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 $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.20	% Computer   : n123.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 07:30:23 CST 2018
56.93/57.06	% done 11603 iterations in 56.856s
56.93/57.06	% SZS status Theorem for 'stdin'
56.93/57.06	% SZS output start Refutation
56.93/57.07	tff(zf_stmt_98, axiom,
56.93/57.07	  (app_encode_app(bool,$o,hBOOL,
56.93/57.07	                  app_encode_app(int,bool,
56.93/57.07	                                 app_encode_app(fun_int_bool,
56.93/57.07	                                                app_encode_fun(int,bool),
56.93/57.07	                                                hAPP_int_bool,
56.93/57.07	                                                app_encode_app(int,
56.93/57.07	                                                               fun_int_bool,
56.93/57.07	                                                               app_encode_app(
56.93/57.07	                                                               fun_int_fun_int_bool,
56.93/57.07	                                                               app_encode_fun(
56.93/57.07	                                                               int,
56.93/57.07	                                                               fun_int_bool),
56.93/57.07	                                                               hAPP_i1948725293t_bool,
56.93/57.07	                                                               ord_less_int),
56.93/57.07	                                                               app_encode_app(
56.93/57.07	                                                               int,int,
56.93/57.07	                                                               app_encode_app(
56.93/57.07	                                                               fun_int_int,
56.93/57.07	                                                               app_encode_fun(
56.93/57.07	                                                               int,int),
56.93/57.07	                                                               hAPP_int_int,
56.93/57.07	                                                               app_encode_app(
56.93/57.07	                                                               int,
56.93/57.07	                                                               fun_int_int,
56.93/57.07	                                                               times_times_int,
56.93/57.07	                                                               app_encode_app(
56.93/57.07	                                                               int,int,
56.93/57.07	                                                               app_encode_app(
56.93/57.07	                                                               fun_int_int,
56.93/57.07	                                                               app_encode_fun(
56.93/57.07	                                                               int,int),
56.93/57.07	                                                               hAPP_int_int,
56.93/57.07	                                                               app_encode_app(
56.93/57.07	                                                               int,
56.93/57.07	                                                               fun_int_int,
56.93/57.07	                                                               plus_plus_int,
56.93/57.07	                                                               app_encode_app(
56.93/57.07	                                                               int,int,
56.93/57.07	                                                               app_encode_app(
56.93/57.07	                                                               fun_int_int,
56.93/57.07	                                                               app_encode_fun(
56.93/57.07	                                                               int,int),
56.93/57.07	                                                               hAPP_int_int,
56.93/57.07	                                                               app_encode_app(
56.93/57.07	                                                               int,
56.93/57.07	                                                               fun_int_int,
56.93/57.07	                                                               times_times_int,
56.93/57.07	                                                               app_encode_app(
56.93/57.07	                                                               int,int,
56.93/57.07	                                                               number_number_of_int,
56.93/57.07	                                                               app_encode_app(
56.93/57.07	                                                               int,int,bit0,
56.93/57.07	                                                               app_encode_app(
56.93/57.07	                                                               int,int,bit0,
56.93/57.07	                                                               app_encode_app(
56.93/57.07	                                                               int,int,bit1,
56.93/57.07	                                                               pls)))))),m))),
56.93/57.07	                                                               one_one_int))),
56.93/57.07	                                                               t))),
56.93/57.07	                                 app_encode_app(int,int,
56.93/57.07	                                                app_encode_app(fun_int_int,
56.93/57.07	                                                               app_encode_fun(
56.93/57.07	                                                               int,int),
56.93/57.07	                                                               hAPP_int_int,
56.93/57.07	                                                               app_encode_app(
56.93/57.07	                                                               int,
56.93/57.07	                                                               fun_int_int,
56.93/57.07	                                                               times_times_int,
56.93/57.07	                                                               app_encode_app(
56.93/57.07	                                                               int,int,
56.93/57.07	                                                               app_encode_app(
56.93/57.07	                                                               fun_int_int,
56.93/57.07	                                                               app_encode_fun(
56.93/57.07	                                                               int,int),
56.93/57.07	                                                               hAPP_int_int,
56.93/57.07	                                                               app_encode_app(
56.93/57.07	                                                               int,
56.93/57.07	                                                               fun_int_int,
56.93/57.07	                                                               plus_plus_int,
56.93/57.07	                                                               app_encode_app(
56.93/57.07	                                                               int,int,
56.93/57.07	                                                               app_encode_app(
56.93/57.07	                                                               fun_int_int,
56.93/57.07	                                                               app_encode_fun(
56.93/57.07	                                                               int,int),
56.93/57.07	                                                               hAPP_int_int,
56.93/57.07	                                                               app_encode_app(
56.93/57.07	                                                               int,
56.93/57.07	                                                               fun_int_int,
56.93/57.07	                                                               times_times_int,
56.93/57.07	                                                               app_encode_app(
56.93/57.07	                                                               int,int,
56.93/57.07	                                                               number_number_of_int,
56.93/57.07	                                                               app_encode_app(
56.93/57.07	                                                               int,int,bit0,
56.93/57.07	                                                               app_encode_app(
56.93/57.07	                                                               int,int,bit0,
56.93/57.07	                                                               app_encode_app(
56.93/57.07	                                                               int,int,bit1,
56.93/57.07	                                                               pls)))))),m))),
56.93/57.07	                                                               one_one_int))),
56.93/57.07	                                                zero_zero_int))))).
56.93/57.07	tff('0', plain,
56.93/57.07	    app_encode_app(bool, $o, hBOOL, 
56.93/57.07	      app_encode_app(int, bool, 
56.93/57.07	        app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
56.93/57.07	          hAPP_int_bool, 
56.93/57.07	          app_encode_app(int, fun_int_bool, 
56.93/57.07	            app_encode_app(fun_int_fun_int_bool, 
56.93/57.07	              app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
56.93/57.07	              ord_less_int), 
56.93/57.07	            app_encode_app(int, int, 
56.93/57.07	              app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	                hAPP_int_int, 
56.93/57.07	                app_encode_app(int, fun_int_int, times_times_int, 
56.93/57.07	                  app_encode_app(int, int, 
56.93/57.07	                    app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	                      hAPP_int_int, 
56.93/57.07	                      app_encode_app(int, fun_int_int, plus_plus_int, 
56.93/57.07	                        app_encode_app(int, int, 
56.93/57.07	                          app_encode_app(fun_int_int, 
56.93/57.07	                            app_encode_fun(int, int), hAPP_int_int, 
56.93/57.07	                            app_encode_app(int, fun_int_int, 
56.93/57.07	                              times_times_int, 
56.93/57.07	                              app_encode_app(int, int, number_number_of_int, 
56.93/57.07	                                app_encode_app(int, int, bit0, 
56.93/57.07	                                  app_encode_app(int, int, bit0, 
56.93/57.07	                                    app_encode_app(int, int, bit1, pls)))))), 
56.93/57.07	                          m))), one_one_int))), t))), 
56.93/57.07	        app_encode_app(int, int, 
56.93/57.07	          app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	            hAPP_int_int, 
56.93/57.07	            app_encode_app(int, fun_int_int, times_times_int, 
56.93/57.07	              app_encode_app(int, int, 
56.93/57.07	                app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	                  hAPP_int_int, 
56.93/57.07	                  app_encode_app(int, fun_int_int, plus_plus_int, 
56.93/57.07	                    app_encode_app(int, int, 
56.93/57.07	                      app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	                        hAPP_int_int, 
56.93/57.07	                        app_encode_app(int, fun_int_int, times_times_int, 
56.93/57.07	                          app_encode_app(int, int, number_number_of_int, 
56.93/57.07	                            app_encode_app(int, int, bit0, 
56.93/57.07	                              app_encode_app(int, int, bit0, 
56.93/57.07	                                app_encode_app(int, int, bit1, pls)))))), m))), 
56.93/57.07	                one_one_int))), zero_zero_int))),
56.93/57.07	    inference('cnf', [status(esa)], [zf_stmt_98])).
56.93/57.07	tff(zf_stmt_268, axiom, (pls = zero_zero_int)).
56.93/57.07	tff('1', plain, pls = zero_zero_int,
56.93/57.07	    inference('cnf', [status(esa)], [zf_stmt_268])).
56.93/57.07	tff(zf_stmt_130, axiom,
56.93/57.07	  (![K_1:int]: (app_encode_app(int,int,number_number_of_int,K_1) = K_1))).
56.93/57.07	tff('2', plain,
56.93/57.07	    ![X31 : int]: app_encode_app(int, int, number_number_of_int, X31) = X31,
56.93/57.07	    inference('cnf', [status(esa)], [zf_stmt_130])).
