0.00/0.00	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : appext
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : kbo
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n170.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 07:39:24 CST 2018
69.36/69.46	% done 13043 iterations in 69.266s
69.36/69.46	% SZS status Theorem for 'stdin'
69.36/69.46	% SZS output start Refutation
69.36/69.47	tff(zf_stmt_97, axiom,
69.36/69.47	  (app_encode_app(bool,$o,hBOOL,
69.36/69.47	                  app_encode_app(int,bool,
69.36/69.47	                                 app_encode_app(fun_int_bool,
69.36/69.47	                                                app_encode_fun(int,bool),
69.36/69.47	                                                hAPP_int_bool,
69.36/69.47	                                                app_encode_app(int,
69.36/69.47	                                                               fun_int_bool,
69.36/69.47	                                                               app_encode_app(
69.36/69.47	                                                               fun_int_fun_int_bool,
69.36/69.47	                                                               app_encode_fun(
69.36/69.47	                                                               int,
69.36/69.47	                                                               fun_int_bool),
69.36/69.47	                                                               hAPP_i1948725293t_bool,
69.36/69.47	                                                               ord_less_eq_int),
69.36/69.47	                                                               one_one_int)),
69.36/69.47	                                 t)))).
69.36/69.47	tff('0', plain,
69.36/69.47	    app_encode_app(bool, $o, hBOOL, 
69.36/69.47	      app_encode_app(int, bool, 
69.36/69.47	        app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
69.36/69.47	          hAPP_int_bool, 
69.36/69.47	          app_encode_app(int, fun_int_bool, 
69.36/69.47	            app_encode_app(fun_int_fun_int_bool, 
69.36/69.47	              app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
69.36/69.47	              ord_less_eq_int), one_one_int)), t)),
69.36/69.47	    inference('cnf', [status(esa)], [zf_stmt_97])).
69.36/69.47	tff(zf_stmt_134, axiom,
69.36/69.47	  (![Z_1:int,W_1:int]:
69.36/69.47	     (app_encode_app(bool,$o,hBOOL,
69.36/69.47	                     app_encode_app(int,bool,
69.36/69.47	                                    app_encode_app(fun_int_bool,
69.36/69.47	                                                   app_encode_fun(int,bool),
69.36/69.47	                                                   hAPP_int_bool,
69.36/69.47	                                                   app_encode_app(int,
69.36/69.47	                                                                  fun_int_bool,
69.36/69.47	                                                                  app_encode_app(
69.36/69.47	                                                                  fun_int_fun_int_bool,
69.36/69.47	                                                                  app_encode_fun(
69.36/69.47	                                                                  int,
69.36/69.47	                                                                  fun_int_bool),
69.36/69.47	                                                                  hAPP_i1948725293t_bool,
69.36/69.47	                                                                  ord_less_int),
69.36/69.47	                                                                  Z_1)),
69.36/69.47	                                    W_1)) <=>
69.36/69.47	      (app_encode_app(bool,$o,hBOOL,
69.36/69.47	                      app_encode_app(int,bool,
69.36/69.47	                                     app_encode_app(fun_int_bool,
69.36/69.47	                                                    app_encode_fun(int,bool),
69.36/69.47	                                                    hAPP_int_bool,
69.36/69.47	                                                    app_encode_app(int,
69.36/69.47	                                                                   fun_int_bool,
69.36/69.47	                                                                   app_encode_app(
69.36/69.47	                                                                   fun_int_fun_int_bool,
69.36/69.47	                                                                   app_encode_fun(
69.36/69.47	                                                                   int,
69.36/69.47	                                                                   fun_int_bool),
69.36/69.47	                                                                   hAPP_i1948725293t_bool,
69.36/69.47	                                                                   ord_less_eq_int),
69.36/69.47	                                                                   Z_1)),
69.36/69.47	                                     W_1)) & 
69.36/69.47	       (Z_1 != W_1))))).
