0.00/0.00	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : app
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : 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 $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.20	% Computer   : n136.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 07:39:38 CST 2018
68.05/68.10	% done 12763 iterations in 67.896s
68.05/68.10	% SZS status Theorem for 'stdin'
68.05/68.10	% SZS output start Refutation
68.05/68.10	tff(zf_stmt_96, axiom,
68.05/68.10	  (app_encode_app(bool,$o,hBOOL,
68.05/68.10	                  app_encode_app(int,bool,
68.05/68.10	                                 app_encode_app(fun_int_bool,
68.05/68.10	                                                app_encode_fun(int,bool),
68.05/68.10	                                                hAPP_int_bool,
68.05/68.10	                                                app_encode_app(int,
68.05/68.10	                                                               fun_int_bool,
68.05/68.10	                                                               app_encode_app(
68.05/68.10	                                                               fun_int_fun_int_bool,
68.05/68.10	                                                               app_encode_fun(
68.05/68.10	                                                               int,
68.05/68.10	                                                               fun_int_bool),
68.05/68.10	                                                               hAPP_i1948725293t_bool,
68.05/68.10	                                                               ord_less_eq_int),
68.05/68.10	                                                               one_one_int)),
68.05/68.10	                                 t)))).
68.05/68.10	tff('0', plain,
68.05/68.10	    app_encode_app(bool, $o, hBOOL, 
68.05/68.10	      app_encode_app(int, bool, 
68.05/68.10	        app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
68.05/68.10	          hAPP_int_bool, 
68.05/68.10	          app_encode_app(int, fun_int_bool, 
68.05/68.10	            app_encode_app(fun_int_fun_int_bool, 
68.05/68.10	              app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
68.05/68.10	              ord_less_eq_int), one_one_int)), t)),
68.05/68.10	    inference('cnf', [status(esa)], [zf_stmt_96])).
68.05/68.10	tff(zf_stmt_133, axiom,
68.05/68.10	  (![Z_1:int,W_1:int]:
68.05/68.10	     (app_encode_app(bool,$o,hBOOL,
68.05/68.10	                     app_encode_app(int,bool,
68.05/68.10	                                    app_encode_app(fun_int_bool,
68.05/68.10	                                                   app_encode_fun(int,bool),
68.05/68.10	                                                   hAPP_int_bool,
68.05/68.10	                                                   app_encode_app(int,
68.05/68.10	                                                                  fun_int_bool,
68.05/68.10	                                                                  app_encode_app(
68.05/68.10	                                                                  fun_int_fun_int_bool,
68.05/68.10	                                                                  app_encode_fun(
68.05/68.10	                                                                  int,
68.05/68.10	                                                                  fun_int_bool),
68.05/68.10	                                                                  hAPP_i1948725293t_bool,
68.05/68.10	                                                                  ord_less_int),
68.05/68.10	                                                                  Z_1)),
68.05/68.10	                                    W_1)) <=>
68.05/68.10	      (app_encode_app(bool,$o,hBOOL,
68.05/68.10	                      app_encode_app(int,bool,
68.05/68.10	                                     app_encode_app(fun_int_bool,
68.05/68.10	                                                    app_encode_fun(int,bool),
68.05/68.10	                                                    hAPP_int_bool,
68.05/68.10	                                                    app_encode_app(int,
68.05/68.10	                                                                   fun_int_bool,
68.05/68.10	                                                                   app_encode_app(
68.05/68.10	                                                                   fun_int_fun_int_bool,
68.05/68.10	                                                                   app_encode_fun(
68.05/68.10	                                                                   int,
68.05/68.10	                                                                   fun_int_bool),
68.05/68.10	                                                                   hAPP_i1948725293t_bool,
68.05/68.10	                                                                   ord_less_eq_int),
68.05/68.10	                                                                   Z_1)),
68.05/68.10	                                     W_1)) & 
68.05/68.10	       (Z_1 != W_1))))).
68.05/68.10	tff('1', plain,
68.05/68.10	    ![X33 : int, X35 : int]:
68.05/68.10	      (app_encode_app(bool, $o, hBOOL, 
68.05/68.10	         app_encode_app(int, bool, 
68.05/68.10	           app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
68.05/68.10	             hAPP_int_bool, 
68.05/68.10	             app_encode_app(int, fun_int_bool, 
68.05/68.10	               app_encode_app(fun_int_fun_int_bool, 
68.05/68.10	                 app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
68.05/68.10	                 ord_less_int), X33)), X35))
68.05/68.10	       | X33 = X35
68.05/68.10	       | ~ app_encode_app(bool, $o, hBOOL, 
68.05/68.10	             app_encode_app(int, bool, 
68.05/68.10	               app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
68.05/68.10	                 hAPP_int_bool, 
68.05/68.10	                 app_encode_app(int, fun_int_bool, 
68.05/68.10	                   app_encode_app(fun_int_fun_int_bool, 
68.05/68.10	                     app_encode_fun(int, fun_int_bool), 
68.05/68.10	                     hAPP_i1948725293t_bool, ord_less_eq_int), X33)), X35))),
68.05/68.10	    inference('cnf', [status(esa)], [zf_stmt_133])).
68.05/68.10	tff('2', plain,
68.05/68.10	    (~ $true
68.05/68.10	     | one_one_int = t
68.05/68.10	     | app_encode_app(bool, $o, hBOOL, 
68.05/68.10	         app_encode_app(int, bool, 
68.05/68.10	           app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
68.05/68.10	             hAPP_int_bool, 
68.05/68.10	             app_encode_app(int, fun_int_bool, 
68.05/68.10	               app_encode_app(fun_int_fun_int_bool, 
68.05/68.10	                 app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
68.05/68.10	                 ord_less_int), one_one_int)), t))),
68.05/68.10	    inference('sup-', [status(thm)], ['0', '1'])).
68.05/68.10	tff('3', plain,
68.05/68.10	    (app_encode_app(bool, $o, hBOOL, 
68.05/68.10	       app_encode_app(int, bool, 
68.05/68.10	         app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
68.05/68.10	           hAPP_int_bool, 
68.05/68.10	           app_encode_app(int, fun_int_bool, 
68.05/68.10	             app_encode_app(fun_int_fun_int_bool, 
68.05/68.10	               app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
68.05/68.10	               ord_less_int), one_one_int)), t))
68.05/68.10	     | one_one_int = t),
68.05/68.10	    inference('simplify', [status(thm)], ['2'])).
68.05/68.10	tff(zf_stmt_97, axiom,
68.05/68.10	  ((t = one_one_int) =>
68.05/68.10	   (?[X:int,Y:int]:
68.05/68.10	      (app_encode_app(int,int,
68.05/68.10	                      app_encode_app(fun_int_int,app_encode_fun(int,int),
68.05/68.10	                                     hAPP_int_int,
68.05/68.10	                                     app_encode_app(int,fun_int_int,
68.05/68.10	                                                    plus_plus_int,
68.05/68.10	                                                    app_encode_app(nat,int,
68.05/68.10	                                                                   app_encode_app(
68.05/68.10	                                                                   fun_nat_int,
68.05/68.10	                                                                   app_encode_fun(
68.05/68.10	                                                                   nat,int),
68.05/68.10	                                                                   hAPP_nat_int,
68.05/68.10	                                                                   app_encode_app(
68.05/68.10	                                                                   int,
68.05/68.10	                                                                   fun_nat_int,
68.05/68.10	                                                                   power_power_int,
68.05/68.10	                                                                   X)),
68.05/68.10	                                                                   app_encode_app(
68.05/68.10	                                                                   int,nat,
68.05/68.10	                                                                   number_number_of_nat,
68.05/68.10	                                                                   app_encode_app(
68.05/68.10	                                                                   int,int,
68.05/68.10	                                                                   bit0,
68.05/68.10	                                                                   app_encode_app(
68.05/68.10	                                                                   int,int,
68.05/68.10	                                                                   bit1,pls)))))),
68.05/68.10	                      app_encode_app(nat,int,
68.05/68.10	                                     app_encode_app(fun_nat_int,
68.05/68.10	                                                    app_encode_fun(nat,int),
68.05/68.10	                                                    hAPP_nat_int,
68.05/68.10	                                                    app_encode_app(int,
68.05/68.10	                                                                   fun_nat_int,
68.05/68.10	                                                                   power_power_int,
68.05/68.10	                                                                   Y)),
68.05/68.10	                                     app_encode_app(int,nat,
68.05/68.10	                                                    number_number_of_nat,
68.05/68.10	                                                    app_encode_app(int,int,
68.05/68.10	                                                                   bit0,
68.05/68.10	                                                                   app_encode_app(
68.05/68.10	                                                                   int,int,
68.05/68.10	                                                                   bit1,pls))))) =
68.05/68.10	       app_encode_app(int,int,
68.05/68.10	                      app_encode_app(fun_int_int,app_encode_fun(int,int),
68.05/68.10	                                     hAPP_int_int,
68.05/68.10	                                     app_encode_app(int,fun_int_int,
68.05/68.10	                                                    plus_plus_int,
68.05/68.10	                                                    app_encode_app(int,int,
68.05/68.10	                                                                   app_encode_app(
68.05/68.10	                                                                   fun_int_int,
68.05/68.10	                                                                   app_encode_fun(
68.05/68.10	                                                                   int,int),
68.05/68.10	                                                                   hAPP_int_int,
68.05/68.10	                                                                   app_encode_app(
68.05/68.10	                                                                   int,
68.05/68.10	                                                                   fun_int_int,
68.05/68.10	                                                                   times_times_int,
68.05/68.10	                                                                   app_encode_app(
68.05/68.10	                                                                   int,int,
68.05/68.10	                                                                   number_number_of_int,
68.05/68.10	                                                                   app_encode_app(
68.05/68.10	                                                                   int,int,
68.05/68.10	                                                                   bit0,
68.05/68.10	                                                                   app_encode_app(
68.05/68.10	                                                                   int,int,
68.05/68.10	                                                                   bit0,
68.05/68.10	                                                                   app_encode_app(
68.05/68.10	                                                                   int,int,
68.05/68.10	                                                                   bit1,pls)))))),
68.05/68.10	                                                                   m))),
68.05/68.10	                      one_one_int))))).
68.05/68.10	tff('4', plain,
68.05/68.10	    (app_encode_app(int, int, 
68.05/68.10	       app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
68.05/68.10	         app_encode_app(int, fun_int_int, plus_plus_int, 
68.05/68.10	           app_encode_app(nat, int, 
68.05/68.10	             app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
68.05/68.10	               hAPP_nat_int, 
68.05/68.10	               app_encode_app(int, fun_nat_int, power_power_int, sk_X)), 
68.05/68.10	             app_encode_app(int, nat, number_number_of_nat, 
68.05/68.10	               app_encode_app(int, int, bit0, 
68.05/68.10	                 app_encode_app(int, int, bit1, pls)))))), 
68.05/68.10	       app_encode_app(nat, int, 
68.05/68.10	         app_encode_app(fun_nat_int, app_encode_fun(nat, int), hAPP_nat_int, 
68.05/68.10	           app_encode_app(int, fun_nat_int, power_power_int, sk_Y)), 
68.05/68.10	         app_encode_app(int, nat, number_number_of_nat, 
68.05/68.10	           app_encode_app(int, int, bit0, 
68.05/68.10	             app_encode_app(int, int, bit1, pls)))))
68.05/68.10	      = app_encode_app(int, int, 
68.05/68.10	          app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.10	            hAPP_int_int, 
68.05/68.10	            app_encode_app(int, fun_int_int, plus_plus_int, 
68.05/68.10	              app_encode_app(int, int, 
68.05/68.10	                app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.10	                  hAPP_int_int, 
68.05/68.10	                  app_encode_app(int, fun_int_int, times_times_int, 
68.05/68.10	                    app_encode_app(int, int, number_number_of_int, 
68.05/68.10	                      app_encode_app(int, int, bit0, 
68.05/68.10	                        app_encode_app(int, int, bit0, 
68.05/68.10	                          app_encode_app(int, int, bit1, pls)))))), m))), 
68.05/68.10	          one_one_int)
68.05/68.10	     | t != one_one_int),
68.05/68.10	    inference('cnf', [status(esa)], [zf_stmt_97])).
68.05/68.10	tff(zf_stmt_454, axiom, (pls = zero_zero_int)).
68.05/68.10	tff('5', plain, pls = zero_zero_int,
68.05/68.10	    inference('cnf', [status(esa)], [zf_stmt_454])).