56.93/57.07	tff('3', plain,
56.93/57.07	    app_encode_app(bool, $o, hBOOL, 
56.93/57.07	      app_encode_app(int, bool, 
56.93/57.07	        app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
56.93/57.07	          hAPP_int_bool, 
56.93/57.07	          app_encode_app(int, fun_int_bool, 
56.93/57.07	            app_encode_app(fun_int_fun_int_bool, 
56.93/57.07	              app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
56.93/57.07	              ord_less_int), 
56.93/57.07	            app_encode_app(int, int, 
56.93/57.07	              app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	                hAPP_int_int, 
56.93/57.07	                app_encode_app(int, fun_int_int, times_times_int, 
56.93/57.07	                  app_encode_app(int, int, 
56.93/57.07	                    app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	                      hAPP_int_int, 
56.93/57.07	                      app_encode_app(int, fun_int_int, plus_plus_int, 
56.93/57.07	                        app_encode_app(int, int, 
56.93/57.07	                          app_encode_app(fun_int_int, 
56.93/57.07	                            app_encode_fun(int, int), hAPP_int_int, 
56.93/57.07	                            app_encode_app(int, fun_int_int, 
56.93/57.07	                              times_times_int, 
56.93/57.07	                              app_encode_app(int, int, bit0, 
56.93/57.07	                                app_encode_app(int, int, bit0, 
56.93/57.07	                                  app_encode_app(int, int, bit1, 
56.93/57.07	                                    zero_zero_int))))), m))), one_one_int))), 
56.93/57.07	              t))), 
56.93/57.07	        app_encode_app(int, int, 
56.93/57.07	          app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	            hAPP_int_int, 
56.93/57.07	            app_encode_app(int, fun_int_int, times_times_int, 
56.93/57.07	              app_encode_app(int, int, 
56.93/57.07	                app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	                  hAPP_int_int, 
56.93/57.07	                  app_encode_app(int, fun_int_int, plus_plus_int, 
56.93/57.07	                    app_encode_app(int, int, 
56.93/57.07	                      app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	                        hAPP_int_int, 
56.93/57.07	                        app_encode_app(int, fun_int_int, times_times_int, 
56.93/57.07	                          app_encode_app(int, int, bit0, 
56.93/57.07	                            app_encode_app(int, int, bit0, 
56.93/57.07	                              app_encode_app(int, int, bit1, zero_zero_int))))), 
56.93/57.07	                      m))), one_one_int))), zero_zero_int))),
56.93/57.07	    inference('demod', [status(thm)], ['0', '1', '2', '1', '2'])).
56.93/57.07	tff(zf_stmt_99, axiom,
56.93/57.07	  (app_encode_app(int,int,
56.93/57.07	                  app_encode_app(fun_int_int,app_encode_fun(int,int),
56.93/57.07	                                 hAPP_int_int,
56.93/57.07	                                 app_encode_app(int,fun_int_int,
56.93/57.07	                                                plus_plus_int,
56.93/57.07	                                                app_encode_app(nat,int,
56.93/57.07	                                                               app_encode_app(
56.93/57.07	                                                               fun_nat_int,
56.93/57.07	                                                               app_encode_fun(
56.93/57.07	                                                               nat,int),
56.93/57.07	                                                               hAPP_nat_int,
56.93/57.07	                                                               app_encode_app(
56.93/57.07	                                                               int,
56.93/57.07	                                                               fun_nat_int,
56.93/57.07	                                                               power_power_int,
56.93/57.07	                                                               s)),
56.93/57.07	                                                               app_encode_app(
56.93/57.07	                                                               int,nat,
56.93/57.07	                                                               number_number_of_nat,
56.93/57.07	                                                               app_encode_app(
56.93/57.07	                                                               int,int,bit0,
56.93/57.07	                                                               app_encode_app(
56.93/57.07	                                                               int,int,bit1,
56.93/57.07	                                                               pls)))))),
56.93/57.07	                  one_one_int) =
56.93/57.07	   app_encode_app(int,int,
56.93/57.07	                  app_encode_app(fun_int_int,app_encode_fun(int,int),
56.93/57.07	                                 hAPP_int_int,
56.93/57.07	                                 app_encode_app(int,fun_int_int,
56.93/57.07	                                                times_times_int,
56.93/57.07	                                                app_encode_app(int,int,
56.93/57.07	                                                               app_encode_app(
56.93/57.07	                                                               fun_int_int,
56.93/57.07	                                                               app_encode_fun(
56.93/57.07	                                                               int,int),
56.93/57.07	                                                               hAPP_int_int,
56.93/57.07	                                                               app_encode_app(
56.93/57.07	                                                               int,
56.93/57.07	                                                               fun_int_int,
56.93/57.07	                                                               plus_plus_int,
56.93/57.07	                                                               app_encode_app(
56.93/57.07	                                                               int,int,
56.93/57.07	                                                               app_encode_app(
56.93/57.07	                                                               fun_int_int,
56.93/57.07	                                                               app_encode_fun(
56.93/57.07	                                                               int,int),
56.93/57.07	                                                               hAPP_int_int,
56.93/57.07	                                                               app_encode_app(
56.93/57.07	                                                               int,
56.93/57.07	                                                               fun_int_int,
56.93/57.07	                                                               times_times_int,
56.93/57.07	                                                               app_encode_app(
56.93/57.07	                                                               int,int,
56.93/57.07	                                                               number_number_of_int,
56.93/57.07	                                                               app_encode_app(
56.93/57.07	                                                               int,int,bit0,
56.93/57.07	                                                               app_encode_app(
56.93/57.07	                                                               int,int,bit0,
56.93/57.07	                                                               app_encode_app(
56.93/57.07	                                                               int,int,bit1,
56.93/57.07	                                                               pls)))))),m))),
56.93/57.07	                                                               one_one_int))),
56.93/57.07	                  t))).
56.93/57.07	tff('4', plain,
56.93/57.07	    app_encode_app(int, int, 
56.93/57.07	      app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
56.93/57.07	        app_encode_app(int, fun_int_int, plus_plus_int, 
56.93/57.07	          app_encode_app(nat, int, 
56.93/57.07	            app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
56.93/57.07	              hAPP_nat_int, 
56.93/57.07	              app_encode_app(int, fun_nat_int, power_power_int, s)), 
56.93/57.07	            app_encode_app(int, nat, number_number_of_nat, 
56.93/57.07	              app_encode_app(int, int, bit0, 
56.93/57.07	                app_encode_app(int, int, bit1, pls)))))), one_one_int)
56.93/57.07	     = app_encode_app(int, int, 
56.93/57.07	         app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
56.93/57.07	           app_encode_app(int, fun_int_int, times_times_int, 
56.93/57.07	             app_encode_app(int, int, 
56.93/57.07	               app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	                 hAPP_int_int, 
56.93/57.07	                 app_encode_app(int, fun_int_int, plus_plus_int, 
56.93/57.07	                   app_encode_app(int, int, 
56.93/57.07	                     app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	                       hAPP_int_int, 
56.93/57.07	                       app_encode_app(int, fun_int_int, times_times_int, 
56.93/57.07	                         app_encode_app(int, int, number_number_of_int, 
56.93/57.07	                           app_encode_app(int, int, bit0, 
56.93/57.07	                             app_encode_app(int, int, bit0, 
56.93/57.07	                               app_encode_app(int, int, bit1, pls)))))), m))), 
56.93/57.07	               one_one_int))), t),
56.93/57.07	    inference('cnf', [status(esa)], [zf_stmt_99])).
56.93/57.07	tff('5', plain,
56.93/57.07	    app_encode_app(int, int, 
56.93/57.07	      app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
56.93/57.07	        app_encode_app(int, fun_int_int, plus_plus_int, 
56.93/57.07	          app_encode_app(nat, int, 
56.93/57.07	            app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
56.93/57.07	              hAPP_nat_int, 
56.93/57.07	              app_encode_app(int, fun_nat_int, power_power_int, s)), 
56.93/57.07	            app_encode_app(int, nat, number_number_of_nat, 
56.93/57.07	              app_encode_app(int, int, bit0, 
56.93/57.07	                app_encode_app(int, int, bit1, zero_zero_int)))))), 
56.93/57.07	      one_one_int)
56.93/57.07	     = app_encode_app(int, int, 
56.93/57.07	         app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
56.93/57.07	           app_encode_app(int, fun_int_int, times_times_int, 
56.93/57.07	             app_encode_app(int, int, 
56.93/57.07	               app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	                 hAPP_int_int, 
56.93/57.07	                 app_encode_app(int, fun_int_int, plus_plus_int, 
56.93/57.07	                   app_encode_app(int, int, 
56.93/57.07	                     app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	                       hAPP_int_int, 
56.93/57.07	                       app_encode_app(int, fun_int_int, times_times_int, 
56.93/57.07	                         app_encode_app(int, int, bit0, 
56.93/57.07	                           app_encode_app(int, int, bit0, 
56.93/57.07	                             app_encode_app(int, int, bit1, zero_zero_int))))), 
56.93/57.07	                     m))), one_one_int))), t),
56.93/57.07	    inference('demod', [status(thm)], ['4', '1', '1', '2'])).
56.93/57.07	tff('6', plain,
56.93/57.07	    app_encode_app(bool, $o, hBOOL, 
56.93/57.07	      app_encode_app(int, bool, 
56.93/57.07	        app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
56.93/57.07	          hAPP_int_bool, 
56.93/57.07	          app_encode_app(int, fun_int_bool, 
56.93/57.07	            app_encode_app(fun_int_fun_int_bool, 
56.93/57.07	              app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
56.93/57.07	              ord_less_int), 
56.93/57.07	            app_encode_app(int, int, 
56.93/57.07	              app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	                hAPP_int_int, 
56.93/57.07	                app_encode_app(int, fun_int_int, plus_plus_int, 
56.93/57.07	                  app_encode_app(nat, int, 
56.93/57.07	                    app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
56.93/57.07	                      hAPP_nat_int, 
56.93/57.07	                      app_encode_app(int, fun_nat_int, power_power_int, s)), 
56.93/57.07	                    app_encode_app(int, nat, number_number_of_nat, 
56.93/57.07	                      app_encode_app(int, int, bit0, 
56.93/57.07	                        app_encode_app(int, int, bit1, zero_zero_int)))))), 
56.93/57.07	              one_one_int))), 
56.93/57.07	        app_encode_app(int, int, 
56.93/57.07	          app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	            hAPP_int_int, 
56.93/57.07	            app_encode_app(int, fun_int_int, times_times_int, 
56.93/57.07	              app_encode_app(int, int, 
56.93/57.07	                app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	                  hAPP_int_int, 
56.93/57.07	                  app_encode_app(int, fun_int_int, plus_plus_int, 
56.93/57.07	                    app_encode_app(int, int, 
56.93/57.07	                      app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	                        hAPP_int_int, 
56.93/57.07	                        app_encode_app(int, fun_int_int, times_times_int, 
56.93/57.07	                          app_encode_app(int, int, bit0, 
56.93/57.07	                            app_encode_app(int, int, bit0, 
56.93/57.07	                              app_encode_app(int, int, bit1, zero_zero_int))))), 
56.93/57.07	                      m))), one_one_int))), zero_zero_int))),
56.93/57.07	    inference('demod', [status(thm)], ['3', '5'])).
