0.00/0.00	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : app
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : kbo
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n139.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 07:55:08 CST 2018
60.68/60.86	% done 4890 iterations in 60.662s
60.68/60.86	% SZS status Theorem for 'stdin'
60.68/60.86	% SZS output start Refutation
60.68/60.87	tff(zf_stmt_160, conjecture,
60.68/60.87	  (app_encode_app(nat,int,
60.68/60.87	                  app_encode_app(int,app_encode_fun(nat,int),
60.68/60.87	                                 power_power(int),
60.68/60.87	                                 app_encode_app(int,int,
60.68/60.87	                                                app_encode_app(int,
60.68/60.87	                                                               app_encode_fun(
60.68/60.87	                                                               int,int),
60.68/60.87	                                                               minus_minus(
60.68/60.87	                                                               int),
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,int,
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,
60.68/60.87	                                                               app_encode_fun(
60.68/60.87	                                                               int,int),
60.68/60.87	                                                               plus_plus(int),
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,int,
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,
60.68/60.87	                                                               app_encode_fun(
60.68/60.87	                                                               int,int),
60.68/60.87	                                                               times_times(
60.68/60.87	                                                               int),
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,int,
60.68/60.87	                                                               number_number_of(
60.68/60.87	                                                               int),
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,int,bit0,
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,int,bit0,
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,int,bit1,
60.68/60.87	                                                               pls))))),m)),
60.68/60.87	                                                               one_one(int))),
60.68/60.87	                                                one_one(int))),
60.68/60.87	                  app_encode_app(int,nat,number_number_of(nat),
60.68/60.87	                                 app_encode_app(int,int,bit0,
60.68/60.87	                                                app_encode_app(int,int,bit1,
60.68/60.87	                                                               pls)))) =
60.68/60.87	   app_encode_app(int,int,
60.68/60.87	                  app_encode_app(int,app_encode_fun(int,int),
60.68/60.87	                                 minus_minus(int),
60.68/60.87	                                 app_encode_app(int,int,
60.68/60.87	                                                app_encode_app(int,
60.68/60.87	                                                               app_encode_fun(
60.68/60.87	                                                               int,int),
60.68/60.87	                                                               times_times(
60.68/60.87	                                                               int),
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,int,
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,
60.68/60.87	                                                               app_encode_fun(
60.68/60.87	                                                               int,int),
60.68/60.87	                                                               plus_plus(int),
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,int,
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,
60.68/60.87	                                                               app_encode_fun(
60.68/60.87	                                                               int,int),
60.68/60.87	                                                               times_times(
60.68/60.87	                                                               int),
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,int,
60.68/60.87	                                                               number_number_of(
60.68/60.87	                                                               int),
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,int,bit0,
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,int,bit0,
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,int,bit1,
60.68/60.87	                                                               pls))))),m)),
60.68/60.87	                                                               one_one(int))),
60.68/60.87	                                                app_encode_app(int,int,
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,
60.68/60.87	                                                               app_encode_fun(
60.68/60.87	                                                               int,int),
60.68/60.87	                                                               minus_minus(
60.68/60.87	                                                               int),
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,int,
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,
60.68/60.87	                                                               app_encode_fun(
60.68/60.87	                                                               int,int),
60.68/60.87	                                                               plus_plus(int),
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,int,
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,
60.68/60.87	                                                               app_encode_fun(
60.68/60.87	                                                               int,int),
60.68/60.87	                                                               times_times(
60.68/60.87	                                                               int),
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,int,
60.68/60.87	                                                               number_number_of(
60.68/60.87	                                                               int),
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,int,bit0,
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,int,bit0,
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,int,bit1,
60.68/60.87	                                                               pls))))),m)),
60.68/60.87	                                                               one_one(int))),
60.68/60.87	                                                               one_one(int)))),
60.68/60.87	                  app_encode_app(int,int,
60.68/60.87	                                 app_encode_app(int,app_encode_fun(int,int),
60.68/60.87	                                                times_times(int),one_one(int)),
60.68/60.87	                                 app_encode_app(int,int,
60.68/60.87	                                                app_encode_app(int,
60.68/60.87	                                                               app_encode_fun(
60.68/60.87	                                                               int,int),
60.68/60.87	                                                               minus_minus(
60.68/60.87	                                                               int),
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,int,
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,
60.68/60.87	                                                               app_encode_fun(
60.68/60.87	                                                               int,int),
60.68/60.87	                                                               plus_plus(int),
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,int,
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,
60.68/60.87	                                                               app_encode_fun(
60.68/60.87	                                                               int,int),
60.68/60.87	                                                               times_times(
60.68/60.87	                                                               int),
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,int,
60.68/60.87	                                                               number_number_of(
60.68/60.87	                                                               int),
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,int,bit0,
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,int,bit0,
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,int,bit1,
60.68/60.87	                                                               pls))))),m)),
60.68/60.87	                                                               one_one(int))),
60.68/60.87	                                                one_one(int)))))).
60.68/60.87	tff(zf_stmt_0, negated_conjecture,
60.68/60.87	  (app_encode_app(nat,int,
60.68/60.87	                  app_encode_app(int,app_encode_fun(nat,int),
60.68/60.87	                                 power_power(int),
60.68/60.87	                                 app_encode_app(int,int,
60.68/60.87	                                                app_encode_app(int,
60.68/60.87	                                                               app_encode_fun(
60.68/60.87	                                                               int,int),
60.68/60.87	                                                               minus_minus(
60.68/60.87	                                                               int),
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,int,
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,
60.68/60.87	                                                               app_encode_fun(
60.68/60.87	                                                               int,int),
60.68/60.87	                                                               plus_plus(int),
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,int,
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,
60.68/60.87	                                                               app_encode_fun(
60.68/60.87	                                                               int,int),
60.68/60.87	                                                               times_times(
60.68/60.87	                                                               int),
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,int,
60.68/60.87	                                                               number_number_of(
60.68/60.87	                                                               int),
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,int,bit0,
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,int,bit0,
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,int,bit1,
60.68/60.87	                                                               pls))))),m)),
60.68/60.87	                                                               one_one(int))),
60.68/60.87	                                                one_one(int))),
60.68/60.87	                  app_encode_app(int,nat,number_number_of(nat),
60.68/60.87	                                 app_encode_app(int,int,bit0,
60.68/60.87	                                                app_encode_app(int,int,bit1,
60.68/60.87	                                                               pls)))) !=
60.68/60.87	   app_encode_app(int,int,
60.68/60.87	                  app_encode_app(int,app_encode_fun(int,int),
60.68/60.87	                                 minus_minus(int),
60.68/60.87	                                 app_encode_app(int,int,
60.68/60.87	                                                app_encode_app(int,
60.68/60.87	                                                               app_encode_fun(
60.68/60.87	                                                               int,int),
60.68/60.87	                                                               times_times(
60.68/60.87	                                                               int),
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,int,
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,
60.68/60.87	                                                               app_encode_fun(
60.68/60.87	                                                               int,int),
60.68/60.87	                                                               plus_plus(int),
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,int,
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,
60.68/60.87	                                                               app_encode_fun(
60.68/60.87	                                                               int,int),
60.68/60.87	                                                               times_times(
60.68/60.87	                                                               int),
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,int,
60.68/60.87	                                                               number_number_of(
60.68/60.87	                                                               int),
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,int,bit0,
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,int,bit0,
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,int,bit1,
60.68/60.87	                                                               pls))))),m)),
60.68/60.87	                                                               one_one(int))),
60.68/60.87	                                                app_encode_app(int,int,
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,
60.68/60.87	                                                               app_encode_fun(
60.68/60.87	                                                               int,int),
60.68/60.87	                                                               minus_minus(
60.68/60.87	                                                               int),
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,int,
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,
60.68/60.87	                                                               app_encode_fun(
60.68/60.87	                                                               int,int),
60.68/60.87	                                                               plus_plus(int),
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,int,
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,
60.68/60.87	                                                               app_encode_fun(
60.68/60.87	                                                               int,int),
60.68/60.87	                                                               times_times(
60.68/60.87	                                                               int),
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,int,
60.68/60.87	                                                               number_number_of(
60.68/60.87	                                                               int),
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,int,bit0,
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,int,bit0,
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,int,bit1,
60.68/60.87	                                                               pls))))),m)),
60.68/60.87	                                                               one_one(int))),
60.68/60.87	                                                               one_one(int)))),
60.68/60.87	                  app_encode_app(int,int,
60.68/60.87	                                 app_encode_app(int,app_encode_fun(int,int),
60.68/60.87	                                                times_times(int),one_one(int)),
60.68/60.87	                                 app_encode_app(int,int,
60.68/60.87	                                                app_encode_app(int,
60.68/60.87	                                                               app_encode_fun(
60.68/60.87	                                                               int,int),
60.68/60.87	                                                               minus_minus(
60.68/60.87	                                                               int),
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,int,
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,
60.68/60.87	                                                               app_encode_fun(
60.68/60.87	                                                               int,int),
60.68/60.87	                                                               plus_plus(int),
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,int,
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,
60.68/60.87	                                                               app_encode_fun(
60.68/60.87	                                                               int,int),
60.68/60.87	                                                               times_times(
60.68/60.87	                                                               int),
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,int,
60.68/60.87	                                                               number_number_of(
60.68/60.87	                                                               int),
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,int,bit0,
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,int,bit0,
60.68/60.87	                                                               app_encode_app(
60.68/60.87	                                                               int,int,bit1,
60.68/60.87	                                                               pls))))),m)),
60.68/60.87	                                                               one_one(int))),
60.68/60.87	                                                one_one(int)))))).