68.05/68.10	tff('6', plain,
68.05/68.10	    (app_encode_app(int, int, 
68.05/68.10	       app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
68.05/68.10	         app_encode_app(int, fun_int_int, plus_plus_int, 
68.05/68.10	           app_encode_app(nat, int, 
68.05/68.10	             app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
68.05/68.10	               hAPP_nat_int, 
68.05/68.10	               app_encode_app(int, fun_nat_int, power_power_int, sk_X)), 
68.05/68.10	             app_encode_app(int, nat, number_number_of_nat, 
68.05/68.10	               app_encode_app(int, int, bit0, 
68.05/68.10	                 app_encode_app(int, int, bit1, zero_zero_int)))))), 
68.05/68.10	       app_encode_app(nat, int, 
68.05/68.10	         app_encode_app(fun_nat_int, app_encode_fun(nat, int), hAPP_nat_int, 
68.05/68.10	           app_encode_app(int, fun_nat_int, power_power_int, sk_Y)), 
68.05/68.10	         app_encode_app(int, nat, number_number_of_nat, 
68.05/68.10	           app_encode_app(int, int, bit0, 
68.05/68.10	             app_encode_app(int, int, bit1, zero_zero_int)))))
68.05/68.10	      = app_encode_app(int, int, 
68.05/68.10	          app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.10	            hAPP_int_int, 
68.05/68.10	            app_encode_app(int, fun_int_int, plus_plus_int, 
68.05/68.10	              app_encode_app(int, int, 
68.05/68.10	                app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.10	                  hAPP_int_int, 
68.05/68.10	                  app_encode_app(int, fun_int_int, times_times_int, 
68.05/68.10	                    app_encode_app(int, int, number_number_of_int, 
68.05/68.10	                      app_encode_app(int, int, bit0, 
68.05/68.10	                        app_encode_app(int, int, bit0, 
68.05/68.10	                          app_encode_app(int, int, bit1, zero_zero_int)))))), 
68.05/68.10	                m))), one_one_int)
68.05/68.10	     | t != one_one_int),
68.05/68.10	    inference('demod', [status(thm)], ['4', '5', '5', '5'])).
68.05/68.10	tff(zf_stmt_240, axiom,
68.05/68.10	  (![K_1:int]: (app_encode_app(int,int,number_number_of_int,K_1) = K_1))).
68.05/68.10	tff('7', plain,
68.05/68.10	    ![X324 : int]:
68.05/68.10	      app_encode_app(int, int, number_number_of_int, X324) = X324,
68.05/68.10	    inference('cnf', [status(esa)], [zf_stmt_240])).
68.05/68.10	tff('8', plain,
68.05/68.10	    (app_encode_app(int, int, 
68.05/68.10	       app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
68.05/68.10	         app_encode_app(int, fun_int_int, plus_plus_int, 
68.05/68.10	           app_encode_app(nat, int, 
68.05/68.10	             app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
68.05/68.10	               hAPP_nat_int, 
68.05/68.10	               app_encode_app(int, fun_nat_int, power_power_int, sk_X)), 
68.05/68.10	             app_encode_app(int, nat, number_number_of_nat, 
68.05/68.10	               app_encode_app(int, int, bit0, 
68.05/68.10	                 app_encode_app(int, int, bit1, zero_zero_int)))))), 
68.05/68.10	       app_encode_app(nat, int, 
68.05/68.10	         app_encode_app(fun_nat_int, app_encode_fun(nat, int), hAPP_nat_int, 
68.05/68.10	           app_encode_app(int, fun_nat_int, power_power_int, sk_Y)), 
68.05/68.10	         app_encode_app(int, nat, number_number_of_nat, 
68.05/68.10	           app_encode_app(int, int, bit0, 
68.05/68.10	             app_encode_app(int, int, bit1, zero_zero_int)))))
68.05/68.10	      = app_encode_app(int, int, 
68.05/68.10	          app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.10	            hAPP_int_int, 
68.05/68.10	            app_encode_app(int, fun_int_int, plus_plus_int, 
68.05/68.10	              app_encode_app(int, int, 
68.05/68.10	                app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.10	                  hAPP_int_int, 
68.05/68.10	                  app_encode_app(int, fun_int_int, times_times_int, 
68.05/68.10	                    app_encode_app(int, int, bit0, 
68.05/68.10	                      app_encode_app(int, int, bit0, 
68.05/68.10	                        app_encode_app(int, int, bit1, zero_zero_int))))), m))), 
68.05/68.10	          one_one_int)
68.05/68.10	     | t != one_one_int),
68.05/68.10	    inference('demod', [status(thm)], ['6', '7'])).
68.05/68.10	tff(zf_stmt_356, axiom,
68.05/68.10	  (app_encode_app(int,int,number_number_of_int,
68.05/68.10	                  app_encode_app(int,int,bit1,pls)) =
68.05/68.10	   one_one_int)).
68.05/68.10	tff('9', plain,
68.05/68.10	    app_encode_app(int, int, number_number_of_int, 
68.05/68.10	      app_encode_app(int, int, bit1, pls))
68.05/68.10	     = one_one_int,
68.05/68.10	    inference('cnf', [status(esa)], [zf_stmt_356])).
68.05/68.10	tff('10', plain, app_encode_app(int, int, bit1, zero_zero_int) = one_one_int,
68.05/68.10	    inference('demod', [status(thm)], ['9', '5', '7'])).
68.05/68.10	tff(zf_stmt_284, axiom,
68.05/68.10	  (![A_99:int]:
68.05/68.10	     (app_encode_app(int,int,
68.05/68.10	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
68.05/68.10	                                    hAPP_int_int,
68.05/68.10	                                    app_encode_app(int,fun_int_int,
68.05/68.10	                                                   times_times_int,
68.05/68.10	                                                   one_one_int)),
68.05/68.10	                     A_99) =
68.05/68.10	      A_99))).
68.05/68.10	tff('11', plain,
68.05/68.10	    ![X442 : int]:
68.05/68.10	      app_encode_app(int, int, 
68.05/68.10	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
68.05/68.10	          app_encode_app(int, fun_int_int, times_times_int, one_one_int)), 
68.05/68.10	        X442)
68.05/68.10	       = X442,
68.05/68.10	    inference('cnf', [status(esa)], [zf_stmt_284])).
68.05/68.10	tff(zf_stmt_686, axiom,
68.05/68.10	  (![A_2:int,B_2:int,Ma:int]:
68.05/68.10	     (app_encode_app(bool,$o,hBOOL,
68.05/68.10	                     app_encode_app(int,bool,
68.05/68.10	                                    app_encode_app(fun_int_bool,
68.05/68.10	                                                   app_encode_fun(int,bool),
68.05/68.10	                                                   hAPP_int_bool,
68.05/68.10	                                                   app_encode_app(int,
68.05/68.10	                                                                  fun_int_bool,
68.05/68.10	                                                                  app_encode_app(
68.05/68.10	                                                                  int,
68.05/68.10	                                                                  app_encode_fun(
68.05/68.10	                                                                  int,
68.05/68.10	                                                                  fun_int_bool),
68.05/68.10	                                                                  zcong,A_2),
68.05/68.10	                                                                  B_2)),
68.05/68.10	                                    Ma)) <=>
68.05/68.10	      (?[K_2:int]:
68.05/68.10	         (B_2 =
68.05/68.10	          app_encode_app(int,int,
68.05/68.10	                         app_encode_app(fun_int_int,app_encode_fun(int,int),
68.05/68.10	                                        hAPP_int_int,
68.05/68.10	                                        app_encode_app(int,fun_int_int,
68.05/68.10	                                                       plus_plus_int,A_2)),
68.05/68.10	                         app_encode_app(int,int,
68.05/68.10	                                        app_encode_app(fun_int_int,
68.05/68.10	                                                       app_encode_fun(
68.05/68.10	                                                       int,int),hAPP_int_int,
68.05/68.10	                                                       app_encode_app(
68.05/68.10	                                                       int,fun_int_int,
68.05/68.10	                                                       times_times_int,Ma)),
68.05/68.10	                                        K_2))))))).
68.05/68.10	tff('12', plain,
68.05/68.10	    ![X1212 : int, X1213 : int, X1214 : int]:
68.05/68.10	      (X1214
68.05/68.10	        = app_encode_app(int, int, 
68.05/68.10	            app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.10	              hAPP_int_int, 
68.05/68.10	              app_encode_app(int, fun_int_int, plus_plus_int, X1212)), 
68.05/68.10	            app_encode_app(int, int, 
68.05/68.10	              app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.10	                hAPP_int_int, 
68.05/68.10	                app_encode_app(int, fun_int_int, times_times_int, X1213)), 
68.05/68.10	              sk_K_2(X1213, X1214, X1212)))
68.05/68.10	       | ~ app_encode_app(bool, $o, hBOOL, 
68.05/68.10	             app_encode_app(int, bool, 
68.05/68.10	               app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
68.05/68.10	                 hAPP_int_bool, 
68.05/68.10	                 app_encode_app(int, fun_int_bool, 
68.05/68.10	                   app_encode_app(int, app_encode_fun(int, fun_int_bool), 
68.05/68.10	                     zcong, X1212), X1214)), X1213))),
68.05/68.10	    inference('cnf', [status(esa)], [zf_stmt_686])).
68.05/68.10	tff('13', plain,
68.05/68.10	    ![X0 : int, X1 : int]:
68.05/68.10	      (X1
68.05/68.10	        = app_encode_app(int, int, 
68.05/68.10	            app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.10	              hAPP_int_int, 
68.05/68.10	              app_encode_app(int, fun_int_int, plus_plus_int, X0)), 
68.05/68.10	            sk_K_2(one_one_int, X1, X0))
68.05/68.10	       | ~ app_encode_app(bool, $o, hBOOL, 
68.05/68.10	             app_encode_app(int, bool, 
68.05/68.10	               app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
68.05/68.10	                 hAPP_int_bool, 
68.05/68.10	                 app_encode_app(int, fun_int_bool, 
68.05/68.10	                   app_encode_app(int, app_encode_fun(int, fun_int_bool), 
68.05/68.10	                     zcong, X0), X1)), one_one_int))),
68.05/68.10	    inference('sup+', [status(thm)], ['11', '12'])).
68.05/68.10	tff(zf_stmt_670, axiom,
68.05/68.10	  (![A:int,B:int]:
68.05/68.10	     app_encode_app(bool,$o,hBOOL,
68.05/68.10	                    app_encode_app(int,bool,
68.05/68.10	                                   app_encode_app(fun_int_bool,
68.05/68.10	                                                  app_encode_fun(int,bool),
68.05/68.10	                                                  hAPP_int_bool,
68.05/68.10	                                                  app_encode_app(int,
68.05/68.10	                                                                 fun_int_bool,
68.05/68.10	                                                                 app_encode_app(
68.05/68.10	                                                                 int,
68.05/68.10	                                                                 app_encode_fun(
68.05/68.10	                                                                 int,
68.05/68.10	                                                                 fun_int_bool),
68.05/68.10	                                                                 zcong,A),B)),
68.05/68.10	                                   one_one_int)))).
68.05/68.10	tff('14', plain,
68.05/68.10	    ![X1169 : int, X1170 : int]:
68.05/68.10	      app_encode_app(bool, $o, hBOOL, 
68.05/68.10	        app_encode_app(int, bool, 
68.05/68.10	          app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
68.05/68.10	            hAPP_int_bool, 
68.05/68.10	            app_encode_app(int, fun_int_bool, 
68.05/68.10	              app_encode_app(int, app_encode_fun(int, fun_int_bool), zcong, 
68.05/68.10	                X1169), X1170)), one_one_int)),
68.05/68.10	    inference('cnf', [status(esa)], [zf_stmt_670])).
68.05/68.10	tff('15', plain,
68.05/68.10	    ![X0 : int, X1 : int]:
68.05/68.10	      (X1
68.05/68.10	        = app_encode_app(int, int, 
68.05/68.10	            app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.10	              hAPP_int_int, 
68.05/68.10	              app_encode_app(int, fun_int_int, plus_plus_int, X0)), 
68.05/68.10	            sk_K_2(one_one_int, X1, X0))
68.05/68.10	       | ~ $true),
68.05/68.10	    inference('demod', [status(thm)], ['13', '14'])).
68.05/68.10	tff('16', plain,
68.05/68.10	    ![X0 : int, X1 : int]:
68.05/68.10	      X1
68.05/68.10	       = app_encode_app(int, int, 
68.05/68.10	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.10	             hAPP_int_int, 
68.05/68.10	             app_encode_app(int, fun_int_int, plus_plus_int, X0)), 
68.05/68.10	           sk_K_2(one_one_int, X1, X0)),
68.05/68.10	    inference('simplify', [status(thm)], ['15'])).
68.05/68.10	tff(zf_stmt_282, axiom,
68.05/68.10	  (![A_100:nat]:
68.05/68.10	     (app_encode_app(nat,nat,
68.05/68.10	                     app_encode_app(fun_nat_nat,app_encode_fun(nat,nat),
68.05/68.10	                                    hAPP_nat_nat,
68.05/68.10	                                    app_encode_app(nat,fun_nat_nat,
68.05/68.10	                                                   times_times_nat,A_100)),
68.05/68.10	                     one_one_nat) =
68.05/68.10	      A_100))).
68.05/68.10	tff('17', plain,
68.05/68.10	    ![X440 : nat]:
68.05/68.10	      app_encode_app(nat, nat, 
68.05/68.10	        app_encode_app(fun_nat_nat, app_encode_fun(nat, nat), hAPP_nat_nat, 
68.05/68.10	          app_encode_app(nat, fun_nat_nat, times_times_nat, X440)), 
68.05/68.10	        one_one_nat)
68.05/68.10	       = X440,
68.05/68.10	    inference('cnf', [status(esa)], [zf_stmt_282])).