56.93/57.07	tff(zf_stmt_256, axiom,
56.93/57.07	  (one_one_int =
56.93/57.07	   app_encode_app(int,int,number_number_of_int,
56.93/57.07	                  app_encode_app(int,int,bit1,pls)))).
56.93/57.07	tff('7', plain,
56.93/57.07	    one_one_int
56.93/57.07	     = app_encode_app(int, int, number_number_of_int, 
56.93/57.07	         app_encode_app(int, int, bit1, pls)),
56.93/57.07	    inference('cnf', [status(esa)], [zf_stmt_256])).
56.93/57.07	tff('8', plain, one_one_int = app_encode_app(int, int, bit1, zero_zero_int),
56.93/57.07	    inference('demod', [status(thm)], ['7', '1', '2'])).
56.93/57.07	tff(zf_stmt_188, axiom,
56.93/57.07	  (![Z:int]:
56.93/57.07	     (app_encode_app(int,int,
56.93/57.07	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
56.93/57.07	                                    hAPP_int_int,
56.93/57.07	                                    app_encode_app(int,fun_int_int,
56.93/57.07	                                                   times_times_int,
56.93/57.07	                                                   one_one_int)),
56.93/57.07	                     Z) =
56.93/57.07	      Z))).
56.93/57.07	tff('9', plain,
56.93/57.07	    ![X160 : int]:
56.93/57.07	      app_encode_app(int, int, 
56.93/57.07	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
56.93/57.07	          app_encode_app(int, fun_int_int, times_times_int, one_one_int)), 
56.93/57.07	        X160)
56.93/57.07	       = X160,
56.93/57.07	    inference('cnf', [status(esa)], [zf_stmt_188])).
56.93/57.07	tff(zf_stmt_840, axiom,
56.93/57.07	  (![A_2:int,B_2:int,Ma:int]:
56.93/57.07	     (app_encode_app(bool,$o,hBOOL,
56.93/57.07	                     app_encode_app(int,bool,
56.93/57.07	                                    app_encode_app(fun_int_bool,
56.93/57.07	                                                   app_encode_fun(int,bool),
56.93/57.07	                                                   hAPP_int_bool,
56.93/57.07	                                                   app_encode_app(int,
56.93/57.07	                                                                  fun_int_bool,
56.93/57.07	                                                                  app_encode_app(
56.93/57.07	                                                                  int,
56.93/57.07	                                                                  app_encode_fun(
56.93/57.07	                                                                  int,
56.93/57.07	                                                                  fun_int_bool),
56.93/57.07	                                                                  zcong,A_2),
56.93/57.07	                                                                  B_2)),
56.93/57.07	                                    Ma)) <=>
56.93/57.07	      (?[K_2:int]:
56.93/57.07	         (B_2 =
56.93/57.07	          app_encode_app(int,int,
56.93/57.07	                         app_encode_app(fun_int_int,app_encode_fun(int,int),
56.93/57.07	                                        hAPP_int_int,
56.93/57.07	                                        app_encode_app(int,fun_int_int,
56.93/57.07	                                                       plus_plus_int,A_2)),
56.93/57.07	                         app_encode_app(int,int,
56.93/57.07	                                        app_encode_app(fun_int_int,
56.93/57.07	                                                       app_encode_fun(
56.93/57.07	                                                       int,int),hAPP_int_int,
56.93/57.07	                                                       app_encode_app(
56.93/57.07	                                                       int,fun_int_int,
56.93/57.07	                                                       times_times_int,Ma)),
56.93/57.07	                                        K_2))))))).
56.93/57.07	tff('10', plain,
56.93/57.07	    ![X1565 : int, X1566 : int, X1567 : int]:
56.93/57.07	      (X1567
56.93/57.07	        = app_encode_app(int, int, 
56.93/57.07	            app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	              hAPP_int_int, 
56.93/57.07	              app_encode_app(int, fun_int_int, plus_plus_int, X1565)), 
56.93/57.07	            app_encode_app(int, int, 
56.93/57.07	              app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	                hAPP_int_int, 
56.93/57.07	                app_encode_app(int, fun_int_int, times_times_int, X1566)), 
56.93/57.07	              sk_K_2(X1566, X1567, X1565)))
56.93/57.07	       | ~ app_encode_app(bool, $o, hBOOL, 
56.93/57.07	             app_encode_app(int, bool, 
56.93/57.07	               app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
56.93/57.07	                 hAPP_int_bool, 
56.93/57.07	                 app_encode_app(int, fun_int_bool, 
56.93/57.07	                   app_encode_app(int, app_encode_fun(int, fun_int_bool), 
56.93/57.07	                     zcong, X1565), X1567)), X1566))),
56.93/57.07	    inference('cnf', [status(esa)], [zf_stmt_840])).
56.93/57.07	tff('11', plain,
56.93/57.07	    ![X0 : int, X1 : int]:
56.93/57.07	      (X1
56.93/57.07	        = app_encode_app(int, int, 
56.93/57.07	            app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	              hAPP_int_int, 
56.93/57.07	              app_encode_app(int, fun_int_int, plus_plus_int, X0)), 
56.93/57.07	            sk_K_2(one_one_int, X1, X0))
56.93/57.07	       | ~ app_encode_app(bool, $o, hBOOL, 
56.93/57.07	             app_encode_app(int, bool, 
56.93/57.07	               app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
56.93/57.07	                 hAPP_int_bool, 
56.93/57.07	                 app_encode_app(int, fun_int_bool, 
56.93/57.07	                   app_encode_app(int, app_encode_fun(int, fun_int_bool), 
56.93/57.07	                     zcong, X0), X1)), one_one_int))),
56.93/57.07	    inference('sup+', [status(thm)], ['9', '10'])).
56.93/57.07	tff(zf_stmt_685, axiom,
56.93/57.07	  (![A:int,B:int]:
56.93/57.07	     app_encode_app(bool,$o,hBOOL,
56.93/57.07	                    app_encode_app(int,bool,
56.93/57.07	                                   app_encode_app(fun_int_bool,
56.93/57.07	                                                  app_encode_fun(int,bool),
56.93/57.07	                                                  hAPP_int_bool,
56.93/57.07	                                                  app_encode_app(int,
56.93/57.07	                                                                 fun_int_bool,
56.93/57.07	                                                                 app_encode_app(
56.93/57.07	                                                                 int,
56.93/57.07	                                                                 app_encode_fun(
56.93/57.07	                                                                 int,
56.93/57.07	                                                                 fun_int_bool),
56.93/57.07	                                                                 zcong,A),B)),
56.93/57.07	                                   one_one_int)))).
56.93/57.07	tff('12', plain,
56.93/57.07	    ![X1188 : int, X1189 : int]:
56.93/57.07	      app_encode_app(bool, $o, hBOOL, 
56.93/57.07	        app_encode_app(int, bool, 
56.93/57.07	          app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
56.93/57.07	            hAPP_int_bool, 
56.93/57.07	            app_encode_app(int, fun_int_bool, 
56.93/57.07	              app_encode_app(int, app_encode_fun(int, fun_int_bool), zcong, 
56.93/57.07	                X1188), X1189)), one_one_int)),
56.93/57.07	    inference('cnf', [status(esa)], [zf_stmt_685])).
56.93/57.07	tff('13', plain,
56.93/57.07	    ![X0 : int, X1 : int]:
56.93/57.07	      (X1
56.93/57.07	        = app_encode_app(int, int, 
56.93/57.07	            app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	              hAPP_int_int, 
56.93/57.07	              app_encode_app(int, fun_int_int, plus_plus_int, X0)), 
56.93/57.07	            sk_K_2(one_one_int, X1, X0))
56.93/57.07	       | ~ $true),
56.93/57.07	    inference('demod', [status(thm)], ['11', '12'])).
56.93/57.07	tff('14', plain,
56.93/57.07	    ![X0 : int, X1 : int]:
56.93/57.07	      X1
56.93/57.07	       = app_encode_app(int, int, 
56.93/57.07	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	             hAPP_int_int, 
56.93/57.07	             app_encode_app(int, fun_int_int, plus_plus_int, X0)), 
56.93/57.07	           sk_K_2(one_one_int, X1, X0)),
56.93/57.07	    inference('simplify', [status(thm)], ['13'])).
56.93/57.07	tff(zf_stmt_576, axiom,
56.93/57.07	  (![Ma:int,N:int]:
56.93/57.07	     ((app_encode_app(int,int,
56.93/57.07	                      app_encode_app(fun_int_int,app_encode_fun(int,int),
56.93/57.07	                                     hAPP_int_int,
56.93/57.07	                                     app_encode_app(int,fun_int_int,
56.93/57.07	                                                    times_times_int,Ma)),
56.93/57.07	                      N) =
56.93/57.07	       one_one_int) <=>
56.93/57.07	      (((Ma = one_one_int) & (N = one_one_int)) | 
56.93/57.07	       ((Ma = app_encode_app(int,int,number_number_of_int,min)) & 
56.93/57.07	        (N = app_encode_app(int,int,number_number_of_int,min))))))).