60.68/60.87	tff('0', plain,
60.68/60.87	    app_encode_app(nat, int, 
60.68/60.87	      app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
60.68/60.87	        app_encode_app(int, int, 
60.68/60.87	          app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
60.68/60.87	            app_encode_app(int, int, 
60.68/60.87	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
60.68/60.87	                app_encode_app(int, int, 
60.68/60.87	                  app_encode_app(int, app_encode_fun(int, int), 
60.68/60.87	                    times_times(int), 
60.68/60.87	                    app_encode_app(int, int, number_number_of(int), 
60.68/60.87	                      app_encode_app(int, int, bit0, 
60.68/60.87	                        app_encode_app(int, int, bit0, 
60.68/60.87	                          app_encode_app(int, int, bit1, pls))))), m)), 
60.68/60.87	              one_one(int))), one_one(int))), 
60.68/60.87	      app_encode_app(int, nat, number_number_of(nat), 
60.68/60.87	        app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls))))
60.68/60.87	     != app_encode_app(int, int, 
60.68/60.87	          app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
60.68/60.87	            app_encode_app(int, int, 
60.68/60.87	              app_encode_app(int, app_encode_fun(int, int), 
60.68/60.87	                times_times(int), 
60.68/60.87	                app_encode_app(int, int, 
60.68/60.87	                  app_encode_app(int, app_encode_fun(int, int), 
60.68/60.87	                    plus_plus(int), 
60.68/60.87	                    app_encode_app(int, int, 
60.68/60.87	                      app_encode_app(int, app_encode_fun(int, int), 
60.68/60.87	                        times_times(int), 
60.68/60.87	                        app_encode_app(int, int, number_number_of(int), 
60.68/60.87	                          app_encode_app(int, int, bit0, 
60.68/60.87	                            app_encode_app(int, int, bit0, 
60.68/60.87	                              app_encode_app(int, int, bit1, pls))))), m)), 
60.68/60.87	                  one_one(int))), 
60.68/60.87	              app_encode_app(int, int, 
60.68/60.87	                app_encode_app(int, app_encode_fun(int, int), 
60.68/60.87	                  minus_minus(int), 
60.68/60.87	                  app_encode_app(int, int, 
60.68/60.87	                    app_encode_app(int, app_encode_fun(int, int), 
60.68/60.87	                      plus_plus(int), 
60.68/60.87	                      app_encode_app(int, int, 
60.68/60.87	                        app_encode_app(int, app_encode_fun(int, int), 
60.68/60.87	                          times_times(int), 
60.68/60.87	                          app_encode_app(int, int, number_number_of(int), 
60.68/60.87	                            app_encode_app(int, int, bit0, 
60.68/60.87	                              app_encode_app(int, int, bit0, 
60.68/60.87	                                app_encode_app(int, int, bit1, pls))))), m)), 
60.68/60.87	                    one_one(int))), one_one(int)))), 
60.68/60.87	          app_encode_app(int, int, 
60.68/60.87	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
60.68/60.87	              one_one(int)), 
60.68/60.87	            app_encode_app(int, int, 
60.68/60.87	              app_encode_app(int, app_encode_fun(int, int), 
60.68/60.87	                minus_minus(int), 
60.68/60.87	                app_encode_app(int, int, 
60.68/60.87	                  app_encode_app(int, app_encode_fun(int, int), 
60.68/60.87	                    plus_plus(int), 
60.68/60.87	                    app_encode_app(int, int, 
60.68/60.87	                      app_encode_app(int, app_encode_fun(int, int), 
60.68/60.87	                        times_times(int), 
60.68/60.87	                        app_encode_app(int, int, number_number_of(int), 
60.68/60.87	                          app_encode_app(int, int, bit0, 
60.68/60.87	                            app_encode_app(int, int, bit0, 
60.68/60.87	                              app_encode_app(int, int, bit1, pls))))), m)), 
60.68/60.87	                  one_one(int))), one_one(int)))),
60.68/60.87	    inference('cnf', [status(esa)], [zf_stmt_0])).
60.68/60.87	tff(zf_stmt_106, axiom,
60.68/60.87	  (one_one(int) =
60.68/60.87	   app_encode_app(int,int,number_number_of(int),
60.68/60.87	                  app_encode_app(int,int,bit1,pls)))).
60.68/60.87	tff('1', plain,
60.68/60.87	    one_one(int)
60.68/60.87	     = app_encode_app(int, int, number_number_of(int), 
60.68/60.87	         app_encode_app(int, int, bit1, pls)),
60.68/60.87	    inference('cnf', [status(esa)], [zf_stmt_106])).
60.68/60.87	tff(zf_stmt_82, axiom,
60.68/60.87	  (![K1:int]: (app_encode_app(int,int,number_number_of(int),K1) = K1))).
60.68/60.87	tff('2', plain,
60.68/60.87	    ![X97 : int]: app_encode_app(int, int, number_number_of(int), X97) = X97,
60.68/60.87	    inference('cnf', [status(esa)], [zf_stmt_82])).
60.68/60.87	tff('3', plain, one_one(int) = app_encode_app(int, int, bit1, pls),
60.68/60.87	    inference('demod', [status(thm)], ['1', '2'])).
60.68/60.87	tff(zf_stmt_58, axiom,
60.68/60.87	  (![L1:int,K1:int]:
60.68/60.87	     (app_encode_app(int,int,
60.68/60.87	                     app_encode_app(int,app_encode_fun(int,int),
60.68/60.87	                                    times_times(int),
60.68/60.87	                                    app_encode_app(int,int,bit0,K1)),
60.68/60.87	                     L1) =
60.68/60.87	      app_encode_app(int,int,bit0,
60.68/60.87	                     app_encode_app(int,int,
60.68/60.87	                                    app_encode_app(int,
60.68/60.87	                                                   app_encode_fun(int,int),
60.68/60.87	                                                   times_times(int),K1),
60.68/60.87	                                    L1))))).
