0.00/0.00	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : app
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : rpo6
0.00/0.00	% Command    : 
0.00/0.00	#!/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   : n043.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 08:18:10 CST 2018
2.68/2.88	% done 1015 iterations in 2.663s
2.68/2.88	% SZS status Theorem for 'stdin'
2.68/2.88	% SZS output start Refutation
2.68/2.88	tff(zf_stmt_176, conjecture,
2.68/2.88	  (app_encode_app(int,int,
2.68/2.88	                  app_encode_app(int,app_encode_fun(int,int),plus_plus(int),
2.68/2.88	                                 app_encode_app(int,int,
2.68/2.88	                                                app_encode_app(int,
2.68/2.88	                                                               app_encode_fun(
2.68/2.88	                                                               int,int),
2.68/2.88	                                                               times_times(
2.68/2.88	                                                               int),
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,int,
2.68/2.88	                                                               number_number_of(
2.68/2.88	                                                               int),
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,int,bit0,
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,int,bit0,
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,int,bit1,
2.68/2.88	                                                               pls))))),
2.68/2.88	                                                app_encode_app(nat,int,
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,
2.68/2.88	                                                               app_encode_fun(
2.68/2.88	                                                               nat,int),
2.68/2.88	                                                               power_power(
2.68/2.88	                                                               int),v),
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,nat,
2.68/2.88	                                                               number_number_of(
2.68/2.88	                                                               nat),
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,int,bit0,
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,int,bit1,
2.68/2.88	                                                               pls)))))),
2.68/2.88	                  app_encode_app(int,int,
2.68/2.88	                                 app_encode_app(int,app_encode_fun(int,int),
2.68/2.88	                                                times_times(int),
2.68/2.88	                                                app_encode_app(int,int,
2.68/2.88	                                                               number_number_of(
2.68/2.88	                                                               int),
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,int,bit0,
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,int,bit0,
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,int,bit1,
2.68/2.88	                                                               pls))))),
2.68/2.88	                                 app_encode_app(nat,int,
2.68/2.88	                                                app_encode_app(int,
2.68/2.88	                                                               app_encode_fun(
2.68/2.88	                                                               nat,int),
2.68/2.88	                                                               power_power(
2.68/2.88	                                                               int),w),
2.68/2.88	                                                app_encode_app(int,nat,
2.68/2.88	                                                               number_number_of(
2.68/2.88	                                                               nat),
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,int,bit0,
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,int,bit1,
2.68/2.88	                                                               pls)))))) =
2.68/2.88	   app_encode_app(int,int,
2.68/2.88	                  app_encode_app(int,app_encode_fun(int,int),plus_plus(int),
2.68/2.88	                                 app_encode_app(nat,int,
2.68/2.88	                                                app_encode_app(int,
2.68/2.88	                                                               app_encode_fun(
2.68/2.88	                                                               nat,int),
2.68/2.88	                                                               power_power(
2.68/2.88	                                                               int),
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,int,
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,
2.68/2.88	                                                               app_encode_fun(
2.68/2.88	                                                               int,int),
2.68/2.88	                                                               times_times(
2.68/2.88	                                                               int),
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,int,
2.68/2.88	                                                               number_number_of(
2.68/2.88	                                                               int),
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,int,bit0,
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,int,bit1,
2.68/2.88	                                                               pls)))),
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,int,
2.68/2.88	                                                               abs_abs(int),v))),
2.68/2.88	                                                app_encode_app(int,nat,
2.68/2.88	                                                               number_number_of(
2.68/2.88	                                                               nat),
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,int,bit0,
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,int,bit1,
2.68/2.88	                                                               pls))))),
2.68/2.88	                  app_encode_app(nat,int,
2.68/2.88	                                 app_encode_app(int,app_encode_fun(nat,int),
2.68/2.88	                                                power_power(int),
2.68/2.88	                                                app_encode_app(int,int,
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,
2.68/2.88	                                                               app_encode_fun(
2.68/2.88	                                                               int,int),
2.68/2.88	                                                               times_times(
2.68/2.88	                                                               int),
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,int,
2.68/2.88	                                                               number_number_of(
2.68/2.88	                                                               int),
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,int,bit0,
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,int,bit1,
2.68/2.88	                                                               pls)))),
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,int,
2.68/2.88	                                                               abs_abs(int),w))),
2.68/2.88	                                 app_encode_app(int,nat,
2.68/2.88	                                                number_number_of(nat),
2.68/2.88	                                                app_encode_app(int,int,bit0,
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,int,bit1,
2.68/2.88	                                                               pls))))))).
2.68/2.88	tff(zf_stmt_0, negated_conjecture,
2.68/2.88	  (app_encode_app(int,int,
2.68/2.88	                  app_encode_app(int,app_encode_fun(int,int),plus_plus(int),
2.68/2.88	                                 app_encode_app(int,int,
2.68/2.88	                                                app_encode_app(int,
2.68/2.88	                                                               app_encode_fun(
2.68/2.88	                                                               int,int),
2.68/2.88	                                                               times_times(
2.68/2.88	                                                               int),
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,int,
2.68/2.88	                                                               number_number_of(
2.68/2.88	                                                               int),
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,int,bit0,
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,int,bit0,
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,int,bit1,
2.68/2.88	                                                               pls))))),
2.68/2.88	                                                app_encode_app(nat,int,
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,
2.68/2.88	                                                               app_encode_fun(
2.68/2.88	                                                               nat,int),
2.68/2.88	                                                               power_power(
2.68/2.88	                                                               int),v),
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,nat,
2.68/2.88	                                                               number_number_of(
2.68/2.88	                                                               nat),
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,int,bit0,
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,int,bit1,
2.68/2.88	                                                               pls)))))),
2.68/2.88	                  app_encode_app(int,int,
2.68/2.88	                                 app_encode_app(int,app_encode_fun(int,int),
2.68/2.88	                                                times_times(int),
2.68/2.88	                                                app_encode_app(int,int,
2.68/2.88	                                                               number_number_of(