69.36/69.47	tff('1', plain,
69.36/69.47	    ![X37 : int, X39 : int]:
69.36/69.47	      (app_encode_app(bool, $o, hBOOL, 
69.36/69.47	         app_encode_app(int, bool, 
69.36/69.47	           app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
69.36/69.47	             hAPP_int_bool, 
69.36/69.47	             app_encode_app(int, fun_int_bool, 
69.36/69.47	               app_encode_app(fun_int_fun_int_bool, 
69.36/69.47	                 app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
69.36/69.47	                 ord_less_int), X37)), X39))
69.36/69.47	       | X37 = X39
69.36/69.47	       | ~ app_encode_app(bool, $o, hBOOL, 
69.36/69.47	             app_encode_app(int, bool, 
69.36/69.47	               app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
69.36/69.47	                 hAPP_int_bool, 
69.36/69.47	                 app_encode_app(int, fun_int_bool, 
69.36/69.47	                   app_encode_app(fun_int_fun_int_bool, 
69.36/69.47	                     app_encode_fun(int, fun_int_bool), 
69.36/69.47	                     hAPP_i1948725293t_bool, ord_less_eq_int), X37)), X39))),
69.36/69.47	    inference('cnf', [status(esa)], [zf_stmt_134])).
69.36/69.47	tff('2', plain,
69.36/69.47	    (~ $true
69.36/69.47	     | one_one_int = t
69.36/69.47	     | app_encode_app(bool, $o, hBOOL, 
69.36/69.47	         app_encode_app(int, bool, 
69.36/69.47	           app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
69.36/69.47	             hAPP_int_bool, 
69.36/69.47	             app_encode_app(int, fun_int_bool, 
69.36/69.47	               app_encode_app(fun_int_fun_int_bool, 
69.36/69.47	                 app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
69.36/69.47	                 ord_less_int), one_one_int)), t))),
69.36/69.47	    inference('sup-', [status(thm)], ['0', '1'])).
69.36/69.47	tff('3', plain,
69.36/69.47	    (app_encode_app(bool, $o, hBOOL, 
69.36/69.47	       app_encode_app(int, bool, 
69.36/69.47	         app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
69.36/69.47	           hAPP_int_bool, 
69.36/69.47	           app_encode_app(int, fun_int_bool, 
69.36/69.47	             app_encode_app(fun_int_fun_int_bool, 
69.36/69.47	               app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
69.36/69.47	               ord_less_int), one_one_int)), t))
69.36/69.47	     | one_one_int = t),
69.36/69.47	    inference('simplify', [status(thm)], ['2'])).
69.36/69.47	tff(zf_stmt_98, axiom,
69.36/69.47	  ((t = one_one_int) =>
69.36/69.47	   (?[X:int,Y:int]:
69.36/69.47	      (app_encode_app(int,int,
69.36/69.47	                      app_encode_app(fun_int_int,app_encode_fun(int,int),
69.36/69.47	                                     hAPP_int_int,
69.36/69.47	                                     app_encode_app(int,fun_int_int,
69.36/69.47	                                                    plus_plus_int,
69.36/69.47	                                                    app_encode_app(nat,int,
69.36/69.47	                                                                   app_encode_app(
69.36/69.47	                                                                   fun_nat_int,
69.36/69.47	                                                                   app_encode_fun(
69.36/69.47	                                                                   nat,int),
69.36/69.47	                                                                   hAPP_nat_int,
69.36/69.47	                                                                   app_encode_app(
69.36/69.47	                                                                   int,
69.36/69.47	                                                                   fun_nat_int,
69.36/69.47	                                                                   power_power_int,
69.36/69.47	                                                                   X)),
69.36/69.47	                                                                   app_encode_app(
69.36/69.47	                                                                   int,nat,
69.36/69.47	                                                                   number_number_of_nat,
69.36/69.47	                                                                   app_encode_app(
69.36/69.47	                                                                   int,int,
69.36/69.47	                                                                   bit0,
69.36/69.47	                                                                   app_encode_app(
69.36/69.47	                                                                   int,int,
69.36/69.47	                                                                   bit1,pls)))))),
69.36/69.47	                      app_encode_app(nat,int,
69.36/69.47	                                     app_encode_app(fun_nat_int,
69.36/69.47	                                                    app_encode_fun(nat,int),
69.36/69.47	                                                    hAPP_nat_int,
69.36/69.47	                                                    app_encode_app(int,
69.36/69.47	                                                                   fun_nat_int,
69.36/69.47	                                                                   power_power_int,
69.36/69.47	                                                                   Y)),
69.36/69.47	                                     app_encode_app(int,nat,
69.36/69.47	                                                    number_number_of_nat,