60.68/60.87	tff('4', plain,
60.68/60.87	    ![X43 : int, X44 : int]:
60.68/60.87	      app_encode_app(int, int, 
60.68/60.87	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
60.68/60.87	          app_encode_app(int, int, bit0, X43)), X44)
60.68/60.87	       = app_encode_app(int, int, bit0, 
60.68/60.87	           app_encode_app(int, int, 
60.68/60.87	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
60.68/60.87	               X43), X44)),
60.68/60.87	    inference('cnf', [status(esa)], [zf_stmt_58])).
60.68/60.87	tff(zf_stmt_57, axiom,
60.68/60.87	  (![W:int]:
60.68/60.87	     (app_encode_app(int,int,
60.68/60.87	                     app_encode_app(int,app_encode_fun(int,int),
60.68/60.87	                                    times_times(int),pls),
60.68/60.87	                     W) =
60.68/60.87	      pls))).
60.68/60.87	tff('5', plain,
60.68/60.87	    ![X42 : int]:
60.68/60.87	      app_encode_app(int, int, 
60.68/60.87	        app_encode_app(int, app_encode_fun(int, int), times_times(int), pls), 
60.68/60.87	        X42)
60.68/60.87	       = pls,
60.68/60.87	    inference('cnf', [status(esa)], [zf_stmt_57])).
60.68/60.87	tff(zf_stmt_40, axiom,
60.68/60.87	  (![L1:int,K1:int]:
60.68/60.87	     (app_encode_app(int,int,
60.68/60.87	                     app_encode_app(int,app_encode_fun(int,int),
60.68/60.87	                                    times_times(int),
60.68/60.87	                                    app_encode_app(int,int,bit1,K1)),
60.68/60.87	                     L1) =
60.68/60.87	      app_encode_app(int,int,
60.68/60.87	                     app_encode_app(int,app_encode_fun(int,int),
60.68/60.87	                                    plus_plus(int),
60.68/60.87	                                    app_encode_app(int,int,bit0,
60.68/60.87	                                                   app_encode_app(int,int,
60.68/60.87	                                                                  app_encode_app(
60.68/60.87	                                                                  int,
60.68/60.87	                                                                  app_encode_fun(
60.68/60.87	                                                                  int,int),
60.68/60.87	                                                                  times_times(
60.68/60.87	                                                                  int),K1),L1))),
60.68/60.87	                     L1)))).
60.68/60.87	tff('6', plain,
60.68/60.87	    ![X8 : int, X9 : int]:
60.68/60.87	      app_encode_app(int, int, 
60.68/60.87	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
60.68/60.87	          app_encode_app(int, int, bit1, X8)), X9)
60.68/60.87	       = app_encode_app(int, int, 
60.68/60.87	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
60.68/60.87	             app_encode_app(int, int, bit0, 
60.68/60.87	               app_encode_app(int, int, 
60.68/60.87	                 app_encode_app(int, app_encode_fun(int, int), 
60.68/60.87	                   times_times(int), X8), X9))), X9),
60.68/60.87	    inference('cnf', [status(esa)], [zf_stmt_40])).
60.68/60.87	tff('7', plain,
60.68/60.87	    ![X0 : int]:
60.68/60.87	      app_encode_app(int, int, 
60.68/60.87	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
60.68/60.87	          app_encode_app(int, int, bit1, pls)), X0)
60.68/60.87	       = app_encode_app(int, int, 
60.68/60.87	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
60.68/60.87	             app_encode_app(int, int, bit0, pls)), X0),
60.68/60.87	    inference('sup+', [status(thm)], ['5', '6'])).
60.68/60.87	tff(zf_stmt_56, axiom, (app_encode_app(int,int,bit0,pls) = pls)).
60.68/60.87	tff('8', plain, app_encode_app(int, int, bit0, pls) = pls,
60.68/60.87	    inference('cnf', [status(esa)], [zf_stmt_56])).
60.68/60.87	tff('9', plain,
60.68/60.87	    ![X0 : int]:
60.68/60.87	      app_encode_app(int, int, 
60.68/60.87	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
60.68/60.87	          one_one(int)), X0)
60.68/60.87	       = app_encode_app(int, int, 
60.68/60.87	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
60.68/60.87	           X0),
60.68/60.87	    inference('demod', [status(thm)], ['7', '3', '8'])).
60.68/60.87	tff(zf_stmt_85, axiom,
60.68/60.87	  (![K1:int]:
60.68/60.87	     (app_encode_app(int,int,
60.68/60.87	                     app_encode_app(int,app_encode_fun(int,int),
60.68/60.87	                                    plus_plus(int),pls),
60.68/60.87	                     K1) =
60.68/60.87	      K1))).
60.68/60.87	tff('10', plain,
60.68/60.87	    ![X102 : int]:
60.68/60.87	      app_encode_app(int, int, 
60.68/60.87	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
60.68/60.87	        X102)
60.68/60.87	       = X102,
60.68/60.87	    inference('cnf', [status(esa)], [zf_stmt_85])).
60.68/60.87	tff('11', plain,
60.68/60.87	    ![X0 : int]:
60.68/60.87	      app_encode_app(int, int, 
60.68/60.87	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
60.68/60.87	          one_one(int)), X0)
60.68/60.87	       = X0,
60.68/60.87	    inference('demod', [status(thm)], ['9', '10'])).
60.68/60.87	tff(zf_stmt_71, axiom,
60.68/60.87	  (![L1:int,K1:int]:
60.68/60.87	     (app_encode_app(int,int,
60.68/60.87	                     app_encode_app(int,app_encode_fun(int,int),
60.68/60.87	                                    plus_plus(int),
60.68/60.87	                                    app_encode_app(int,int,bit0,K1)),
60.68/60.87	                     app_encode_app(int,int,bit1,L1)) =
60.68/60.87	      app_encode_app(int,int,bit1,
60.68/60.87	                     app_encode_app(int,int,
60.68/60.87	                                    app_encode_app(int,
60.68/60.87	                                                   app_encode_fun(int,int),
60.68/60.87	                                                   plus_plus(int),K1),
60.68/60.87	                                    L1))))).
60.68/60.87	tff('12', plain,
60.68/60.87	    ![X81 : int, X82 : int]:
60.68/60.87	      app_encode_app(int, int, 
60.68/60.87	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
60.68/60.87	          app_encode_app(int, int, bit0, X81)), 
60.68/60.87	        app_encode_app(int, int, bit1, X82))
60.68/60.87	       = app_encode_app(int, int, bit1, 
60.68/60.87	           app_encode_app(int, int, 
60.68/60.87	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
60.68/60.87	               X81), X82)),
60.68/60.87	    inference('cnf', [status(esa)], [zf_stmt_71])).
60.68/60.87	tff('13', plain,
60.68/60.87	    ![X0 : int]:
60.68/60.87	      app_encode_app(int, int, 
60.68/60.87	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
60.68/60.87	          app_encode_app(int, int, bit0, X0)), one_one(int))
60.68/60.87	       = app_encode_app(int, int, bit1, 
60.68/60.87	           app_encode_app(int, int, 
60.68/60.87	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
60.68/60.87	               X0), pls)),
60.68/60.87	    inference('sup+', [status(thm)], ['3', '12'])).
