0.00/0.00	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : appext
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : kbo
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.20	% Computer   : n173.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 07:55:08 CST 2018
46.85/47.06	% done 4870 iterations in 46.854s
46.85/47.06	% SZS status Theorem for 'stdin'
46.85/47.06	% SZS output start Refutation
46.85/47.06	tff(zf_stmt_161, conjecture,
46.85/47.06	  (app_encode_app(nat,int,
46.85/47.06	                  app_encode_app(int,app_encode_fun(nat,int),
46.85/47.06	                                 power_power(int),
46.85/47.06	                                 app_encode_app(int,int,
46.85/47.06	                                                app_encode_app(int,
46.85/47.06	                                                               app_encode_fun(
46.85/47.06	                                                               int,int),
46.85/47.06	                                                               minus_minus(
46.85/47.06	                                                               int),
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,int,
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,
46.85/47.06	                                                               app_encode_fun(
46.85/47.06	                                                               int,int),
46.85/47.06	                                                               plus_plus(int),
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,int,
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,
46.85/47.06	                                                               app_encode_fun(
46.85/47.06	                                                               int,int),
46.85/47.06	                                                               times_times(
46.85/47.06	                                                               int),
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,int,
46.85/47.06	                                                               number_number_of(
46.85/47.06	                                                               int),
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,int,bit0,
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,int,bit0,
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,int,bit1,
46.85/47.06	                                                               pls))))),m)),
46.85/47.06	                                                               one_one(int))),
46.85/47.06	                                                one_one(int))),
46.85/47.06	                  app_encode_app(int,nat,number_number_of(nat),
46.85/47.06	                                 app_encode_app(int,int,bit0,
46.85/47.06	                                                app_encode_app(int,int,bit1,
46.85/47.06	                                                               pls)))) =
46.85/47.06	   app_encode_app(int,int,
46.85/47.06	                  app_encode_app(int,app_encode_fun(int,int),
46.85/47.06	                                 minus_minus(int),
46.85/47.06	                                 app_encode_app(int,int,
46.85/47.06	                                                app_encode_app(int,
46.85/47.06	                                                               app_encode_fun(
46.85/47.06	                                                               int,int),
46.85/47.06	                                                               times_times(
46.85/47.06	                                                               int),
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,int,
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,
46.85/47.06	                                                               app_encode_fun(
46.85/47.06	                                                               int,int),
46.85/47.06	                                                               plus_plus(int),
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,int,
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,
46.85/47.06	                                                               app_encode_fun(
46.85/47.06	                                                               int,int),
46.85/47.06	                                                               times_times(
46.85/47.06	                                                               int),
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,int,
46.85/47.06	                                                               number_number_of(
46.85/47.06	                                                               int),
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,int,bit0,
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,int,bit0,
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,int,bit1,
46.85/47.06	                                                               pls))))),m)),
46.85/47.06	                                                               one_one(int))),
46.85/47.06	                                                app_encode_app(int,int,
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,
46.85/47.06	                                                               app_encode_fun(
46.85/47.06	                                                               int,int),
46.85/47.06	                                                               minus_minus(
46.85/47.06	                                                               int),
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,int,
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,
46.85/47.06	                                                               app_encode_fun(
46.85/47.06	                                                               int,int),
46.85/47.06	                                                               plus_plus(int),
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,int,
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,
46.85/47.06	                                                               app_encode_fun(
46.85/47.06	                                                               int,int),
46.85/47.06	                                                               times_times(
46.85/47.06	                                                               int),
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,int,
46.85/47.06	                                                               number_number_of(
46.85/47.06	                                                               int),
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,int,bit0,
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,int,bit0,
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,int,bit1,
46.85/47.06	                                                               pls))))),m)),
46.85/47.06	                                                               one_one(int))),
46.85/47.06	                                                               one_one(int)))),
46.85/47.06	                  app_encode_app(int,int,
46.85/47.06	                                 app_encode_app(int,app_encode_fun(int,int),
46.85/47.06	                                                times_times(int),one_one(int)),
46.85/47.06	                                 app_encode_app(int,int,
46.85/47.06	                                                app_encode_app(int,
46.85/47.06	                                                               app_encode_fun(
46.85/47.06	                                                               int,int),
46.85/47.06	                                                               minus_minus(
46.85/47.06	                                                               int),
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,int,
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,
46.85/47.06	                                                               app_encode_fun(
46.85/47.06	                                                               int,int),
46.85/47.06	                                                               plus_plus(int),
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,int,
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,
46.85/47.06	                                                               app_encode_fun(
46.85/47.06	                                                               int,int),
46.85/47.06	                                                               times_times(
46.85/47.06	                                                               int),
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,int,
46.85/47.06	                                                               number_number_of(
46.85/47.06	                                                               int),
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,int,bit0,
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,int,bit0,
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,int,bit1,
46.85/47.06	                                                               pls))))),m)),
46.85/47.06	                                                               one_one(int))),
46.85/47.06	                                                one_one(int)))))).
46.85/47.06	tff(zf_stmt_0, negated_conjecture,
46.85/47.06	  (app_encode_app(nat,int,
46.85/47.06	                  app_encode_app(int,app_encode_fun(nat,int),
46.85/47.06	                                 power_power(int),
46.85/47.06	                                 app_encode_app(int,int,
46.85/47.06	                                                app_encode_app(int,
46.85/47.06	                                                               app_encode_fun(
46.85/47.06	                                                               int,int),
46.85/47.06	                                                               minus_minus(
46.85/47.06	                                                               int),
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,int,
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,
46.85/47.06	                                                               app_encode_fun(
46.85/47.06	                                                               int,int),
46.85/47.06	                                                               plus_plus(int),
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,int,
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,
46.85/47.06	                                                               app_encode_fun(
46.85/47.06	                                                               int,int),
46.85/47.06	                                                               times_times(
46.85/47.06	                                                               int),
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,int,
46.85/47.06	                                                               number_number_of(
46.85/47.06	                                                               int),
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,int,bit0,
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,int,bit0,
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,int,bit1,
46.85/47.06	                                                               pls))))),m)),
46.85/47.06	                                                               one_one(int))),
46.85/47.06	                                                one_one(int))),
46.85/47.06	                  app_encode_app(int,nat,number_number_of(nat),
46.85/47.06	                                 app_encode_app(int,int,bit0,
46.85/47.06	                                                app_encode_app(int,int,bit1,
46.85/47.06	                                                               pls)))) !=
46.85/47.06	   app_encode_app(int,int,
46.85/47.06	                  app_encode_app(int,app_encode_fun(int,int),
46.85/47.06	                                 minus_minus(int),
46.85/47.06	                                 app_encode_app(int,int,
46.85/47.06	                                                app_encode_app(int,
46.85/47.06	                                                               app_encode_fun(
46.85/47.06	                                                               int,int),
46.85/47.06	                                                               times_times(
46.85/47.06	                                                               int),
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,int,
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,
46.85/47.06	                                                               app_encode_fun(
46.85/47.06	                                                               int,int),
46.85/47.06	                                                               plus_plus(int),
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,int,
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,
46.85/47.06	                                                               app_encode_fun(
46.85/47.06	                                                               int,int),
46.85/47.06	                                                               times_times(
46.85/47.06	                                                               int),
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,int,
46.85/47.06	                                                               number_number_of(
46.85/47.06	                                                               int),
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,int,bit0,
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,int,bit0,
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,int,bit1,
46.85/47.06	                                                               pls))))),m)),
46.85/47.06	                                                               one_one(int))),
46.85/47.06	                                                app_encode_app(int,int,
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,
46.85/47.06	                                                               app_encode_fun(
46.85/47.06	                                                               int,int),
46.85/47.06	                                                               minus_minus(
46.85/47.06	                                                               int),
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,int,
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,
46.85/47.06	                                                               app_encode_fun(
46.85/47.06	                                                               int,int),
46.85/47.06	                                                               plus_plus(int),
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,int,
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,
46.85/47.06	                                                               app_encode_fun(
46.85/47.06	                                                               int,int),
46.85/47.06	                                                               times_times(
46.85/47.06	                                                               int),
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,int,
46.85/47.06	                                                               number_number_of(
46.85/47.06	                                                               int),
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,int,bit0,
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,int,bit0,
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,int,bit1,
46.85/47.06	                                                               pls))))),m)),
46.85/47.06	                                                               one_one(int))),
46.85/47.06	                                                               one_one(int)))),
46.85/47.06	                  app_encode_app(int,int,
46.85/47.06	                                 app_encode_app(int,app_encode_fun(int,int),
46.85/47.06	                                                times_times(int),one_one(int)),
46.85/47.06	                                 app_encode_app(int,int,
46.85/47.06	                                                app_encode_app(int,
46.85/47.06	                                                               app_encode_fun(
46.85/47.06	                                                               int,int),
46.85/47.06	                                                               minus_minus(
46.85/47.06	                                                               int),
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,int,
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,
46.85/47.06	                                                               app_encode_fun(
46.85/47.06	                                                               int,int),
46.85/47.06	                                                               plus_plus(int),
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,int,
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,
46.85/47.06	                                                               app_encode_fun(
46.85/47.06	                                                               int,int),
46.85/47.06	                                                               times_times(
46.85/47.06	                                                               int),
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,int,
46.85/47.06	                                                               number_number_of(
46.85/47.06	                                                               int),
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,int,bit0,
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,int,bit0,
46.85/47.06	                                                               app_encode_app(
46.85/47.06	                                                               int,int,bit1,
46.85/47.06	                                                               pls))))),m)),
46.85/47.06	                                                               one_one(int))),
46.85/47.06	                                                one_one(int)))))).