69.36/69.47	                                                    app_encode_app(int,int,
69.36/69.47	                                                                   bit0,
69.36/69.47	                                                                   app_encode_app(
69.36/69.47	                                                                   int,int,
69.36/69.47	                                                                   bit1,pls))))) =
69.36/69.47	       app_encode_app(int,int,
69.36/69.47	                      app_encode_app(fun_int_int,app_encode_fun(int,int),
69.36/69.47	                                     hAPP_int_int,
69.36/69.47	                                     app_encode_app(int,fun_int_int,
69.36/69.47	                                                    plus_plus_int,
69.36/69.47	                                                    app_encode_app(int,int,
69.36/69.47	                                                                   app_encode_app(
69.36/69.47	                                                                   fun_int_int,
69.36/69.47	                                                                   app_encode_fun(
69.36/69.47	                                                                   int,int),
69.36/69.47	                                                                   hAPP_int_int,
69.36/69.47	                                                                   app_encode_app(
69.36/69.47	                                                                   int,
69.36/69.47	                                                                   fun_int_int,
69.36/69.47	                                                                   times_times_int,
69.36/69.47	                                                                   app_encode_app(
69.36/69.47	                                                                   int,int,
69.36/69.47	                                                                   number_number_of_int,
69.36/69.47	                                                                   app_encode_app(
69.36/69.47	                                                                   int,int,
69.36/69.47	                                                                   bit0,
69.36/69.47	                                                                   app_encode_app(
69.36/69.47	                                                                   int,int,
69.36/69.47	                                                                   bit0,
69.36/69.47	                                                                   app_encode_app(
69.36/69.47	                                                                   int,int,
69.36/69.47	                                                                   bit1,pls)))))),
69.36/69.47	                                                                   m))),
69.36/69.47	                      one_one_int))))).
69.36/69.47	tff('4', plain,
69.36/69.47	    (app_encode_app(int, int, 
69.36/69.47	       app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
69.36/69.47	         app_encode_app(int, fun_int_int, plus_plus_int, 
69.36/69.47	           app_encode_app(nat, int, 
69.36/69.47	             app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
69.36/69.47	               hAPP_nat_int, 
69.36/69.47	               app_encode_app(int, fun_nat_int, power_power_int, sk_X)), 
69.36/69.47	             app_encode_app(int, nat, number_number_of_nat, 
69.36/69.47	               app_encode_app(int, int, bit0, 
69.36/69.47	                 app_encode_app(int, int, bit1, pls)))))), 
69.36/69.47	       app_encode_app(nat, int, 
69.36/69.47	         app_encode_app(fun_nat_int, app_encode_fun(nat, int), hAPP_nat_int, 
69.36/69.47	           app_encode_app(int, fun_nat_int, power_power_int, sk_Y)), 
69.36/69.47	         app_encode_app(int, nat, number_number_of_nat, 
69.36/69.47	           app_encode_app(int, int, bit0, 
69.36/69.47	             app_encode_app(int, int, bit1, pls)))))
69.36/69.47	      = app_encode_app(int, int, 
69.36/69.47	          app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	            hAPP_int_int, 
69.36/69.47	            app_encode_app(int, fun_int_int, plus_plus_int, 
69.36/69.47	              app_encode_app(int, int, 
69.36/69.47	                app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	                  hAPP_int_int, 
69.36/69.47	                  app_encode_app(int, fun_int_int, times_times_int, 
69.36/69.47	                    app_encode_app(int, int, number_number_of_int, 
69.36/69.47	                      app_encode_app(int, int, bit0, 
69.36/69.47	                        app_encode_app(int, int, bit0, 
69.36/69.47	                          app_encode_app(int, int, bit1, pls)))))), m))), 
69.36/69.47	          one_one_int)
69.36/69.47	     | t != one_one_int),
69.36/69.47	    inference('cnf', [status(esa)], [zf_stmt_98])).
69.36/69.47	tff(zf_stmt_455, axiom, (pls = zero_zero_int)).
69.36/69.47	tff('5', plain, pls = zero_zero_int,
69.36/69.47	    inference('cnf', [status(esa)], [zf_stmt_455])).
69.36/69.47	tff(zf_stmt_241, axiom,
69.36/69.47	  (![K_1:int]: (app_encode_app(int,int,number_number_of_int,K_1) = K_1))).
69.36/69.47	tff('6', plain,
69.36/69.47	    ![X328 : int]:
69.36/69.47	      app_encode_app(int, int, number_number_of_int, X328) = X328,
69.36/69.47	    inference('cnf', [status(esa)], [zf_stmt_241])).