60.68/60.87	tff(zf_stmt_84, axiom,
60.68/60.87	  (![K1:int]:
60.68/60.87	     (app_encode_app(int,int,
60.68/60.87	                     app_encode_app(int,app_encode_fun(int,int),
60.68/60.87	                                    plus_plus(int),K1),
60.68/60.87	                     pls) =
60.68/60.87	      K1))).
60.68/60.87	tff('14', plain,
60.68/60.87	    ![X101 : int]:
60.68/60.87	      app_encode_app(int, int, 
60.68/60.87	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X101), 
60.68/60.87	        pls)
60.68/60.87	       = X101,
60.68/60.87	    inference('cnf', [status(esa)], [zf_stmt_84])).
60.68/60.87	tff('15', plain,
60.68/60.87	    ![X0 : int]:
60.68/60.87	      app_encode_app(int, int, 
60.68/60.87	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
60.68/60.87	          app_encode_app(int, int, bit0, X0)), one_one(int))
60.68/60.87	       = app_encode_app(int, int, bit1, X0),
60.68/60.87	    inference('demod', [status(thm)], ['13', '14'])).
60.68/60.87	tff(zf_stmt_72, axiom,
60.68/60.87	  (![L1:int,K1:int]:
60.68/60.87	     (app_encode_app(int,int,
60.68/60.87	                     app_encode_app(int,app_encode_fun(int,int),
60.68/60.87	                                    minus_minus(int),
60.68/60.87	                                    app_encode_app(int,int,bit1,K1)),
60.68/60.87	                     app_encode_app(int,int,bit1,L1)) =
60.68/60.87	      app_encode_app(int,int,bit0,
60.68/60.87	                     app_encode_app(int,int,
60.68/60.87	                                    app_encode_app(int,
60.68/60.87	                                                   app_encode_fun(int,int),
60.68/60.87	                                                   minus_minus(int),K1),
60.68/60.87	                                    L1))))).
60.68/60.87	tff('16', plain,
60.68/60.87	    ![X83 : int, X84 : int]:
60.68/60.87	      app_encode_app(int, int, 
60.68/60.87	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
60.68/60.87	          app_encode_app(int, int, bit1, X83)), 
60.68/60.87	        app_encode_app(int, int, bit1, X84))
60.68/60.87	       = app_encode_app(int, int, bit0, 
60.68/60.87	           app_encode_app(int, int, 
60.68/60.87	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
60.68/60.87	               X83), X84)),
60.68/60.87	    inference('cnf', [status(esa)], [zf_stmt_72])).
60.68/60.87	tff('17', plain,
60.68/60.87	    ![X0 : int]:
60.68/60.87	      app_encode_app(int, int, 
60.68/60.87	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
60.68/60.87	          app_encode_app(int, int, bit1, X0)), one_one(int))
60.68/60.87	       = app_encode_app(int, int, bit0, 
60.68/60.87	           app_encode_app(int, int, 
60.68/60.87	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
60.68/60.87	               X0), pls)),
60.68/60.87	    inference('sup+', [status(thm)], ['3', '16'])).
60.68/60.87	tff(zf_stmt_88, axiom,
60.68/60.87	  (![K1:int]:
60.68/60.87	     (app_encode_app(int,int,
60.68/60.87	                     app_encode_app(int,app_encode_fun(int,int),
60.68/60.87	                                    minus_minus(int),K1),
60.68/60.87	                     pls) =
60.68/60.87	      K1))).
60.68/60.87	tff('18', plain,
60.68/60.87	    ![X106 : int]:
60.68/60.87	      app_encode_app(int, int, 
60.68/60.87	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), X106), 
60.68/60.87	        pls)
60.68/60.87	       = X106,
60.68/60.87	    inference('cnf', [status(esa)], [zf_stmt_88])).
60.68/60.87	tff('19', plain,
60.68/60.87	    ![X0 : int]:
60.68/60.87	      app_encode_app(int, int, 
60.68/60.87	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
60.68/60.87	          app_encode_app(int, int, bit1, X0)), one_one(int))
60.68/60.87	       = app_encode_app(int, int, bit0, X0),
60.68/60.87	    inference('demod', [status(thm)], ['17', '18'])).
60.68/60.87	tff(zf_stmt_35, axiom,
60.68/60.87	  (![B1:$tType]:
60.68/60.87	     ((monoid_mult(B1) & number(B1)) =>
60.68/60.87	      (![W:int]:
60.68/60.87	         (app_encode_app(nat,B1,
60.68/60.87	                         app_encode_app(B1,app_encode_fun(nat,B1),
60.68/60.87	                                        power_power(B1),
60.68/60.87	                                        app_encode_app(int,B1,
60.68/60.87	                                                       number_number_of(B1),W)),
60.68/60.87	                         app_encode_app(int,nat,number_number_of(nat),
60.68/60.87	                                        app_encode_app(int,int,bit0,
60.68/60.87	                                                       app_encode_app(
60.68/60.87	                                                       int,int,bit1,pls)))) =
60.68/60.87	          app_encode_app(B1,B1,
60.68/60.87	                         app_encode_app(B1,app_encode_fun(B1,B1),
60.68/60.87	                                        times_times(B1),
60.68/60.87	                                        app_encode_app(int,B1,
60.68/60.87	                                                       number_number_of(B1),W)),
60.68/60.87	                         app_encode_app(int,B1,number_number_of(B1),W))))))).
60.68/60.87	tff('20', plain,
60.68/60.87	    ![X0 : $tType, X1 : int]:
60.68/60.87	      (app_encode_app(nat, X0, 
60.68/60.87	         app_encode_app(X0, app_encode_fun(nat, X0), power_power(X0), 
60.68/60.87	           app_encode_app(int, X0, number_number_of(X0), X1)), 
60.68/60.87	         app_encode_app(int, nat, number_number_of(nat), 
60.68/60.87	           app_encode_app(int, int, bit0, 
60.68/60.87	             app_encode_app(int, int, bit1, pls))))
60.68/60.87	        = app_encode_app(X0, X0, 
60.68/60.87	            app_encode_app(X0, app_encode_fun(X0, X0), times_times(X0), 
60.68/60.87	              app_encode_app(int, X0, number_number_of(X0), X1)), 
60.68/60.87	            app_encode_app(int, X0, number_number_of(X0), X1))
60.68/60.87	       | ~ number(X0)
60.68/60.87	       | ~ monoid_mult(X0)),
60.68/60.87	    inference('cnf', [status(esa)], [zf_stmt_35])).
60.68/60.87	tff('21', plain,
60.68/60.87	    ![X0 : int]:
60.68/60.87	      (app_encode_app(nat, int, 
60.68/60.87	         app_encode_app(int, app_encode_fun(nat, int), power_power(int), X0), 
60.68/60.87	         app_encode_app(int, nat, number_number_of(nat), 
60.68/60.87	           app_encode_app(int, int, bit0, 
60.68/60.87	             app_encode_app(int, int, bit1, pls))))
60.68/60.87	        = app_encode_app(int, int, 
60.68/60.87	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
60.68/60.87	              app_encode_app(int, int, number_number_of(int), X0)), 
60.68/60.87	            app_encode_app(int, int, number_number_of(int), X0))
60.68/60.87	       | ~ monoid_mult(int)
60.68/60.87	       | ~ number(int)),
60.68/60.87	    inference('sup+', [status(thm)], ['2', '20'])).
60.68/60.87	tff(zf_stmt_135, axiom, (monoid_mult(int))).
60.68/60.87	tff('22', plain, monoid_mult(int),
60.68/60.87	    inference('cnf', [status(esa)], [zf_stmt_135])).