68.05/68.10	tff(zf_stmt_676, axiom,
68.05/68.10	  (![N_4:nat]:
68.05/68.10	     (app_encode_app(nat,real,
68.05/68.10	                     app_encode_app(fun_nat_real,app_encode_fun(nat,real),
68.05/68.10	                                    hAPP_nat_real,
68.05/68.10	                                    app_encode_app(real,fun_nat_real,
68.05/68.10	                                                   power_power_real,
68.05/68.10	                                                   app_encode_app(int,real,
68.05/68.10	                                                                  number267125858f_real,
68.05/68.10	                                                                  min))),
68.05/68.10	                     app_encode_app(nat,nat,
68.05/68.10	                                    app_encode_app(fun_nat_nat,
68.05/68.10	                                                   app_encode_fun(nat,nat),
68.05/68.10	                                                   hAPP_nat_nat,
68.05/68.10	                                                   app_encode_app(nat,
68.05/68.10	                                                                  fun_nat_nat,
68.05/68.10	                                                                  times_times_nat,
68.05/68.10	                                                                  app_encode_app(
68.05/68.10	                                                                  int,nat,
68.05/68.10	                                                                  number_number_of_nat,
68.05/68.10	                                                                  app_encode_app(
68.05/68.10	                                                                  int,int,
68.05/68.10	                                                                  bit0,
68.05/68.10	                                                                  app_encode_app(
68.05/68.10	                                                                  int,int,
68.05/68.10	                                                                  bit1,pls))))),
68.05/68.10	                                    N_4)) =
68.05/68.10	      one_one_real))).
68.05/68.10	tff('18', plain,
68.05/68.10	    ![X1192 : nat]:
68.05/68.10	      app_encode_app(nat, real, 
68.05/68.10	        app_encode_app(fun_nat_real, app_encode_fun(nat, real), 
68.05/68.10	          hAPP_nat_real, 
68.05/68.10	          app_encode_app(real, fun_nat_real, power_power_real, 
68.05/68.10	            app_encode_app(int, real, number267125858f_real, min))), 
68.05/68.10	        app_encode_app(nat, nat, 
68.05/68.10	          app_encode_app(fun_nat_nat, app_encode_fun(nat, nat), 
68.05/68.10	            hAPP_nat_nat, 
68.05/68.10	            app_encode_app(nat, fun_nat_nat, times_times_nat, 
68.05/68.10	              app_encode_app(int, nat, number_number_of_nat, 
68.05/68.10	                app_encode_app(int, int, bit0, 
68.05/68.10	                  app_encode_app(int, int, bit1, pls))))), X1192))
68.05/68.10	       = one_one_real,
68.05/68.10	    inference('cnf', [status(esa)], [zf_stmt_676])).
68.05/68.10	tff('19', plain,
68.05/68.10	    ![X1192 : nat]:
68.05/68.10	      app_encode_app(nat, real, 
68.05/68.10	        app_encode_app(fun_nat_real, app_encode_fun(nat, real), 
68.05/68.10	          hAPP_nat_real, 
68.05/68.10	          app_encode_app(real, fun_nat_real, power_power_real, 
68.05/68.10	            app_encode_app(int, real, number267125858f_real, min))), 
68.05/68.10	        app_encode_app(nat, nat, 
68.05/68.10	          app_encode_app(fun_nat_nat, app_encode_fun(nat, nat), 
68.05/68.10	            hAPP_nat_nat, 
68.05/68.10	            app_encode_app(nat, fun_nat_nat, times_times_nat, 
68.05/68.10	              app_encode_app(int, nat, number_number_of_nat, 
68.05/68.10	                app_encode_app(int, int, bit0, one_one_int)))), X1192))
68.05/68.10	       = one_one_real,
68.05/68.10	    inference('demod', [status(thm)], ['18', '5', '10'])).
68.05/68.10	tff('20', plain,
68.05/68.10	    app_encode_app(nat, real, 
68.05/68.10	      app_encode_app(fun_nat_real, app_encode_fun(nat, real), hAPP_nat_real, 
68.05/68.10	        app_encode_app(real, fun_nat_real, power_power_real, 
68.05/68.10	          app_encode_app(int, real, number267125858f_real, min))), 
68.05/68.10	      app_encode_app(int, nat, number_number_of_nat, 
68.05/68.10	        app_encode_app(int, int, bit0, one_one_int)))
68.05/68.10	     = one_one_real,
68.05/68.10	    inference('sup+', [status(thm)], ['17', '19'])).
68.05/68.10	tff(zf_stmt_116, axiom,
68.05/68.10	  (![X_26:real]:
68.05/68.10	     (app_encode_app(real,real,
68.05/68.10	                     app_encode_app(fun_real_real,app_encode_fun(real,real),
68.05/68.10	                                    hAPP_real_real,
68.05/68.10	                                    app_encode_app(real,fun_real_real,
68.05/68.10	                                                   times_times_real,X_26)),
68.05/68.10	                     X_26) =
68.05/68.10	      app_encode_app(nat,real,
68.05/68.10	                     app_encode_app(fun_nat_real,app_encode_fun(nat,real),
68.05/68.10	                                    hAPP_nat_real,
68.05/68.10	                                    app_encode_app(real,fun_nat_real,
68.05/68.10	                                                   power_power_real,X_26)),
68.05/68.10	                     app_encode_app(int,nat,number_number_of_nat,
68.05/68.10	                                    app_encode_app(int,int,bit0,
68.05/68.10	                                                   app_encode_app(int,int,
68.05/68.10	                                                                  bit1,pls))))))).
68.05/68.10	tff('21', plain,
68.05/68.10	    ![X15 : real]:
68.05/68.10	      app_encode_app(real, real, 
68.05/68.10	        app_encode_app(fun_real_real, app_encode_fun(real, real), 
68.05/68.10	          hAPP_real_real, 
68.05/68.10	          app_encode_app(real, fun_real_real, times_times_real, X15)), X15)
68.05/68.10	       = app_encode_app(nat, real, 
68.05/68.10	           app_encode_app(fun_nat_real, app_encode_fun(nat, real), 
68.05/68.10	             hAPP_nat_real, 
68.05/68.10	             app_encode_app(real, fun_nat_real, power_power_real, X15)), 
68.05/68.10	           app_encode_app(int, nat, number_number_of_nat, 
68.05/68.10	             app_encode_app(int, int, bit0, 
68.05/68.10	               app_encode_app(int, int, bit1, pls)))),
68.05/68.10	    inference('cnf', [status(esa)], [zf_stmt_116])).
68.05/68.10	tff('22', plain,
68.05/68.10	    ![X15 : real]:
68.05/68.10	      app_encode_app(real, real, 
68.05/68.10	        app_encode_app(fun_real_real, app_encode_fun(real, real), 
68.05/68.10	          hAPP_real_real, 
68.05/68.10	          app_encode_app(real, fun_real_real, times_times_real, X15)), X15)
68.05/68.10	       = app_encode_app(nat, real, 
68.05/68.10	           app_encode_app(fun_nat_real, app_encode_fun(nat, real), 
68.05/68.10	             hAPP_nat_real, 
68.05/68.10	             app_encode_app(real, fun_nat_real, power_power_real, X15)), 
68.05/68.10	           app_encode_app(int, nat, number_number_of_nat, 
68.05/68.10	             app_encode_app(int, int, bit0, one_one_int))),
68.05/68.10	    inference('demod', [status(thm)], ['21', '5', '10'])).
68.05/68.10	tff(zf_stmt_338, axiom,
68.05/68.10	  (![V_13:int,W_12:int]:
68.05/68.10	     (app_encode_app(real,real,
68.05/68.10	                     app_encode_app(fun_real_real,app_encode_fun(real,real),
68.05/68.10	                                    hAPP_real_real,
68.05/68.10	                                    app_encode_app(real,fun_real_real,
68.05/68.10	                                                   times_times_real,
68.05/68.10	                                                   app_encode_app(int,real,
68.05/68.10	                                                                  number267125858f_real,
68.05/68.10	                                                                  V_13))),
68.05/68.10	                     app_encode_app(int,real,number267125858f_real,W_12)) =
68.05/68.10	      app_encode_app(int,real,number267125858f_real,
68.05/68.10	                     app_encode_app(int,int,
68.05/68.10	                                    app_encode_app(fun_int_int,
68.05/68.10	                                                   app_encode_fun(int,int),
68.05/68.10	                                                   hAPP_int_int,
68.05/68.10	                                                   app_encode_app(int,
68.05/68.10	                                                                  fun_int_int,
68.05/68.10	                                                                  times_times_int,
68.05/68.10	                                                                  V_13)),
68.05/68.10	                                    W_12))))).
68.05/68.10	tff('23', plain,
68.05/68.10	    ![X542 : int, X543 : int]:
68.05/68.10	      app_encode_app(real, real, 
68.05/68.10	        app_encode_app(fun_real_real, app_encode_fun(real, real), 
68.05/68.10	          hAPP_real_real, 
68.05/68.10	          app_encode_app(real, fun_real_real, times_times_real, 
68.05/68.10	            app_encode_app(int, real, number267125858f_real, X542))), 
68.05/68.10	        app_encode_app(int, real, number267125858f_real, X543))
68.05/68.10	       = app_encode_app(int, real, number267125858f_real, 
68.05/68.10	           app_encode_app(int, int, 
68.05/68.10	             app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.10	               hAPP_int_int, 
68.05/68.10	               app_encode_app(int, fun_int_int, times_times_int, X542)), 
68.05/68.10	             X543)),
68.05/68.10	    inference('cnf', [status(esa)], [zf_stmt_338])).
68.05/68.10	tff(zf_stmt_210, axiom,
68.05/68.10	  (![A_111:real,B_63:real]:
68.05/68.10	     (app_encode_app(real,real,
68.05/68.10	                     app_encode_app(fun_real_real,app_encode_fun(real,real),
68.05/68.10	                                    hAPP_real_real,
68.05/68.10	                                    app_encode_app(real,fun_real_real,
68.05/68.10	                                                   times_times_real,A_111)),
68.05/68.10	                     B_63) =
68.05/68.10	      app_encode_app(real,real,
68.05/68.10	                     app_encode_app(fun_real_real,app_encode_fun(real,real),
68.05/68.10	                                    hAPP_real_real,
68.05/68.10	                                    app_encode_app(real,fun_real_real,
68.05/68.10	                                                   times_times_real,B_63)),
68.05/68.10	                     A_111)))).
68.05/68.10	tff('24', plain,
68.05/68.10	    ![X238 : real, X239 : real]:
68.05/68.10	      app_encode_app(real, real, 
68.05/68.10	        app_encode_app(fun_real_real, app_encode_fun(real, real), 
68.05/68.10	          hAPP_real_real, 
68.05/68.10	          app_encode_app(real, fun_real_real, times_times_real, X239)), X238)
68.05/68.10	       = app_encode_app(real, real, 
68.05/68.10	           app_encode_app(fun_real_real, app_encode_fun(real, real), 
68.05/68.10	             hAPP_real_real, 
68.05/68.10	             app_encode_app(real, fun_real_real, times_times_real, X238)), 
68.05/68.10	           X239),
68.05/68.10	    inference('cnf', [status(esa)], [zf_stmt_210])).
68.05/68.10	tff('25', plain,
68.05/68.10	    ![X0 : int, X1 : int]:
68.05/68.10	      app_encode_app(real, real, 
68.05/68.10	        app_encode_app(fun_real_real, app_encode_fun(real, real), 
68.05/68.10	          hAPP_real_real, 
68.05/68.10	          app_encode_app(real, fun_real_real, times_times_real, 
68.05/68.10	            app_encode_app(int, real, number267125858f_real, X0))), 
68.05/68.10	        app_encode_app(int, real, number267125858f_real, X1))
68.05/68.10	       = app_encode_app(int, real, number267125858f_real, 
68.05/68.10	           app_encode_app(int, int, 
68.05/68.10	             app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.10	               hAPP_int_int, 
68.05/68.10	               app_encode_app(int, fun_int_int, times_times_int, X1)), X0)),
68.05/68.10	    inference('sup+', [status(thm)], ['23', '24'])).
68.05/68.10	tff('26', plain,
68.05/68.10	    app_encode_app(int, real, number267125858f_real, 
68.05/68.10	      app_encode_app(int, int, 
68.05/68.10	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
68.05/68.10	          app_encode_app(int, fun_int_int, times_times_int, min)), min))
68.05/68.10	     = one_one_real,
68.05/68.10	    inference('demod', [status(thm)], ['20', '22', '25'])).
68.05/68.10	tff(zf_stmt_358, axiom,
68.05/68.10	  (app_encode_app(int,real,number267125858f_real,
68.05/68.10	                  app_encode_app(int,int,bit1,pls)) =
68.05/68.10	   one_one_real)).