2.68/2.88	                                                               int),
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,int,bit0,
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,int,bit0,
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,int,bit1,
2.68/2.88	                                                               pls))))),
2.68/2.88	                                 app_encode_app(nat,int,
2.68/2.88	                                                app_encode_app(int,
2.68/2.88	                                                               app_encode_fun(
2.68/2.88	                                                               nat,int),
2.68/2.88	                                                               power_power(
2.68/2.88	                                                               int),w),
2.68/2.88	                                                app_encode_app(int,nat,
2.68/2.88	                                                               number_number_of(
2.68/2.88	                                                               nat),
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,int,bit0,
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,int,bit1,
2.68/2.88	                                                               pls)))))) !=
2.68/2.88	   app_encode_app(int,int,
2.68/2.88	                  app_encode_app(int,app_encode_fun(int,int),plus_plus(int),
2.68/2.88	                                 app_encode_app(nat,int,
2.68/2.88	                                                app_encode_app(int,
2.68/2.88	                                                               app_encode_fun(
2.68/2.88	                                                               nat,int),
2.68/2.88	                                                               power_power(
2.68/2.88	                                                               int),
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,int,
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,
2.68/2.88	                                                               app_encode_fun(
2.68/2.88	                                                               int,int),
2.68/2.88	                                                               times_times(
2.68/2.88	                                                               int),
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,int,
2.68/2.88	                                                               number_number_of(
2.68/2.88	                                                               int),
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,int,bit0,
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,int,bit1,
2.68/2.88	                                                               pls)))),
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,int,
2.68/2.88	                                                               abs_abs(int),v))),
2.68/2.88	                                                app_encode_app(int,nat,
2.68/2.88	                                                               number_number_of(
2.68/2.88	                                                               nat),
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,int,bit0,
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,int,bit1,
2.68/2.88	                                                               pls))))),
2.68/2.88	                  app_encode_app(nat,int,
2.68/2.88	                                 app_encode_app(int,app_encode_fun(nat,int),
2.68/2.88	                                                power_power(int),
2.68/2.88	                                                app_encode_app(int,int,
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,
2.68/2.88	                                                               app_encode_fun(
2.68/2.88	                                                               int,int),
2.68/2.88	                                                               times_times(
2.68/2.88	                                                               int),
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,int,
2.68/2.88	                                                               number_number_of(
2.68/2.88	                                                               int),
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,int,bit0,
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,int,bit1,
2.68/2.88	                                                               pls)))),
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,int,
2.68/2.88	                                                               abs_abs(int),w))),
2.68/2.88	                                 app_encode_app(int,nat,
2.68/2.88	                                                number_number_of(nat),
2.68/2.88	                                                app_encode_app(int,int,bit0,
2.68/2.88	                                                               app_encode_app(
2.68/2.88	                                                               int,int,bit1,
2.68/2.88	                                                               pls))))))).
2.68/2.88	tff('0', plain,
2.68/2.88	    app_encode_app(int, int, 
2.68/2.88	      app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.68/2.88	        app_encode_app(int, int, 
2.68/2.88	          app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.68/2.88	            app_encode_app(int, int, number_number_of(int), 
2.68/2.88	              app_encode_app(int, int, bit0, 
2.68/2.88	                app_encode_app(int, int, bit0, 
2.68/2.88	                  app_encode_app(int, int, bit1, pls))))), 
2.68/2.88	          app_encode_app(nat, int, 
2.68/2.88	            app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
2.68/2.88	              v), 
2.68/2.88	            app_encode_app(int, nat, number_number_of(nat), 
2.68/2.88	              app_encode_app(int, int, bit0, 
2.68/2.88	                app_encode_app(int, int, bit1, pls)))))), 
2.68/2.88	      app_encode_app(int, int, 
2.68/2.88	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.68/2.88	          app_encode_app(int, int, number_number_of(int), 
2.68/2.88	            app_encode_app(int, int, bit0, 
2.68/2.88	              app_encode_app(int, int, bit0, 
2.68/2.88	                app_encode_app(int, int, bit1, pls))))), 
2.68/2.88	        app_encode_app(nat, int, 
2.68/2.88	          app_encode_app(int, app_encode_fun(nat, int), power_power(int), w), 
2.68/2.88	          app_encode_app(int, nat, number_number_of(nat), 
2.68/2.88	            app_encode_app(int, int, bit0, 
2.68/2.88	              app_encode_app(int, int, bit1, pls))))))
2.68/2.88	     != app_encode_app(int, int, 
2.68/2.88	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.68/2.88	            app_encode_app(nat, int, 
2.68/2.88	              app_encode_app(int, app_encode_fun(nat, int), 
2.68/2.88	                power_power(int), 
2.68/2.88	                app_encode_app(int, int, 
2.68/2.88	                  app_encode_app(int, app_encode_fun(int, int), 
2.68/2.88	                    times_times(int), 
2.68/2.88	                    app_encode_app(int, int, number_number_of(int), 
2.68/2.88	                      app_encode_app(int, int, bit0, 
2.68/2.88	                        app_encode_app(int, int, bit1, pls)))), 
2.68/2.88	                  app_encode_app(int, int, abs_abs(int), v))), 
2.68/2.88	              app_encode_app(int, nat, number_number_of(nat), 
2.68/2.88	                app_encode_app(int, int, bit0, 
2.68/2.88	                  app_encode_app(int, int, bit1, pls))))), 
2.68/2.88	          app_encode_app(nat, int, 
2.68/2.88	            app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
2.68/2.88	              app_encode_app(int, int, 
2.68/2.88	                app_encode_app(int, app_encode_fun(int, int), 
2.68/2.88	                  times_times(int), 
2.68/2.88	                  app_encode_app(int, int, number_number_of(int), 
2.68/2.88	                    app_encode_app(int, int, bit0, 
2.68/2.88	                      app_encode_app(int, int, bit1, pls)))), 
2.68/2.88	                app_encode_app(int, int, abs_abs(int), w))), 
2.68/2.88	            app_encode_app(int, nat, number_number_of(nat), 
2.68/2.88	              app_encode_app(int, int, bit0, 
2.68/2.88	                app_encode_app(int, int, bit1, pls))))),
2.68/2.88	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.68/2.88	tff(zf_stmt_57, axiom,
2.68/2.88	  (![W:int]:
2.68/2.88	     (app_encode_app(int,int,
2.68/2.88	                     app_encode_app(int,app_encode_fun(int,int),
2.68/2.88	                                    times_times(int),pls),
2.68/2.88	                     W) =
2.68/2.88	      pls))).
2.68/2.88	tff('1', plain,
2.68/2.88	    ![X49 : int]:
2.68/2.88	      app_encode_app(int, int, 
2.68/2.88	        app_encode_app(int, app_encode_fun(int, int), times_times(int), pls), 
2.68/2.88	        X49)
2.68/2.88	       = pls,
2.68/2.88	    inference('cnf', [status(esa)], [zf_stmt_57])).
2.68/2.88	tff(zf_stmt_38, axiom,
2.68/2.88	  (![L:int,K:int]:
2.68/2.88	     (app_encode_app(int,int,
2.68/2.88	                     app_encode_app(int,app_encode_fun(int,int),
2.68/2.88	                                    times_times(int),
2.68/2.88	                                    app_encode_app(int,int,bit1,K)),
2.68/2.88	                     L) =
2.68/2.88	      app_encode_app(int,int,
2.68/2.88	                     app_encode_app(int,app_encode_fun(int,int),
2.68/2.88	                                    plus_plus(int),
2.68/2.88	                                    app_encode_app(int,int,bit0,
2.68/2.88	                                                   app_encode_app(int,int,
2.68/2.88	                                                                  app_encode_app(
2.68/2.88	                                                                  int,
2.68/2.88	                                                                  app_encode_fun(
2.68/2.88	                                                                  int,int),
2.68/2.88	                                                                  times_times(
2.68/2.88	                                                                  int),K),L))),
2.68/2.88	                     L)))).