60.68/60.87	tff(zf_stmt_141, axiom, (number(int))).
60.68/60.87	tff('23', plain, number(int), inference('cnf', [status(esa)], [zf_stmt_141])).
60.68/60.87	tff('24', plain,
60.68/60.87	    ![X0 : int]:
60.68/60.87	      (app_encode_app(nat, int, 
60.68/60.87	         app_encode_app(int, app_encode_fun(nat, int), power_power(int), X0), 
60.68/60.87	         app_encode_app(int, nat, number_number_of(nat), 
60.68/60.87	           app_encode_app(int, int, bit0, 
60.68/60.87	             app_encode_app(int, int, bit1, pls))))
60.68/60.87	        = app_encode_app(int, int, 
60.68/60.87	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
60.68/60.87	              X0), X0)
60.68/60.87	       | ~ $true
60.68/60.87	       | ~ $true),
60.68/60.87	    inference('demod', [status(thm)], ['21', '2', '2', '22', '23'])).
60.68/60.87	tff('25', plain,
60.68/60.87	    ![X0 : int]:
60.68/60.87	      app_encode_app(nat, int, 
60.68/60.87	        app_encode_app(int, app_encode_fun(nat, int), power_power(int), X0), 
60.68/60.87	        app_encode_app(int, nat, number_number_of(nat), 
60.68/60.87	          app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls))))
60.68/60.87	       = app_encode_app(int, int, 
60.68/60.87	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
60.68/60.87	             X0), X0),
60.68/60.87	    inference('simplify', [status(thm)], ['24'])).
60.68/60.87	tff('26', plain,
60.68/60.87	    ![X0 : int]:
60.68/60.87	      app_encode_app(nat, int, 
60.68/60.87	        app_encode_app(int, app_encode_fun(nat, int), power_power(int), X0), 
60.68/60.87	        app_encode_app(int, nat, number_number_of(nat), 
60.68/60.87	          app_encode_app(int, int, bit0, one_one(int))))
60.68/60.87	       = app_encode_app(int, int, 
60.68/60.87	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
60.68/60.87	             X0), X0),
60.68/60.87	    inference('demod', [status(thm)], ['25', '3'])).
60.68/60.87	tff('27', plain,
60.68/60.87	    ![X0 : int]:
60.68/60.87	      app_encode_app(nat, int, 
60.68/60.87	        app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
60.68/60.87	          app_encode_app(int, int, bit0, X0)), 
60.68/60.87	        app_encode_app(int, nat, number_number_of(nat), 
60.68/60.87	          app_encode_app(int, int, bit0, one_one(int))))
60.68/60.87	       = app_encode_app(int, int, bit0, 
60.68/60.87	           app_encode_app(int, int, 
60.68/60.87	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
60.68/60.87	               X0), app_encode_app(int, int, bit0, X0))),
60.68/60.87	    inference('sup+', [status(thm)], ['26', '4'])).
60.68/60.87	tff(zf_stmt_86, axiom,
60.68/60.87	  (![K1:int]:
60.68/60.87	     (app_encode_app(int,int,bit0,K1) =
60.68/60.87	      app_encode_app(int,int,
60.68/60.87	                     app_encode_app(int,app_encode_fun(int,int),
60.68/60.87	                                    plus_plus(int),K1),
60.68/60.87	                     K1)))).
60.68/60.87	tff('28', plain,
60.68/60.87	    ![X103 : int]:
60.68/60.87	      app_encode_app(int, int, bit0, X103)
60.68/60.87	       = app_encode_app(int, int, 
60.68/60.87	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
60.68/60.87	             X103), X103),
60.68/60.87	    inference('cnf', [status(esa)], [zf_stmt_86])).
60.68/60.87	tff(zf_stmt_62, axiom,
60.68/60.87	  (![B1:$tType]:
60.68/60.87	     ((number(B1) & semiring(B1)) =>
60.68/60.87	      (![C:B1,B:B1,V:int]:
60.68/60.87	         (app_encode_app(B1,B1,
60.68/60.87	                         app_encode_app(B1,app_encode_fun(B1,B1),
60.68/60.87	                                        times_times(B1),
60.68/60.87	                                        app_encode_app(int,B1,
60.68/60.87	                                                       number_number_of(B1),V)),
60.68/60.87	                         app_encode_app(B1,B1,
60.68/60.87	                                        app_encode_app(B1,
60.68/60.87	                                                       app_encode_fun(B1,B1),
60.68/60.87	                                                       plus_plus(B1),B),
60.68/60.87	                                        C)) =
60.68/60.87	          app_encode_app(B1,B1,
60.68/60.87	                         app_encode_app(B1,app_encode_fun(B1,B1),
60.68/60.87	                                        plus_plus(B1),
60.68/60.87	                                        app_encode_app(B1,B1,
60.68/60.87	                                                       app_encode_app(
60.68/60.87	                                                       B1,
60.68/60.87	                                                       app_encode_fun(B1,B1),
60.68/60.87	                                                       times_times(B1),
60.68/60.87	                                                       app_encode_app(
60.68/60.87	                                                       int,B1,
60.68/60.87	                                                       number_number_of(B1),V)),
60.68/60.87	                                                       B)),
60.68/60.87	                         app_encode_app(B1,B1,
60.68/60.87	                                        app_encode_app(B1,
60.68/60.87	                                                       app_encode_fun(B1,B1),
60.68/60.87	                                                       times_times(B1),
60.68/60.87	                                                       app_encode_app(
60.68/60.87	                                                       int,B1,
60.68/60.87	                                                       number_number_of(B1),V)),
60.68/60.87	                                        C))))))).
60.68/60.87	tff('29', plain,
60.68/60.87	    ![X53 : $tType, X54 : int, X55 : X53, X56 : X53]:
60.68/60.87	      (app_encode_app(X53, X53, 
60.68/60.87	         app_encode_app(X53, app_encode_fun(X53, X53), times_times(X53), 
60.68/60.87	           app_encode_app(int, X53, number_number_of(X53), X54)), 
60.68/60.87	         app_encode_app(X53, X53, 
60.68/60.87	           app_encode_app(X53, app_encode_fun(X53, X53), plus_plus(X53), X55), 
60.68/60.87	           X56))
60.68/60.87	        = app_encode_app(X53, X53, 
60.68/60.87	            app_encode_app(X53, app_encode_fun(X53, X53), plus_plus(X53), 
60.68/60.87	              app_encode_app(X53, X53, 
60.68/60.87	                app_encode_app(X53, app_encode_fun(X53, X53), 
60.68/60.87	                  times_times(X53), 
60.68/60.87	                  app_encode_app(int, X53, number_number_of(X53), X54)), X55)), 
60.68/60.87	            app_encode_app(X53, X53, 
60.68/60.87	              app_encode_app(X53, app_encode_fun(X53, X53), 
60.68/60.87	                times_times(X53), 
60.68/60.87	                app_encode_app(int, X53, number_number_of(X53), X54)), X56))
60.68/60.87	       | ~ semiring(X53)
60.68/60.87	       | ~ number(X53)),
60.68/60.87	    inference('cnf', [status(esa)], [zf_stmt_62])).
60.68/60.87	tff('30', plain,
60.68/60.87	    ![X0 : int, X1 : int]:
60.68/60.87	      (app_encode_app(int, int, 
60.68/60.87	         app_encode_app(int, app_encode_fun(int, int), times_times(int), 
60.68/60.87	           app_encode_app(int, int, number_number_of(int), X1)), 
60.68/60.87	         app_encode_app(int, int, 
60.68/60.87	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
60.68/60.87	           X0))
60.68/60.87	        = app_encode_app(int, int, bit0, 
60.68/60.87	            app_encode_app(int, int, 
60.68/60.87	              app_encode_app(int, app_encode_fun(int, int), 
60.68/60.87	                times_times(int), 
60.68/60.87	                app_encode_app(int, int, number_number_of(int), X1)), X0))
60.68/60.87	       | ~ number(int)
60.68/60.87	       | ~ semiring(int)),
60.68/60.87	    inference('sup+', [status(thm)], ['28', '29'])).