56.93/57.07	tff('15', plain,
56.93/57.07	    ![X930 : int, X932 : int]:
56.93/57.07	      (app_encode_app(int, int, 
56.93/57.07	         app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
56.93/57.07	           app_encode_app(int, fun_int_int, times_times_int, X930)), X932)
56.93/57.07	        = one_one_int
56.93/57.07	       | X930 != app_encode_app(int, int, number_number_of_int, min)
56.93/57.07	       | X932 != app_encode_app(int, int, number_number_of_int, min)),
56.93/57.07	    inference('cnf', [status(esa)], [zf_stmt_576])).
56.93/57.07	tff('16', plain,
56.93/57.07	    app_encode_app(int, int, 
56.93/57.07	      app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
56.93/57.07	        app_encode_app(int, fun_int_int, times_times_int, 
56.93/57.07	          app_encode_app(int, int, number_number_of_int, min))), 
56.93/57.07	      app_encode_app(int, int, number_number_of_int, min))
56.93/57.07	     = one_one_int,
56.93/57.07	    inference('simplify', [status(thm)], ['15'])).
56.93/57.07	tff('17', plain,
56.93/57.07	    app_encode_app(int, int, 
56.93/57.07	      app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
56.93/57.07	        app_encode_app(int, fun_int_int, times_times_int, min)), min)
56.93/57.07	     = one_one_int,
56.93/57.07	    inference('demod', [status(thm)], ['16', '2', '2'])).
56.93/57.07	tff(zf_stmt_257, axiom,
56.93/57.07	  (![K_1:int,L:int]:
56.93/57.07	     (app_encode_app(int,int,
56.93/57.07	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
56.93/57.07	                                    hAPP_int_int,
56.93/57.07	                                    app_encode_app(int,fun_int_int,
56.93/57.07	                                                   times_times_int,
56.93/57.07	                                                   app_encode_app(int,int,
56.93/57.07	                                                                  bit1,K_1))),
56.93/57.07	                     L) =
56.93/57.07	      app_encode_app(int,int,
56.93/57.07	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
56.93/57.07	                                    hAPP_int_int,
56.93/57.07	                                    app_encode_app(int,fun_int_int,
56.93/57.07	                                                   plus_plus_int,
56.93/57.07	                                                   app_encode_app(int,int,
56.93/57.07	                                                                  bit0,
56.93/57.07	                                                                  app_encode_app(
56.93/57.07	                                                                  int,int,
56.93/57.07	                                                                  app_encode_app(
56.93/57.07	                                                                  fun_int_int,
56.93/57.07	                                                                  app_encode_fun(
56.93/57.07	                                                                  int,int),
56.93/57.07	                                                                  hAPP_int_int,
56.93/57.07	                                                                  app_encode_app(
56.93/57.07	                                                                  int,
56.93/57.07	                                                                  fun_int_int,
56.93/57.07	                                                                  times_times_int,
56.93/57.07	                                                                  K_1)),L)))),
56.93/57.07	                     L)))).
56.93/57.07	tff('18', plain,
56.93/57.07	    ![X314 : int, X315 : int]:
56.93/57.07	      app_encode_app(int, int, 
56.93/57.07	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
56.93/57.07	          app_encode_app(int, fun_int_int, times_times_int, 
56.93/57.07	            app_encode_app(int, int, bit1, X314))), X315)
56.93/57.07	       = app_encode_app(int, int, 
56.93/57.07	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	             hAPP_int_int, 
56.93/57.07	             app_encode_app(int, fun_int_int, plus_plus_int, 
56.93/57.07	               app_encode_app(int, int, bit0, 
56.93/57.07	                 app_encode_app(int, int, 
56.93/57.07	                   app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	                     hAPP_int_int, 
56.93/57.07	                     app_encode_app(int, fun_int_int, times_times_int, X314)), 
56.93/57.07	                   X315)))), X315),
56.93/57.07	    inference('cnf', [status(esa)], [zf_stmt_257])).
56.93/57.07	tff(zf_stmt_230, axiom,
56.93/57.07	  (![Z:int,W:int]:
56.93/57.07	     (app_encode_app(int,int,
56.93/57.07	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
56.93/57.07	                                    hAPP_int_int,
56.93/57.07	                                    app_encode_app(int,fun_int_int,
56.93/57.07	                                                   plus_plus_int,Z)),
56.93/57.07	                     W) =
56.93/57.07	      app_encode_app(int,int,
56.93/57.07	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
56.93/57.07	                                    hAPP_int_int,
56.93/57.07	                                    app_encode_app(int,fun_int_int,
56.93/57.07	                                                   plus_plus_int,W)),
56.93/57.07	                     Z)))).
56.93/57.07	tff('19', plain,
56.93/57.07	    ![X265 : int, X266 : int]:
56.93/57.07	      app_encode_app(int, int, 
56.93/57.07	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
56.93/57.07	          app_encode_app(int, fun_int_int, plus_plus_int, X266)), X265)
56.93/57.07	       = app_encode_app(int, int, 
56.93/57.07	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	             hAPP_int_int, 
56.93/57.07	             app_encode_app(int, fun_int_int, plus_plus_int, X265)), X266),
56.93/57.07	    inference('cnf', [status(esa)], [zf_stmt_230])).
56.93/57.07	tff('20', plain,
56.93/57.07	    ![X314 : int, X315 : int]:
56.93/57.07	      app_encode_app(int, int, 
56.93/57.07	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
56.93/57.07	          app_encode_app(int, fun_int_int, times_times_int, 
56.93/57.07	            app_encode_app(int, int, bit1, X314))), X315)
56.93/57.07	       = app_encode_app(int, int, 
56.93/57.07	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	             hAPP_int_int, 
56.93/57.07	             app_encode_app(int, fun_int_int, plus_plus_int, X315)), 
56.93/57.07	           app_encode_app(int, int, bit0, 
56.93/57.07	             app_encode_app(int, int, 
56.93/57.07	               app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	                 hAPP_int_int, 
56.93/57.07	                 app_encode_app(int, fun_int_int, times_times_int, X314)), 
56.93/57.07	               X315))),
56.93/57.07	    inference('demod', [status(thm)], ['18', '19'])).
56.93/57.07	tff('21', plain,
56.93/57.07	    app_encode_app(int, int, 
56.93/57.07	      app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
56.93/57.07	        app_encode_app(int, fun_int_int, times_times_int, 
56.93/57.07	          app_encode_app(int, int, bit1, min))), min)
56.93/57.07	     = app_encode_app(int, int, 
56.93/57.07	         app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
56.93/57.07	           app_encode_app(int, fun_int_int, plus_plus_int, min)), 
56.93/57.07	         app_encode_app(int, int, bit0, one_one_int)),
56.93/57.07	    inference('sup+', [status(thm)], ['17', '20'])).
56.93/57.07	tff(zf_stmt_555, axiom, (app_encode_app(int,int,bit1,min) = min)).
56.93/57.07	tff('22', plain, app_encode_app(int, int, bit1, min) = min,
56.93/57.07	    inference('cnf', [status(esa)], [zf_stmt_555])).
56.93/57.07	tff(zf_stmt_330, axiom,
56.93/57.07	  (![K_1:int,L:int]:
56.93/57.07	     (app_encode_app(int,int,
56.93/57.07	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
56.93/57.07	                                    hAPP_int_int,
56.93/57.07	                                    app_encode_app(int,fun_int_int,
56.93/57.07	                                                   plus_plus_int,
56.93/57.07	                                                   app_encode_app(int,int,
56.93/57.07	                                                                  bit0,K_1))),
56.93/57.07	                     app_encode_app(int,int,bit1,L)) =
56.93/57.07	      app_encode_app(int,int,bit1,
56.93/57.07	                     app_encode_app(int,int,
56.93/57.07	                                    app_encode_app(fun_int_int,
56.93/57.07	                                                   app_encode_fun(int,int),
56.93/57.07	                                                   hAPP_int_int,
56.93/57.07	                                                   app_encode_app(int,
56.93/57.07	                                                                  fun_int_int,
56.93/57.07	                                                                  plus_plus_int,
56.93/57.07	                                                                  K_1)),
56.93/57.07	                                    L))))).
56.93/57.07	tff('23', plain,
56.93/57.07	    ![X418 : int, X419 : int]:
56.93/57.07	      app_encode_app(int, int, 
56.93/57.07	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
56.93/57.07	          app_encode_app(int, fun_int_int, plus_plus_int, 
56.93/57.07	            app_encode_app(int, int, bit0, X418))), 
56.93/57.07	        app_encode_app(int, int, bit1, X419))
56.93/57.07	       = app_encode_app(int, int, bit1, 
56.93/57.07	           app_encode_app(int, int, 
56.93/57.07	             app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	               hAPP_int_int, 
56.93/57.07	               app_encode_app(int, fun_int_int, plus_plus_int, X418)), X419)),
56.93/57.07	    inference('cnf', [status(esa)], [zf_stmt_330])).
56.93/57.07	tff('24', plain,
56.93/57.07	    ![X0 : int]:
56.93/57.07	      app_encode_app(int, int, 
56.93/57.07	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
56.93/57.07	          app_encode_app(int, fun_int_int, plus_plus_int, 
56.93/57.07	            app_encode_app(int, int, bit0, X0))), min)
56.93/57.07	       = app_encode_app(int, int, bit1, 
56.93/57.07	           app_encode_app(int, int, 
56.93/57.07	             app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	               hAPP_int_int, 
56.93/57.07	               app_encode_app(int, fun_int_int, plus_plus_int, X0)), min)),
56.93/57.07	    inference('sup+', [status(thm)], ['22', '23'])).