2.68/2.88	tff('2', plain,
2.68/2.88	    ![X6 : int, X7 : int]:
2.68/2.88	      app_encode_app(int, int, 
2.68/2.88	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.68/2.88	          app_encode_app(int, int, bit1, X6)), X7)
2.68/2.88	       = app_encode_app(int, int, 
2.68/2.88	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.68/2.88	             app_encode_app(int, int, bit0, 
2.68/2.88	               app_encode_app(int, int, 
2.68/2.88	                 app_encode_app(int, app_encode_fun(int, int), 
2.68/2.88	                   times_times(int), X6), X7))), X7),
2.68/2.88	    inference('cnf', [status(esa)], [zf_stmt_38])).
2.68/2.88	tff('3', plain,
2.68/2.88	    ![X0 : int]:
2.68/2.88	      app_encode_app(int, int, 
2.68/2.88	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.68/2.88	          app_encode_app(int, int, bit1, pls)), X0)
2.68/2.88	       = app_encode_app(int, int, 
2.68/2.88	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.68/2.88	             app_encode_app(int, int, bit0, pls)), X0),
2.68/2.88	    inference('sup+', [status(thm)], ['1', '2'])).
2.68/2.88	tff(zf_stmt_56, axiom, (app_encode_app(int,int,bit0,pls) = pls)).
2.68/2.88	tff('4', plain, app_encode_app(int, int, bit0, pls) = pls,
2.68/2.88	    inference('cnf', [status(esa)], [zf_stmt_56])).
2.68/2.88	tff('5', plain,
2.68/2.88	    ![X0 : int]:
2.68/2.88	      app_encode_app(int, int, 
2.68/2.88	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.68/2.88	          app_encode_app(int, int, bit1, pls)), X0)
2.68/2.88	       = app_encode_app(int, int, 
2.68/2.88	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
2.68/2.88	           X0),
2.68/2.88	    inference('demod', [status(thm)], ['3', '4'])).
2.68/2.88	tff(zf_stmt_70, axiom,
2.68/2.88	  (![K:int]:
2.68/2.88	     (app_encode_app(int,int,
2.68/2.88	                     app_encode_app(int,app_encode_fun(int,int),
2.68/2.88	                                    plus_plus(int),pls),
2.68/2.88	                     K) =
2.68/2.88	      K))).
2.68/2.88	tff('6', plain,
2.68/2.88	    ![X80 : int]:
2.68/2.88	      app_encode_app(int, int, 
2.68/2.88	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
2.68/2.88	        X80)
2.68/2.88	       = X80,
2.68/2.88	    inference('cnf', [status(esa)], [zf_stmt_70])).
2.68/2.88	tff('7', plain,
2.68/2.88	    ![X0 : int]:
2.68/2.88	      app_encode_app(int, int, 
2.68/2.88	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.68/2.88	          app_encode_app(int, int, bit1, pls)), X0)
2.68/2.88	       = X0,
2.68/2.88	    inference('sup+', [status(thm)], ['5', '6'])).
2.68/2.88	tff(zf_stmt_71, axiom,
2.68/2.88	  (![K:int]:
2.68/2.88	     (app_encode_app(int,int,bit0,K) =
2.68/2.88	      app_encode_app(int,int,
2.68/2.88	                     app_encode_app(int,app_encode_fun(int,int),
2.68/2.88	                                    plus_plus(int),K),
2.68/2.88	                     K)))).
2.68/2.88	tff('8', plain,
2.68/2.88	    ![X81 : int]:
2.68/2.88	      app_encode_app(int, int, bit0, X81)
2.68/2.88	       = app_encode_app(int, int, 
2.68/2.88	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X81), 
2.68/2.88	           X81),
2.68/2.88	    inference('cnf', [status(esa)], [zf_stmt_71])).
2.68/2.88	tff(zf_stmt_58, axiom,
2.68/2.88	  (![L:int,K:int]:
2.68/2.88	     (app_encode_app(int,int,
2.68/2.88	                     app_encode_app(int,app_encode_fun(int,int),
2.68/2.88	                                    times_times(int),
2.68/2.88	                                    app_encode_app(int,int,bit0,K)),
2.68/2.88	                     L) =
2.68/2.88	      app_encode_app(int,int,bit0,
2.68/2.88	                     app_encode_app(int,int,
2.68/2.88	                                    app_encode_app(int,
2.68/2.88	                                                   app_encode_fun(int,int),
2.68/2.88	                                                   times_times(int),K),
2.68/2.88	                                    L))))).
2.68/2.88	tff('9', plain,
2.68/2.88	    ![X50 : int, X51 : int]:
2.68/2.88	      app_encode_app(int, int, 
2.68/2.88	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.68/2.88	          app_encode_app(int, int, bit0, X50)), X51)
2.68/2.88	       = app_encode_app(int, int, bit0, 
2.68/2.88	           app_encode_app(int, int, 
2.68/2.88	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.68/2.88	               X50), X51)),
2.68/2.88	    inference('cnf', [status(esa)], [zf_stmt_58])).
2.68/2.88	tff('10', plain,
2.68/2.88	    ![X0 : int, X1 : int]:
2.68/2.88	      app_encode_app(int, int, 
2.68/2.88	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.68/2.88	          app_encode_app(int, int, 
2.68/2.88	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
2.68/2.88	            X0)), X1)
2.68/2.88	       = app_encode_app(int, int, bit0, 
2.68/2.88	           app_encode_app(int, int, 
2.68/2.88	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.68/2.88	               X0), X1)),
2.68/2.88	    inference('sup+', [status(thm)], ['8', '9'])).
2.68/2.88	tff('11', plain,
2.68/2.88	    ![X0 : int]:
2.68/2.88	      app_encode_app(int, int, 
2.68/2.88	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.68/2.88	          app_encode_app(int, int, 
2.68/2.88	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.68/2.88	              app_encode_app(int, int, bit1, pls)), 
2.68/2.88	            app_encode_app(int, int, bit1, pls))), X0)
2.68/2.88	       = app_encode_app(int, int, bit0, X0),
2.68/2.88	    inference('sup+', [status(thm)], ['7', '10'])).