60.68/60.87	tff(zf_stmt_139, axiom, (semiring(int))).
60.68/60.87	tff('31', plain, semiring(int),
60.68/60.87	    inference('cnf', [status(esa)], [zf_stmt_139])).
60.68/60.87	tff('32', plain,
60.68/60.87	    ![X0 : int, X1 : int]:
60.68/60.87	      (app_encode_app(int, int, 
60.68/60.87	         app_encode_app(int, app_encode_fun(int, int), times_times(int), X1), 
60.68/60.87	         app_encode_app(int, int, bit0, X0))
60.68/60.87	        = app_encode_app(int, int, bit0, 
60.68/60.87	            app_encode_app(int, int, 
60.68/60.87	              app_encode_app(int, app_encode_fun(int, int), 
60.68/60.87	                times_times(int), X1), X0))
60.68/60.87	       | ~ $true
60.68/60.87	       | ~ $true),
60.68/60.87	    inference('demod', [status(thm)], ['30', '2', '28', '2', '23', '31'])).
60.68/60.87	tff('33', plain,
60.68/60.87	    ![X0 : int, X1 : int]:
60.68/60.87	      app_encode_app(int, int, 
60.68/60.87	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X1), 
60.68/60.87	        app_encode_app(int, int, bit0, X0))
60.68/60.87	       = app_encode_app(int, int, bit0, 
60.68/60.87	           app_encode_app(int, int, 
60.68/60.87	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
60.68/60.87	               X1), X0)),
60.68/60.87	    inference('simplify', [status(thm)], ['32'])).
60.68/60.87	tff('34', plain,
60.68/60.87	    ![X0 : int]:
60.68/60.87	      app_encode_app(nat, int, 
60.68/60.87	        app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
60.68/60.87	          app_encode_app(int, int, bit0, X0)), 
60.68/60.87	        app_encode_app(int, nat, number_number_of(nat), 
60.68/60.87	          app_encode_app(int, int, bit0, one_one(int))))
60.68/60.87	       = app_encode_app(int, int, bit0, 
60.68/60.87	           app_encode_app(int, int, bit0, 
60.68/60.87	             app_encode_app(int, int, 
60.68/60.87	               app_encode_app(int, app_encode_fun(int, int), 
60.68/60.87	                 times_times(int), X0), X0))),
60.68/60.87	    inference('demod', [status(thm)], ['27', '33'])).
60.68/60.87	tff(zf_stmt_60, axiom,
60.68/60.87	  (![L1:int,K1:int]:
60.68/60.87	     (app_encode_app(int,int,
60.68/60.87	                     app_encode_app(int,app_encode_fun(int,int),
60.68/60.87	                                    minus_minus(int),
60.68/60.87	                                    app_encode_app(int,int,bit0,K1)),
60.68/60.87	                     app_encode_app(int,int,bit0,L1)) =
60.68/60.87	      app_encode_app(int,int,bit0,
60.68/60.87	                     app_encode_app(int,int,
60.68/60.87	                                    app_encode_app(int,
60.68/60.87	                                                   app_encode_fun(int,int),
60.68/60.87	                                                   minus_minus(int),K1),
60.68/60.87	                                    L1))))).
60.68/60.87	tff('35', plain,
60.68/60.87	    ![X47 : int, X48 : int]:
60.68/60.87	      app_encode_app(int, int, 
60.68/60.87	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
60.68/60.87	          app_encode_app(int, int, bit0, X47)), 
60.68/60.87	        app_encode_app(int, int, bit0, X48))
60.68/60.87	       = app_encode_app(int, int, bit0, 
60.68/60.87	           app_encode_app(int, int, 
60.68/60.87	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
60.68/60.87	               X47), X48)),
60.68/60.87	    inference('cnf', [status(esa)], [zf_stmt_60])).
60.68/60.87	tff('36', plain,
60.68/60.87	    app_encode_app(int, int, bit0, 
60.68/60.87	      app_encode_app(int, int, bit0, 
60.68/60.87	        app_encode_app(int, int, bit0, 
60.68/60.87	          app_encode_app(int, int, bit0, 
60.68/60.87	            app_encode_app(int, int, 
60.68/60.87	              app_encode_app(int, app_encode_fun(int, int), 
60.68/60.87	                times_times(int), m), m)))))
60.68/60.87	     != app_encode_app(int, int, bit0, 
60.68/60.87	          app_encode_app(int, int, bit0, 
60.68/60.87	            app_encode_app(int, int, 
60.68/60.87	              app_encode_app(int, app_encode_fun(int, int), 
60.68/60.87	                minus_minus(int), 
60.68/60.87	                app_encode_app(int, int, 
60.68/60.87	                  app_encode_app(int, app_encode_fun(int, int), 
60.68/60.87	                    times_times(int), 
60.68/60.87	                    app_encode_app(int, int, bit1, 
60.68/60.87	                      app_encode_app(int, int, bit0, m))), m)), m))),
60.68/60.87	    inference('demod', [status(thm)],
60.68/60.87	              ['0', '3', '2', '4', '4', '11', '15', '19', '3', '34', '4', 
60.68/60.87	               '33', '3', '2', '4', '4', '11', '15', '3', '2', '4', '4', 
60.68/60.87	               '11', '15', '19', '33', '33', '3', '2', '4', '4', '11', '15', 
60.68/60.87	               '19', '11', '35', '35'])).
60.68/60.87	tff('37', plain,
60.68/60.87	    app_encode_app(int, int, 
60.68/60.87	      app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
60.68/60.87	        one_one(int)), one_one(int))
60.68/60.87	     = app_encode_app(int, int, bit0, pls),
60.68/60.87	    inference('sup+', [status(thm)], ['3', '19'])).
60.68/60.87	tff('38', plain,
60.68/60.87	    app_encode_app(int, int, 
60.68/60.87	      app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
60.68/60.87	        one_one(int)), one_one(int))
60.68/60.87	     = pls,
60.68/60.87	    inference('demod', [status(thm)], ['37', '8'])).
60.68/60.87	tff(zf_stmt_64, axiom,
60.68/60.87	  (![B1:$tType]:
60.68/60.87	     ((number(B1) & ring(B1)) =>
60.68/60.87	      (![C:B1,B:B1,V:int]:
60.68/60.87	         (app_encode_app(B1,B1,
60.68/60.87	                         app_encode_app(B1,app_encode_fun(B1,B1),
60.68/60.87	                                        times_times(B1),
60.68/60.87	                                        app_encode_app(int,B1,
60.68/60.87	                                                       number_number_of(B1),V)),
60.68/60.87	                         app_encode_app(B1,B1,
60.68/60.87	                                        app_encode_app(B1,
60.68/60.87	                                                       app_encode_fun(B1,B1),
60.68/60.87	                                                       minus_minus(B1),B),
60.68/60.87	                                        C)) =
60.68/60.87	          app_encode_app(B1,B1,
60.68/60.87	                         app_encode_app(B1,app_encode_fun(B1,B1),
60.68/60.87	                                        minus_minus(B1),
60.68/60.87	                                        app_encode_app(B1,B1,
60.68/60.87	                                                       app_encode_app(
60.68/60.87	                                                       B1,
60.68/60.87	                                                       app_encode_fun(B1,B1),
60.68/60.87	                                                       times_times(B1),
60.68/60.87	                                                       app_encode_app(
60.68/60.87	                                                       int,B1,
60.68/60.87	                                                       number_number_of(B1),V)),
60.68/60.87	                                                       B)),
60.68/60.87	                         app_encode_app(B1,B1,
60.68/60.87	                                        app_encode_app(B1,
60.68/60.87	                                                       app_encode_fun(B1,B1),
60.68/60.87	                                                       times_times(B1),
60.68/60.87	                                                       app_encode_app(
60.68/60.87	                                                       int,B1,
60.68/60.87	                                                       number_number_of(B1),V)),
60.68/60.87	                                        C))))))).