46.85/47.06	tff('0', plain,
46.85/47.06	    app_encode_app(nat, int, 
46.85/47.06	      app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
46.85/47.06	        app_encode_app(int, int, 
46.85/47.06	          app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
46.85/47.06	            app_encode_app(int, int, 
46.85/47.06	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
46.85/47.06	                app_encode_app(int, int, 
46.85/47.06	                  app_encode_app(int, app_encode_fun(int, int), 
46.85/47.06	                    times_times(int), 
46.85/47.06	                    app_encode_app(int, int, number_number_of(int), 
46.85/47.06	                      app_encode_app(int, int, bit0, 
46.85/47.06	                        app_encode_app(int, int, bit0, 
46.85/47.06	                          app_encode_app(int, int, bit1, pls))))), m)), 
46.85/47.06	              one_one(int))), one_one(int))), 
46.85/47.06	      app_encode_app(int, nat, number_number_of(nat), 
46.85/47.06	        app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls))))
46.85/47.06	     != app_encode_app(int, int, 
46.85/47.06	          app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
46.85/47.06	            app_encode_app(int, int, 
46.85/47.06	              app_encode_app(int, app_encode_fun(int, int), 
46.85/47.06	                times_times(int), 
46.85/47.06	                app_encode_app(int, int, 
46.85/47.06	                  app_encode_app(int, app_encode_fun(int, int), 
46.85/47.06	                    plus_plus(int), 
46.85/47.06	                    app_encode_app(int, int, 
46.85/47.06	                      app_encode_app(int, app_encode_fun(int, int), 
46.85/47.06	                        times_times(int), 
46.85/47.06	                        app_encode_app(int, int, number_number_of(int), 
46.85/47.06	                          app_encode_app(int, int, bit0, 
46.85/47.06	                            app_encode_app(int, int, bit0, 
46.85/47.06	                              app_encode_app(int, int, bit1, pls))))), m)), 
46.85/47.06	                  one_one(int))), 
46.85/47.06	              app_encode_app(int, int, 
46.85/47.06	                app_encode_app(int, app_encode_fun(int, int), 
46.85/47.06	                  minus_minus(int), 
46.85/47.06	                  app_encode_app(int, int, 
46.85/47.06	                    app_encode_app(int, app_encode_fun(int, int), 
46.85/47.06	                      plus_plus(int), 
46.85/47.06	                      app_encode_app(int, int, 
46.85/47.06	                        app_encode_app(int, app_encode_fun(int, int), 
46.85/47.06	                          times_times(int), 
46.85/47.06	                          app_encode_app(int, int, number_number_of(int), 
46.85/47.06	                            app_encode_app(int, int, bit0, 
46.85/47.06	                              app_encode_app(int, int, bit0, 
46.85/47.06	                                app_encode_app(int, int, bit1, pls))))), m)), 
46.85/47.06	                    one_one(int))), one_one(int)))), 
46.85/47.06	          app_encode_app(int, int, 
46.85/47.06	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
46.85/47.06	              one_one(int)), 
46.85/47.06	            app_encode_app(int, int, 
46.85/47.06	              app_encode_app(int, app_encode_fun(int, int), 
46.85/47.06	                minus_minus(int), 
46.85/47.06	                app_encode_app(int, int, 
46.85/47.06	                  app_encode_app(int, app_encode_fun(int, int), 
46.85/47.06	                    plus_plus(int), 
46.85/47.06	                    app_encode_app(int, int, 
46.85/47.06	                      app_encode_app(int, app_encode_fun(int, int), 
46.85/47.06	                        times_times(int), 
46.85/47.06	                        app_encode_app(int, int, number_number_of(int), 
46.85/47.06	                          app_encode_app(int, int, bit0, 
46.85/47.06	                            app_encode_app(int, int, bit0, 
46.85/47.06	                              app_encode_app(int, int, bit1, pls))))), m)), 
46.85/47.06	                  one_one(int))), one_one(int)))),
46.85/47.06	    inference('cnf', [status(esa)], [zf_stmt_0])).
46.85/47.06	tff(zf_stmt_107, axiom,
46.85/47.06	  (one_one(int) =
46.85/47.06	   app_encode_app(int,int,number_number_of(int),
46.85/47.06	                  app_encode_app(int,int,bit1,pls)))).
46.85/47.06	tff('1', plain,
46.85/47.06	    one_one(int)
46.85/47.06	     = app_encode_app(int, int, number_number_of(int), 
46.85/47.06	         app_encode_app(int, int, bit1, pls)),
46.85/47.06	    inference('cnf', [status(esa)], [zf_stmt_107])).
46.85/47.06	tff(zf_stmt_83, axiom,
46.85/47.06	  (![K1:int]: (app_encode_app(int,int,number_number_of(int),K1) = K1))).
46.85/47.06	tff('2', plain,
46.85/47.06	    ![X101 : int]:
46.85/47.06	      app_encode_app(int, int, number_number_of(int), X101) = X101,
46.85/47.06	    inference('cnf', [status(esa)], [zf_stmt_83])).
46.85/47.06	tff('3', plain, one_one(int) = app_encode_app(int, int, bit1, pls),
46.85/47.06	    inference('demod', [status(thm)], ['1', '2'])).
46.85/47.06	tff(zf_stmt_59, axiom,
46.85/47.06	  (![L1:int,K1:int]:
46.85/47.06	     (app_encode_app(int,int,
46.85/47.06	                     app_encode_app(int,app_encode_fun(int,int),
46.85/47.06	                                    times_times(int),
46.85/47.06	                                    app_encode_app(int,int,bit0,K1)),
46.85/47.06	                     L1) =
46.85/47.06	      app_encode_app(int,int,bit0,
46.85/47.06	                     app_encode_app(int,int,
46.85/47.06	                                    app_encode_app(int,
46.85/47.06	                                                   app_encode_fun(int,int),
46.85/47.06	                                                   times_times(int),K1),
46.85/47.06	                                    L1))))).