2.68/2.88	tff(zf_stmt_74, axiom,
2.68/2.88	  (![Z2:int,Z11:int,W:int]:
2.68/2.88	     (app_encode_app(int,int,
2.68/2.88	                     app_encode_app(int,app_encode_fun(int,int),
2.68/2.88	                                    times_times(int),W),
2.68/2.88	                     app_encode_app(int,int,
2.68/2.88	                                    app_encode_app(int,
2.68/2.88	                                                   app_encode_fun(int,int),
2.68/2.88	                                                   plus_plus(int),Z11),
2.68/2.88	                                    Z2)) =
2.68/2.88	      app_encode_app(int,int,
2.68/2.88	                     app_encode_app(int,app_encode_fun(int,int),
2.68/2.88	                                    plus_plus(int),
2.68/2.88	                                    app_encode_app(int,int,
2.68/2.88	                                                   app_encode_app(int,
2.68/2.88	                                                                  app_encode_fun(
2.68/2.88	                                                                  int,int),
2.68/2.88	                                                                  times_times(
2.68/2.88	                                                                  int),W),
2.68/2.88	                                                   Z11)),
2.68/2.88	                     app_encode_app(int,int,
2.68/2.88	                                    app_encode_app(int,
2.68/2.88	                                                   app_encode_fun(int,int),
2.68/2.88	                                                   times_times(int),W),
2.68/2.88	                                    Z2))))).
2.68/2.88	tff('12', plain,
2.68/2.88	    ![X87 : int, X88 : int, X89 : int]:
2.68/2.88	      app_encode_app(int, int, 
2.68/2.88	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X87), 
2.68/2.88	        app_encode_app(int, int, 
2.68/2.88	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X88), 
2.68/2.88	          X89))
2.68/2.88	       = app_encode_app(int, int, 
2.68/2.88	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.68/2.88	             app_encode_app(int, int, 
2.68/2.88	               app_encode_app(int, app_encode_fun(int, int), 
2.68/2.88	                 times_times(int), X87), X88)), 
2.68/2.88	           app_encode_app(int, int, 
2.68/2.88	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.68/2.88	               X87), X89)),
2.68/2.88	    inference('cnf', [status(esa)], [zf_stmt_74])).
2.68/2.88	tff(zf_stmt_73, axiom,
2.68/2.88	  (![W:int,Z2:int,Z11:int]:
2.68/2.88	     (app_encode_app(int,int,
2.68/2.88	                     app_encode_app(int,app_encode_fun(int,int),
2.68/2.88	                                    times_times(int),
2.68/2.88	                                    app_encode_app(int,int,
2.68/2.88	                                                   app_encode_app(int,
2.68/2.88	                                                                  app_encode_fun(
2.68/2.88	                                                                  int,int),
2.68/2.88	                                                                  plus_plus(
2.68/2.88	                                                                  int),Z11),
2.68/2.88	                                                   Z2)),
2.68/2.88	                     W) =
2.68/2.88	      app_encode_app(int,int,
2.68/2.88	                     app_encode_app(int,app_encode_fun(int,int),
2.68/2.88	                                    plus_plus(int),
2.68/2.88	                                    app_encode_app(int,int,
2.68/2.88	                                                   app_encode_app(int,
2.68/2.88	                                                                  app_encode_fun(
2.68/2.88	                                                                  int,int),
2.68/2.88	                                                                  times_times(
2.68/2.88	                                                                  int),Z11),
2.68/2.88	                                                   W)),
2.68/2.88	                     app_encode_app(int,int,
2.68/2.88	                                    app_encode_app(int,
2.68/2.88	                                                   app_encode_fun(int,int),
2.68/2.88	                                                   times_times(int),Z2),
2.68/2.88	                                    W))))).
2.68/2.88	tff('13', plain,
2.68/2.88	    ![X84 : int, X85 : int, X86 : int]:
2.68/2.88	      app_encode_app(int, int, 
2.68/2.88	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.68/2.88	          app_encode_app(int, int, 
2.68/2.88	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.68/2.88	              X84), X86)), X85)
2.68/2.88	       = app_encode_app(int, int, 
2.68/2.88	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.68/2.88	             app_encode_app(int, int, 
2.68/2.88	               app_encode_app(int, app_encode_fun(int, int), 
2.68/2.88	                 times_times(int), X84), X85)), 
2.68/2.88	           app_encode_app(int, int, 
2.68/2.88	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.68/2.88	               X86), X85)),
2.68/2.88	    inference('cnf', [status(esa)], [zf_stmt_73])).
2.68/2.88	tff('14', plain,
2.68/2.88	    ![X0 : int, X1 : int]:
2.68/2.88	      app_encode_app(int, int, 
2.68/2.88	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.68/2.88	          app_encode_app(int, int, 
2.68/2.88	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X1), 
2.68/2.88	            X1)), X0)
2.68/2.88	       = app_encode_app(int, int, 
2.68/2.88	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.68/2.88	             X1), 
2.68/2.88	           app_encode_app(int, int, 
2.68/2.88	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.68/2.88	               X0), X0)),
2.68/2.88	    inference('sup+', [status(thm)], ['12', '13'])).
2.68/2.88	tff(zf_stmt_67, axiom,
2.68/2.88	  (![K:int]: (app_encode_app(int,int,number_number_of(int),K) = K))).
2.68/2.88	tff('15', plain,
2.68/2.88	    ![X75 : int]: app_encode_app(int, int, number_number_of(int), X75) = X75,
2.68/2.88	    inference('cnf', [status(esa)], [zf_stmt_67])).
2.68/2.88	tff(zf_stmt_140, axiom, (comm_semiring_1(int))).
2.68/2.88	tff('16', plain, comm_semiring_1(int),
2.68/2.88	    inference('cnf', [status(esa)], [zf_stmt_140])).
2.68/2.88	tff(zf_stmt_104, axiom,
2.68/2.88	  (![A:$tType]:
2.68/2.88	     (comm_semiring_1(A) =>
2.68/2.88	      (![B:A,A1:A]:
2.68/2.88	         (app_encode_app(A,A,
2.68/2.88	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
2.68/2.88	                                        A1),
2.68/2.88	                         B) =
2.68/2.88	          app_encode_app(A,A,
2.68/2.88	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
2.68/2.88	                                        B),
2.68/2.88	                         A1)))))).
2.68/2.88	tff('17', plain,
2.68/2.88	    ![X155 : $tType, X156 : X155, X157 : X155]:
2.68/2.88	      (app_encode_app(X155, X155, 
2.68/2.88	         app_encode_app(X155, app_encode_fun(X155, X155), times_times(X155), 
2.68/2.88	           X157), X156)
2.68/2.88	        = app_encode_app(X155, X155, 
2.68/2.88	            app_encode_app(X155, app_encode_fun(X155, X155), 
2.68/2.88	              times_times(X155), X156), X157)
2.68/2.88	       | ~ comm_semiring_1(X155)),
2.68/2.88	    inference('cnf', [status(esa)], [zf_stmt_104])).
