3.01/3.18	                times_times(int), X0), X0)),
3.01/3.18	    inference('sup-', [status(thm)], ['36', '37'])).
3.01/3.18	tff('39', plain,
3.01/3.18	    ![X0 : int]:
3.01/3.18	      app_encode_app(int, int, 
3.01/3.18	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.01/3.18	          app_encode_app(int, int, abs_abs(int), X0)), 
3.01/3.18	        app_encode_app(int, int, abs_abs(int), X0))
3.01/3.18	       = app_encode_app(int, int, 
3.01/3.18	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.01/3.18	             X0), X0),
3.01/3.18	    inference('simplify', [status(thm)], ['38'])).
3.01/3.18	tff('40', plain,
3.01/3.18	    app_encode_app(int, int, 
3.01/3.18	      app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.01/3.18	        app_encode_app(int, int, 
3.01/3.18	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.01/3.18	            app_encode_app(int, int, bit1, pls)), 
3.01/3.18	          app_encode_app(int, int, bit1, pls))), 
3.01/3.18	      app_encode_app(int, int, 
3.01/3.18	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.01/3.18	          app_encode_app(int, int, 
3.01/3.18	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.01/3.18	              app_encode_app(int, int, bit1, pls)), 
3.01/3.18	            app_encode_app(int, int, bit1, pls))), 
3.01/3.18	        app_encode_app(int, int, 
3.01/3.18	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.01/3.18	            app_encode_app(int, int, 
3.01/3.18	              app_encode_app(int, app_encode_fun(int, int), 
3.01/3.18	                times_times(int), v), v)), 
3.01/3.18	          app_encode_app(int, int, 
3.01/3.18	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.01/3.18	              w), w))))
3.01/3.18	     != app_encode_app(int, int, 
3.01/3.18	          app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.01/3.18	            app_encode_app(int, int, 
3.01/3.18	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.01/3.18	                app_encode_app(int, int, bit1, pls)), 
3.01/3.18	              app_encode_app(int, int, bit1, pls))), 
3.01/3.18	          app_encode_app(int, int, 
3.01/3.18	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.01/3.18	              app_encode_app(int, int, 
3.01/3.18	                app_encode_app(int, app_encode_fun(int, int), 
3.01/3.18	                  plus_plus(int), app_encode_app(int, int, bit1, pls)), 
3.01/3.18	                app_encode_app(int, int, bit1, pls))), 
3.01/3.18	            app_encode_app(int, int, 
3.01/3.18	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.01/3.18	                app_encode_app(int, int, 
3.01/3.18	                  app_encode_app(int, app_encode_fun(int, int), 
3.01/3.18	                    times_times(int), v), v)), 
3.01/3.18	              app_encode_app(int, int, 
3.01/3.18	                app_encode_app(int, app_encode_fun(int, int), 
3.01/3.18	                  times_times(int), w), w)))),
3.01/3.18	    inference('demod', [status(thm)],
3.01/3.18	              ['25', '32', '32', '32', '23', '35', '35', '39', '32', '23', 
3.01/3.18	               '35', '35', '39', '24', '24'])).
3.01/3.18	tff('41', plain, $false, inference('simplify', [status(thm)], ['40'])).
3.01/3.18	
3.01/3.18	% SZS output end Refutation
3.01/3.18	EOF