68.05/68.10	tff('27', plain,
68.05/68.10	    app_encode_app(int, real, number267125858f_real, 
68.05/68.10	      app_encode_app(int, int, bit1, pls))
68.05/68.10	     = one_one_real,
68.05/68.10	    inference('cnf', [status(esa)], [zf_stmt_358])).
68.05/68.10	tff('28', plain,
68.05/68.10	    app_encode_app(int, real, number267125858f_real, one_one_int)
68.05/68.10	     = one_one_real,
68.05/68.10	    inference('demod', [status(thm)], ['27', '5', '10'])).
68.05/68.10	tff(zf_stmt_232, axiom,
68.05/68.10	  (![X_2:int,Y_2:int]:
68.05/68.10	     ((app_encode_app(int,real,number267125858f_real,X_2) =
68.05/68.10	       app_encode_app(int,real,number267125858f_real,Y_2)) <=>
68.05/68.10	      (X_2 = Y_2)))).
68.05/68.10	tff('29', plain,
68.05/68.10	    ![X301 : int, X302 : int]:
68.05/68.10	      (X302 = X301
68.05/68.10	       | app_encode_app(int, real, number267125858f_real, X302)
68.05/68.10	          != app_encode_app(int, real, number267125858f_real, X301)),
68.05/68.10	    inference('cnf', [status(esa)], [zf_stmt_232])).
68.05/68.10	tff('30', plain,
68.05/68.10	    ![X0 : int]:
68.05/68.10	      (one_one_real != app_encode_app(int, real, number267125858f_real, X0)
68.05/68.10	       | one_one_int = X0),
68.05/68.10	    inference('sup-', [status(thm)], ['28', '29'])).
68.05/68.10	tff('31', plain,
68.05/68.10	    (one_one_real != one_one_real
68.05/68.10	     | one_one_int
68.05/68.10	        = app_encode_app(int, int, 
68.05/68.10	            app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.10	              hAPP_int_int, 
68.05/68.10	              app_encode_app(int, fun_int_int, times_times_int, min)), min)),
68.05/68.10	    inference('sup-', [status(thm)], ['26', '30'])).
68.05/68.10	tff('32', plain,
68.05/68.10	    one_one_int
68.05/68.10	     = app_encode_app(int, int, 
68.05/68.10	         app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
68.05/68.10	           app_encode_app(int, fun_int_int, times_times_int, min)), min),
68.05/68.10	    inference('simplify', [status(thm)], ['31'])).
68.05/68.10	tff(zf_stmt_364, axiom,
68.05/68.10	  (![K_1:int,L:int]:
68.05/68.10	     (app_encode_app(int,int,
68.05/68.10	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
68.05/68.10	                                    hAPP_int_int,
68.05/68.10	                                    app_encode_app(int,fun_int_int,
68.05/68.10	                                                   times_times_int,
68.05/68.10	                                                   app_encode_app(int,int,
68.05/68.10	                                                                  bit1,K_1))),
68.05/68.10	                     L) =
68.05/68.10	      app_encode_app(int,int,
68.05/68.10	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
68.05/68.10	                                    hAPP_int_int,
68.05/68.10	                                    app_encode_app(int,fun_int_int,
68.05/68.10	                                                   plus_plus_int,
68.05/68.10	                                                   app_encode_app(int,int,
68.05/68.10	                                                                  bit0,
68.05/68.10	                                                                  app_encode_app(
68.05/68.10	                                                                  int,int,
68.05/68.10	                                                                  app_encode_app(
68.05/68.10	                                                                  fun_int_int,
68.05/68.10	                                                                  app_encode_fun(
68.05/68.10	                                                                  int,int),
68.05/68.10	                                                                  hAPP_int_int,
68.05/68.10	                                                                  app_encode_app(
68.05/68.10	                                                                  int,
68.05/68.10	                                                                  fun_int_int,
68.05/68.10	                                                                  times_times_int,
68.05/68.10	                                                                  K_1)),L)))),
68.05/68.10	                     L)))).
68.05/68.10	tff('33', plain,
68.05/68.10	    ![X573 : int, X574 : int]:
68.05/68.10	      app_encode_app(int, int, 
68.05/68.10	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
68.05/68.10	          app_encode_app(int, fun_int_int, times_times_int, 
68.05/68.10	            app_encode_app(int, int, bit1, X573))), X574)
68.05/68.10	       = app_encode_app(int, int, 
68.05/68.10	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.10	             hAPP_int_int, 
68.05/68.10	             app_encode_app(int, fun_int_int, plus_plus_int, 
68.05/68.10	               app_encode_app(int, int, bit0, 
68.05/68.10	                 app_encode_app(int, int, 
68.05/68.10	                   app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.10	                     hAPP_int_int, 
68.05/68.10	                     app_encode_app(int, fun_int_int, times_times_int, X573)), 
68.05/68.10	                   X574)))), X574),
68.05/68.10	    inference('cnf', [status(esa)], [zf_stmt_364])).
68.05/68.10	tff(zf_stmt_228, axiom,
68.05/68.10	  (![A_104:int,C_30:int]:
68.05/68.10	     (app_encode_app(int,int,
68.05/68.10	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
68.05/68.10	                                    hAPP_int_int,
68.05/68.10	                                    app_encode_app(int,fun_int_int,
68.05/68.10	                                                   plus_plus_int,A_104)),
68.05/68.10	                     C_30) =
68.05/68.10	      app_encode_app(int,int,
68.05/68.10	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
68.05/68.10	                                    hAPP_int_int,
68.05/68.10	                                    app_encode_app(int,fun_int_int,
68.05/68.10	                                                   plus_plus_int,C_30)),
68.05/68.10	                     A_104)))).
68.05/68.10	tff('34', plain,
68.05/68.10	    ![X292 : int, X293 : int]:
68.05/68.10	      app_encode_app(int, int, 
68.05/68.10	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
68.05/68.10	          app_encode_app(int, fun_int_int, plus_plus_int, X293)), X292)
68.05/68.10	       = app_encode_app(int, int, 
68.05/68.10	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.10	             hAPP_int_int, 
68.05/68.10	             app_encode_app(int, fun_int_int, plus_plus_int, X292)), X293),
68.05/68.10	    inference('cnf', [status(esa)], [zf_stmt_228])).
68.05/68.10	tff('35', plain,
68.05/68.10	    ![X573 : int, X574 : int]:
68.05/68.10	      app_encode_app(int, int, 
68.05/68.10	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
68.05/68.10	          app_encode_app(int, fun_int_int, times_times_int, 
68.05/68.10	            app_encode_app(int, int, bit1, X573))), X574)
68.05/68.10	       = app_encode_app(int, int, 
68.05/68.10	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.10	             hAPP_int_int, 
68.05/68.10	             app_encode_app(int, fun_int_int, plus_plus_int, X574)), 
68.05/68.10	           app_encode_app(int, int, bit0, 
68.05/68.10	             app_encode_app(int, int, 
68.05/68.10	               app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.10	                 hAPP_int_int, 
68.05/68.10	                 app_encode_app(int, fun_int_int, times_times_int, X573)), 
68.05/68.10	               X574))),
68.05/68.10	    inference('demod', [status(thm)], ['33', '34'])).
68.05/68.10	tff('36', plain,
68.05/68.10	    app_encode_app(int, int, 
68.05/68.10	      app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
68.05/68.11	        app_encode_app(int, fun_int_int, times_times_int, 
68.05/68.11	          app_encode_app(int, int, bit1, min))), min)
68.05/68.11	     = app_encode_app(int, int, 
68.05/68.11	         app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
68.05/68.11	           app_encode_app(int, fun_int_int, plus_plus_int, min)), 
68.05/68.11	         app_encode_app(int, int, bit0, one_one_int)),
68.05/68.11	    inference('sup+', [status(thm)], ['32', '35'])).
68.05/68.11	tff(zf_stmt_616, axiom, (app_encode_app(int,int,bit1,min) = min)).
68.05/68.11	tff('37', plain, app_encode_app(int, int, bit1, min) = min,
68.05/68.11	    inference('cnf', [status(esa)], [zf_stmt_616])).
68.05/68.11	tff(zf_stmt_348, axiom,
68.05/68.11	  (![K_1:int,L:int]:
68.05/68.11	     (app_encode_app(int,int,
68.05/68.11	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
68.05/68.11	                                    hAPP_int_int,
68.05/68.11	                                    app_encode_app(int,fun_int_int,
68.05/68.11	                                                   plus_plus_int,
68.05/68.11	                                                   app_encode_app(int,int,
68.05/68.11	                                                                  bit0,K_1))),
68.05/68.11	                     app_encode_app(int,int,bit1,L)) =
68.05/68.11	      app_encode_app(int,int,bit1,
68.05/68.11	                     app_encode_app(int,int,
68.05/68.11	                                    app_encode_app(fun_int_int,
68.05/68.11	                                                   app_encode_fun(int,int),
68.05/68.11	                                                   hAPP_int_int,
68.05/68.11	                                                   app_encode_app(int,
68.05/68.11	                                                                  fun_int_int,
68.05/68.11	                                                                  plus_plus_int,
68.05/68.11	                                                                  K_1)),
68.05/68.11	                                    L))))).
68.05/68.11	tff('38', plain,
68.05/68.11	    ![X564 : int, X565 : int]:
68.05/68.11	      app_encode_app(int, int, 
68.05/68.11	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
68.05/68.11	          app_encode_app(int, fun_int_int, plus_plus_int, 
68.05/68.11	            app_encode_app(int, int, bit0, X564))), 
68.05/68.11	        app_encode_app(int, int, bit1, X565))
68.05/68.11	       = app_encode_app(int, int, bit1, 
68.05/68.11	           app_encode_app(int, int, 
68.05/68.11	             app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.11	               hAPP_int_int, 
68.05/68.11	               app_encode_app(int, fun_int_int, plus_plus_int, X564)), X565)),
68.05/68.11	    inference('cnf', [status(esa)], [zf_stmt_348])).
68.05/68.11	tff('39', plain,
68.05/68.11	    ![X0 : int]:
68.05/68.11	      app_encode_app(int, int, 
68.05/68.11	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
68.05/68.11	          app_encode_app(int, fun_int_int, plus_plus_int, 
68.05/68.11	            app_encode_app(int, int, bit0, X0))), min)
68.05/68.11	       = app_encode_app(int, int, bit1, 
68.05/68.11	           app_encode_app(int, int, 
68.05/68.11	             app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.11	               hAPP_int_int, 
68.05/68.11	               app_encode_app(int, fun_int_int, plus_plus_int, X0)), min)),
68.05/68.11	    inference('sup+', [status(thm)], ['37', '38'])).
68.05/68.11	tff('40', plain,
68.05/68.11	    ![X0 : int]:
68.05/68.11	      app_encode_app(int, int, 
68.05/68.11	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
68.05/68.11	          app_encode_app(int, fun_int_int, plus_plus_int, min)), 
68.05/68.11	        app_encode_app(int, int, bit0, X0))
68.05/68.11	       = app_encode_app(int, int, bit1, 
68.05/68.11	           app_encode_app(int, int, 
68.05/68.11	             app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.11	               hAPP_int_int, 
68.05/68.11	               app_encode_app(int, fun_int_int, plus_plus_int, X0)), min)),
68.05/68.11	    inference('demod', [status(thm)], ['39', '34'])).
68.05/68.11	tff('41', plain,
68.05/68.11	    app_encode_app(int, int, 
68.05/68.11	      app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
68.05/68.11	        app_encode_app(int, fun_int_int, times_times_int, min)), min)
68.05/68.11	     = app_encode_app(int, int, bit1, 
68.05/68.11	         app_encode_app(int, int, 
68.05/68.11	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.11	             hAPP_int_int, 
68.05/68.11	             app_encode_app(int, fun_int_int, plus_plus_int, one_one_int)), 
68.05/68.11	           min)),
68.05/68.11	    inference('demod', [status(thm)], ['36', '37', '40'])).
68.05/68.11	tff('42', plain,
68.05/68.11	    one_one_int
68.05/68.11	     = app_encode_app(int, int, bit1, 
68.05/68.11	         app_encode_app(int, int, 
68.05/68.11	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.11	             hAPP_int_int, 
68.05/68.11	             app_encode_app(int, fun_int_int, plus_plus_int, one_one_int)), 
68.05/68.11	           min)),
68.05/68.11	    inference('demod', [status(thm)], ['41', '32'])).
68.05/68.11	tff(zf_stmt_236, axiom,
68.05/68.11	  (![K:int,L_1:int]:
68.05/68.11	     ((app_encode_app(int,int,bit1,K) = app_encode_app(int,int,bit1,L_1)) <=>
68.05/68.11	      (K = L_1)))).
68.05/68.11	tff('43', plain,
68.05/68.11	    ![X313 : int, X314 : int]:
68.05/68.11	      (X314 = X313
68.05/68.11	       | app_encode_app(int, int, bit1, X314)
68.05/68.11	          != app_encode_app(int, int, bit1, X313)),
68.05/68.11	    inference('cnf', [status(esa)], [zf_stmt_236])).