2.68/2.88	tff('18', plain,
2.68/2.88	    ![X0 : int, X1 : int]:
2.68/2.88	      (~ $true
2.68/2.88	       | app_encode_app(int, int, 
2.68/2.88	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.68/2.88	             X1), X0)
2.68/2.88	          = app_encode_app(int, int, 
2.68/2.88	              app_encode_app(int, app_encode_fun(int, int), 
2.68/2.88	                times_times(int), X0), X1)),
2.68/2.88	    inference('sup-', [status(thm)], ['16', '17'])).
2.68/2.88	tff('19', plain,
2.68/2.88	    ![X0 : int, X1 : int]:
2.68/2.88	      app_encode_app(int, int, 
2.68/2.88	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X1), 
2.68/2.88	        X0)
2.68/2.88	       = app_encode_app(int, int, 
2.68/2.88	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.68/2.88	             X0), X1),
2.68/2.88	    inference('simplify', [status(thm)], ['18'])).
2.68/2.88	tff(zf_stmt_145, axiom, (number_ring(int))).
2.68/2.88	tff('20', plain, number_ring(int),
2.68/2.88	    inference('cnf', [status(esa)], [zf_stmt_145])).
2.68/2.88	tff(zf_stmt_62, axiom,
2.68/2.88	  (![A:$tType]:
2.68/2.88	     (number_ring(A) =>
2.68/2.88	      (![Z1:A,W:int,V:int]:
2.68/2.88	         (app_encode_app(A,A,
2.68/2.88	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
2.68/2.88	                                        app_encode_app(int,A,
2.68/2.88	                                                       number_number_of(A),V)),
2.68/2.88	                         app_encode_app(A,A,
2.68/2.88	                                        app_encode_app(A,app_encode_fun(A,A),
2.68/2.88	                                                       times_times(A),
2.68/2.88	                                                       app_encode_app(
2.68/2.88	                                                       int,A,
2.68/2.88	                                                       number_number_of(A),W)),
2.68/2.88	                                        Z1)) =
2.68/2.88	          app_encode_app(A,A,
2.68/2.88	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
2.68/2.88	                                        app_encode_app(int,A,
2.68/2.88	                                                       number_number_of(A),
2.68/2.88	                                                       app_encode_app(
2.68/2.88	                                                       int,int,
2.68/2.88	                                                       app_encode_app(
2.68/2.88	                                                       int,
2.68/2.88	                                                       app_encode_fun(
2.68/2.88	                                                       int,int),
2.68/2.88	                                                       times_times(int),V),W))),
2.68/2.88	                         Z1)))))).
2.68/2.88	tff('21', plain,
2.68/2.88	    ![X62 : $tType, X63 : int, X64 : int, X65 : X62]:
2.68/2.88	      (app_encode_app(X62, X62, 
2.68/2.88	         app_encode_app(X62, app_encode_fun(X62, X62), times_times(X62), 
2.68/2.88	           app_encode_app(int, X62, number_number_of(X62), X63)), 
2.68/2.88	         app_encode_app(X62, X62, 
2.68/2.88	           app_encode_app(X62, app_encode_fun(X62, X62), times_times(X62), 
2.68/2.88	             app_encode_app(int, X62, number_number_of(X62), X64)), X65))
2.68/2.88	        = app_encode_app(X62, X62, 
2.68/2.88	            app_encode_app(X62, app_encode_fun(X62, X62), times_times(X62), 
2.68/2.88	              app_encode_app(int, X62, number_number_of(X62), 
2.68/2.88	                app_encode_app(int, int, 
2.68/2.88	                  app_encode_app(int, app_encode_fun(int, int), 
2.68/2.88	                    times_times(int), X63), X64))), X65)
2.68/2.88	       | ~ number_ring(X62)),
2.68/2.88	    inference('cnf', [status(esa)], [zf_stmt_62])).
2.68/2.88	tff('22', plain,
2.68/2.88	    ![X0 : int, X1 : int, X2 : int]:
2.68/2.88	      (~ $true
2.68/2.88	       | app_encode_app(int, int, 
2.68/2.88	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.68/2.88	             app_encode_app(int, int, number_number_of(int), X2)), 
2.68/2.88	           app_encode_app(int, int, 
2.68/2.88	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.68/2.88	               app_encode_app(int, int, number_number_of(int), X1)), X0))
2.68/2.88	          = app_encode_app(int, int, 
2.68/2.88	              app_encode_app(int, app_encode_fun(int, int), 
2.68/2.88	                times_times(int), 
2.68/2.88	                app_encode_app(int, int, number_number_of(int), 
2.68/2.88	                  app_encode_app(int, int, 
2.68/2.88	                    app_encode_app(int, app_encode_fun(int, int), 
2.68/2.88	                      times_times(int), X2), X1))), X0)),
2.68/2.88	    inference('sup-', [status(thm)], ['20', '21'])).
2.68/2.88	tff('23', plain,
2.68/2.88	    ![X0 : int, X1 : int, X2 : int]:
2.68/2.88	      (~ $true
2.68/2.88	       | app_encode_app(int, int, 
2.68/2.88	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.68/2.88	             X2), 
2.68/2.88	           app_encode_app(int, int, 
2.68/2.88	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.68/2.88	               X1), X0))
2.68/2.88	          = app_encode_app(int, int, 
2.68/2.88	              app_encode_app(int, app_encode_fun(int, int), 
2.68/2.88	                times_times(int), 
2.68/2.88	                app_encode_app(int, int, 
2.68/2.88	                  app_encode_app(int, app_encode_fun(int, int), 
2.68/2.88	                    times_times(int), X2), X1)), X0)),
2.68/2.88	    inference('demod', [status(thm)], ['22', '15', '15', '15'])).
2.68/2.88	tff('24', plain,
2.68/2.88	    ![X0 : int, X1 : int, X2 : int]:
2.68/2.88	      app_encode_app(int, int, 
2.68/2.88	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X2), 
2.68/2.88	        app_encode_app(int, int, 
2.68/2.88	          app_encode_app(int, app_encode_fun(int, int), times_times(int), X1), 
2.68/2.88	          X0))
2.68/2.88	       = app_encode_app(int, int, 
2.68/2.88	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.68/2.88	             app_encode_app(int, int, 
2.68/2.88	               app_encode_app(int, app_encode_fun(int, int), 
2.68/2.88	                 times_times(int), X2), X1)), X0),
2.68/2.88	    inference('simplify', [status(thm)], ['23'])).