56.93/57.07	tff('25', plain,
56.93/57.07	    ![X0 : int]:
56.93/57.07	      app_encode_app(int, int, 
56.93/57.07	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
56.93/57.07	          app_encode_app(int, fun_int_int, plus_plus_int, min)), 
56.93/57.07	        app_encode_app(int, int, bit0, X0))
56.93/57.07	       = app_encode_app(int, int, bit1, 
56.93/57.07	           app_encode_app(int, int, 
56.93/57.07	             app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	               hAPP_int_int, 
56.93/57.07	               app_encode_app(int, fun_int_int, plus_plus_int, X0)), min)),
56.93/57.07	    inference('demod', [status(thm)], ['24', '19'])).
56.93/57.07	tff('26', plain,
56.93/57.07	    app_encode_app(int, int, 
56.93/57.07	      app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
56.93/57.07	        app_encode_app(int, fun_int_int, times_times_int, min)), min)
56.93/57.07	     = app_encode_app(int, int, bit1, 
56.93/57.07	         app_encode_app(int, int, 
56.93/57.07	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	             hAPP_int_int, 
56.93/57.07	             app_encode_app(int, fun_int_int, plus_plus_int, one_one_int)), 
56.93/57.07	           min)),
56.93/57.07	    inference('demod', [status(thm)], ['21', '22', '25'])).
56.93/57.07	tff('27', plain,
56.93/57.07	    one_one_int
56.93/57.07	     = app_encode_app(int, int, bit1, 
56.93/57.07	         app_encode_app(int, int, 
56.93/57.07	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	             hAPP_int_int, 
56.93/57.07	             app_encode_app(int, fun_int_int, plus_plus_int, one_one_int)), 
56.93/57.07	           min)),
56.93/57.07	    inference('demod', [status(thm)], ['26', '17'])).
56.93/57.07	tff(zf_stmt_217, axiom,
56.93/57.07	  (![K:int,L_1:int]:
56.93/57.07	     ((app_encode_app(int,int,bit1,K) = app_encode_app(int,int,bit1,L_1)) <=>
56.93/57.07	      (K = L_1)))).
56.93/57.07	tff('28', plain,
56.93/57.07	    ![X227 : int, X228 : int]:
56.93/57.07	      (X228 = X227
56.93/57.07	       | app_encode_app(int, int, bit1, X228)
56.93/57.07	          != app_encode_app(int, int, bit1, X227)),
56.93/57.07	    inference('cnf', [status(esa)], [zf_stmt_217])).
56.93/57.07	tff('29', plain,
56.93/57.07	    ![X0 : int]:
56.93/57.07	      (one_one_int != app_encode_app(int, int, bit1, X0) | zero_zero_int = X0),
56.93/57.07	    inference('sup-', [status(thm)], ['8', '28'])).
56.93/57.07	tff('30', plain,
56.93/57.07	    (one_one_int != one_one_int
56.93/57.07	     | zero_zero_int
56.93/57.07	        = app_encode_app(int, int, 
56.93/57.07	            app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	              hAPP_int_int, 
56.93/57.07	              app_encode_app(int, fun_int_int, plus_plus_int, one_one_int)), 
56.93/57.07	            min)),
56.93/57.07	    inference('sup-', [status(thm)], ['27', '29'])).
56.93/57.07	tff('31', plain,
56.93/57.07	    zero_zero_int
56.93/57.07	     = app_encode_app(int, int, 
56.93/57.07	         app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
56.93/57.07	           app_encode_app(int, fun_int_int, plus_plus_int, one_one_int)), 
56.93/57.07	         min),
56.93/57.07	    inference('simplify', [status(thm)], ['30'])).
56.93/57.07	tff(zf_stmt_228, axiom,
56.93/57.07	  (![Z1:int,Z2:int,Z3:int]:
56.93/57.07	     (app_encode_app(int,int,
56.93/57.07	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
56.93/57.07	                                    hAPP_int_int,
56.93/57.07	                                    app_encode_app(int,fun_int_int,
56.93/57.07	                                                   plus_plus_int,
56.93/57.07	                                                   app_encode_app(int,int,
56.93/57.07	                                                                  app_encode_app(
56.93/57.07	                                                                  fun_int_int,
56.93/57.07	                                                                  app_encode_fun(
56.93/57.07	                                                                  int,int),
56.93/57.07	                                                                  hAPP_int_int,
56.93/57.07	                                                                  app_encode_app(
56.93/57.07	                                                                  int,
56.93/57.07	                                                                  fun_int_int,
56.93/57.07	                                                                  plus_plus_int,
56.93/57.07	                                                                  Z1)),Z2))),
56.93/57.07	                     Z3) =
56.93/57.07	      app_encode_app(int,int,
56.93/57.07	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
56.93/57.07	                                    hAPP_int_int,
56.93/57.07	                                    app_encode_app(int,fun_int_int,
56.93/57.07	                                                   plus_plus_int,Z1)),
56.93/57.07	                     app_encode_app(int,int,
56.93/57.07	                                    app_encode_app(fun_int_int,
56.93/57.07	                                                   app_encode_fun(int,int),
56.93/57.07	                                                   hAPP_int_int,
56.93/57.07	                                                   app_encode_app(int,
56.93/57.07	                                                                  fun_int_int,
56.93/57.07	                                                                  plus_plus_int,
56.93/57.07	                                                                  Z2)),
56.93/57.07	                                    Z3))))).
56.93/57.07	tff('32', plain,
56.93/57.07	    ![X259 : int, X260 : int, X261 : int]:
56.93/57.07	      app_encode_app(int, int, 
56.93/57.07	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
56.93/57.07	          app_encode_app(int, fun_int_int, plus_plus_int, 
56.93/57.07	            app_encode_app(int, int, 
56.93/57.07	              app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	                hAPP_int_int, 
56.93/57.07	                app_encode_app(int, fun_int_int, plus_plus_int, X259)), X260))), 
56.93/57.07	        X261)
56.93/57.07	       = app_encode_app(int, int, 
56.93/57.07	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	             hAPP_int_int, 
56.93/57.07	             app_encode_app(int, fun_int_int, plus_plus_int, X259)), 
56.93/57.07	           app_encode_app(int, int, 
56.93/57.07	             app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	               hAPP_int_int, 
56.93/57.07	               app_encode_app(int, fun_int_int, plus_plus_int, X260)), X261)),
56.93/57.07	    inference('cnf', [status(esa)], [zf_stmt_228])).
56.93/57.07	tff('33', plain,
56.93/57.07	    ![X0 : int]:
56.93/57.07	      app_encode_app(int, int, 
56.93/57.07	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
56.93/57.07	          app_encode_app(int, fun_int_int, plus_plus_int, zero_zero_int)), 
56.93/57.07	        X0)
56.93/57.07	       = app_encode_app(int, int, 
56.93/57.07	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	             hAPP_int_int, 
56.93/57.07	             app_encode_app(int, fun_int_int, plus_plus_int, one_one_int)), 
56.93/57.07	           app_encode_app(int, int, 
56.93/57.07	             app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	               hAPP_int_int, 
56.93/57.07	               app_encode_app(int, fun_int_int, plus_plus_int, min)), X0)),
56.93/57.07	    inference('sup+', [status(thm)], ['31', '32'])).
56.93/57.07	tff(zf_stmt_276, axiom,
56.93/57.07	  (![K_1:int]:
56.93/57.07	     (app_encode_app(int,int,
56.93/57.07	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
56.93/57.07	                                    hAPP_int_int,
56.93/57.07	                                    app_encode_app(int,fun_int_int,
56.93/57.07	                                                   plus_plus_int,pls)),
56.93/57.07	                     K_1) =
56.93/57.07	      K_1))).
56.93/57.07	tff('34', plain,
56.93/57.07	    ![X345 : int]:
56.93/57.07	      app_encode_app(int, int, 
56.93/57.07	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
56.93/57.07	          app_encode_app(int, fun_int_int, plus_plus_int, pls)), X345)
56.93/57.07	       = X345,
56.93/57.07	    inference('cnf', [status(esa)], [zf_stmt_276])).
56.93/57.07	tff('35', plain,
56.93/57.07	    ![X345 : int]:
56.93/57.07	      app_encode_app(int, int, 
56.93/57.07	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
56.93/57.07	          app_encode_app(int, fun_int_int, plus_plus_int, zero_zero_int)), 
56.93/57.07	        X345)
56.93/57.07	       = X345,
56.93/57.07	    inference('demod', [status(thm)], ['34', '1'])).
56.93/57.07	tff('36', plain,
56.93/57.07	    ![X0 : int]:
56.93/57.07	      X0
56.93/57.07	       = app_encode_app(int, int, 
56.93/57.07	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	             hAPP_int_int, 
56.93/57.07	             app_encode_app(int, fun_int_int, plus_plus_int, one_one_int)), 
56.93/57.07	           app_encode_app(int, int, 
56.93/57.07	             app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	               hAPP_int_int, 
56.93/57.07	               app_encode_app(int, fun_int_int, plus_plus_int, min)), X0)),
56.93/57.07	    inference('demod', [status(thm)], ['33', '35'])).
56.93/57.07	tff('37', plain,
56.93/57.07	    ![X0 : int]:
56.93/57.07	      sk_K_2(one_one_int, X0, min)
56.93/57.07	       = app_encode_app(int, int, 
56.93/57.07	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	             hAPP_int_int, 
56.93/57.07	             app_encode_app(int, fun_int_int, plus_plus_int, one_one_int)), 
56.93/57.07	           X0),
56.93/57.07	    inference('sup+', [status(thm)], ['14', '36'])).