68.05/68.11	tff('44', plain,
68.05/68.11	    ![X0 : int]:
68.05/68.11	      (one_one_int != app_encode_app(int, int, bit1, X0) | zero_zero_int = X0),
68.05/68.11	    inference('sup-', [status(thm)], ['10', '43'])).
68.05/68.11	tff('45', plain,
68.05/68.11	    (one_one_int != one_one_int
68.05/68.11	     | zero_zero_int
68.05/68.11	        = app_encode_app(int, int, 
68.05/68.11	            app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.11	              hAPP_int_int, 
68.05/68.11	              app_encode_app(int, fun_int_int, plus_plus_int, one_one_int)), 
68.05/68.11	            min)),
68.05/68.11	    inference('sup-', [status(thm)], ['42', '44'])).
68.05/68.11	tff('46', plain,
68.05/68.11	    zero_zero_int
68.05/68.11	     = app_encode_app(int, int, 
68.05/68.11	         app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
68.05/68.11	           app_encode_app(int, fun_int_int, plus_plus_int, one_one_int)), 
68.05/68.11	         min),
68.05/68.11	    inference('simplify', [status(thm)], ['45'])).
68.05/68.11	tff(zf_stmt_219, axiom,
68.05/68.11	  (![A_107:int,B_60:int,C_33:int]:
68.05/68.11	     (app_encode_app(int,int,
68.05/68.11	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
68.05/68.11	                                    hAPP_int_int,
68.05/68.11	                                    app_encode_app(int,fun_int_int,
68.05/68.11	                                                   plus_plus_int,
68.05/68.11	                                                   app_encode_app(int,int,
68.05/68.11	                                                                  app_encode_app(
68.05/68.11	                                                                  fun_int_int,
68.05/68.11	                                                                  app_encode_fun(
68.05/68.11	                                                                  int,int),
68.05/68.11	                                                                  hAPP_int_int,
68.05/68.11	                                                                  app_encode_app(
68.05/68.11	                                                                  int,
68.05/68.11	                                                                  fun_int_int,
68.05/68.11	                                                                  plus_plus_int,
68.05/68.11	                                                                  A_107)),
68.05/68.11	                                                                  B_60))),
68.05/68.11	                     C_33) =
68.05/68.11	      app_encode_app(int,int,
68.05/68.11	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
68.05/68.11	                                    hAPP_int_int,
68.05/68.11	                                    app_encode_app(int,fun_int_int,
68.05/68.11	                                                   plus_plus_int,A_107)),
68.05/68.11	                     app_encode_app(int,int,
68.05/68.11	                                    app_encode_app(fun_int_int,
68.05/68.11	                                                   app_encode_fun(int,int),
68.05/68.11	                                                   hAPP_int_int,
68.05/68.11	                                                   app_encode_app(int,
68.05/68.11	                                                                  fun_int_int,
68.05/68.11	                                                                  plus_plus_int,
68.05/68.11	                                                                  B_60)),
68.05/68.11	                                    C_33))))).
68.05/68.11	tff('47', plain,
68.05/68.11	    ![X265 : int, X266 : int, X267 : int]:
68.05/68.11	      app_encode_app(int, int, 
68.05/68.11	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
68.05/68.11	          app_encode_app(int, fun_int_int, plus_plus_int, 
68.05/68.11	            app_encode_app(int, int, 
68.05/68.11	              app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.11	                hAPP_int_int, 
68.05/68.11	                app_encode_app(int, fun_int_int, plus_plus_int, X265)), X266))), 
68.05/68.11	        X267)
68.05/68.11	       = app_encode_app(int, int, 
68.05/68.11	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.11	             hAPP_int_int, 
68.05/68.11	             app_encode_app(int, fun_int_int, plus_plus_int, X265)), 
68.05/68.11	           app_encode_app(int, int, 
68.05/68.11	             app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.11	               hAPP_int_int, 
68.05/68.11	               app_encode_app(int, fun_int_int, plus_plus_int, X266)), X267)),
68.05/68.11	    inference('cnf', [status(esa)], [zf_stmt_219])).
68.05/68.11	tff('48', plain,
68.05/68.11	    ![X0 : int]:
68.05/68.11	      app_encode_app(int, int, 
68.05/68.11	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
68.05/68.11	          app_encode_app(int, fun_int_int, plus_plus_int, zero_zero_int)), 
68.05/68.11	        X0)
68.05/68.11	       = app_encode_app(int, int, 
68.05/68.11	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.11	             hAPP_int_int, 
68.05/68.11	             app_encode_app(int, fun_int_int, plus_plus_int, one_one_int)), 
68.05/68.11	           app_encode_app(int, int, 
68.05/68.11	             app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.11	               hAPP_int_int, 
68.05/68.11	               app_encode_app(int, fun_int_int, plus_plus_int, min)), X0)),
68.05/68.11	    inference('sup+', [status(thm)], ['46', '47'])).
68.05/68.11	tff(zf_stmt_300, axiom,
68.05/68.11	  (![K_1:int]:
68.05/68.11	     (app_encode_app(int,int,
68.05/68.11	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
68.05/68.11	                                    hAPP_int_int,
68.05/68.11	                                    app_encode_app(int,fun_int_int,
68.05/68.11	                                                   plus_plus_int,pls)),
68.05/68.11	                     K_1) =
68.05/68.11	      K_1))).
68.05/68.11	tff('49', plain,
68.05/68.11	    ![X468 : int]:
68.05/68.11	      app_encode_app(int, int, 
68.05/68.11	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
68.05/68.11	          app_encode_app(int, fun_int_int, plus_plus_int, pls)), X468)
68.05/68.11	       = X468,
68.05/68.11	    inference('cnf', [status(esa)], [zf_stmt_300])).
68.05/68.11	tff('50', plain,
68.05/68.11	    ![X468 : int]:
68.05/68.11	      app_encode_app(int, int, 
68.05/68.11	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
68.05/68.11	          app_encode_app(int, fun_int_int, plus_plus_int, zero_zero_int)), 
68.05/68.11	        X468)
68.05/68.11	       = X468,
68.05/68.11	    inference('demod', [status(thm)], ['49', '5'])).
68.05/68.11	tff('51', plain,
68.05/68.11	    ![X0 : int]:
68.05/68.11	      X0
68.05/68.11	       = app_encode_app(int, int, 
68.05/68.11	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.11	             hAPP_int_int, 
68.05/68.11	             app_encode_app(int, fun_int_int, plus_plus_int, one_one_int)), 
68.05/68.11	           app_encode_app(int, int, 
68.05/68.11	             app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.11	               hAPP_int_int, 
68.05/68.11	               app_encode_app(int, fun_int_int, plus_plus_int, min)), X0)),
68.05/68.11	    inference('demod', [status(thm)], ['48', '50'])).
68.05/68.11	tff('52', plain,
68.05/68.11	    ![X0 : int]:
68.05/68.11	      sk_K_2(one_one_int, X0, min)
68.05/68.11	       = app_encode_app(int, int, 
68.05/68.11	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.11	             hAPP_int_int, 
68.05/68.11	             app_encode_app(int, fun_int_int, plus_plus_int, one_one_int)), 
68.05/68.11	           X0),
68.05/68.11	    inference('sup+', [status(thm)], ['16', '51'])).
68.05/68.11	tff(zf_stmt_302, axiom,
68.05/68.11	  (![K_1:int]:
68.05/68.11	     (app_encode_app(int,int,bit0,K_1) =
68.05/68.11	      app_encode_app(int,int,
68.05/68.11	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
68.05/68.11	                                    hAPP_int_int,
68.05/68.11	                                    app_encode_app(int,fun_int_int,
68.05/68.11	                                                   plus_plus_int,K_1)),
68.05/68.11	                     K_1)))).
68.05/68.11	tff('53', plain,
68.05/68.11	    ![X471 : int]:
68.05/68.11	      app_encode_app(int, int, bit0, X471)
68.05/68.11	       = app_encode_app(int, int, 
68.05/68.11	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.11	             hAPP_int_int, 
68.05/68.11	             app_encode_app(int, fun_int_int, plus_plus_int, X471)), X471),
68.05/68.11	    inference('cnf', [status(esa)], [zf_stmt_302])).
68.05/68.11	tff('54', plain,
68.05/68.11	    app_encode_app(int, int, bit0, one_one_int)
68.05/68.11	     = sk_K_2(one_one_int, one_one_int, min),
68.05/68.11	    inference('sup+', [status(thm)], ['52', '53'])).
68.05/68.11	tff(zf_stmt_278, axiom,
68.05/68.11	  (![X_21:int,Y_18:int,Z_9:int]:
68.05/68.11	     (app_encode_app(int,int,
68.05/68.11	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
68.05/68.11	                                    hAPP_int_int,
68.05/68.11	                                    app_encode_app(int,fun_int_int,
68.05/68.11	                                                   times_times_int,X_21)),
68.05/68.11	                     app_encode_app(int,int,
68.05/68.11	                                    app_encode_app(fun_int_int,
68.05/68.11	                                                   app_encode_fun(int,int),
68.05/68.11	                                                   hAPP_int_int,
68.05/68.11	                                                   app_encode_app(int,
68.05/68.11	                                                                  fun_int_int,
68.05/68.11	                                                                  plus_plus_int,
68.05/68.11	                                                                  Y_18)),
68.05/68.11	                                    Z_9)) =
68.05/68.11	      app_encode_app(int,int,
68.05/68.11	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
68.05/68.11	                                    hAPP_int_int,
68.05/68.11	                                    app_encode_app(int,fun_int_int,
68.05/68.11	                                                   plus_plus_int,
68.05/68.11	                                                   app_encode_app(int,int,
68.05/68.11	                                                                  app_encode_app(
68.05/68.11	                                                                  fun_int_int,
68.05/68.11	                                                                  app_encode_fun(
68.05/68.11	                                                                  int,int),
68.05/68.11	                                                                  hAPP_int_int,
68.05/68.11	                                                                  app_encode_app(
68.05/68.11	                                                                  int,
68.05/68.11	                                                                  fun_int_int,
68.05/68.11	                                                                  times_times_int,
68.05/68.11	                                                                  X_21)),Y_18))),
68.05/68.11	                     app_encode_app(int,int,
68.05/68.11	                                    app_encode_app(fun_int_int,
68.05/68.11	                                                   app_encode_fun(int,int),
68.05/68.11	                                                   hAPP_int_int,
68.05/68.11	                                                   app_encode_app(int,
68.05/68.11	                                                                  fun_int_int,
68.05/68.11	                                                                  times_times_int,
68.05/68.11	                                                                  X_21)),
68.05/68.11	                                    Z_9))))).
68.05/68.11	tff('55', plain,
68.05/68.11	    ![X430 : int, X431 : int, X432 : int]:
68.05/68.11	      app_encode_app(int, int, 
68.05/68.11	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
68.05/68.11	          app_encode_app(int, fun_int_int, times_times_int, X430)), 
68.05/68.11	        app_encode_app(int, int, 
68.05/68.11	          app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.11	            hAPP_int_int, 
68.05/68.11	            app_encode_app(int, fun_int_int, plus_plus_int, X431)), X432))
68.05/68.11	       = app_encode_app(int, int, 
68.05/68.11	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.11	             hAPP_int_int, 
68.05/68.11	             app_encode_app(int, fun_int_int, plus_plus_int, 
68.05/68.11	               app_encode_app(int, int, 
68.05/68.11	                 app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.11	                   hAPP_int_int, 
68.05/68.11	                   app_encode_app(int, fun_int_int, times_times_int, X430)), 
68.05/68.11	                 X431))), 
68.05/68.11	           app_encode_app(int, int, 
68.05/68.11	             app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.11	               hAPP_int_int, 
68.05/68.11	               app_encode_app(int, fun_int_int, times_times_int, X430)), 
68.05/68.11	             X432)),
68.05/68.11	    inference('cnf', [status(esa)], [zf_stmt_278])).
68.05/68.11	tff('56', plain,
68.05/68.11	    ![X0 : int, X1 : int]:
68.05/68.11	      app_encode_app(int, int, 
68.05/68.11	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
68.05/68.11	          app_encode_app(int, fun_int_int, times_times_int, X1)), 
68.05/68.11	        app_encode_app(int, int, 
68.05/68.11	          app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.11	            hAPP_int_int, 
68.05/68.11	            app_encode_app(int, fun_int_int, plus_plus_int, X0)), X0))
68.05/68.11	       = app_encode_app(int, int, bit0, 
68.05/68.11	           app_encode_app(int, int, 
68.05/68.11	             app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.11	               hAPP_int_int, 
68.05/68.11	               app_encode_app(int, fun_int_int, times_times_int, X1)), X0)),
68.05/68.11	    inference('sup+', [status(thm)], ['53', '55'])).
68.05/68.11	tff('57', plain,
68.05/68.11	    ![X0 : int, X1 : int]:
68.05/68.11	      app_encode_app(int, int, 
68.05/68.11	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
68.05/68.11	          app_encode_app(int, fun_int_int, times_times_int, X1)), 
68.05/68.11	        app_encode_app(int, int, bit0, X0))
68.05/68.11	       = app_encode_app(int, int, bit0, 
68.05/68.11	           app_encode_app(int, int, 
68.05/68.11	             app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.11	               hAPP_int_int, 
68.05/68.11	               app_encode_app(int, fun_int_int, times_times_int, X1)), X0)),
68.05/68.11	    inference('demod', [status(thm)], ['56', '53'])).