60.68/60.87	tff('39', plain,
60.68/60.87	    ![X61 : $tType, X62 : int, X63 : X61, X64 : X61]:
60.68/60.87	      (app_encode_app(X61, X61, 
60.68/60.87	         app_encode_app(X61, app_encode_fun(X61, X61), times_times(X61), 
60.68/60.87	           app_encode_app(int, X61, number_number_of(X61), X62)), 
60.68/60.87	         app_encode_app(X61, X61, 
60.68/60.87	           app_encode_app(X61, app_encode_fun(X61, X61), minus_minus(X61), 
60.68/60.87	             X63), X64))
60.68/60.87	        = app_encode_app(X61, X61, 
60.68/60.87	            app_encode_app(X61, app_encode_fun(X61, X61), minus_minus(X61), 
60.68/60.87	              app_encode_app(X61, X61, 
60.68/60.87	                app_encode_app(X61, app_encode_fun(X61, X61), 
60.68/60.87	                  times_times(X61), 
60.68/60.87	                  app_encode_app(int, X61, number_number_of(X61), X62)), X63)), 
60.68/60.87	            app_encode_app(X61, X61, 
60.68/60.87	              app_encode_app(X61, app_encode_fun(X61, X61), 
60.68/60.87	                times_times(X61), 
60.68/60.87	                app_encode_app(int, X61, number_number_of(X61), X62)), X64))
60.68/60.87	       | ~ ring(X61)
60.68/60.87	       | ~ number(X61)),
60.68/60.87	    inference('cnf', [status(esa)], [zf_stmt_64])).
60.68/60.87	tff(zf_stmt_92, axiom,
60.68/60.87	  (![W:int,Z2:int,Z1:int]:
60.68/60.87	     (app_encode_app(int,int,
60.68/60.87	                     app_encode_app(int,app_encode_fun(int,int),
60.68/60.87	                                    times_times(int),
60.68/60.87	                                    app_encode_app(int,int,
60.68/60.87	                                                   app_encode_app(int,
60.68/60.87	                                                                  app_encode_fun(
60.68/60.87	                                                                  int,int),
60.68/60.87	                                                                  minus_minus(
60.68/60.87	                                                                  int),Z1),
60.68/60.87	                                                   Z2)),
60.68/60.87	                     W) =
60.68/60.87	      app_encode_app(int,int,
60.68/60.87	                     app_encode_app(int,app_encode_fun(int,int),
60.68/60.87	                                    minus_minus(int),
60.68/60.87	                                    app_encode_app(int,int,
60.68/60.87	                                                   app_encode_app(int,
60.68/60.87	                                                                  app_encode_fun(
60.68/60.87	                                                                  int,int),
60.68/60.87	                                                                  times_times(
60.68/60.87	                                                                  int),Z1),
60.68/60.87	                                                   W)),
60.68/60.87	                     app_encode_app(int,int,
60.68/60.87	                                    app_encode_app(int,
60.68/60.87	                                                   app_encode_fun(int,int),
60.68/60.87	                                                   times_times(int),Z2),
60.68/60.87	                                    W))))).
60.68/60.87	tff('40', plain,
60.68/60.87	    ![X115 : int, X116 : int, X117 : int]:
60.68/60.87	      app_encode_app(int, int, 
60.68/60.87	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
60.68/60.87	          app_encode_app(int, int, 
60.68/60.87	            app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
60.68/60.87	              X115), X117)), X116)
60.68/60.87	       = app_encode_app(int, int, 
60.68/60.87	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
60.68/60.87	             app_encode_app(int, int, 
60.68/60.87	               app_encode_app(int, app_encode_fun(int, int), 
60.68/60.87	                 times_times(int), X115), X116)), 
60.68/60.87	           app_encode_app(int, int, 
60.68/60.87	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
60.68/60.87	               X117), X116)),
60.68/60.87	    inference('cnf', [status(esa)], [zf_stmt_92])).
60.68/60.87	tff('41', plain,
60.68/60.87	    ![X0 : int, X1 : int]:
60.68/60.87	      (app_encode_app(int, int, 
60.68/60.87	         app_encode_app(int, app_encode_fun(int, int), times_times(int), 
60.68/60.87	           app_encode_app(int, int, 
60.68/60.87	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
60.68/60.87	               app_encode_app(int, int, number_number_of(int), X1)), 
60.68/60.87	             app_encode_app(int, int, number_number_of(int), X1))), X0)
60.68/60.87	        = app_encode_app(int, int, 
60.68/60.87	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
60.68/60.87	              app_encode_app(int, int, number_number_of(int), X1)), 
60.68/60.87	            app_encode_app(int, int, 
60.68/60.87	              app_encode_app(int, app_encode_fun(int, int), 
60.68/60.87	                minus_minus(int), X0), X0))
60.68/60.87	       | ~ number(int)
60.68/60.87	       | ~ ring(int)),
60.68/60.87	    inference('sup+', [status(thm)], ['39', '40'])).
60.68/60.87	tff(zf_stmt_140, axiom, (ring(int))).
60.68/60.87	tff('42', plain, ring(int), inference('cnf', [status(esa)], [zf_stmt_140])).
60.68/60.87	tff('43', plain,
60.68/60.87	    ![X0 : int, X1 : int]:
60.68/60.87	      (app_encode_app(int, int, 
60.68/60.87	         app_encode_app(int, app_encode_fun(int, int), times_times(int), 
60.68/60.87	           app_encode_app(int, int, 
60.68/60.87	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
60.68/60.87	               X1), X1)), X0)
60.68/60.87	        = app_encode_app(int, int, 
60.68/60.87	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
60.68/60.87	              X1), 
60.68/60.87	            app_encode_app(int, int, 
60.68/60.87	              app_encode_app(int, app_encode_fun(int, int), 
60.68/60.87	                minus_minus(int), X0), X0))
60.68/60.87	       | ~ $true
60.68/60.87	       | ~ $true),
60.68/60.87	    inference('demod', [status(thm)], ['41', '2', '2', '2', '23', '42'])).
60.68/60.87	tff('44', plain,
60.68/60.87	    ![X0 : int, X1 : int]:
60.68/60.87	      app_encode_app(int, int, 
60.68/60.87	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
60.68/60.87	          app_encode_app(int, int, 
60.68/60.87	            app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
60.68/60.87	              X1), X1)), X0)
60.68/60.87	       = app_encode_app(int, int, 
60.68/60.87	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
60.68/60.87	             X1), 
60.68/60.87	           app_encode_app(int, int, 
60.68/60.87	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
60.68/60.87	               X0), X0)),
60.68/60.87	    inference('simplify', [status(thm)], ['43'])).