56.93/57.07	tff(zf_stmt_278, axiom,
56.93/57.07	  (![K_1:int]:
56.93/57.07	     (app_encode_app(int,int,bit0,K_1) =
56.93/57.07	      app_encode_app(int,int,
56.93/57.07	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
56.93/57.07	                                    hAPP_int_int,
56.93/57.07	                                    app_encode_app(int,fun_int_int,
56.93/57.07	                                                   plus_plus_int,K_1)),
56.93/57.07	                     K_1)))).
56.93/57.07	tff('38', plain,
56.93/57.07	    ![X348 : int]:
56.93/57.07	      app_encode_app(int, int, bit0, X348)
56.93/57.07	       = app_encode_app(int, int, 
56.93/57.07	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	             hAPP_int_int, 
56.93/57.07	             app_encode_app(int, fun_int_int, plus_plus_int, X348)), X348),
56.93/57.07	    inference('cnf', [status(esa)], [zf_stmt_278])).
56.93/57.07	tff('39', plain,
56.93/57.07	    app_encode_app(int, int, bit0, one_one_int)
56.93/57.07	     = sk_K_2(one_one_int, one_one_int, min),
56.93/57.07	    inference('sup+', [status(thm)], ['37', '38'])).
56.93/57.07	tff('40', plain,
56.93/57.07	    ![X0 : int]:
56.93/57.07	      app_encode_app(int, int, 
56.93/57.07	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
56.93/57.07	          app_encode_app(int, fun_int_int, plus_plus_int, X0)), one_one_int)
56.93/57.07	       = sk_K_2(one_one_int, X0, min),
56.93/57.07	    inference('sup+', [status(thm)], ['37', '19'])).
56.93/57.07	tff(zf_stmt_185, axiom,
56.93/57.07	  (![K_1:int,L:int]:
56.93/57.07	     (app_encode_app(int,int,
56.93/57.07	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
56.93/57.07	                                    hAPP_int_int,
56.93/57.07	                                    app_encode_app(int,fun_int_int,
56.93/57.07	                                                   times_times_int,
56.93/57.07	                                                   app_encode_app(int,int,
56.93/57.07	                                                                  bit0,K_1))),
56.93/57.07	                     L) =
56.93/57.07	      app_encode_app(int,int,bit0,
56.93/57.07	                     app_encode_app(int,int,
56.93/57.07	                                    app_encode_app(fun_int_int,
56.93/57.07	                                                   app_encode_fun(int,int),
56.93/57.07	                                                   hAPP_int_int,
56.93/57.07	                                                   app_encode_app(int,
56.93/57.07	                                                                  fun_int_int,
56.93/57.07	                                                                  times_times_int,
56.93/57.07	                                                                  K_1)),
56.93/57.07	                                    L))))).
56.93/57.07	tff('41', plain,
56.93/57.07	    ![X154 : int, X155 : int]:
56.93/57.07	      app_encode_app(int, int, 
56.93/57.07	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
56.93/57.07	          app_encode_app(int, fun_int_int, times_times_int, 
56.93/57.07	            app_encode_app(int, int, bit0, X154))), X155)
56.93/57.07	       = app_encode_app(int, int, bit0, 
56.93/57.07	           app_encode_app(int, int, 
56.93/57.07	             app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	               hAPP_int_int, 
56.93/57.07	               app_encode_app(int, fun_int_int, times_times_int, X154)), 
56.93/57.07	             X155)),
56.93/57.07	    inference('cnf', [status(esa)], [zf_stmt_185])).
56.93/57.07	tff(zf_stmt_514, axiom,
56.93/57.07	  (![M_10:int,A_81:int]:
56.93/57.07	     (app_encode_app(int,int,
56.93/57.07	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
56.93/57.07	                                    hAPP_int_int,
56.93/57.07	                                    app_encode_app(int,fun_int_int,
56.93/57.07	                                                   plus_plus_int,M_10)),
56.93/57.07	                     app_encode_app(int,int,
56.93/57.07	                                    app_encode_app(fun_int_int,
56.93/57.07	                                                   app_encode_fun(int,int),
56.93/57.07	                                                   hAPP_int_int,
56.93/57.07	                                                   app_encode_app(int,
56.93/57.07	                                                                  fun_int_int,
56.93/57.07	                                                                  times_times_int,
56.93/57.07	                                                                  A_81)),
56.93/57.07	                                    M_10)) =
56.93/57.07	      app_encode_app(int,int,
56.93/57.07	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
56.93/57.07	                                    hAPP_int_int,
56.93/57.07	                                    app_encode_app(int,fun_int_int,
56.93/57.07	                                                   times_times_int,
56.93/57.07	                                                   app_encode_app(int,int,
56.93/57.07	                                                                  app_encode_app(
56.93/57.07	                                                                  fun_int_int,
56.93/57.07	                                                                  app_encode_fun(
56.93/57.07	                                                                  int,int),
56.93/57.07	                                                                  hAPP_int_int,
56.93/57.07	                                                                  app_encode_app(
56.93/57.07	                                                                  int,
56.93/57.07	                                                                  fun_int_int,
56.93/57.07	                                                                  plus_plus_int,
56.93/57.07	                                                                  A_81)),
56.93/57.07	                                                                  one_one_int))),
56.93/57.07	                     M_10)))).
56.93/57.07	tff('42', plain,
56.93/57.07	    ![X816 : int, X817 : int]:
56.93/57.07	      app_encode_app(int, int, 
56.93/57.07	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
56.93/57.07	          app_encode_app(int, fun_int_int, plus_plus_int, X817)), 
56.93/57.07	        app_encode_app(int, int, 
56.93/57.07	          app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	            hAPP_int_int, 
56.93/57.07	            app_encode_app(int, fun_int_int, times_times_int, X816)), X817))
56.93/57.07	       = app_encode_app(int, int, 
56.93/57.07	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	             hAPP_int_int, 
56.93/57.07	             app_encode_app(int, fun_int_int, times_times_int, 
56.93/57.07	               app_encode_app(int, int, 
56.93/57.07	                 app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	                   hAPP_int_int, 
56.93/57.07	                   app_encode_app(int, fun_int_int, plus_plus_int, X816)), 
56.93/57.07	                 one_one_int))), X817),
56.93/57.07	    inference('cnf', [status(esa)], [zf_stmt_514])).
56.93/57.07	tff('43', plain,
56.93/57.07	    ![X0 : int]:
56.93/57.07	      app_encode_app(int, int, 
56.93/57.07	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
56.93/57.07	          app_encode_app(int, fun_int_int, plus_plus_int, X0)), 
56.93/57.07	        app_encode_app(int, int, 
56.93/57.07	          app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	            hAPP_int_int, 
56.93/57.07	            app_encode_app(int, fun_int_int, times_times_int, one_one_int)), 
56.93/57.07	          X0))
56.93/57.07	       = app_encode_app(int, int, 
56.93/57.07	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	             hAPP_int_int, 
56.93/57.07	             app_encode_app(int, fun_int_int, times_times_int, 
56.93/57.07	               sk_K_2(one_one_int, one_one_int, min))), X0),
56.93/57.07	    inference('sup+', [status(thm)], ['37', '42'])).
56.93/57.07	tff('44', plain,
56.93/57.07	    ![X0 : int]:
56.93/57.07	      app_encode_app(int, int, 
56.93/57.07	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
56.93/57.07	          app_encode_app(int, fun_int_int, plus_plus_int, X0)), X0)
56.93/57.07	       = app_encode_app(int, int, 
56.93/57.07	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	             hAPP_int_int, 
56.93/57.07	             app_encode_app(int, fun_int_int, times_times_int, 
56.93/57.07	               sk_K_2(one_one_int, one_one_int, min))), X0),
56.93/57.07	    inference('demod', [status(thm)], ['43', '9'])).
56.93/57.07	tff('45', plain,
56.93/57.07	    ![X0 : int]:
56.93/57.07	      app_encode_app(int, int, bit0, X0)
56.93/57.07	       = app_encode_app(int, int, 
56.93/57.07	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	             hAPP_int_int, 
56.93/57.07	             app_encode_app(int, fun_int_int, times_times_int, 
56.93/57.07	               sk_K_2(one_one_int, one_one_int, min))), X0),
56.93/57.07	    inference('demod', [status(thm)], ['44', '38'])).
56.93/57.07	tff(zf_stmt_332, axiom,
56.93/57.07	  (![K_1:int]:
56.93/57.07	     (app_encode_app(int,int,bit1,K_1) =
56.93/57.07	      app_encode_app(int,int,
56.93/57.07	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
56.93/57.07	                                    hAPP_int_int,
56.93/57.07	                                    app_encode_app(int,fun_int_int,
56.93/57.07	                                                   plus_plus_int,
56.93/57.07	                                                   app_encode_app(int,int,
56.93/57.07	                                                                  app_encode_app(
56.93/57.07	                                                                  fun_int_int,
56.93/57.07	                                                                  app_encode_fun(
56.93/57.07	                                                                  int,int),
56.93/57.07	                                                                  hAPP_int_int,
56.93/57.07	                                                                  app_encode_app(
56.93/57.07	                                                                  int,
56.93/57.07	                                                                  fun_int_int,
56.93/57.07	                                                                  plus_plus_int,
56.93/57.07	                                                                  one_one_int)),
56.93/57.07	                                                                  K_1))),
56.93/57.07	                     K_1)))).
56.93/57.07	tff('46', plain,
56.93/57.07	    ![X420 : int]:
56.93/57.07	      app_encode_app(int, int, bit1, X420)
56.93/57.07	       = app_encode_app(int, int, 
56.93/57.07	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	             hAPP_int_int, 
56.93/57.07	             app_encode_app(int, fun_int_int, plus_plus_int, 
56.93/57.07	               app_encode_app(int, int, 
56.93/57.07	                 app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	                   hAPP_int_int, 
56.93/57.07	                   app_encode_app(int, fun_int_int, plus_plus_int, 
56.93/57.07	                     one_one_int)), X420))), X420),
56.93/57.07	    inference('cnf', [status(esa)], [zf_stmt_332])).