68.05/68.11	tff(zf_stmt_208, axiom,
68.05/68.11	  (![A_111:int,B_63:int]:
68.05/68.11	     (app_encode_app(int,int,
68.05/68.11	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
68.05/68.11	                                    hAPP_int_int,
68.05/68.11	                                    app_encode_app(int,fun_int_int,
68.05/68.11	                                                   times_times_int,A_111)),
68.05/68.11	                     B_63) =
68.05/68.11	      app_encode_app(int,int,
68.05/68.11	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
68.05/68.11	                                    hAPP_int_int,
68.05/68.11	                                    app_encode_app(int,fun_int_int,
68.05/68.11	                                                   times_times_int,B_63)),
68.05/68.11	                     A_111)))).
68.05/68.11	tff('58', plain,
68.05/68.11	    ![X234 : int, X235 : int]:
68.05/68.11	      app_encode_app(int, int, 
68.05/68.11	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
68.05/68.11	          app_encode_app(int, fun_int_int, times_times_int, X235)), X234)
68.05/68.11	       = app_encode_app(int, int, 
68.05/68.11	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.11	             hAPP_int_int, 
68.05/68.11	             app_encode_app(int, fun_int_int, times_times_int, X234)), X235),
68.05/68.11	    inference('cnf', [status(esa)], [zf_stmt_208])).
68.05/68.11	tff('59', plain,
68.05/68.11	    ![X0 : int, X1 : int]:
68.05/68.11	      app_encode_app(int, int, 
68.05/68.11	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
68.05/68.11	          app_encode_app(int, fun_int_int, times_times_int, 
68.05/68.11	            app_encode_app(int, int, bit0, X0))), X1)
68.05/68.11	       = app_encode_app(int, int, bit0, 
68.05/68.11	           app_encode_app(int, int, 
68.05/68.11	             app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.11	               hAPP_int_int, 
68.05/68.11	               app_encode_app(int, fun_int_int, times_times_int, X1)), X0)),
68.05/68.11	    inference('sup+', [status(thm)], ['57', '58'])).
68.05/68.11	tff('60', plain,
68.05/68.11	    ![X0 : int]:
68.05/68.11	      app_encode_app(int, int, 
68.05/68.11	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
68.05/68.11	          app_encode_app(int, fun_int_int, times_times_int, X0)), 
68.05/68.11	        sk_K_2(one_one_int, one_one_int, min))
68.05/68.11	       = app_encode_app(int, int, bit0, 
68.05/68.11	           app_encode_app(int, int, 
68.05/68.11	             app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.11	               hAPP_int_int, 
68.05/68.11	               app_encode_app(int, fun_int_int, times_times_int, X0)), 
68.05/68.11	             one_one_int)),
68.05/68.11	    inference('sup+', [status(thm)], ['54', '57'])).
68.05/68.11	tff(zf_stmt_281, axiom,
68.05/68.11	  (![A_100:int]:
68.05/68.11	     (app_encode_app(int,int,
68.05/68.11	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
68.05/68.11	                                    hAPP_int_int,
68.05/68.11	                                    app_encode_app(int,fun_int_int,
68.05/68.11	                                                   times_times_int,A_100)),
68.05/68.11	                     one_one_int) =
68.05/68.11	      A_100))).
68.05/68.11	tff('61', plain,
68.05/68.11	    ![X439 : int]:
68.05/68.11	      app_encode_app(int, int, 
68.05/68.11	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
68.05/68.11	          app_encode_app(int, fun_int_int, times_times_int, X439)), 
68.05/68.11	        one_one_int)
68.05/68.11	       = X439,
68.05/68.11	    inference('cnf', [status(esa)], [zf_stmt_281])).
68.05/68.11	tff('62', plain,
68.05/68.11	    ![X0 : int]:
68.05/68.11	      app_encode_app(int, int, 
68.05/68.11	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
68.05/68.11	          app_encode_app(int, fun_int_int, times_times_int, X0)), 
68.05/68.11	        sk_K_2(one_one_int, one_one_int, min))
68.05/68.11	       = app_encode_app(int, int, bit0, X0),
68.05/68.11	    inference('demod', [status(thm)], ['60', '61'])).
68.05/68.11	tff('63', plain,
68.05/68.11	    ![X0 : int]:
68.05/68.11	      app_encode_app(int, int, 
68.05/68.11	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
68.05/68.11	          app_encode_app(int, fun_int_int, plus_plus_int, X0)), one_one_int)
68.05/68.11	       = sk_K_2(one_one_int, X0, min),
68.05/68.11	    inference('sup+', [status(thm)], ['52', '34'])).
68.05/68.11	tff(zf_stmt_349, axiom,
68.05/68.11	  (![K_1:int]:
68.05/68.11	     (app_encode_app(int,int,bit1,K_1) =
68.05/68.11	      app_encode_app(int,int,
68.05/68.11	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
68.05/68.11	                                    hAPP_int_int,
68.05/68.11	                                    app_encode_app(int,fun_int_int,
68.05/68.11	                                                   plus_plus_int,
68.05/68.11	                                                   app_encode_app(int,int,
68.05/68.11	                                                                  app_encode_app(
68.05/68.11	                                                                  fun_int_int,
68.05/68.11	                                                                  app_encode_fun(
68.05/68.11	                                                                  int,int),
68.05/68.11	                                                                  hAPP_int_int,
68.05/68.11	                                                                  app_encode_app(
68.05/68.11	                                                                  int,
68.05/68.11	                                                                  fun_int_int,
68.05/68.11	                                                                  plus_plus_int,
68.05/68.11	                                                                  one_one_int)),
68.05/68.11	                                                                  K_1))),
68.05/68.11	                     K_1)))).
68.05/68.11	tff('64', plain,
68.05/68.11	    ![X566 : int]:
68.05/68.11	      app_encode_app(int, int, bit1, X566)
68.05/68.11	       = app_encode_app(int, int, 
68.05/68.11	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.11	             hAPP_int_int, 
68.05/68.11	             app_encode_app(int, fun_int_int, plus_plus_int, 
68.05/68.11	               app_encode_app(int, int, 
68.05/68.11	                 app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.11	                   hAPP_int_int, 
68.05/68.11	                   app_encode_app(int, fun_int_int, plus_plus_int, 
68.05/68.11	                     one_one_int)), X566))), X566),
68.05/68.11	    inference('cnf', [status(esa)], [zf_stmt_349])).
68.05/68.11	tff('65', plain,
68.05/68.11	    ![X566 : int]:
68.05/68.11	      app_encode_app(int, int, bit1, X566)
68.05/68.11	       = app_encode_app(int, int, 
68.05/68.11	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.11	             hAPP_int_int, 
68.05/68.11	             app_encode_app(int, fun_int_int, plus_plus_int, X566)), 
68.05/68.11	           app_encode_app(int, int, 
68.05/68.11	             app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.11	               hAPP_int_int, 
68.05/68.11	               app_encode_app(int, fun_int_int, plus_plus_int, one_one_int)), 
68.05/68.11	             X566)),
68.05/68.11	    inference('demod', [status(thm)], ['64', '34'])).
68.05/68.11	tff(zf_stmt_225, axiom,
68.05/68.11	  (![A_105:int,C_31:int,D_9:int]:
68.05/68.11	     (app_encode_app(int,int,
68.05/68.11	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
68.05/68.11	                                    hAPP_int_int,
68.05/68.11	                                    app_encode_app(int,fun_int_int,
68.05/68.11	                                                   plus_plus_int,A_105)),
68.05/68.11	                     app_encode_app(int,int,
68.05/68.11	                                    app_encode_app(fun_int_int,
68.05/68.11	                                                   app_encode_fun(int,int),
68.05/68.11	                                                   hAPP_int_int,
68.05/68.11	                                                   app_encode_app(int,
68.05/68.11	                                                                  fun_int_int,
68.05/68.11	                                                                  plus_plus_int,
68.05/68.11	                                                                  C_31)),
68.05/68.11	                                    D_9)) =
68.05/68.11	      app_encode_app(int,int,
68.05/68.11	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
68.05/68.11	                                    hAPP_int_int,
68.05/68.11	                                    app_encode_app(int,fun_int_int,
68.05/68.11	                                                   plus_plus_int,C_31)),
68.05/68.11	                     app_encode_app(int,int,
68.05/68.11	                                    app_encode_app(fun_int_int,
68.05/68.11	                                                   app_encode_fun(int,int),
68.05/68.11	                                                   hAPP_int_int,
68.05/68.11	                                                   app_encode_app(int,
68.05/68.11	                                                                  fun_int_int,
68.05/68.11	                                                                  plus_plus_int,
68.05/68.11	                                                                  A_105)),
68.05/68.11	                                    D_9))))).
68.05/68.11	tff('66', plain,
68.05/68.11	    ![X283 : int, X284 : int, X285 : int]:
68.05/68.11	      app_encode_app(int, int, 
68.05/68.11	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
68.05/68.11	          app_encode_app(int, fun_int_int, plus_plus_int, X284)), 
68.05/68.11	        app_encode_app(int, int, 
68.05/68.11	          app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.11	            hAPP_int_int, 
68.05/68.11	            app_encode_app(int, fun_int_int, plus_plus_int, X283)), X285))
68.05/68.11	       = app_encode_app(int, int, 
68.05/68.11	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.11	             hAPP_int_int, 
68.05/68.11	             app_encode_app(int, fun_int_int, plus_plus_int, X283)), 
68.05/68.11	           app_encode_app(int, int, 
68.05/68.11	             app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.11	               hAPP_int_int, 
68.05/68.11	               app_encode_app(int, fun_int_int, plus_plus_int, X284)), X285)),
68.05/68.11	    inference('cnf', [status(esa)], [zf_stmt_225])).
68.05/68.11	tff('67', plain,
68.05/68.11	    ![X0 : int]:
68.05/68.11	      app_encode_app(int, int, bit1, X0)
68.05/68.11	       = app_encode_app(int, int, 
68.05/68.11	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.11	             hAPP_int_int, 
68.05/68.11	             app_encode_app(int, fun_int_int, plus_plus_int, one_one_int)), 
68.05/68.11	           app_encode_app(int, int, 
68.05/68.11	             app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.11	               hAPP_int_int, 
68.05/68.11	               app_encode_app(int, fun_int_int, plus_plus_int, X0)), X0)),
68.05/68.11	    inference('sup+', [status(thm)], ['65', '66'])).
68.05/68.11	tff('68', plain,
68.05/68.11	    ![X0 : int]:
68.05/68.11	      app_encode_app(int, int, bit1, X0)
68.05/68.11	       = app_encode_app(int, int, 
68.05/68.11	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.11	             hAPP_int_int, 
68.05/68.11	             app_encode_app(int, fun_int_int, plus_plus_int, one_one_int)), 
68.05/68.11	           app_encode_app(int, int, bit0, X0)),
68.05/68.11	    inference('demod', [status(thm)], ['67', '53'])).
68.05/68.11	tff('69', plain,
68.05/68.11	    ![X0 : int]:
68.05/68.11	      app_encode_app(int, int, bit1, X0)
68.05/68.11	       = sk_K_2(one_one_int, app_encode_app(int, int, bit0, X0), min),
68.05/68.11	    inference('demod', [status(thm)], ['68', '52'])).
68.05/68.11	tff('70', plain,
68.05/68.11	    (app_encode_app(int, int, 
68.05/68.11	       app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
68.05/68.11	         app_encode_app(int, fun_int_int, plus_plus_int, 
68.05/68.11	           app_encode_app(nat, int, 
68.05/68.11	             app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
68.05/68.11	               hAPP_nat_int, 
68.05/68.11	               app_encode_app(int, fun_nat_int, power_power_int, sk_X)), 
68.05/68.11	             app_encode_app(int, nat, number_number_of_nat, 
68.05/68.11	               sk_K_2(one_one_int, one_one_int, min))))), 
68.05/68.11	       app_encode_app(nat, int, 
68.05/68.11	         app_encode_app(fun_nat_int, app_encode_fun(nat, int), hAPP_nat_int, 
68.05/68.11	           app_encode_app(int, fun_nat_int, power_power_int, sk_Y)), 
68.05/68.11	         app_encode_app(int, nat, number_number_of_nat, 
68.05/68.11	           sk_K_2(one_one_int, one_one_int, min))))
68.05/68.11	      = app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m))
68.05/68.11	     | t != one_one_int),
68.05/68.11	    inference('demod', [status(thm)],
68.05/68.11	              ['8', '10', '54', '10', '54', '10', '54', '59', '62', '63', 
68.05/68.11	               '69'])).