60.68/60.87	tff('45', plain,
60.68/60.87	    ![X0 : int]:
60.68/60.87	      app_encode_app(int, int, 
60.68/60.87	        app_encode_app(int, app_encode_fun(int, int), times_times(int), pls), 
60.68/60.87	        X0)
60.68/60.87	       = app_encode_app(int, int, 
60.68/60.87	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
60.68/60.87	             one_one(int)), 
60.68/60.87	           app_encode_app(int, int, 
60.68/60.87	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
60.68/60.87	               X0), X0)),
60.68/60.87	    inference('sup+', [status(thm)], ['38', '44'])).
60.68/60.87	tff('46', plain,
60.68/60.87	    ![X0 : int]:
60.68/60.87	      pls
60.68/60.87	       = app_encode_app(int, int, 
60.68/60.87	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
60.68/60.87	             X0), X0),
60.68/60.87	    inference('demod', [status(thm)], ['45', '5', '11'])).
60.68/60.87	tff(zf_stmt_105, axiom,
60.68/60.87	  (![A:$tType]:
60.68/60.87	     (number_ring(A) =>
60.68/60.87	      (![C:A,W:int,V:int]:
60.68/60.87	         (app_encode_app(A,A,
60.68/60.87	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
60.68/60.87	                                        app_encode_app(int,A,
60.68/60.87	                                                       number_number_of(A),V)),
60.68/60.87	                         app_encode_app(A,A,
60.68/60.87	                                        app_encode_app(A,app_encode_fun(A,A),
60.68/60.87	                                                       minus_minus(A),
60.68/60.87	                                                       app_encode_app(
60.68/60.87	                                                       int,A,
60.68/60.87	                                                       number_number_of(A),W)),
60.68/60.87	                                        C)) =
60.68/60.87	          app_encode_app(A,A,
60.68/60.87	                         app_encode_app(A,app_encode_fun(A,A),minus_minus(A),
60.68/60.87	                                        app_encode_app(int,A,
60.68/60.87	                                                       number_number_of(A),
60.68/60.87	                                                       app_encode_app(
60.68/60.87	                                                       int,int,
60.68/60.87	                                                       app_encode_app(
60.68/60.87	                                                       int,
60.68/60.87	                                                       app_encode_fun(
60.68/60.87	                                                       int,int),
60.68/60.87	                                                       plus_plus(int),V),W))),
60.68/60.87	                         C)))))).
60.68/60.87	tff('47', plain,
60.68/60.87	    ![X143 : $tType, X144 : int, X145 : int, X146 : X143]:
60.68/60.87	      (app_encode_app(X143, X143, 
60.68/60.87	         app_encode_app(X143, app_encode_fun(X143, X143), plus_plus(X143), 
60.68/60.87	           app_encode_app(int, X143, number_number_of(X143), X144)), 
60.68/60.87	         app_encode_app(X143, X143, 
60.68/60.87	           app_encode_app(X143, app_encode_fun(X143, X143), 
60.68/60.87	             minus_minus(X143), 
60.68/60.87	             app_encode_app(int, X143, number_number_of(X143), X145)), X146))
60.68/60.87	        = app_encode_app(X143, X143, 
60.68/60.87	            app_encode_app(X143, app_encode_fun(X143, X143), 
60.68/60.87	              minus_minus(X143), 
60.68/60.87	              app_encode_app(int, X143, number_number_of(X143), 
60.68/60.87	                app_encode_app(int, int, 
60.68/60.87	                  app_encode_app(int, app_encode_fun(int, int), 
60.68/60.87	                    plus_plus(int), X144), X145))), X146)
60.68/60.87	       | ~ number_ring(X143)),
60.68/60.87	    inference('cnf', [status(esa)], [zf_stmt_105])).
60.68/60.87	tff('48', plain,
60.68/60.87	    ![X0 : int, X1 : int]:
60.68/60.87	      (app_encode_app(int, int, 
60.68/60.87	         app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
60.68/60.87	           app_encode_app(int, int, number_number_of(int), X1)), pls)
60.68/60.87	        = app_encode_app(int, int, 
60.68/60.87	            app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
60.68/60.87	              app_encode_app(int, int, number_number_of(int), 
60.68/60.87	                app_encode_app(int, int, 
60.68/60.87	                  app_encode_app(int, app_encode_fun(int, int), 
60.68/60.87	                    plus_plus(int), X1), X0))), 
60.68/60.87	            app_encode_app(int, int, number_number_of(int), X0))
60.68/60.87	       | ~ number_ring(int)),
60.68/60.87	    inference('sup+', [status(thm)], ['46', '47'])).
60.68/60.87	tff(zf_stmt_138, axiom, (number_ring(int))).
60.68/60.87	tff('49', plain, number_ring(int),
60.68/60.87	    inference('cnf', [status(esa)], [zf_stmt_138])).
60.68/60.87	tff('50', plain,
60.68/60.87	    ![X0 : int, X1 : int]:
60.68/60.87	      (X1
60.68/60.87	        = app_encode_app(int, int, 
60.68/60.87	            app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
60.68/60.87	              app_encode_app(int, int, 
60.68/60.87	                app_encode_app(int, app_encode_fun(int, int), 
60.68/60.87	                  plus_plus(int), X1), X0)), X0)
60.68/60.87	       | ~ $true),
60.68/60.87	    inference('demod', [status(thm)], ['48', '2', '14', '2', '2', '49'])).
60.68/60.87	tff('51', plain,
60.68/60.87	    ![X0 : int, X1 : int]:
60.68/60.87	      X1
60.68/60.87	       = app_encode_app(int, int, 
60.68/60.87	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
60.68/60.87	             app_encode_app(int, int, 
60.68/60.87	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
60.68/60.87	                 X1), X0)), X0),
60.68/60.87	    inference('simplify', [status(thm)], ['50'])).
60.68/60.87	tff('52', plain,
60.68/60.87	    ![X0 : int, X1 : int]:
60.68/60.87	      app_encode_app(int, int, bit0, 
60.68/60.87	        app_encode_app(int, int, 
60.68/60.87	          app_encode_app(int, app_encode_fun(int, int), times_times(int), X1), 
60.68/60.87	          X0))
60.68/60.87	       = app_encode_app(int, int, 
60.68/60.87	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
60.68/60.87	             app_encode_app(int, int, 
60.68/60.87	               app_encode_app(int, app_encode_fun(int, int), 
60.68/60.87	                 times_times(int), app_encode_app(int, int, bit1, X1)), X0)), 
60.68/60.87	           X0),
60.68/60.87	    inference('sup+', [status(thm)], ['6', '51'])).
60.68/60.87	tff('53', plain,
60.68/60.87	    app_encode_app(int, int, bit0, 
60.68/60.87	      app_encode_app(int, int, bit0, 
60.68/60.87	        app_encode_app(int, int, bit0, 
60.68/60.87	          app_encode_app(int, int, bit0, 
60.68/60.87	            app_encode_app(int, int, 
60.68/60.87	              app_encode_app(int, app_encode_fun(int, int), 
60.68/60.87	                times_times(int), m), m)))))
60.68/60.87	     != app_encode_app(int, int, bit0, 
60.68/60.87	          app_encode_app(int, int, bit0, 
60.68/60.87	            app_encode_app(int, int, bit0, 
60.68/60.87	              app_encode_app(int, int, bit0, 
60.68/60.87	                app_encode_app(int, int, 
60.68/60.87	                  app_encode_app(int, app_encode_fun(int, int), 
60.68/60.87	                    times_times(int), m), m))))),
60.68/60.87	    inference('demod', [status(thm)], ['36', '52', '4'])).
60.68/60.87	tff('54', plain, $false, inference('simplify', [status(thm)], ['53'])).
60.68/60.87	
60.68/60.87	% SZS output end Refutation
60.68/60.88	EOF