46.85/47.06	tff('4', plain,
46.85/47.06	    ![X47 : int, X48 : int]:
46.85/47.06	      app_encode_app(int, int, 
46.85/47.06	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
46.85/47.06	          app_encode_app(int, int, bit0, X47)), X48)
46.85/47.06	       = app_encode_app(int, int, bit0, 
46.85/47.06	           app_encode_app(int, int, 
46.85/47.06	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
46.85/47.06	               X47), X48)),
46.85/47.06	    inference('cnf', [status(esa)], [zf_stmt_59])).
46.85/47.06	tff(zf_stmt_58, axiom,
46.85/47.06	  (![W:int]:
46.85/47.06	     (app_encode_app(int,int,
46.85/47.06	                     app_encode_app(int,app_encode_fun(int,int),
46.85/47.06	                                    times_times(int),pls),
46.85/47.06	                     W) =
46.85/47.06	      pls))).
46.85/47.06	tff('5', plain,
46.85/47.06	    ![X46 : int]:
46.85/47.06	      app_encode_app(int, int, 
46.85/47.06	        app_encode_app(int, app_encode_fun(int, int), times_times(int), pls), 
46.85/47.06	        X46)
46.85/47.06	       = pls,
46.85/47.06	    inference('cnf', [status(esa)], [zf_stmt_58])).
46.85/47.06	tff(zf_stmt_41, axiom,
46.85/47.06	  (![L1:int,K1:int]:
46.85/47.06	     (app_encode_app(int,int,
46.85/47.06	                     app_encode_app(int,app_encode_fun(int,int),
46.85/47.06	                                    times_times(int),
46.85/47.06	                                    app_encode_app(int,int,bit1,K1)),
46.85/47.06	                     L1) =
46.85/47.06	      app_encode_app(int,int,
46.85/47.06	                     app_encode_app(int,app_encode_fun(int,int),
46.85/47.06	                                    plus_plus(int),
46.85/47.06	                                    app_encode_app(int,int,bit0,
46.85/47.06	                                                   app_encode_app(int,int,
46.85/47.06	                                                                  app_encode_app(
46.85/47.06	                                                                  int,
46.85/47.06	                                                                  app_encode_fun(
46.85/47.06	                                                                  int,int),
46.85/47.06	                                                                  times_times(
46.85/47.06	                                                                  int),K1),L1))),
46.85/47.06	                     L1)))).
46.85/47.06	tff('6', plain,
46.85/47.06	    ![X12 : int, X13 : int]:
46.85/47.06	      app_encode_app(int, int, 
46.85/47.06	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
46.85/47.06	          app_encode_app(int, int, bit1, X12)), X13)
46.85/47.06	       = app_encode_app(int, int, 
46.85/47.06	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
46.85/47.06	             app_encode_app(int, int, bit0, 
46.85/47.06	               app_encode_app(int, int, 
46.85/47.06	                 app_encode_app(int, app_encode_fun(int, int), 
46.85/47.06	                   times_times(int), X12), X13))), X13),
46.85/47.06	    inference('cnf', [status(esa)], [zf_stmt_41])).
46.85/47.06	tff('7', plain,
46.85/47.06	    ![X0 : int]:
46.85/47.06	      app_encode_app(int, int, 
46.85/47.06	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
46.85/47.06	          app_encode_app(int, int, bit1, pls)), X0)
46.85/47.06	       = app_encode_app(int, int, 
46.85/47.06	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
46.85/47.06	             app_encode_app(int, int, bit0, pls)), X0),
46.85/47.06	    inference('sup+', [status(thm)], ['5', '6'])).
46.85/47.06	tff(zf_stmt_57, axiom, (app_encode_app(int,int,bit0,pls) = pls)).
46.85/47.06	tff('8', plain, app_encode_app(int, int, bit0, pls) = pls,
46.85/47.06	    inference('cnf', [status(esa)], [zf_stmt_57])).
46.85/47.06	tff('9', plain,
46.85/47.06	    ![X0 : int]:
46.85/47.06	      app_encode_app(int, int, 
46.85/47.06	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
46.85/47.06	          one_one(int)), X0)
46.85/47.06	       = app_encode_app(int, int, 
46.85/47.06	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
46.85/47.06	           X0),
46.85/47.06	    inference('demod', [status(thm)], ['7', '3', '8'])).
46.85/47.06	tff(zf_stmt_86, axiom,
46.85/47.06	  (![K1:int]:
46.85/47.06	     (app_encode_app(int,int,
46.85/47.06	                     app_encode_app(int,app_encode_fun(int,int),
46.85/47.06	                                    plus_plus(int),pls),
46.85/47.06	                     K1) =
46.85/47.06	      K1))).
46.85/47.06	tff('10', plain,
46.85/47.06	    ![X106 : int]:
46.85/47.06	      app_encode_app(int, int, 
46.85/47.06	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
46.85/47.06	        X106)
46.85/47.06	       = X106,
46.85/47.06	    inference('cnf', [status(esa)], [zf_stmt_86])).
46.85/47.06	tff('11', plain,
46.85/47.06	    ![X0 : int]:
46.85/47.06	      app_encode_app(int, int, 
46.85/47.06	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
46.85/47.06	          one_one(int)), X0)
46.85/47.06	       = X0,
46.85/47.06	    inference('demod', [status(thm)], ['9', '10'])).
46.85/47.06	tff(zf_stmt_2, axiom,
46.85/47.06	  (![X:app_encode_fun(Alpha,Beta),Y:app_encode_fun(Alpha,Beta)]:
46.85/47.06	     ((![Z:Alpha]:
46.85/47.06	         (app_encode_app(Alpha,Beta,X,Z) = app_encode_app(Alpha,Beta,Y,Z))) =>
46.85/47.06	      (X = Y)))).
46.85/47.06	tff('12', plain,
46.85/47.06	    ![X0 : $tType, X1 : $tType, X2 : app_encode_fun(X0, X1), 
46.85/47.06	      X3 : app_encode_fun(X0, X1)]:
46.85/47.06	      (X3 = X2
46.85/47.06	       | app_encode_app(X0, X1, X3, sk_Z(X1, X0, X2, X3))
46.85/47.06	          != app_encode_app(X0, X1, X2, sk_Z(X1, X0, X2, X3))),
46.85/47.06	    inference('cnf', [status(esa)], [zf_stmt_2])).
46.85/47.06	tff('13', plain,
46.85/47.06	    ![X0 : app_encode_fun(int, int)]:
46.85/47.06	      (app_encode_app(int, int, X0, 
46.85/47.06	         sk_Z(int, int, number_number_of(int), X0))
46.85/47.06	        != sk_Z(int, int, number_number_of(int), X0)
46.85/47.06	       | X0 = number_number_of(int)),
46.85/47.06	    inference('sup-', [status(thm)], ['2', '12'])).
46.85/47.06	tff('14', plain,
46.85/47.06	    (sk_Z(int, int, number_number_of(int), 
46.85/47.06	       app_encode_app(int, app_encode_fun(int, int), times_times(int), 
46.85/47.06	         one_one(int)))
46.85/47.06	      != sk_Z(int, int, number_number_of(int), 
46.85/47.06	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
46.85/47.06	             one_one(int)))
46.85/47.06	     | app_encode_app(int, app_encode_fun(int, int), times_times(int), 
46.85/47.06	         one_one(int))
46.85/47.06	        = number_number_of(int)),
46.85/47.06	    inference('sup-', [status(thm)], ['11', '13'])).
46.85/47.06	tff('15', plain,
46.85/47.06	    app_encode_app(int, app_encode_fun(int, int), times_times(int), 
46.85/47.06	      one_one(int))
46.85/47.06	     = number_number_of(int),
46.85/47.06	    inference('simplify', [status(thm)], ['14'])).
46.85/47.06	tff(zf_stmt_72, axiom,
46.85/47.06	  (![L1:int,K1:int]:
46.85/47.06	     (app_encode_app(int,int,
46.85/47.06	                     app_encode_app(int,app_encode_fun(int,int),
46.85/47.06	                                    plus_plus(int),
46.85/47.06	                                    app_encode_app(int,int,bit0,K1)),
46.85/47.06	                     app_encode_app(int,int,bit1,L1)) =
46.85/47.06	      app_encode_app(int,int,bit1,
46.85/47.06	                     app_encode_app(int,int,
46.85/47.06	                                    app_encode_app(int,
46.85/47.06	                                                   app_encode_fun(int,int),
46.85/47.06	                                                   plus_plus(int),K1),
46.85/47.06	                                    L1))))).