69.36/69.47	tff('7', plain,
69.36/69.47	    (app_encode_app(int, int, 
69.36/69.47	       app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
69.36/69.47	         app_encode_app(int, fun_int_int, plus_plus_int, 
69.36/69.47	           app_encode_app(nat, int, 
69.36/69.47	             app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
69.36/69.47	               hAPP_nat_int, 
69.36/69.47	               app_encode_app(int, fun_nat_int, power_power_int, sk_X)), 
69.36/69.47	             app_encode_app(int, nat, number_number_of_nat, 
69.36/69.47	               app_encode_app(int, int, bit0, 
69.36/69.47	                 app_encode_app(int, int, bit1, zero_zero_int)))))), 
69.36/69.47	       app_encode_app(nat, int, 
69.36/69.47	         app_encode_app(fun_nat_int, app_encode_fun(nat, int), hAPP_nat_int, 
69.36/69.47	           app_encode_app(int, fun_nat_int, power_power_int, sk_Y)), 
69.36/69.47	         app_encode_app(int, nat, number_number_of_nat, 
69.36/69.47	           app_encode_app(int, int, bit0, 
69.36/69.47	             app_encode_app(int, int, bit1, zero_zero_int)))))
69.36/69.47	      = app_encode_app(int, int, 
69.36/69.47	          app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	            hAPP_int_int, 
69.36/69.47	            app_encode_app(int, fun_int_int, plus_plus_int, 
69.36/69.47	              app_encode_app(int, int, 
69.36/69.47	                app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	                  hAPP_int_int, 
69.36/69.47	                  app_encode_app(int, fun_int_int, times_times_int, 
69.36/69.47	                    app_encode_app(int, int, bit0, 
69.36/69.47	                      app_encode_app(int, int, bit0, 
69.36/69.47	                        app_encode_app(int, int, bit1, zero_zero_int))))), m))), 
69.36/69.47	          one_one_int)
69.36/69.47	     | t != one_one_int),
69.36/69.47	    inference('demod', [status(thm)], ['4', '5', '5', '5', '6'])).
69.36/69.47	tff(zf_stmt_357, axiom,
69.36/69.47	  (app_encode_app(int,int,number_number_of_int,
69.36/69.47	                  app_encode_app(int,int,bit1,pls)) =
69.36/69.47	   one_one_int)).
69.36/69.47	tff('8', plain,
69.36/69.47	    app_encode_app(int, int, number_number_of_int, 
69.36/69.47	      app_encode_app(int, int, bit1, pls))
69.36/69.47	     = one_one_int,
69.36/69.47	    inference('cnf', [status(esa)], [zf_stmt_357])).
69.36/69.47	tff('9', plain, app_encode_app(int, int, bit1, zero_zero_int) = one_one_int,
69.36/69.47	    inference('demod', [status(thm)], ['8', '5', '6'])).
69.36/69.47	tff('10', plain,
69.36/69.47	    (app_encode_app(int, int, 
69.36/69.47	       app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
69.36/69.47	         app_encode_app(int, fun_int_int, plus_plus_int, 
69.36/69.47	           app_encode_app(nat, int, 
69.36/69.47	             app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
69.36/69.47	               hAPP_nat_int, 
69.36/69.47	               app_encode_app(int, fun_nat_int, power_power_int, sk_X)), 
69.36/69.47	             app_encode_app(int, nat, number_number_of_nat, 
69.36/69.47	               app_encode_app(int, int, bit0, one_one_int))))), 
69.36/69.47	       app_encode_app(nat, int, 
69.36/69.47	         app_encode_app(fun_nat_int, app_encode_fun(nat, int), hAPP_nat_int, 
69.36/69.47	           app_encode_app(int, fun_nat_int, power_power_int, sk_Y)), 
69.36/69.47	         app_encode_app(int, nat, number_number_of_nat, 
69.36/69.47	           app_encode_app(int, int, bit0, one_one_int))))
69.36/69.47	      = app_encode_app(int, int, 
69.36/69.47	          app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	            hAPP_int_int, 
69.36/69.47	            app_encode_app(int, fun_int_int, plus_plus_int, 
69.36/69.47	              app_encode_app(int, int, 
69.36/69.47	                app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	                  hAPP_int_int, 
69.36/69.47	                  app_encode_app(int, fun_int_int, times_times_int, 
69.36/69.47	                    app_encode_app(int, int, bit0, 
69.36/69.47	                      app_encode_app(int, int, bit0, one_one_int)))), m))), 
69.36/69.47	          one_one_int)
69.36/69.47	     | t != one_one_int),
69.36/69.47	    inference('demod', [status(thm)], ['7', '9', '9', '9'])).