56.93/57.07	tff('47', plain,
56.93/57.07	    ![X420 : int]:
56.93/57.07	      app_encode_app(int, int, bit1, X420)
56.93/57.07	       = app_encode_app(int, int, 
56.93/57.07	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	             hAPP_int_int, 
56.93/57.07	             app_encode_app(int, fun_int_int, plus_plus_int, X420)), 
56.93/57.07	           app_encode_app(int, int, 
56.93/57.07	             app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	               hAPP_int_int, 
56.93/57.07	               app_encode_app(int, fun_int_int, plus_plus_int, one_one_int)), 
56.93/57.07	             X420)),
56.93/57.07	    inference('demod', [status(thm)], ['46', '19'])).
56.93/57.07	tff(zf_stmt_229, axiom,
56.93/57.07	  (![X_1:int,Y:int,Z:int]:
56.93/57.07	     (app_encode_app(int,int,
56.93/57.07	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
56.93/57.07	                                    hAPP_int_int,
56.93/57.07	                                    app_encode_app(int,fun_int_int,
56.93/57.07	                                                   plus_plus_int,X_1)),
56.93/57.07	                     app_encode_app(int,int,
56.93/57.07	                                    app_encode_app(fun_int_int,
56.93/57.07	                                                   app_encode_fun(int,int),
56.93/57.07	                                                   hAPP_int_int,
56.93/57.07	                                                   app_encode_app(int,
56.93/57.07	                                                                  fun_int_int,
56.93/57.07	                                                                  plus_plus_int,
56.93/57.07	                                                                  Y)),
56.93/57.07	                                    Z)) =
56.93/57.07	      app_encode_app(int,int,
56.93/57.07	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
56.93/57.07	                                    hAPP_int_int,
56.93/57.07	                                    app_encode_app(int,fun_int_int,
56.93/57.07	                                                   plus_plus_int,Y)),
56.93/57.07	                     app_encode_app(int,int,
56.93/57.07	                                    app_encode_app(fun_int_int,
56.93/57.07	                                                   app_encode_fun(int,int),
56.93/57.07	                                                   hAPP_int_int,
56.93/57.07	                                                   app_encode_app(int,
56.93/57.07	                                                                  fun_int_int,
56.93/57.07	                                                                  plus_plus_int,
56.93/57.07	                                                                  X_1)),
56.93/57.07	                                    Z))))).
56.93/57.07	tff('48', plain,
56.93/57.07	    ![X262 : int, X263 : int, X264 : int]:
56.93/57.07	      app_encode_app(int, int, 
56.93/57.07	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
56.93/57.07	          app_encode_app(int, fun_int_int, plus_plus_int, X263)), 
56.93/57.07	        app_encode_app(int, int, 
56.93/57.07	          app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	            hAPP_int_int, 
56.93/57.07	            app_encode_app(int, fun_int_int, plus_plus_int, X262)), X264))
56.93/57.07	       = app_encode_app(int, int, 
56.93/57.07	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	             hAPP_int_int, 
56.93/57.07	             app_encode_app(int, fun_int_int, plus_plus_int, X262)), 
56.93/57.07	           app_encode_app(int, int, 
56.93/57.07	             app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	               hAPP_int_int, 
56.93/57.07	               app_encode_app(int, fun_int_int, plus_plus_int, X263)), X264)),
56.93/57.07	    inference('cnf', [status(esa)], [zf_stmt_229])).
56.93/57.07	tff('49', plain,
56.93/57.07	    ![X0 : int]:
56.93/57.07	      app_encode_app(int, int, bit1, X0)
56.93/57.07	       = app_encode_app(int, int, 
56.93/57.07	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	             hAPP_int_int, 
56.93/57.07	             app_encode_app(int, fun_int_int, plus_plus_int, one_one_int)), 
56.93/57.07	           app_encode_app(int, int, 
56.93/57.07	             app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	               hAPP_int_int, 
56.93/57.07	               app_encode_app(int, fun_int_int, plus_plus_int, X0)), X0)),
56.93/57.07	    inference('sup+', [status(thm)], ['47', '48'])).
56.93/57.07	tff('50', plain,
56.93/57.07	    ![X0 : int]:
56.93/57.07	      app_encode_app(int, int, bit1, X0)
56.93/57.07	       = app_encode_app(int, int, 
56.93/57.07	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	             hAPP_int_int, 
56.93/57.07	             app_encode_app(int, fun_int_int, plus_plus_int, one_one_int)), 
56.93/57.07	           app_encode_app(int, int, bit0, X0)),
56.93/57.07	    inference('demod', [status(thm)], ['49', '38'])).
56.93/57.07	tff('51', plain,
56.93/57.07	    ![X0 : int]:
56.93/57.07	      app_encode_app(int, int, bit1, X0)
56.93/57.07	       = sk_K_2(one_one_int, app_encode_app(int, int, bit0, X0), min),
56.93/57.07	    inference('demod', [status(thm)], ['50', '37'])).
56.93/57.07	tff(zf_stmt_131, axiom,
56.93/57.07	  (![Z:int,W:int]:
56.93/57.07	     (app_encode_app(int,int,
56.93/57.07	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
56.93/57.07	                                    hAPP_int_int,
56.93/57.07	                                    app_encode_app(int,fun_int_int,
56.93/57.07	                                                   times_times_int,Z)),
56.93/57.07	                     W) =
56.93/57.07	      app_encode_app(int,int,
56.93/57.07	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
56.93/57.07	                                    hAPP_int_int,
56.93/57.07	                                    app_encode_app(int,fun_int_int,
56.93/57.07	                                                   times_times_int,W)),
56.93/57.07	                     Z)))).
56.93/57.07	tff('52', plain,
56.93/57.07	    ![X32 : int, X33 : int]:
56.93/57.07	      app_encode_app(int, int, 
56.93/57.07	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
56.93/57.07	          app_encode_app(int, fun_int_int, times_times_int, X33)), X32)
56.93/57.07	       = app_encode_app(int, int, 
56.93/57.07	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	             hAPP_int_int, 
56.93/57.07	             app_encode_app(int, fun_int_int, times_times_int, X32)), X33),
56.93/57.07	    inference('cnf', [status(esa)], [zf_stmt_131])).
56.93/57.07	tff(zf_stmt_184, axiom,
56.93/57.07	  (![W:int]:
56.93/57.07	     (app_encode_app(int,int,
56.93/57.07	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
56.93/57.07	                                    hAPP_int_int,
56.93/57.07	                                    app_encode_app(int,fun_int_int,
56.93/57.07	                                                   times_times_int,pls)),
56.93/57.07	                     W) =
56.93/57.07	      pls))).
56.93/57.07	tff('53', plain,
56.93/57.07	    ![X153 : int]:
56.93/57.07	      app_encode_app(int, int, 
56.93/57.07	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
56.93/57.07	          app_encode_app(int, fun_int_int, times_times_int, pls)), X153)
56.93/57.07	       = pls,
56.93/57.07	    inference('cnf', [status(esa)], [zf_stmt_184])).
56.93/57.07	tff('54', plain,
56.93/57.07	    ![X153 : int]:
56.93/57.07	      app_encode_app(int, int, 
56.93/57.07	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
56.93/57.07	          app_encode_app(int, fun_int_int, times_times_int, zero_zero_int)), 
56.93/57.07	        X153)
56.93/57.07	       = zero_zero_int,
56.93/57.07	    inference('demod', [status(thm)], ['53', '1', '1'])).
56.93/57.07	tff(zf_stmt_1297, axiom,
56.93/57.07	  (![P:fun_int_fun_int_bool,Q:int,R:int]:
56.93/57.07	     (app_encode_app(int,bool,
56.93/57.07	                     app_encode_app(fun_int_bool,app_encode_fun(int,bool),
56.93/57.07	                                    hAPP_int_bool,
56.93/57.07	                                    app_encode_app(int,fun_int_bool,
56.93/57.07	                                                   app_encode_app(fun_int_fun_int_bool,
56.93/57.07	                                                                  app_encode_fun(
56.93/57.07	                                                                  int,
56.93/57.07	                                                                  fun_int_bool),
56.93/57.07	                                                                  cOMBC_int_int_bool,
56.93/57.07	                                                                  P),
56.93/57.07	                                                   Q)),
56.93/57.07	                     R) =
56.93/57.07	      app_encode_app(int,bool,
56.93/57.07	                     app_encode_app(fun_int_bool,app_encode_fun(int,bool),
56.93/57.07	                                    hAPP_int_bool,
56.93/57.07	                                    app_encode_app(int,fun_int_bool,
56.93/57.07	                                                   app_encode_app(fun_int_fun_int_bool,
56.93/57.07	                                                                  app_encode_fun(
56.93/57.07	                                                                  int,
56.93/57.07	                                                                  fun_int_bool),
56.93/57.07	                                                                  hAPP_i1948725293t_bool,
56.93/57.07	                                                                  P),
56.93/57.07	                                                   R)),
56.93/57.07	                     Q)))).