46.85/47.06	tff('16', plain,
46.85/47.06	    ![X85 : int, X86 : int]:
46.85/47.06	      app_encode_app(int, int, 
46.85/47.06	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
46.85/47.06	          app_encode_app(int, int, bit0, X85)), 
46.85/47.06	        app_encode_app(int, int, bit1, X86))
46.85/47.06	       = app_encode_app(int, int, bit1, 
46.85/47.06	           app_encode_app(int, int, 
46.85/47.06	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
46.85/47.06	               X85), X86)),
46.85/47.06	    inference('cnf', [status(esa)], [zf_stmt_72])).
46.85/47.06	tff('17', plain,
46.85/47.06	    ![X0 : int]:
46.85/47.06	      app_encode_app(int, int, 
46.85/47.06	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
46.85/47.06	          app_encode_app(int, int, bit0, X0)), one_one(int))
46.85/47.06	       = app_encode_app(int, int, bit1, 
46.85/47.06	           app_encode_app(int, int, 
46.85/47.06	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
46.85/47.06	               X0), pls)),
46.85/47.06	    inference('sup+', [status(thm)], ['3', '16'])).
46.85/47.06	tff(zf_stmt_85, axiom,
46.85/47.06	  (![K1:int]:
46.85/47.06	     (app_encode_app(int,int,
46.85/47.06	                     app_encode_app(int,app_encode_fun(int,int),
46.85/47.06	                                    plus_plus(int),K1),
46.85/47.06	                     pls) =
46.85/47.06	      K1))).
46.85/47.06	tff('18', plain,
46.85/47.06	    ![X105 : int]:
46.85/47.06	      app_encode_app(int, int, 
46.85/47.06	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X105), 
46.85/47.06	        pls)
46.85/47.06	       = X105,
46.85/47.06	    inference('cnf', [status(esa)], [zf_stmt_85])).
46.85/47.06	tff('19', plain,
46.85/47.06	    ![X0 : int]:
46.85/47.06	      app_encode_app(int, int, 
46.85/47.06	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
46.85/47.06	          app_encode_app(int, int, bit0, X0)), one_one(int))
46.85/47.06	       = app_encode_app(int, int, bit1, X0),
46.85/47.06	    inference('demod', [status(thm)], ['17', '18'])).
46.85/47.06	tff(zf_stmt_73, axiom,
46.85/47.06	  (![L1:int,K1:int]:
46.85/47.06	     (app_encode_app(int,int,
46.85/47.06	                     app_encode_app(int,app_encode_fun(int,int),
46.85/47.06	                                    minus_minus(int),
46.85/47.06	                                    app_encode_app(int,int,bit1,K1)),
46.85/47.06	                     app_encode_app(int,int,bit1,L1)) =
46.85/47.06	      app_encode_app(int,int,bit0,
46.85/47.06	                     app_encode_app(int,int,
46.85/47.06	                                    app_encode_app(int,
46.85/47.06	                                                   app_encode_fun(int,int),
46.85/47.06	                                                   minus_minus(int),K1),
46.85/47.06	                                    L1))))).
46.85/47.06	tff('20', plain,
46.85/47.06	    ![X87 : int, X88 : int]:
46.85/47.06	      app_encode_app(int, int, 
46.85/47.06	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
46.85/47.06	          app_encode_app(int, int, bit1, X87)), 
46.85/47.06	        app_encode_app(int, int, bit1, X88))
46.85/47.06	       = app_encode_app(int, int, bit0, 
46.85/47.06	           app_encode_app(int, int, 
46.85/47.06	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
46.85/47.06	               X87), X88)),
46.85/47.06	    inference('cnf', [status(esa)], [zf_stmt_73])).
46.85/47.06	tff('21', plain,
46.85/47.06	    ![X0 : int]:
46.85/47.06	      app_encode_app(int, int, 
46.85/47.06	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
46.85/47.06	          app_encode_app(int, int, bit1, X0)), one_one(int))
46.85/47.06	       = app_encode_app(int, int, bit0, 
46.85/47.06	           app_encode_app(int, int, 
46.85/47.06	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
46.85/47.06	               X0), pls)),
46.85/47.06	    inference('sup+', [status(thm)], ['3', '20'])).
46.85/47.06	tff(zf_stmt_89, axiom,
46.85/47.06	  (![K1:int]:
46.85/47.06	     (app_encode_app(int,int,
46.85/47.06	                     app_encode_app(int,app_encode_fun(int,int),
46.85/47.06	                                    minus_minus(int),K1),
46.85/47.06	                     pls) =
46.85/47.06	      K1))).
46.85/47.06	tff('22', plain,
46.85/47.06	    ![X110 : int]:
46.85/47.06	      app_encode_app(int, int, 
46.85/47.06	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), X110), 
46.85/47.06	        pls)
46.85/47.06	       = X110,
46.85/47.06	    inference('cnf', [status(esa)], [zf_stmt_89])).
46.85/47.06	tff('23', plain,
46.85/47.06	    ![X0 : int]:
46.85/47.06	      app_encode_app(int, int, 
46.85/47.06	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
46.85/47.06	          app_encode_app(int, int, bit1, X0)), one_one(int))
46.85/47.06	       = app_encode_app(int, int, bit0, X0),
46.85/47.06	    inference('demod', [status(thm)], ['21', '22'])).
46.85/47.06	tff(zf_stmt_36, axiom,
46.85/47.06	  (![B1:$tType]:
46.85/47.06	     ((monoid_mult(B1) & number(B1)) =>
46.85/47.06	      (![W:int]:
46.85/47.06	         (app_encode_app(nat,B1,
46.85/47.06	                         app_encode_app(B1,app_encode_fun(nat,B1),
46.85/47.06	                                        power_power(B1),
46.85/47.06	                                        app_encode_app(int,B1,
46.85/47.06	                                                       number_number_of(B1),W)),
46.85/47.06	                         app_encode_app(int,nat,number_number_of(nat),
46.85/47.06	                                        app_encode_app(int,int,bit0,
46.85/47.06	                                                       app_encode_app(
46.85/47.06	                                                       int,int,bit1,pls)))) =
46.85/47.06	          app_encode_app(B1,B1,
46.85/47.06	                         app_encode_app(B1,app_encode_fun(B1,B1),
46.85/47.06	                                        times_times(B1),
46.85/47.06	                                        app_encode_app(int,B1,
46.85/47.06	                                                       number_number_of(B1),W)),
46.85/47.06	                         app_encode_app(int,B1,number_number_of(B1),W))))))).
46.85/47.06	tff('24', plain,
46.85/47.06	    ![X4 : $tType, X5 : int]:
46.85/47.06	      (app_encode_app(nat, X4, 
46.85/47.06	         app_encode_app(X4, app_encode_fun(nat, X4), power_power(X4), 
46.85/47.06	           app_encode_app(int, X4, number_number_of(X4), X5)), 
46.85/47.06	         app_encode_app(int, nat, number_number_of(nat), 
46.85/47.06	           app_encode_app(int, int, bit0, 
46.85/47.06	             app_encode_app(int, int, bit1, pls))))
46.85/47.06	        = app_encode_app(X4, X4, 
46.85/47.06	            app_encode_app(X4, app_encode_fun(X4, X4), times_times(X4), 
46.85/47.06	              app_encode_app(int, X4, number_number_of(X4), X5)), 
46.85/47.06	            app_encode_app(int, X4, number_number_of(X4), X5))
46.85/47.06	       | ~ number(X4)
46.85/47.06	       | ~ monoid_mult(X4)),
46.85/47.06	    inference('cnf', [status(esa)], [zf_stmt_36])).