68.05/68.11	tff(zf_stmt_1300, conjecture,
68.05/68.11	  (?[X:int,Y:int]:
68.05/68.11	     (app_encode_app(int,int,
68.05/68.11	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
68.05/68.11	                                    hAPP_int_int,
68.05/68.11	                                    app_encode_app(int,fun_int_int,
68.05/68.11	                                                   plus_plus_int,
68.05/68.11	                                                   app_encode_app(nat,int,
68.05/68.11	                                                                  app_encode_app(
68.05/68.11	                                                                  fun_nat_int,
68.05/68.11	                                                                  app_encode_fun(
68.05/68.11	                                                                  nat,int),
68.05/68.11	                                                                  hAPP_nat_int,
68.05/68.11	                                                                  app_encode_app(
68.05/68.11	                                                                  int,
68.05/68.11	                                                                  fun_nat_int,
68.05/68.11	                                                                  power_power_int,
68.05/68.11	                                                                  X)),
68.05/68.11	                                                                  app_encode_app(
68.05/68.11	                                                                  int,nat,
68.05/68.11	                                                                  number_number_of_nat,
68.05/68.11	                                                                  app_encode_app(
68.05/68.11	                                                                  int,int,
68.05/68.11	                                                                  bit0,
68.05/68.11	                                                                  app_encode_app(
68.05/68.11	                                                                  int,int,
68.05/68.11	                                                                  bit1,pls)))))),
68.05/68.11	                     app_encode_app(nat,int,
68.05/68.11	                                    app_encode_app(fun_nat_int,
68.05/68.11	                                                   app_encode_fun(nat,int),
68.05/68.11	                                                   hAPP_nat_int,
68.05/68.11	                                                   app_encode_app(int,
68.05/68.11	                                                                  fun_nat_int,
68.05/68.11	                                                                  power_power_int,
68.05/68.11	                                                                  Y)),
68.05/68.11	                                    app_encode_app(int,nat,
68.05/68.11	                                                   number_number_of_nat,
68.05/68.11	                                                   app_encode_app(int,int,
68.05/68.11	                                                                  bit0,
68.05/68.11	                                                                  app_encode_app(
68.05/68.11	                                                                  int,int,
68.05/68.11	                                                                  bit1,pls))))) =
68.05/68.11	      app_encode_app(int,int,
68.05/68.11	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
68.05/68.11	                                    hAPP_int_int,
68.05/68.11	                                    app_encode_app(int,fun_int_int,
68.05/68.11	                                                   plus_plus_int,
68.05/68.11	                                                   app_encode_app(int,int,
68.05/68.11	                                                                  app_encode_app(
68.05/68.11	                                                                  fun_int_int,
68.05/68.11	                                                                  app_encode_fun(
68.05/68.11	                                                                  int,int),
68.05/68.11	                                                                  hAPP_int_int,
68.05/68.11	                                                                  app_encode_app(
68.05/68.11	                                                                  int,
68.05/68.11	                                                                  fun_int_int,
68.05/68.11	                                                                  times_times_int,
68.05/68.11	                                                                  app_encode_app(
68.05/68.11	                                                                  int,int,
68.05/68.11	                                                                  number_number_of_int,
68.05/68.11	                                                                  app_encode_app(
68.05/68.11	                                                                  int,int,
68.05/68.11	                                                                  bit0,
68.05/68.11	                                                                  app_encode_app(
68.05/68.11	                                                                  int,int,
68.05/68.11	                                                                  bit0,
68.05/68.11	                                                                  app_encode_app(
68.05/68.11	                                                                  int,int,
68.05/68.11	                                                                  bit1,pls)))))),
68.05/68.11	                                                                  m))),
68.05/68.11	                     one_one_int)))).
68.05/68.11	tff(zf_stmt_0, negated_conjecture,
68.05/68.11	  (~
68.05/68.11	    (?[X:int,Y:int]:
68.05/68.11	       (app_encode_app(int,int,
68.05/68.11	                       app_encode_app(fun_int_int,app_encode_fun(int,int),
68.05/68.11	                                      hAPP_int_int,
68.05/68.11	                                      app_encode_app(int,fun_int_int,
68.05/68.11	                                                     plus_plus_int,
68.05/68.11	                                                     app_encode_app(nat,int,
68.05/68.11	                                                                    app_encode_app(
68.05/68.11	                                                                    fun_nat_int,
68.05/68.11	                                                                    app_encode_fun(
68.05/68.11	                                                                    nat,int),
68.05/68.11	                                                                    hAPP_nat_int,
68.05/68.11	                                                                    app_encode_app(
68.05/68.11	                                                                    int,
68.05/68.11	                                                                    fun_nat_int,
68.05/68.11	                                                                    power_power_int,
68.05/68.11	                                                                    X)),
68.05/68.11	                                                                    app_encode_app(
68.05/68.11	                                                                    int,nat,
68.05/68.11	                                                                    number_number_of_nat,
68.05/68.11	                                                                    app_encode_app(
68.05/68.11	                                                                    int,int,
68.05/68.11	                                                                    bit0,
68.05/68.11	                                                                    app_encode_app(
68.05/68.11	                                                                    int,int,
68.05/68.11	                                                                    bit1,pls)))))),
68.05/68.11	                       app_encode_app(nat,int,
68.05/68.11	                                      app_encode_app(fun_nat_int,
68.05/68.11	                                                     app_encode_fun(nat,int),
68.05/68.11	                                                     hAPP_nat_int,
68.05/68.11	                                                     app_encode_app(int,
68.05/68.11	                                                                    fun_nat_int,
68.05/68.11	                                                                    power_power_int,
68.05/68.11	                                                                    Y)),
68.05/68.11	                                      app_encode_app(int,nat,
68.05/68.11	                                                     number_number_of_nat,
68.05/68.11	                                                     app_encode_app(int,int,
68.05/68.11	                                                                    bit0,
68.05/68.11	                                                                    app_encode_app(
68.05/68.11	                                                                    int,int,
68.05/68.11	                                                                    bit1,pls))))) =
68.05/68.11	        app_encode_app(int,int,
68.05/68.11	                       app_encode_app(fun_int_int,app_encode_fun(int,int),
68.05/68.11	                                      hAPP_int_int,
68.05/68.11	                                      app_encode_app(int,fun_int_int,
68.05/68.11	                                                     plus_plus_int,
68.05/68.11	                                                     app_encode_app(int,int,
68.05/68.11	                                                                    app_encode_app(
68.05/68.11	                                                                    fun_int_int,
68.05/68.11	                                                                    app_encode_fun(
68.05/68.11	                                                                    int,int),
68.05/68.11	                                                                    hAPP_int_int,
68.05/68.11	                                                                    app_encode_app(
68.05/68.11	                                                                    int,
68.05/68.11	                                                                    fun_int_int,
68.05/68.11	                                                                    times_times_int,
68.05/68.11	                                                                    app_encode_app(
68.05/68.11	                                                                    int,int,
68.05/68.11	                                                                    number_number_of_int,
68.05/68.11	                                                                    app_encode_app(
68.05/68.11	                                                                    int,int,
68.05/68.11	                                                                    bit0,
68.05/68.11	                                                                    app_encode_app(
68.05/68.11	                                                                    int,int,
68.05/68.11	                                                                    bit0,
68.05/68.11	                                                                    app_encode_app(
68.05/68.11	                                                                    int,int,
68.05/68.11	                                                                    bit1,pls)))))),
68.05/68.11	                                                                    m))),
68.05/68.11	                       one_one_int))))).
68.05/68.11	tff('71', plain,
68.05/68.11	    ![X2821 : int, X2822 : int]:
68.05/68.11	      app_encode_app(int, int, 
68.05/68.11	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
68.05/68.11	          app_encode_app(int, fun_int_int, plus_plus_int, 
68.05/68.11	            app_encode_app(nat, int, 
68.05/68.11	              app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
68.05/68.11	                hAPP_nat_int, 
68.05/68.11	                app_encode_app(int, fun_nat_int, power_power_int, X2821)), 
68.05/68.11	              app_encode_app(int, nat, number_number_of_nat, 
68.05/68.11	                app_encode_app(int, int, bit0, 
68.05/68.11	                  app_encode_app(int, int, bit1, pls)))))), 
68.05/68.11	        app_encode_app(nat, int, 
68.05/68.11	          app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
68.05/68.11	            hAPP_nat_int, 
68.05/68.11	            app_encode_app(int, fun_nat_int, power_power_int, X2822)), 
68.05/68.11	          app_encode_app(int, nat, number_number_of_nat, 
68.05/68.11	            app_encode_app(int, int, bit0, 
68.05/68.11	              app_encode_app(int, int, bit1, pls)))))
68.05/68.11	       != app_encode_app(int, int, 
68.05/68.11	            app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.11	              hAPP_int_int, 
68.05/68.11	              app_encode_app(int, fun_int_int, plus_plus_int, 
68.05/68.11	                app_encode_app(int, int, 
68.05/68.11	                  app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.11	                    hAPP_int_int, 
68.05/68.11	                    app_encode_app(int, fun_int_int, times_times_int, 
68.05/68.11	                      app_encode_app(int, int, number_number_of_int, 
68.05/68.11	                        app_encode_app(int, int, bit0, 
68.05/68.11	                          app_encode_app(int, int, bit0, 
68.05/68.11	                            app_encode_app(int, int, bit1, pls)))))), m))), 
68.05/68.11	            one_one_int),
68.05/68.11	    inference('cnf', [status(esa)], [zf_stmt_0])).
68.05/68.11	tff('72', plain,
68.05/68.11	    ![X2821 : int, X2822 : int]:
68.05/68.11	      app_encode_app(int, int, 
68.05/68.11	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
68.05/68.11	          app_encode_app(int, fun_int_int, plus_plus_int, 
68.05/68.11	            app_encode_app(nat, int, 
68.05/68.11	              app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
68.05/68.11	                hAPP_nat_int, 
68.05/68.11	                app_encode_app(int, fun_nat_int, power_power_int, X2821)), 
68.05/68.11	              app_encode_app(int, nat, number_number_of_nat, 
68.05/68.11	                sk_K_2(one_one_int, one_one_int, min))))), 
68.05/68.11	        app_encode_app(nat, int, 
68.05/68.11	          app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
68.05/68.11	            hAPP_nat_int, 
68.05/68.11	            app_encode_app(int, fun_nat_int, power_power_int, X2822)), 
68.05/68.11	          app_encode_app(int, nat, number_number_of_nat, 
68.05/68.11	            sk_K_2(one_one_int, one_one_int, min))))
68.05/68.11	       != app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m)),
68.05/68.11	    inference('demod', [status(thm)],
68.05/68.11	              ['71', '5', '10', '54', '5', '10', '54', '5', '10', '54', '7', 
68.05/68.11	               '59', '62', '63', '69'])).
68.05/68.11	tff('73', plain, t != one_one_int,
68.05/68.11	    inference('simplify_reflect-', [status(thm)], ['70', '72'])).
68.05/68.11	tff('74', plain,
68.05/68.11	    app_encode_app(bool, $o, hBOOL, 
68.05/68.11	      app_encode_app(int, bool, 
68.05/68.11	        app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
68.05/68.11	          hAPP_int_bool, 
68.05/68.11	          app_encode_app(int, fun_int_bool, 
68.05/68.11	            app_encode_app(fun_int_fun_int_bool, 
68.05/68.11	              app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
68.05/68.11	              ord_less_int), one_one_int)), t)),
68.05/68.11	    inference('simplify_reflect-', [status(thm)], ['3', '73'])).