56.93/57.07	tff('55', plain,
56.93/57.07	    ![X2790 : fun_int_fun_int_bool, X2791 : int, X2792 : int]:
56.93/57.07	      app_encode_app(int, bool, 
56.93/57.07	        app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
56.93/57.07	          hAPP_int_bool, 
56.93/57.07	          app_encode_app(int, fun_int_bool, 
56.93/57.07	            app_encode_app(fun_int_fun_int_bool, 
56.93/57.07	              app_encode_fun(int, fun_int_bool), cOMBC_int_int_bool, X2790), 
56.93/57.07	            X2792)), X2791)
56.93/57.07	       = app_encode_app(int, bool, 
56.93/57.07	           app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
56.93/57.07	             hAPP_int_bool, 
56.93/57.07	             app_encode_app(int, fun_int_bool, 
56.93/57.07	               app_encode_app(fun_int_fun_int_bool, 
56.93/57.07	                 app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
56.93/57.07	                 X2790), X2791)), X2792),
56.93/57.07	    inference('cnf', [status(esa)], [zf_stmt_1297])).
56.93/57.07	tff('56', plain,
56.93/57.07	    app_encode_app(bool, $o, hBOOL, 
56.93/57.07	      app_encode_app(int, bool, 
56.93/57.07	        app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
56.93/57.07	          hAPP_int_bool, 
56.93/57.07	          app_encode_app(int, fun_int_bool, 
56.93/57.07	            app_encode_app(fun_int_fun_int_bool, 
56.93/57.07	              app_encode_fun(int, fun_int_bool), cOMBC_int_int_bool, 
56.93/57.07	              ord_less_int), zero_zero_int)), 
56.93/57.07	        sk_K_2(one_one_int, 
56.93/57.07	          app_encode_app(nat, int, 
56.93/57.07	            app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
56.93/57.07	              hAPP_nat_int, 
56.93/57.07	              app_encode_app(int, fun_nat_int, power_power_int, s)), 
56.93/57.07	            app_encode_app(int, nat, number_number_of_nat, 
56.93/57.07	              sk_K_2(one_one_int, one_one_int, min))), min))),
56.93/57.07	    inference('demod', [status(thm)],
56.93/57.07	              ['6', '8', '39', '40', '8', '39', '41', '45', '40', '51', 
56.93/57.07	               '52', '54', '55'])).
56.93/57.07	tff(zf_stmt_1300, conjecture,
56.93/57.07	  (app_encode_app(bool,$o,hBOOL,
56.93/57.07	                  app_encode_app(int,bool,
56.93/57.07	                                 app_encode_app(fun_int_bool,
56.93/57.07	                                                app_encode_fun(int,bool),
56.93/57.07	                                                hAPP_int_bool,
56.93/57.07	                                                app_encode_app(int,
56.93/57.07	                                                               fun_int_bool,
56.93/57.07	                                                               app_encode_app(
56.93/57.07	                                                               fun_int_fun_int_bool,
56.93/57.07	                                                               app_encode_fun(
56.93/57.07	                                                               int,
56.93/57.07	                                                               fun_int_bool),
56.93/57.07	                                                               hAPP_i1948725293t_bool,
56.93/57.07	                                                               ord_less_int),
56.93/57.07	                                                               app_encode_app(
56.93/57.07	                                                               int,int,
56.93/57.07	                                                               app_encode_app(
56.93/57.07	                                                               fun_int_int,
56.93/57.07	                                                               app_encode_fun(
56.93/57.07	                                                               int,int),
56.93/57.07	                                                               hAPP_int_int,
56.93/57.07	                                                               app_encode_app(
56.93/57.07	                                                               int,
56.93/57.07	                                                               fun_int_int,
56.93/57.07	                                                               plus_plus_int,
56.93/57.07	                                                               app_encode_app(
56.93/57.07	                                                               nat,int,
56.93/57.07	                                                               app_encode_app(
56.93/57.07	                                                               fun_nat_int,
56.93/57.07	                                                               app_encode_fun(
56.93/57.07	                                                               nat,int),
56.93/57.07	                                                               hAPP_nat_int,
56.93/57.07	                                                               app_encode_app(
56.93/57.07	                                                               int,
56.93/57.07	                                                               fun_nat_int,
56.93/57.07	                                                               power_power_int,
56.93/57.07	                                                               s)),
56.93/57.07	                                                               app_encode_app(
56.93/57.07	                                                               int,nat,
56.93/57.07	                                                               number_number_of_nat,
56.93/57.07	                                                               app_encode_app(
56.93/57.07	                                                               int,int,bit0,
56.93/57.07	                                                               app_encode_app(
56.93/57.07	                                                               int,int,bit1,
56.93/57.07	                                                               pls)))))),
56.93/57.07	                                                               one_one_int))),
56.93/57.07	                                 zero_zero_int)))).
56.93/57.07	tff(zf_stmt_0, negated_conjecture,
56.93/57.07	  (~
56.93/57.07	    app_encode_app(bool,$o,hBOOL,
56.93/57.07	                   app_encode_app(int,bool,
56.93/57.07	                                  app_encode_app(fun_int_bool,
56.93/57.07	                                                 app_encode_fun(int,bool),
56.93/57.07	                                                 hAPP_int_bool,
56.93/57.07	                                                 app_encode_app(int,
56.93/57.07	                                                                fun_int_bool,
56.93/57.07	                                                                app_encode_app(
56.93/57.07	                                                                fun_int_fun_int_bool,
56.93/57.07	                                                                app_encode_fun(
56.93/57.07	                                                                int,
56.93/57.07	                                                                fun_int_bool),
56.93/57.07	                                                                hAPP_i1948725293t_bool,
56.93/57.07	                                                                ord_less_int),
56.93/57.07	                                                                app_encode_app(
56.93/57.07	                                                                int,int,
56.93/57.07	                                                                app_encode_app(
56.93/57.07	                                                                fun_int_int,
56.93/57.07	                                                                app_encode_fun(
56.93/57.07	                                                                int,int),
56.93/57.07	                                                                hAPP_int_int,
56.93/57.07	                                                                app_encode_app(
56.93/57.07	                                                                int,
56.93/57.07	                                                                fun_int_int,
56.93/57.07	                                                                plus_plus_int,
56.93/57.07	                                                                app_encode_app(
56.93/57.07	                                                                nat,int,
56.93/57.07	                                                                app_encode_app(
56.93/57.07	                                                                fun_nat_int,
56.93/57.07	                                                                app_encode_fun(
56.93/57.07	                                                                nat,int),
56.93/57.07	                                                                hAPP_nat_int,
56.93/57.07	                                                                app_encode_app(
56.93/57.07	                                                                int,
56.93/57.07	                                                                fun_nat_int,
56.93/57.07	                                                                power_power_int,
56.93/57.07	                                                                s)),
56.93/57.07	                                                                app_encode_app(
56.93/57.07	                                                                int,nat,
56.93/57.07	                                                                number_number_of_nat,
56.93/57.07	                                                                app_encode_app(
56.93/57.07	                                                                int,int,bit0,
56.93/57.07	                                                                app_encode_app(
56.93/57.07	                                                                int,int,bit1,
56.93/57.07	                                                                pls)))))),
56.93/57.07	                                                                one_one_int))),
56.93/57.07	                                  zero_zero_int)))).
56.93/57.07	tff('57', plain,
56.93/57.07	    ~ app_encode_app(bool, $o, hBOOL, 
56.93/57.07	        app_encode_app(int, bool, 
56.93/57.07	          app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
56.93/57.07	            hAPP_int_bool, 
56.93/57.07	            app_encode_app(int, fun_int_bool, 
56.93/57.07	              app_encode_app(fun_int_fun_int_bool, 
56.93/57.07	                app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
56.93/57.07	                ord_less_int), 
56.93/57.07	              app_encode_app(int, int, 
56.93/57.07	                app_encode_app(fun_int_int, app_encode_fun(int, int), 
56.93/57.07	                  hAPP_int_int, 
56.93/57.07	                  app_encode_app(int, fun_int_int, plus_plus_int, 
56.93/57.07	                    app_encode_app(nat, int, 
56.93/57.07	                      app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
56.93/57.07	                        hAPP_nat_int, 
56.93/57.07	                        app_encode_app(int, fun_nat_int, power_power_int, s)), 
56.93/57.07	                      app_encode_app(int, nat, number_number_of_nat, 
56.93/57.07	                        app_encode_app(int, int, bit0, 
56.93/57.07	                          app_encode_app(int, int, bit1, pls)))))), 
56.93/57.07	                one_one_int))), zero_zero_int)),
56.93/57.07	    inference('cnf', [status(esa)], [zf_stmt_0])).
56.93/57.07	tff('58', plain,
56.93/57.07	    ~ app_encode_app(bool, $o, hBOOL, 
56.93/57.07	        app_encode_app(int, bool, 
56.93/57.07	          app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
56.93/57.07	            hAPP_int_bool, 
56.93/57.07	            app_encode_app(int, fun_int_bool, 
56.93/57.07	              app_encode_app(fun_int_fun_int_bool, 
56.93/57.07	                app_encode_fun(int, fun_int_bool), cOMBC_int_int_bool, 
56.93/57.07	                ord_less_int), zero_zero_int)), 
56.93/57.07	          sk_K_2(one_one_int, 
56.93/57.07	            app_encode_app(nat, int, 
56.93/57.07	              app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
56.93/57.07	                hAPP_nat_int, 
56.93/57.07	                app_encode_app(int, fun_nat_int, power_power_int, s)), 
56.93/57.07	              app_encode_app(int, nat, number_number_of_nat, 
56.93/57.07	                sk_K_2(one_one_int, one_one_int, min))), min))),
56.93/57.07	    inference('demod', [status(thm)], ['57', '1', '8', '39', '40', '55'])).
56.93/57.07	tff('59', plain, ~ $true, inference('sup-', [status(thm)], ['56', '58'])).
56.93/57.07	tff('60', plain, $false, inference('simplify', [status(thm)], ['59'])).
56.93/57.07	
56.93/57.07	% SZS output end Refutation
56.93/57.07	EOF