46.85/47.06	tff('25', plain,
46.85/47.06	    ![X0 : int]:
46.85/47.06	      (app_encode_app(nat, int, 
46.85/47.06	         app_encode_app(int, app_encode_fun(nat, int), power_power(int), X0), 
46.85/47.06	         app_encode_app(int, nat, number_number_of(nat), 
46.85/47.06	           app_encode_app(int, int, bit0, 
46.85/47.06	             app_encode_app(int, int, bit1, pls))))
46.85/47.06	        = app_encode_app(int, int, 
46.85/47.06	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
46.85/47.06	              app_encode_app(int, int, number_number_of(int), X0)), 
46.85/47.06	            app_encode_app(int, int, number_number_of(int), X0))
46.85/47.06	       | ~ monoid_mult(int)
46.85/47.06	       | ~ number(int)),
46.85/47.06	    inference('sup+', [status(thm)], ['2', '24'])).
46.85/47.06	tff(zf_stmt_136, axiom, (monoid_mult(int))).
46.85/47.06	tff('26', plain, monoid_mult(int),
46.85/47.06	    inference('cnf', [status(esa)], [zf_stmt_136])).
46.85/47.06	tff(zf_stmt_142, axiom, (number(int))).
46.85/47.06	tff('27', plain, number(int), inference('cnf', [status(esa)], [zf_stmt_142])).
46.85/47.06	tff('28', plain,
46.85/47.06	    ![X0 : int]:
46.85/47.06	      (app_encode_app(nat, int, 
46.85/47.06	         app_encode_app(int, app_encode_fun(nat, int), power_power(int), X0), 
46.85/47.06	         app_encode_app(int, nat, number_number_of(nat), 
46.85/47.06	           app_encode_app(int, int, bit0, 
46.85/47.06	             app_encode_app(int, int, bit1, pls))))
46.85/47.06	        = app_encode_app(int, int, 
46.85/47.06	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
46.85/47.06	              X0), X0)
46.85/47.06	       | ~ $true
46.85/47.06	       | ~ $true),
46.85/47.06	    inference('demod', [status(thm)], ['25', '2', '2', '26', '27'])).
46.85/47.06	tff('29', plain,
46.85/47.06	    ![X0 : int]:
46.85/47.06	      app_encode_app(nat, int, 
46.85/47.06	        app_encode_app(int, app_encode_fun(nat, int), power_power(int), X0), 
46.85/47.06	        app_encode_app(int, nat, number_number_of(nat), 
46.85/47.06	          app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls))))
46.85/47.06	       = app_encode_app(int, int, 
46.85/47.06	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
46.85/47.06	             X0), X0),
46.85/47.06	    inference('simplify', [status(thm)], ['28'])).
46.85/47.06	tff('30', plain,
46.85/47.06	    ![X0 : int]:
46.85/47.06	      app_encode_app(nat, int, 
46.85/47.06	        app_encode_app(int, app_encode_fun(nat, int), power_power(int), X0), 
46.85/47.06	        app_encode_app(int, nat, number_number_of(nat), 
46.85/47.06	          app_encode_app(int, int, bit0, one_one(int))))
46.85/47.06	       = app_encode_app(int, int, 
46.85/47.06	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
46.85/47.06	             X0), X0),
46.85/47.06	    inference('demod', [status(thm)], ['29', '3'])).
46.85/47.06	tff('31', plain,
46.85/47.06	    ![X0 : int]:
46.85/47.06	      app_encode_app(nat, int, 
46.85/47.06	        app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
46.85/47.06	          app_encode_app(int, int, bit0, X0)), 
46.85/47.06	        app_encode_app(int, nat, number_number_of(nat), 
46.85/47.06	          app_encode_app(int, int, bit0, one_one(int))))
46.85/47.06	       = app_encode_app(int, int, bit0, 
46.85/47.06	           app_encode_app(int, int, 
46.85/47.06	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
46.85/47.06	               X0), app_encode_app(int, int, bit0, X0))),
46.85/47.06	    inference('sup+', [status(thm)], ['30', '4'])).
46.85/47.06	tff(zf_stmt_87, axiom,
46.85/47.06	  (![K1:int]:
46.85/47.06	     (app_encode_app(int,int,bit0,K1) =
46.85/47.06	      app_encode_app(int,int,
46.85/47.06	                     app_encode_app(int,app_encode_fun(int,int),
46.85/47.06	                                    plus_plus(int),K1),
46.85/47.06	                     K1)))).
46.85/47.06	tff('32', plain,
46.85/47.06	    ![X107 : int]:
46.85/47.06	      app_encode_app(int, int, bit0, X107)
46.85/47.06	       = app_encode_app(int, int, 
46.85/47.06	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
46.85/47.06	             X107), X107),
46.85/47.06	    inference('cnf', [status(esa)], [zf_stmt_87])).
46.85/47.06	tff(zf_stmt_63, axiom,
46.85/47.06	  (![B1:$tType]:
46.85/47.06	     ((number(B1) & semiring(B1)) =>
46.85/47.06	      (![C:B1,B:B1,V:int]:
46.85/47.06	         (app_encode_app(B1,B1,
46.85/47.06	                         app_encode_app(B1,app_encode_fun(B1,B1),
46.85/47.06	                                        times_times(B1),
46.85/47.06	                                        app_encode_app(int,B1,
46.85/47.06	                                                       number_number_of(B1),V)),
46.85/47.06	                         app_encode_app(B1,B1,
46.85/47.06	                                        app_encode_app(B1,
46.85/47.06	                                                       app_encode_fun(B1,B1),
46.85/47.06	                                                       plus_plus(B1),B),
46.85/47.06	                                        C)) =
46.85/47.06	          app_encode_app(B1,B1,
46.85/47.06	                         app_encode_app(B1,app_encode_fun(B1,B1),
46.85/47.07	                                        plus_plus(B1),
46.85/47.07	                                        app_encode_app(B1,B1,
46.85/47.07	                                                       app_encode_app(
46.85/47.07	                                                       B1,
46.85/47.07	                                                       app_encode_fun(B1,B1),
46.85/47.07	                                                       times_times(B1),
46.85/47.07	                                                       app_encode_app(
46.85/47.07	                                                       int,B1,
46.85/47.07	                                                       number_number_of(B1),V)),
46.85/47.07	                                                       B)),
46.85/47.07	                         app_encode_app(B1,B1,
46.85/47.07	                                        app_encode_app(B1,
46.85/47.07	                                                       app_encode_fun(B1,B1),
46.85/47.07	                                                       times_times(B1),
46.85/47.07	                                                       app_encode_app(
46.85/47.07	                                                       int,B1,
46.85/47.07	                                                       number_number_of(B1),V)),
46.85/47.07	                                        C))))))).
46.85/47.07	tff('33', plain,
46.85/47.07	    ![X57 : $tType, X58 : int, X59 : X57, X60 : X57]:
46.85/47.07	      (app_encode_app(X57, X57, 
46.85/47.07	         app_encode_app(X57, app_encode_fun(X57, X57), times_times(X57), 
46.85/47.07	           app_encode_app(int, X57, number_number_of(X57), X58)), 
46.85/47.07	         app_encode_app(X57, X57, 
46.85/47.07	           app_encode_app(X57, app_encode_fun(X57, X57), plus_plus(X57), X59), 
46.85/47.07	           X60))
46.85/47.07	        = app_encode_app(X57, X57, 
46.85/47.07	            app_encode_app(X57, app_encode_fun(X57, X57), plus_plus(X57), 
46.85/47.07	              app_encode_app(X57, X57, 
46.85/47.07	                app_encode_app(X57, app_encode_fun(X57, X57), 
46.85/47.07	                  times_times(X57), 
46.85/47.07	                  app_encode_app(int, X57, number_number_of(X57), X58)), X59)), 
46.85/47.07	            app_encode_app(X57, X57, 
46.85/47.07	              app_encode_app(X57, app_encode_fun(X57, X57), 
46.85/47.07	                times_times(X57), 
46.85/47.07	                app_encode_app(int, X57, number_number_of(X57), X58)), X60))
46.85/47.07	       | ~ semiring(X57)
46.85/47.07	       | ~ number(X57)),
46.85/47.07	    inference('cnf', [status(esa)], [zf_stmt_63])).