68.05/68.11	tff(zf_stmt_98, axiom,
68.05/68.11	  (app_encode_app(bool,$o,hBOOL,
68.05/68.11	                  app_encode_app(int,bool,
68.05/68.11	                                 app_encode_app(fun_int_bool,
68.05/68.11	                                                app_encode_fun(int,bool),
68.05/68.11	                                                hAPP_int_bool,
68.05/68.11	                                                app_encode_app(int,
68.05/68.11	                                                               fun_int_bool,
68.05/68.11	                                                               app_encode_app(
68.05/68.11	                                                               fun_int_fun_int_bool,
68.05/68.11	                                                               app_encode_fun(
68.05/68.11	                                                               int,
68.05/68.11	                                                               fun_int_bool),
68.05/68.11	                                                               hAPP_i1948725293t_bool,
68.05/68.11	                                                               ord_less_int),
68.05/68.11	                                                               one_one_int)),
68.05/68.11	                                 t)) =>
68.05/68.11	   (?[X:int,Y:int]:
68.05/68.11	      (app_encode_app(int,int,
68.05/68.11	                      app_encode_app(fun_int_int,app_encode_fun(int,int),
68.05/68.11	                                     hAPP_int_int,
68.05/68.11	                                     app_encode_app(int,fun_int_int,
68.05/68.11	                                                    plus_plus_int,
68.05/68.11	                                                    app_encode_app(nat,int,
68.05/68.11	                                                                   app_encode_app(
68.05/68.11	                                                                   fun_nat_int,
68.05/68.11	                                                                   app_encode_fun(
68.05/68.11	                                                                   nat,int),
68.05/68.11	                                                                   hAPP_nat_int,
68.05/68.11	                                                                   app_encode_app(
68.05/68.11	                                                                   int,
68.05/68.11	                                                                   fun_nat_int,
68.05/68.11	                                                                   power_power_int,
68.05/68.11	                                                                   X)),
68.05/68.11	                                                                   app_encode_app(
68.05/68.11	                                                                   int,nat,
68.05/68.11	                                                                   number_number_of_nat,
68.05/68.11	                                                                   app_encode_app(
68.05/68.11	                                                                   int,int,
68.05/68.11	                                                                   bit0,
68.05/68.11	                                                                   app_encode_app(
68.05/68.11	                                                                   int,int,
68.05/68.11	                                                                   bit1,pls)))))),
68.05/68.11	                      app_encode_app(nat,int,
68.05/68.11	                                     app_encode_app(fun_nat_int,
68.05/68.11	                                                    app_encode_fun(nat,int),
68.05/68.11	                                                    hAPP_nat_int,
68.05/68.11	                                                    app_encode_app(int,
68.05/68.11	                                                                   fun_nat_int,
68.05/68.11	                                                                   power_power_int,
68.05/68.11	                                                                   Y)),
68.05/68.11	                                     app_encode_app(int,nat,
68.05/68.11	                                                    number_number_of_nat,
68.05/68.11	                                                    app_encode_app(int,int,
68.05/68.11	                                                                   bit0,
68.05/68.11	                                                                   app_encode_app(
68.05/68.11	                                                                   int,int,
68.05/68.11	                                                                   bit1,pls))))) =
68.05/68.11	       app_encode_app(int,int,
68.05/68.11	                      app_encode_app(fun_int_int,app_encode_fun(int,int),
68.05/68.11	                                     hAPP_int_int,
68.05/68.11	                                     app_encode_app(int,fun_int_int,
68.05/68.11	                                                    plus_plus_int,
68.05/68.11	                                                    app_encode_app(int,int,
68.05/68.11	                                                                   app_encode_app(
68.05/68.11	                                                                   fun_int_int,
68.05/68.11	                                                                   app_encode_fun(
68.05/68.11	                                                                   int,int),
68.05/68.11	                                                                   hAPP_int_int,
68.05/68.11	                                                                   app_encode_app(
68.05/68.11	                                                                   int,
68.05/68.11	                                                                   fun_int_int,
68.05/68.11	                                                                   times_times_int,
68.05/68.11	                                                                   app_encode_app(
68.05/68.11	                                                                   int,int,
68.05/68.11	                                                                   number_number_of_int,
68.05/68.11	                                                                   app_encode_app(
68.05/68.11	                                                                   int,int,
68.05/68.11	                                                                   bit0,
68.05/68.11	                                                                   app_encode_app(
68.05/68.11	                                                                   int,int,
68.05/68.11	                                                                   bit0,
68.05/68.11	                                                                   app_encode_app(
68.05/68.11	                                                                   int,int,
68.05/68.11	                                                                   bit1,pls)))))),
68.05/68.11	                                                                   m))),
68.05/68.11	                      one_one_int))))).
68.05/68.11	tff('75', plain,
68.05/68.11	    (app_encode_app(int, int, 
68.05/68.11	       app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
68.05/68.11	         app_encode_app(int, fun_int_int, plus_plus_int, 
68.05/68.11	           app_encode_app(nat, int, 
68.05/68.11	             app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
68.05/68.11	               hAPP_nat_int, 
68.05/68.11	               app_encode_app(int, fun_nat_int, power_power_int, sk_X1)), 
68.05/68.11	             app_encode_app(int, nat, number_number_of_nat, 
68.05/68.11	               app_encode_app(int, int, bit0, 
68.05/68.11	                 app_encode_app(int, int, bit1, pls)))))), 
68.05/68.11	       app_encode_app(nat, int, 
68.05/68.11	         app_encode_app(fun_nat_int, app_encode_fun(nat, int), hAPP_nat_int, 
68.05/68.11	           app_encode_app(int, fun_nat_int, power_power_int, sk_Y1)), 
68.05/68.11	         app_encode_app(int, nat, number_number_of_nat, 
68.05/68.11	           app_encode_app(int, int, bit0, 
68.05/68.11	             app_encode_app(int, int, bit1, pls)))))
68.05/68.11	      = app_encode_app(int, int, 
68.05/68.11	          app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.11	            hAPP_int_int, 
68.05/68.11	            app_encode_app(int, fun_int_int, plus_plus_int, 
68.05/68.11	              app_encode_app(int, int, 
68.05/68.11	                app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.11	                  hAPP_int_int, 
68.05/68.11	                  app_encode_app(int, fun_int_int, times_times_int, 
68.05/68.11	                    app_encode_app(int, int, number_number_of_int, 
68.05/68.11	                      app_encode_app(int, int, bit0, 
68.05/68.11	                        app_encode_app(int, int, bit0, 
68.05/68.11	                          app_encode_app(int, int, bit1, pls)))))), m))), 
68.05/68.11	          one_one_int)
68.05/68.11	     | ~ app_encode_app(bool, $o, hBOOL, 
68.05/68.11	           app_encode_app(int, bool, 
68.05/68.11	             app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
68.05/68.11	               hAPP_int_bool, 
68.05/68.11	               app_encode_app(int, fun_int_bool, 
68.05/68.11	                 app_encode_app(fun_int_fun_int_bool, 
68.05/68.11	                   app_encode_fun(int, fun_int_bool), 
68.05/68.11	                   hAPP_i1948725293t_bool, ord_less_int), one_one_int)), t))),
68.05/68.11	    inference('cnf', [status(esa)], [zf_stmt_98])).
68.05/68.11	tff('76', plain,
68.05/68.11	    (app_encode_app(int, int, 
68.05/68.11	       app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
68.05/68.11	         app_encode_app(int, fun_int_int, plus_plus_int, 
68.05/68.11	           app_encode_app(nat, int, 
68.05/68.11	             app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
68.05/68.11	               hAPP_nat_int, 
68.05/68.11	               app_encode_app(int, fun_nat_int, power_power_int, sk_X1)), 
68.05/68.11	             app_encode_app(int, nat, number_number_of_nat, 
68.05/68.11	               app_encode_app(int, int, bit0, 
68.05/68.11	                 app_encode_app(int, int, bit1, zero_zero_int)))))), 
68.05/68.11	       app_encode_app(nat, int, 
68.05/68.11	         app_encode_app(fun_nat_int, app_encode_fun(nat, int), hAPP_nat_int, 
68.05/68.11	           app_encode_app(int, fun_nat_int, power_power_int, sk_Y1)), 
68.05/68.11	         app_encode_app(int, nat, number_number_of_nat, 
68.05/68.11	           app_encode_app(int, int, bit0, 
68.05/68.11	             app_encode_app(int, int, bit1, zero_zero_int)))))
68.05/68.11	      = app_encode_app(int, int, 
68.05/68.11	          app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.11	            hAPP_int_int, 
68.05/68.11	            app_encode_app(int, fun_int_int, plus_plus_int, 
68.05/68.11	              app_encode_app(int, int, 
68.05/68.11	                app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.11	                  hAPP_int_int, 
68.05/68.11	                  app_encode_app(int, fun_int_int, times_times_int, 
68.05/68.11	                    app_encode_app(int, int, bit0, 
68.05/68.11	                      app_encode_app(int, int, bit0, 
68.05/68.11	                        app_encode_app(int, int, bit1, zero_zero_int))))), m))), 
68.05/68.11	          one_one_int)
68.05/68.11	     | ~ app_encode_app(bool, $o, hBOOL, 
68.05/68.11	           app_encode_app(int, bool, 
68.05/68.11	             app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
68.05/68.11	               hAPP_int_bool, 
68.05/68.11	               app_encode_app(int, fun_int_bool, 
68.05/68.11	                 app_encode_app(fun_int_fun_int_bool, 
68.05/68.11	                   app_encode_fun(int, fun_int_bool), 
68.05/68.11	                   hAPP_i1948725293t_bool, ord_less_int), one_one_int)), t))),
68.05/68.11	    inference('demod', [status(thm)], ['75', '5', '5', '5', '7'])).
68.05/68.11	tff('77', plain,
68.05/68.11	    (app_encode_app(int, int, 
68.05/68.11	       app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
68.05/68.11	         app_encode_app(int, fun_int_int, plus_plus_int, 
68.05/68.11	           app_encode_app(nat, int, 
68.05/68.11	             app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
68.05/68.11	               hAPP_nat_int, 
68.05/68.11	               app_encode_app(int, fun_nat_int, power_power_int, sk_X1)), 
68.05/68.11	             app_encode_app(int, nat, number_number_of_nat, 
68.05/68.11	               app_encode_app(int, int, bit0, one_one_int))))), 
68.05/68.11	       app_encode_app(nat, int, 
68.05/68.11	         app_encode_app(fun_nat_int, app_encode_fun(nat, int), hAPP_nat_int, 
68.05/68.11	           app_encode_app(int, fun_nat_int, power_power_int, sk_Y1)), 
68.05/68.11	         app_encode_app(int, nat, number_number_of_nat, 
68.05/68.11	           app_encode_app(int, int, bit0, one_one_int))))
68.05/68.11	      = app_encode_app(int, int, 
68.05/68.11	          app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.11	            hAPP_int_int, 
68.05/68.11	            app_encode_app(int, fun_int_int, plus_plus_int, 
68.05/68.11	              app_encode_app(int, int, 
68.05/68.11	                app_encode_app(fun_int_int, app_encode_fun(int, int), 
68.05/68.11	                  hAPP_int_int, 
68.05/68.11	                  app_encode_app(int, fun_int_int, times_times_int, 
68.05/68.11	                    app_encode_app(int, int, bit0, 
68.05/68.11	                      app_encode_app(int, int, bit0, one_one_int)))), m))), 
68.05/68.11	          one_one_int)
68.05/68.11	     | ~ app_encode_app(bool, $o, hBOOL, 
68.05/68.11	           app_encode_app(int, bool, 
68.05/68.11	             app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
68.05/68.11	               hAPP_int_bool, 
68.05/68.11	               app_encode_app(int, fun_int_bool, 
68.05/68.11	                 app_encode_app(fun_int_fun_int_bool, 
68.05/68.11	                   app_encode_fun(int, fun_int_bool), 
68.05/68.11	                   hAPP_i1948725293t_bool, ord_less_int), one_one_int)), t))),
68.05/68.11	    inference('demod', [status(thm)], ['76', '10', '10', '10'])).
68.05/68.11	tff('78', plain,
68.05/68.11	    (app_encode_app(int, int, 
68.05/68.11	       app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
68.05/68.11	         app_encode_app(int, fun_int_int, plus_plus_int, 
68.05/68.11	           app_encode_app(nat, int, 
68.05/68.11	             app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
68.05/68.11	               hAPP_nat_int, 
68.05/68.11	               app_encode_app(int, fun_nat_int, power_power_int, sk_X1)), 
68.05/68.11	             app_encode_app(int, nat, number_number_of_nat, 
68.05/68.11	               sk_K_2(one_one_int, one_one_int, min))))), 
68.05/68.11	       app_encode_app(nat, int, 
68.05/68.11	         app_encode_app(fun_nat_int, app_encode_fun(nat, int), hAPP_nat_int, 
68.05/68.11	           app_encode_app(int, fun_nat_int, power_power_int, sk_Y1)), 
68.05/68.11	         app_encode_app(int, nat, number_number_of_nat, 
68.05/68.11	           sk_K_2(one_one_int, one_one_int, min))))
68.05/68.11	      = app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m))
68.05/68.11	     | ~ app_encode_app(bool, $o, hBOOL, 
68.05/68.11	           app_encode_app(int, bool, 
68.05/68.11	             app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
68.05/68.11	               hAPP_int_bool, 
68.05/68.11	               app_encode_app(int, fun_int_bool, 
68.05/68.11	                 app_encode_app(fun_int_fun_int_bool, 
68.05/68.11	                   app_encode_fun(int, fun_int_bool), 
68.05/68.11	                   hAPP_i1948725293t_bool, ord_less_int), one_one_int)), t))),
68.05/68.11	    inference('demod', [status(thm)],
68.05/68.11	              ['77', '54', '54', '54', '59', '62', '63', '69'])).
68.05/68.11	tff('79', plain,
68.05/68.11	    ~ app_encode_app(bool, $o, hBOOL, 
68.05/68.11	        app_encode_app(int, bool, 
68.05/68.11	          app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
68.05/68.11	            hAPP_int_bool, 
68.05/68.11	            app_encode_app(int, fun_int_bool, 
68.05/68.11	              app_encode_app(fun_int_fun_int_bool, 
68.05/68.11	                app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
68.05/68.11	                ord_less_int), one_one_int)), t)),
68.05/68.11	    inference('simplify_reflect-', [status(thm)], ['78', '72'])).
68.05/68.11	tff('80', plain, ~ $true, inference('sup-', [status(thm)], ['74', '79'])).
68.05/68.11	tff('81', plain, $false, inference('simplify', [status(thm)], ['80'])).
68.05/68.11	
68.05/68.11	% SZS output end Refutation
68.05/68.11	EOF