2.68/2.88	tff('25', plain,
2.68/2.88	    ![X0 : int, X1 : int, X2 : int]:
2.68/2.88	      app_encode_app(int, int, 
2.68/2.88	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X0), 
2.68/2.88	        app_encode_app(int, int, 
2.68/2.88	          app_encode_app(int, app_encode_fun(int, int), times_times(int), X1), 
2.68/2.88	          X2))
2.68/2.88	       = app_encode_app(int, int, 
2.68/2.88	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.68/2.88	             app_encode_app(int, int, 
2.68/2.88	               app_encode_app(int, app_encode_fun(int, int), 
2.68/2.88	                 times_times(int), X1), X0)), X2),
2.68/2.88	    inference('sup+', [status(thm)], ['19', '24'])).
2.68/2.88	tff('26', plain,
2.68/2.88	    app_encode_app(int, int, 
2.68/2.88	      app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.68/2.88	        app_encode_app(int, int, 
2.68/2.88	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.68/2.88	            app_encode_app(int, int, bit1, pls)), 
2.68/2.88	          app_encode_app(int, int, bit1, pls))), 
2.68/2.88	      app_encode_app(int, int, 
2.68/2.88	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.68/2.88	          app_encode_app(int, int, 
2.68/2.88	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.68/2.88	              app_encode_app(int, int, bit1, pls)), 
2.68/2.88	            app_encode_app(int, int, bit1, pls))), 
2.68/2.88	        app_encode_app(int, int, 
2.68/2.88	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.68/2.88	            app_encode_app(nat, int, 
2.68/2.88	              app_encode_app(int, app_encode_fun(nat, int), 
2.68/2.88	                power_power(int), v), 
2.68/2.88	              app_encode_app(int, nat, number_number_of(nat), 
2.68/2.88	                app_encode_app(int, int, 
2.68/2.88	                  app_encode_app(int, app_encode_fun(int, int), 
2.68/2.88	                    plus_plus(int), app_encode_app(int, int, bit1, pls)), 
2.68/2.88	                  app_encode_app(int, int, bit1, pls))))), 
2.68/2.88	          app_encode_app(nat, int, 
2.68/2.88	            app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
2.68/2.88	              w), 
2.68/2.88	            app_encode_app(int, nat, number_number_of(nat), 
2.68/2.88	              app_encode_app(int, int, 
2.68/2.88	                app_encode_app(int, app_encode_fun(int, int), 
2.68/2.88	                  plus_plus(int), app_encode_app(int, int, bit1, pls)), 
2.68/2.88	                app_encode_app(int, int, bit1, pls)))))))
2.68/2.88	     != app_encode_app(int, int, 
2.68/2.88	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.68/2.88	            app_encode_app(nat, int, 
2.68/2.88	              app_encode_app(int, app_encode_fun(nat, int), 
2.68/2.88	                power_power(int), 
2.68/2.88	                app_encode_app(int, int, 
2.68/2.88	                  app_encode_app(int, app_encode_fun(int, int), 
2.68/2.88	                    times_times(int), 
2.68/2.88	                    app_encode_app(int, int, 
2.68/2.88	                      app_encode_app(int, app_encode_fun(int, int), 
2.68/2.88	                        plus_plus(int), app_encode_app(int, int, bit1, pls)), 
2.68/2.88	                      app_encode_app(int, int, bit1, pls))), 
2.68/2.88	                  app_encode_app(int, int, abs_abs(int), v))), 
2.68/2.88	              app_encode_app(int, nat, number_number_of(nat), 
2.68/2.88	                app_encode_app(int, int, 
2.68/2.88	                  app_encode_app(int, app_encode_fun(int, int), 
2.68/2.88	                    plus_plus(int), app_encode_app(int, int, bit1, pls)), 
2.68/2.88	                  app_encode_app(int, int, bit1, pls))))), 
2.68/2.88	          app_encode_app(nat, int, 
2.68/2.88	            app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
2.68/2.88	              app_encode_app(int, int, 
2.68/2.88	                app_encode_app(int, app_encode_fun(int, int), 
2.68/2.88	                  times_times(int), 
2.68/2.88	                  app_encode_app(int, int, 
2.68/2.88	                    app_encode_app(int, app_encode_fun(int, int), 
2.68/2.88	                      plus_plus(int), app_encode_app(int, int, bit1, pls)), 
2.68/2.88	                    app_encode_app(int, int, bit1, pls))), 
2.68/2.88	                app_encode_app(int, int, abs_abs(int), w))), 
2.68/2.88	            app_encode_app(int, nat, number_number_of(nat), 
2.68/2.88	              app_encode_app(int, int, 
2.68/2.88	                app_encode_app(int, app_encode_fun(int, int), 
2.68/2.88	                  plus_plus(int), app_encode_app(int, int, bit1, pls)), 
2.68/2.88	                app_encode_app(int, int, bit1, pls))))),
2.68/2.88	    inference('demod', [status(thm)],
2.68/2.88	              ['0', '11', '14', '7', '11', '15', '11', '14', '7', '25', 
2.68/2.88	               '11', '14', '7', '11', '15', '11', '14', '7', '25', '12', 
2.68/2.88	               '12', '11', '14', '7', '15', '11', '14', '7', '11', '14', 
2.68/2.88	               '7', '15', '11', '14', '7'])).
2.68/2.88	tff(zf_stmt_143, axiom, (monoid_mult(int))).
2.68/2.88	tff('27', plain, monoid_mult(int),
2.68/2.88	    inference('cnf', [status(esa)], [zf_stmt_143])).
2.68/2.88	tff(zf_stmt_35, axiom,
2.68/2.88	  (![B2:$tType]:
2.68/2.88	     ((monoid_mult(B2) & number(B2)) =>
2.68/2.88	      (![W:int]:
2.68/2.88	         (app_encode_app(nat,B2,
2.68/2.88	                         app_encode_app(B2,app_encode_fun(nat,B2),
2.68/2.88	                                        power_power(B2),
2.68/2.88	                                        app_encode_app(int,B2,
2.68/2.88	                                                       number_number_of(B2),W)),
2.68/2.88	                         app_encode_app(int,nat,number_number_of(nat),
2.68/2.88	                                        app_encode_app(int,int,bit0,
2.68/2.88	                                                       app_encode_app(
2.68/2.88	                                                       int,int,bit1,pls)))) =
2.68/2.88	          app_encode_app(B2,B2,
2.68/2.88	                         app_encode_app(B2,app_encode_fun(B2,B2),
2.68/2.88	                                        times_times(B2),
2.68/2.88	                                        app_encode_app(int,B2,
2.68/2.88	                                                       number_number_of(B2),W)),
2.68/2.88	                         app_encode_app(int,B2,number_number_of(B2),W))))))).