46.85/47.07	tff('34', plain,
46.85/47.07	    ![X0 : int, X1 : int]:
46.85/47.07	      (app_encode_app(int, int, 
46.85/47.07	         app_encode_app(int, app_encode_fun(int, int), times_times(int), 
46.85/47.07	           app_encode_app(int, int, number_number_of(int), X1)), 
46.85/47.07	         app_encode_app(int, int, 
46.85/47.07	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
46.85/47.07	           X0))
46.85/47.07	        = app_encode_app(int, int, bit0, 
46.85/47.07	            app_encode_app(int, int, 
46.85/47.07	              app_encode_app(int, app_encode_fun(int, int), 
46.85/47.07	                times_times(int), 
46.85/47.07	                app_encode_app(int, int, number_number_of(int), X1)), X0))
46.85/47.07	       | ~ number(int)
46.85/47.07	       | ~ semiring(int)),
46.85/47.07	    inference('sup+', [status(thm)], ['32', '33'])).
46.85/47.07	tff(zf_stmt_140, axiom, (semiring(int))).
46.85/47.07	tff('35', plain, semiring(int),
46.85/47.07	    inference('cnf', [status(esa)], [zf_stmt_140])).
46.85/47.07	tff('36', plain,
46.85/47.07	    ![X0 : int, X1 : int]:
46.85/47.07	      (app_encode_app(int, int, 
46.85/47.07	         app_encode_app(int, app_encode_fun(int, int), times_times(int), X1), 
46.85/47.07	         app_encode_app(int, int, bit0, X0))
46.85/47.07	        = app_encode_app(int, int, bit0, 
46.85/47.07	            app_encode_app(int, int, 
46.85/47.07	              app_encode_app(int, app_encode_fun(int, int), 
46.85/47.07	                times_times(int), X1), X0))
46.85/47.07	       | ~ $true
46.85/47.07	       | ~ $true),
46.85/47.07	    inference('demod', [status(thm)], ['34', '2', '32', '2', '27', '35'])).
46.85/47.07	tff('37', plain,
46.85/47.07	    ![X0 : int, X1 : int]:
46.85/47.07	      app_encode_app(int, int, 
46.85/47.07	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X1), 
46.85/47.07	        app_encode_app(int, int, bit0, X0))
46.85/47.07	       = app_encode_app(int, int, bit0, 
46.85/47.07	           app_encode_app(int, int, 
46.85/47.07	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
46.85/47.07	               X1), X0)),
46.85/47.07	    inference('simplify', [status(thm)], ['36'])).
46.85/47.07	tff('38', plain,
46.85/47.07	    ![X0 : int]:
46.85/47.07	      app_encode_app(nat, int, 
46.85/47.07	        app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
46.85/47.07	          app_encode_app(int, int, bit0, X0)), 
46.85/47.07	        app_encode_app(int, nat, number_number_of(nat), 
46.85/47.07	          app_encode_app(int, int, bit0, one_one(int))))
46.85/47.07	       = app_encode_app(int, int, bit0, 
46.85/47.07	           app_encode_app(int, int, bit0, 
46.85/47.07	             app_encode_app(int, int, 
46.85/47.07	               app_encode_app(int, app_encode_fun(int, int), 
46.85/47.07	                 times_times(int), X0), X0))),
46.85/47.07	    inference('demod', [status(thm)], ['31', '37'])).
46.85/47.07	tff(zf_stmt_61, axiom,
46.85/47.07	  (![L1:int,K1:int]:
46.85/47.07	     (app_encode_app(int,int,
46.85/47.07	                     app_encode_app(int,app_encode_fun(int,int),
46.85/47.07	                                    minus_minus(int),
46.85/47.07	                                    app_encode_app(int,int,bit0,K1)),
46.85/47.07	                     app_encode_app(int,int,bit0,L1)) =
46.85/47.07	      app_encode_app(int,int,bit0,
46.85/47.07	                     app_encode_app(int,int,
46.85/47.07	                                    app_encode_app(int,
46.85/47.07	                                                   app_encode_fun(int,int),
46.85/47.07	                                                   minus_minus(int),K1),
46.85/47.07	                                    L1))))).
46.85/47.07	tff('39', plain,
46.85/47.07	    ![X51 : int, X52 : int]:
46.85/47.07	      app_encode_app(int, int, 
46.85/47.07	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
46.85/47.07	          app_encode_app(int, int, bit0, X51)), 
46.85/47.07	        app_encode_app(int, int, bit0, X52))
46.85/47.07	       = app_encode_app(int, int, bit0, 
46.85/47.07	           app_encode_app(int, int, 
46.85/47.07	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
46.85/47.07	               X51), X52)),
46.85/47.07	    inference('cnf', [status(esa)], [zf_stmt_61])).
46.85/47.07	tff('40', plain,
46.85/47.07	    app_encode_app(int, int, bit0, 
46.85/47.07	      app_encode_app(int, int, bit0, 
46.85/47.07	        app_encode_app(int, int, bit0, 
46.85/47.07	          app_encode_app(int, int, bit0, 
46.85/47.07	            app_encode_app(int, int, 
46.85/47.07	              app_encode_app(int, app_encode_fun(int, int), 
46.85/47.07	                times_times(int), m), m)))))
46.85/47.07	     != app_encode_app(int, int, bit0, 
46.85/47.07	          app_encode_app(int, int, bit0, 
46.85/47.07	            app_encode_app(int, int, 
46.85/47.07	              app_encode_app(int, app_encode_fun(int, int), 
46.85/47.07	                minus_minus(int), 
46.85/47.07	                app_encode_app(int, int, 
46.85/47.07	                  app_encode_app(int, app_encode_fun(int, int), 
46.85/47.07	                    times_times(int), 
46.85/47.07	                    app_encode_app(int, int, bit1, 
46.85/47.07	                      app_encode_app(int, int, bit0, m))), m)), m))),
46.85/47.07	    inference('demod', [status(thm)],
46.85/47.07	              ['0', '3', '2', '4', '4', '15', '2', '19', '23', '3', '38', 
46.85/47.07	               '4', '37', '3', '2', '4', '4', '15', '2', '19', '3', '2', 
46.85/47.07	               '4', '4', '15', '2', '19', '23', '37', '37', '15', '3', '2', 
46.85/47.07	               '4', '4', '15', '2', '19', '23', '2', '39', '39'])).
46.85/47.07	tff('41', plain,
46.85/47.07	    app_encode_app(int, int, 
46.85/47.07	      app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
46.85/47.07	        one_one(int)), one_one(int))
46.85/47.07	     = app_encode_app(int, int, bit0, pls),
46.85/47.07	    inference('sup+', [status(thm)], ['3', '23'])).
46.85/47.07	tff('42', plain,
46.85/47.07	    app_encode_app(int, int, 
46.85/47.07	      app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
46.85/47.07	        one_one(int)), one_one(int))
46.85/47.07	     = pls,
46.85/47.07	    inference('demod', [status(thm)], ['41', '8'])).
46.85/47.07	tff(zf_stmt_65, axiom,
46.85/47.07	  (![B1:$tType]:
46.85/47.07	     ((number(B1) & ring(B1)) =>
46.85/47.07	      (![C:B1,B:B1,V:int]:
46.85/47.07	         (app_encode_app(B1,B1,
46.85/47.07	                         app_encode_app(B1,app_encode_fun(B1,B1),
46.85/47.07	                                        times_times(B1),
46.85/47.07	                                        app_encode_app(int,B1,
46.85/47.07	                                                       number_number_of(B1),V)),
46.85/47.07	                         app_encode_app(B1,B1,
46.85/47.07	                                        app_encode_app(B1,
46.85/47.07	                                                       app_encode_fun(B1,B1),
46.85/47.07	                                                       minus_minus(B1),B),
46.85/47.07	                                        C)) =
46.85/47.07	          app_encode_app(B1,B1,
46.85/47.07	                         app_encode_app(B1,app_encode_fun(B1,B1),
46.85/47.07	                                        minus_minus(B1),
46.85/47.07	                                        app_encode_app(B1,B1,
46.85/47.07	                                                       app_encode_app(
46.85/47.07	                                                       B1,
46.85/47.07	                                                       app_encode_fun(B1,B1),
46.85/47.07	                                                       times_times(B1),
46.85/47.07	                                                       app_encode_app(
46.85/47.07	                                                       int,B1,
46.85/47.07	                                                       number_number_of(B1),V)),
46.85/47.07	                                                       B)),
46.85/47.07	                         app_encode_app(B1,B1,
46.85/47.07	                                        app_encode_app(B1,
46.85/47.07	                                                       app_encode_fun(B1,B1),
46.85/47.07	                                                       times_times(B1),
46.85/47.07	                                                       app_encode_app(
46.85/47.07	                                                       int,B1,
46.85/47.07	                                                       number_number_of(B1),V)),
46.85/47.07	                                        C))))))).
46.85/47.07	tff('43', plain,
46.85/47.07	    ![X65 : $tType, X66 : int, X67 : X65, X68 : X65]:
46.85/47.07	      (app_encode_app(X65, X65, 
46.85/47.07	         app_encode_app(X65, app_encode_fun(X65, X65), times_times(X65), 
46.85/47.07	           app_encode_app(int, X65, number_number_of(X65), X66)), 
46.85/47.07	         app_encode_app(X65, X65, 
46.85/47.07	           app_encode_app(X65, app_encode_fun(X65, X65), minus_minus(X65), 
46.85/47.07	             X67), X68))
46.85/47.07	        = app_encode_app(X65, X65, 
46.85/47.07	            app_encode_app(X65, app_encode_fun(X65, X65), minus_minus(X65), 
46.85/47.07	              app_encode_app(X65, X65, 
46.85/47.07	                app_encode_app(X65, app_encode_fun(X65, X65), 
46.85/47.07	                  times_times(X65), 
46.85/47.07	                  app_encode_app(int, X65, number_number_of(X65), X66)), X67)), 
46.85/47.07	            app_encode_app(X65, X65, 
46.85/47.07	              app_encode_app(X65, app_encode_fun(X65, X65), 
46.85/47.07	                times_times(X65), 
46.85/47.07	                app_encode_app(int, X65, number_number_of(X65), X66)), X68))
46.85/47.07	       | ~ ring(X65)
46.85/47.07	       | ~ number(X65)),
46.85/47.07	    inference('cnf', [status(esa)], [zf_stmt_65])).
46.85/47.07	tff(zf_stmt_93, axiom,
46.85/47.07	  (![W:int,Z2:int,Z1:int]:
46.85/47.07	     (app_encode_app(int,int,
46.85/47.07	                     app_encode_app(int,app_encode_fun(int,int),
46.85/47.07	                                    times_times(int),
46.85/47.07	                                    app_encode_app(int,int,
46.85/47.07	                                                   app_encode_app(int,
46.85/47.07	                                                                  app_encode_fun(
46.85/47.07	                                                                  int,int),
46.85/47.07	                                                                  minus_minus(
46.85/47.07	                                                                  int),Z1),
46.85/47.07	                                                   Z2)),
46.85/47.07	                     W) =
46.85/47.07	      app_encode_app(int,int,
46.85/47.07	                     app_encode_app(int,app_encode_fun(int,int),
46.85/47.07	                                    minus_minus(int),
46.85/47.07	                                    app_encode_app(int,int,
46.85/47.07	                                                   app_encode_app(int,
46.85/47.07	                                                                  app_encode_fun(
46.85/47.07	                                                                  int,int),
46.85/47.07	                                                                  times_times(
46.85/47.07	                                                                  int),Z1),
46.85/47.07	                                                   W)),
46.85/47.07	                     app_encode_app(int,int,
46.85/47.07	                                    app_encode_app(int,
46.85/47.07	                                                   app_encode_fun(int,int),
46.85/47.07	                                                   times_times(int),Z2),
46.85/47.07	                                    W))))).
46.85/47.07	tff('44', plain,
46.85/47.07	    ![X119 : int, X120 : int, X121 : int]:
46.85/47.07	      app_encode_app(int, int, 
46.85/47.07	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
46.85/47.07	          app_encode_app(int, int, 
46.85/47.07	            app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
46.85/47.07	              X119), X121)), X120)
46.85/47.07	       = app_encode_app(int, int, 
46.85/47.07	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
46.85/47.07	             app_encode_app(int, int, 
46.85/47.07	               app_encode_app(int, app_encode_fun(int, int), 
46.85/47.07	                 times_times(int), X119), X120)), 
46.85/47.07	           app_encode_app(int, int, 
46.85/47.07	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
46.85/47.07	               X121), X120)),
46.85/47.07	    inference('cnf', [status(esa)], [zf_stmt_93])).
46.85/47.07	tff('45', plain,
46.85/47.07	    ![X0 : int, X1 : int]:
46.85/47.07	      (app_encode_app(int, int, 
46.85/47.07	         app_encode_app(int, app_encode_fun(int, int), times_times(int), 
46.85/47.07	           app_encode_app(int, int, 
46.85/47.07	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
46.85/47.07	               app_encode_app(int, int, number_number_of(int), X1)), 
46.85/47.07	             app_encode_app(int, int, number_number_of(int), X1))), X0)
46.85/47.07	        = app_encode_app(int, int, 
46.85/47.07	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
46.85/47.07	              app_encode_app(int, int, number_number_of(int), X1)), 
46.85/47.07	            app_encode_app(int, int, 
46.85/47.07	              app_encode_app(int, app_encode_fun(int, int), 
46.85/47.07	                minus_minus(int), X0), X0))
46.85/47.07	       | ~ number(int)
46.85/47.07	       | ~ ring(int)),
46.85/47.07	    inference('sup+', [status(thm)], ['43', '44'])).
46.85/47.07	tff(zf_stmt_141, axiom, (ring(int))).
46.85/47.07	tff('46', plain, ring(int), inference('cnf', [status(esa)], [zf_stmt_141])).
46.85/47.07	tff('47', plain,
46.85/47.07	    ![X0 : int, X1 : int]:
46.85/47.07	      (app_encode_app(int, int, 
46.85/47.07	         app_encode_app(int, app_encode_fun(int, int), times_times(int), 
46.85/47.07	           app_encode_app(int, int, 
46.85/47.07	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
46.85/47.07	               X1), X1)), X0)
46.85/47.07	        = app_encode_app(int, int, 
46.85/47.07	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
46.85/47.07	              X1), 
46.85/47.07	            app_encode_app(int, int, 
46.85/47.07	              app_encode_app(int, app_encode_fun(int, int), 
46.85/47.07	                minus_minus(int), X0), X0))
46.85/47.07	       | ~ $true
46.85/47.07	       | ~ $true),
46.85/47.07	    inference('demod', [status(thm)], ['45', '2', '2', '2', '27', '46'])).
46.85/47.07	tff('48', plain,
46.85/47.07	    ![X0 : int, X1 : int]:
46.85/47.07	      app_encode_app(int, int, 
46.85/47.07	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
46.85/47.07	          app_encode_app(int, int, 
46.85/47.07	            app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
46.85/47.07	              X1), X1)), X0)
46.85/47.07	       = app_encode_app(int, int, 
46.85/47.07	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
46.85/47.07	             X1), 
46.85/47.07	           app_encode_app(int, int, 
46.85/47.07	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
46.85/47.07	               X0), X0)),
46.85/47.07	    inference('simplify', [status(thm)], ['47'])).