2.68/2.88	tff('28', plain,
2.68/2.88	    ![X0 : $tType, X1 : int]:
2.68/2.88	      (app_encode_app(nat, X0, 
2.68/2.88	         app_encode_app(X0, app_encode_fun(nat, X0), power_power(X0), 
2.68/2.88	           app_encode_app(int, X0, number_number_of(X0), X1)), 
2.68/2.88	         app_encode_app(int, nat, number_number_of(nat), 
2.68/2.88	           app_encode_app(int, int, bit0, 
2.68/2.88	             app_encode_app(int, int, bit1, pls))))
2.68/2.88	        = app_encode_app(X0, X0, 
2.68/2.88	            app_encode_app(X0, app_encode_fun(X0, X0), times_times(X0), 
2.68/2.88	              app_encode_app(int, X0, number_number_of(X0), X1)), 
2.68/2.88	            app_encode_app(int, X0, number_number_of(X0), X1))
2.68/2.88	       | ~ number(X0)
2.68/2.88	       | ~ monoid_mult(X0)),
2.68/2.88	    inference('cnf', [status(esa)], [zf_stmt_35])).
2.68/2.88	tff('29', plain,
2.68/2.88	    ![X0 : int]:
2.68/2.88	      (~ $true
2.68/2.88	       | ~ number(int)
2.68/2.88	       | app_encode_app(nat, int, 
2.68/2.88	           app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
2.68/2.88	             app_encode_app(int, int, number_number_of(int), X0)), 
2.68/2.88	           app_encode_app(int, nat, number_number_of(nat), 
2.68/2.88	             app_encode_app(int, int, bit0, 
2.68/2.88	               app_encode_app(int, int, bit1, pls))))
2.68/2.88	          = app_encode_app(int, int, 
2.68/2.88	              app_encode_app(int, app_encode_fun(int, int), 
2.68/2.88	                times_times(int), 
2.68/2.88	                app_encode_app(int, int, number_number_of(int), X0)), 
2.68/2.88	              app_encode_app(int, int, number_number_of(int), X0))),
2.68/2.88	    inference('sup-', [status(thm)], ['27', '28'])).
2.68/2.88	tff('30', plain,
2.68/2.88	    ![X0 : int]:
2.68/2.88	      (app_encode_app(nat, int, 
2.68/2.88	         app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
2.68/2.88	           app_encode_app(int, int, number_number_of(int), X0)), 
2.68/2.88	         app_encode_app(int, nat, number_number_of(nat), 
2.68/2.88	           app_encode_app(int, int, bit0, 
2.68/2.88	             app_encode_app(int, int, bit1, pls))))
2.68/2.88	        = app_encode_app(int, int, 
2.68/2.88	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.68/2.88	              app_encode_app(int, int, number_number_of(int), X0)), 
2.68/2.88	            app_encode_app(int, int, number_number_of(int), X0))
2.68/2.88	       | ~ number(int)),
2.68/2.88	    inference('simplify', [status(thm)], ['29'])).
2.68/2.88	tff(zf_stmt_147, axiom, (number(int))).
2.68/2.88	tff('31', plain, number(int), inference('cnf', [status(esa)], [zf_stmt_147])).
2.68/2.88	tff('32', plain,
2.68/2.88	    ![X0 : int]:
2.68/2.88	      (app_encode_app(nat, int, 
2.68/2.88	         app_encode_app(int, app_encode_fun(nat, int), power_power(int), X0), 
2.68/2.88	         app_encode_app(int, nat, number_number_of(nat), 
2.68/2.88	           app_encode_app(int, int, 
2.68/2.88	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.68/2.88	               app_encode_app(int, int, bit1, pls)), 
2.68/2.88	             app_encode_app(int, int, bit1, pls))))
2.68/2.88	        = app_encode_app(int, int, 
2.68/2.88	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.68/2.88	              X0), X0)
2.68/2.88	       | ~ $true),
2.68/2.88	    inference('demod', [status(thm)],
2.68/2.88	              ['30', '15', '11', '14', '7', '15', '15', '31'])).
2.68/2.88	tff('33', plain,
2.68/2.88	    ![X0 : int]:
2.68/2.88	      app_encode_app(nat, int, 
2.68/2.88	        app_encode_app(int, app_encode_fun(nat, int), power_power(int), X0), 
2.68/2.88	        app_encode_app(int, nat, number_number_of(nat), 
2.68/2.88	          app_encode_app(int, int, 
2.68/2.88	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.68/2.88	              app_encode_app(int, int, bit1, pls)), 
2.68/2.88	            app_encode_app(int, int, bit1, pls))))
2.68/2.88	       = app_encode_app(int, int, 
2.68/2.88	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.68/2.88	             X0), X0),
2.68/2.88	    inference('simplify', [status(thm)], ['32'])).
2.68/2.88	tff(zf_stmt_105, axiom,
2.68/2.88	  (![A:$tType]:
2.68/2.88	     (comm_semiring_1(A) =>
2.68/2.88	      (![Ry:A,Rx:A,Lx:A]:
2.68/2.88	         (app_encode_app(A,A,
2.68/2.88	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
2.68/2.88	                                        Lx),
2.68/2.88	                         app_encode_app(A,A,
2.68/2.88	                                        app_encode_app(A,app_encode_fun(A,A),
2.68/2.88	                                                       times_times(A),Rx),
2.68/2.88	                                        Ry)) =
2.68/2.88	          app_encode_app(A,A,
2.68/2.88	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
2.68/2.88	                                        Rx),
2.68/2.88	                         app_encode_app(A,A,
2.68/2.88	                                        app_encode_app(A,app_encode_fun(A,A),
2.68/2.88	                                                       times_times(A),Lx),
2.68/2.88	                                        Ry))))))).
2.68/2.88	tff('34', plain,
2.68/2.88	    ![X158 : $tType, X159 : X158, X160 : X158, X161 : X158]:
2.68/2.88	      (app_encode_app(X158, X158, 
2.68/2.88	         app_encode_app(X158, app_encode_fun(X158, X158), times_times(X158), 
2.68/2.88	           X160), 
2.68/2.88	         app_encode_app(X158, X158, 
2.68/2.88	           app_encode_app(X158, app_encode_fun(X158, X158), 
2.68/2.88	             times_times(X158), X159), X161))
2.68/2.88	        = app_encode_app(X158, X158, 
2.68/2.88	            app_encode_app(X158, app_encode_fun(X158, X158), 
2.68/2.88	              times_times(X158), X159), 
2.68/2.88	            app_encode_app(X158, X158, 
2.68/2.88	              app_encode_app(X158, app_encode_fun(X158, X158), 
2.68/2.88	                times_times(X158), X160), X161))
2.68/2.88	       | ~ comm_semiring_1(X158)),
2.68/2.88	    inference('cnf', [status(esa)], [zf_stmt_105])).
2.68/2.88	tff('35', plain,
2.68/2.88	    ![X0 : int, X1 : int, X2 : int]:
2.68/2.88	      (~ $true
2.68/2.88	       | app_encode_app(int, int, 
2.68/2.88	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.68/2.88	             X2), 
2.68/2.88	           app_encode_app(int, int, 
2.68/2.88	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.68/2.88	               X1), X0))
2.68/2.88	          = app_encode_app(int, int, 
2.68/2.88	              app_encode_app(int, app_encode_fun(int, int), 
2.68/2.88	                times_times(int), X1), 
2.68/2.88	              app_encode_app(int, int, 
2.68/2.88	                app_encode_app(int, app_encode_fun(int, int), 
2.68/2.88	                  times_times(int), X2), X0))),
2.68/2.88	    inference('sup-', [status(thm)], ['16', '34'])).
2.68/2.88	tff('36', plain,
2.68/2.88	    ![X0 : int, X1 : int, X2 : int]:
2.68/2.88	      app_encode_app(int, int, 
2.68/2.88	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X2), 
2.68/2.88	        app_encode_app(int, int, 
2.68/2.88	          app_encode_app(int, app_encode_fun(int, int), times_times(int), X1), 
2.68/2.88	          X0))
2.68/2.88	       = app_encode_app(int, int, 
2.68/2.88	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.68/2.88	             X1), 
2.68/2.88	           app_encode_app(int, int, 
2.68/2.88	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.68/2.88	               X2), X0)),
2.68/2.88	    inference('simplify', [status(thm)], ['35'])).
2.68/2.88	tff(zf_stmt_139, axiom, (linordered_idom(int))).
2.68/2.88	tff('37', plain, linordered_idom(int),
2.68/2.88	    inference('cnf', [status(esa)], [zf_stmt_139])).
2.68/2.88	tff(zf_stmt_96, axiom,
2.68/2.88	  (![A:$tType]:
2.68/2.88	     (linordered_idom(A) =>
2.68/2.88	      (![A1:A]:
2.68/2.88	         (app_encode_app(A,A,
2.68/2.88	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
2.68/2.88	                                        app_encode_app(A,A,abs_abs(A),A1)),
2.68/2.88	                         app_encode_app(A,A,abs_abs(A),A1)) =
2.68/2.88	          app_encode_app(A,A,
2.68/2.88	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
2.68/2.88	                                        A1),
2.68/2.88	                         A1)))))).
2.68/2.88	tff('38', plain,
2.68/2.88	    ![X133 : $tType, X134 : X133]:
2.68/2.88	      (app_encode_app(X133, X133, 
2.68/2.88	         app_encode_app(X133, app_encode_fun(X133, X133), times_times(X133), 
2.68/2.88	           app_encode_app(X133, X133, abs_abs(X133), X134)), 
2.68/2.88	         app_encode_app(X133, X133, abs_abs(X133), X134))
2.68/2.88	        = app_encode_app(X133, X133, 
2.68/2.88	            app_encode_app(X133, app_encode_fun(X133, X133), 
2.68/2.88	              times_times(X133), X134), X134)
2.68/2.88	       | ~ linordered_idom(X133)),
2.68/2.88	    inference('cnf', [status(esa)], [zf_stmt_96])).
2.68/2.88	tff('39', plain,
2.68/2.88	    ![X0 : int]:
2.68/2.88	      (~ $true
2.68/2.88	       | app_encode_app(int, int, 
2.68/2.88	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.68/2.88	             app_encode_app(int, int, abs_abs(int), X0)), 
2.68/2.88	           app_encode_app(int, int, abs_abs(int), X0))
2.68/2.88	          = app_encode_app(int, int, 
2.68/2.88	              app_encode_app(int, app_encode_fun(int, int), 
2.68/2.88	                times_times(int), X0), X0)),
2.68/2.88	    inference('sup-', [status(thm)], ['37', '38'])).
2.68/2.88	tff('40', plain,
2.68/2.88	    ![X0 : int]:
2.68/2.88	      app_encode_app(int, int, 
2.68/2.88	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.68/2.88	          app_encode_app(int, int, abs_abs(int), X0)), 
2.68/2.88	        app_encode_app(int, int, abs_abs(int), X0))
2.68/2.88	       = app_encode_app(int, int, 
2.68/2.88	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.68/2.88	             X0), X0),
2.68/2.88	    inference('simplify', [status(thm)], ['39'])).
2.68/2.88	tff('41', plain,
2.68/2.88	    app_encode_app(int, int, 
2.68/2.88	      app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.68/2.88	        app_encode_app(int, int, 
2.68/2.88	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.68/2.88	            app_encode_app(int, int, bit1, pls)), 
2.68/2.88	          app_encode_app(int, int, bit1, pls))), 
2.68/2.88	      app_encode_app(int, int, 
2.68/2.88	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.68/2.88	          app_encode_app(int, int, 
2.68/2.88	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.68/2.88	              app_encode_app(int, int, bit1, pls)), 
2.68/2.88	            app_encode_app(int, int, bit1, pls))), 
2.68/2.88	        app_encode_app(int, int, 
2.68/2.88	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.68/2.88	            app_encode_app(int, int, 
2.68/2.88	              app_encode_app(int, app_encode_fun(int, int), 
2.68/2.88	                times_times(int), v), v)), 
2.68/2.88	          app_encode_app(int, int, 
2.68/2.88	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.68/2.88	              w), w))))
2.68/2.88	     != app_encode_app(int, int, 
2.68/2.88	          app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.68/2.88	            app_encode_app(int, int, 
2.68/2.88	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.68/2.88	                app_encode_app(int, int, bit1, pls)), 
2.68/2.88	              app_encode_app(int, int, bit1, pls))), 
2.68/2.88	          app_encode_app(int, int, 
2.68/2.88	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.68/2.88	              app_encode_app(int, int, 
2.68/2.88	                app_encode_app(int, app_encode_fun(int, int), 
2.68/2.88	                  plus_plus(int), app_encode_app(int, int, bit1, pls)), 
2.68/2.88	                app_encode_app(int, int, bit1, pls))), 
2.68/2.88	            app_encode_app(int, int, 
2.68/2.88	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.68/2.88	                app_encode_app(int, int, 
2.68/2.88	                  app_encode_app(int, app_encode_fun(int, int), 
2.68/2.88	                    times_times(int), v), v)), 
2.68/2.88	              app_encode_app(int, int, 
2.68/2.88	                app_encode_app(int, app_encode_fun(int, int), 
2.68/2.88	                  times_times(int), w), w)))),
2.68/2.88	    inference('demod', [status(thm)],
2.68/2.88	              ['26', '33', '33', '33', '25', '36', '36', '40', '33', '25', 
2.68/2.88	               '36', '36', '40', '12', '12'])).
2.68/2.88	tff('42', plain, $false, inference('simplify', [status(thm)], ['41'])).
2.68/2.88	
2.68/2.88	% SZS output end Refutation
2.68/2.88	EOF