46.85/47.07	tff('49', plain,
46.85/47.07	    ![X0 : int]:
46.85/47.07	      app_encode_app(int, int, 
46.85/47.07	        app_encode_app(int, app_encode_fun(int, int), times_times(int), pls), 
46.85/47.07	        X0)
46.85/47.07	       = app_encode_app(int, int, 
46.85/47.07	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
46.85/47.07	             one_one(int)), 
46.85/47.07	           app_encode_app(int, int, 
46.85/47.07	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
46.85/47.07	               X0), X0)),
46.85/47.07	    inference('sup+', [status(thm)], ['42', '48'])).
46.85/47.07	tff('50', plain,
46.85/47.07	    ![X0 : int]:
46.85/47.07	      pls
46.85/47.07	       = app_encode_app(int, int, 
46.85/47.07	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
46.85/47.07	             X0), X0),
46.85/47.07	    inference('demod', [status(thm)], ['49', '5', '15', '2'])).
46.85/47.07	tff(zf_stmt_106, axiom,
46.85/47.07	  (![A:$tType]:
46.85/47.07	     (number_ring(A) =>
46.85/47.07	      (![C:A,W:int,V:int]:
46.85/47.07	         (app_encode_app(A,A,
46.85/47.07	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
46.85/47.07	                                        app_encode_app(int,A,
46.85/47.07	                                                       number_number_of(A),V)),
46.85/47.07	                         app_encode_app(A,A,
46.85/47.07	                                        app_encode_app(A,app_encode_fun(A,A),
46.85/47.07	                                                       minus_minus(A),
46.85/47.07	                                                       app_encode_app(
46.85/47.07	                                                       int,A,
46.85/47.07	                                                       number_number_of(A),W)),
46.85/47.07	                                        C)) =
46.85/47.07	          app_encode_app(A,A,
46.85/47.07	                         app_encode_app(A,app_encode_fun(A,A),minus_minus(A),
46.85/47.07	                                        app_encode_app(int,A,
46.85/47.07	                                                       number_number_of(A),
46.85/47.07	                                                       app_encode_app(
46.85/47.07	                                                       int,int,
46.85/47.07	                                                       app_encode_app(
46.85/47.07	                                                       int,
46.85/47.07	                                                       app_encode_fun(
46.85/47.07	                                                       int,int),
46.85/47.07	                                                       plus_plus(int),V),W))),
46.85/47.07	                         C)))))).
46.85/47.07	tff('51', plain,
46.85/47.07	    ![X147 : $tType, X148 : int, X149 : int, X150 : X147]:
46.85/47.07	      (app_encode_app(X147, X147, 
46.85/47.07	         app_encode_app(X147, app_encode_fun(X147, X147), plus_plus(X147), 
46.85/47.07	           app_encode_app(int, X147, number_number_of(X147), X148)), 
46.85/47.07	         app_encode_app(X147, X147, 
46.85/47.07	           app_encode_app(X147, app_encode_fun(X147, X147), 
46.85/47.07	             minus_minus(X147), 
46.85/47.07	             app_encode_app(int, X147, number_number_of(X147), X149)), X150))
46.85/47.07	        = app_encode_app(X147, X147, 
46.85/47.07	            app_encode_app(X147, app_encode_fun(X147, X147), 
46.85/47.07	              minus_minus(X147), 
46.85/47.07	              app_encode_app(int, X147, number_number_of(X147), 
46.85/47.07	                app_encode_app(int, int, 
46.85/47.07	                  app_encode_app(int, app_encode_fun(int, int), 
46.85/47.07	                    plus_plus(int), X148), X149))), X150)
46.85/47.07	       | ~ number_ring(X147)),
46.85/47.07	    inference('cnf', [status(esa)], [zf_stmt_106])).
46.85/47.07	tff('52', plain,
46.85/47.07	    ![X0 : int, X1 : int]:
46.85/47.07	      (app_encode_app(int, int, 
46.85/47.07	         app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
46.85/47.07	           app_encode_app(int, int, number_number_of(int), X1)), pls)
46.85/47.07	        = app_encode_app(int, int, 
46.85/47.07	            app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
46.85/47.07	              app_encode_app(int, int, number_number_of(int), 
46.85/47.07	                app_encode_app(int, int, 
46.85/47.07	                  app_encode_app(int, app_encode_fun(int, int), 
46.85/47.07	                    plus_plus(int), X1), X0))), 
46.85/47.07	            app_encode_app(int, int, number_number_of(int), X0))
46.85/47.07	       | ~ number_ring(int)),
46.85/47.07	    inference('sup+', [status(thm)], ['50', '51'])).
46.85/47.07	tff(zf_stmt_139, axiom, (number_ring(int))).
46.85/47.07	tff('53', plain, number_ring(int),
46.85/47.07	    inference('cnf', [status(esa)], [zf_stmt_139])).
46.85/47.07	tff('54', plain,
46.85/47.07	    ![X0 : int, X1 : int]:
46.85/47.07	      (X1
46.85/47.07	        = app_encode_app(int, int, 
46.85/47.07	            app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
46.85/47.07	              app_encode_app(int, int, 
46.85/47.07	                app_encode_app(int, app_encode_fun(int, int), 
46.85/47.07	                  plus_plus(int), X1), X0)), X0)
46.85/47.07	       | ~ $true),
46.85/47.07	    inference('demod', [status(thm)], ['52', '2', '18', '2', '2', '53'])).
46.85/47.07	tff('55', plain,
46.85/47.07	    ![X0 : int, X1 : int]:
46.85/47.07	      X1
46.85/47.07	       = app_encode_app(int, int, 
46.85/47.07	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
46.85/47.07	             app_encode_app(int, int, 
46.85/47.07	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
46.85/47.07	                 X1), X0)), X0),
46.85/47.07	    inference('simplify', [status(thm)], ['54'])).
46.85/47.07	tff('56', plain,
46.85/47.07	    ![X0 : int, X1 : int]:
46.85/47.07	      app_encode_app(int, int, bit0, 
46.85/47.07	        app_encode_app(int, int, 
46.85/47.07	          app_encode_app(int, app_encode_fun(int, int), times_times(int), X1), 
46.85/47.07	          X0))
46.85/47.07	       = app_encode_app(int, int, 
46.85/47.07	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
46.85/47.07	             app_encode_app(int, int, 
46.85/47.07	               app_encode_app(int, app_encode_fun(int, int), 
46.85/47.07	                 times_times(int), app_encode_app(int, int, bit1, X1)), X0)), 
46.85/47.07	           X0),
46.85/47.07	    inference('sup+', [status(thm)], ['6', '55'])).
46.85/47.07	tff('57', plain,
46.85/47.07	    app_encode_app(int, int, bit0, 
46.85/47.07	      app_encode_app(int, int, bit0, 
46.85/47.07	        app_encode_app(int, int, bit0, 
46.85/47.07	          app_encode_app(int, int, bit0, 
46.85/47.07	            app_encode_app(int, int, 
46.85/47.07	              app_encode_app(int, app_encode_fun(int, int), 
46.85/47.07	                times_times(int), m), m)))))
46.85/47.07	     != app_encode_app(int, int, bit0, 
46.85/47.07	          app_encode_app(int, int, bit0, 
46.85/47.07	            app_encode_app(int, int, bit0, 
46.85/47.07	              app_encode_app(int, int, bit0, 
46.85/47.07	                app_encode_app(int, int, 
46.85/47.07	                  app_encode_app(int, app_encode_fun(int, int), 
46.85/47.07	                    times_times(int), m), m))))),
46.85/47.07	    inference('demod', [status(thm)], ['40', '56', '4'])).
46.85/47.07	tff('58', plain, $false, inference('simplify', [status(thm)], ['57'])).
46.85/47.07	
46.85/47.07	% SZS output end Refutation
46.85/47.07	EOF