69.36/69.47	tff(zf_stmt_285, axiom,
69.36/69.47	  (![A_99:int]:
69.36/69.47	     (app_encode_app(int,int,
69.36/69.47	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
69.36/69.47	                                    hAPP_int_int,
69.36/69.47	                                    app_encode_app(int,fun_int_int,
69.36/69.47	                                                   times_times_int,
69.36/69.47	                                                   one_one_int)),
69.36/69.47	                     A_99) =
69.36/69.47	      A_99))).
69.36/69.47	tff('11', plain,
69.36/69.47	    ![X446 : int]:
69.36/69.47	      app_encode_app(int, int, 
69.36/69.47	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
69.36/69.47	          app_encode_app(int, fun_int_int, times_times_int, one_one_int)), 
69.36/69.47	        X446)
69.36/69.47	       = X446,
69.36/69.47	    inference('cnf', [status(esa)], [zf_stmt_285])).
69.36/69.47	tff(zf_stmt_2, axiom,
69.36/69.47	  (![X:app_encode_fun(Alpha,Beta),Y:app_encode_fun(Alpha,Beta)]:
69.36/69.47	     ((![Z:Alpha]:
69.36/69.47	         (app_encode_app(Alpha,Beta,X,Z) = app_encode_app(Alpha,Beta,Y,Z))) =>
69.36/69.47	      (X = Y)))).
69.36/69.47	tff('12', plain,
69.36/69.47	    ![X0 : $tType, X1 : $tType, X2 : app_encode_fun(X0, X1), 
69.36/69.47	      X3 : app_encode_fun(X0, X1)]:
69.36/69.47	      (X3 = X2
69.36/69.47	       | app_encode_app(X0, X1, X3, sk_Z(X1, X0, X2, X3))
69.36/69.47	          != app_encode_app(X0, X1, X2, sk_Z(X1, X0, X2, X3))),
69.36/69.47	    inference('cnf', [status(esa)], [zf_stmt_2])).
69.36/69.47	tff('13', plain,
69.36/69.47	    ![X0 : app_encode_fun(int, int)]:
69.36/69.47	      (app_encode_app(int, int, X0, sk_Z(int, int, number_number_of_int, X0))
69.36/69.47	        != sk_Z(int, int, number_number_of_int, X0)
69.36/69.47	       | X0 = number_number_of_int),
69.36/69.47	    inference('sup-', [status(thm)], ['6', '12'])).
69.36/69.47	tff('14', plain,
69.36/69.47	    (sk_Z(int, int, number_number_of_int, 
69.36/69.47	       app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
69.36/69.47	         app_encode_app(int, fun_int_int, times_times_int, one_one_int)))
69.36/69.47	      != sk_Z(int, int, number_number_of_int, 
69.36/69.47	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	             hAPP_int_int, 
69.36/69.47	             app_encode_app(int, fun_int_int, times_times_int, one_one_int)))
69.36/69.47	     | app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
69.36/69.47	         app_encode_app(int, fun_int_int, times_times_int, one_one_int))
69.36/69.47	        = number_number_of_int),
69.36/69.47	    inference('sup-', [status(thm)], ['11', '13'])).
69.36/69.47	tff('15', plain,
69.36/69.47	    app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
69.36/69.47	      app_encode_app(int, fun_int_int, times_times_int, one_one_int))
69.36/69.47	     = number_number_of_int,
69.36/69.47	    inference('simplify', [status(thm)], ['14'])).
69.36/69.47	tff(zf_stmt_687, axiom,
69.36/69.47	  (![A_2:int,B_2:int,Ma:int]:
69.36/69.47	     (app_encode_app(bool,$o,hBOOL,
69.36/69.47	                     app_encode_app(int,bool,
69.36/69.47	                                    app_encode_app(fun_int_bool,
69.36/69.47	                                                   app_encode_fun(int,bool),
69.36/69.47	                                                   hAPP_int_bool,
69.36/69.47	                                                   app_encode_app(int,
69.36/69.47	                                                                  fun_int_bool,
69.36/69.47	                                                                  app_encode_app(
69.36/69.47	                                                                  int,
69.36/69.47	                                                                  app_encode_fun(
69.36/69.47	                                                                  int,
69.36/69.47	                                                                  fun_int_bool),
69.36/69.47	                                                                  zcong,A_2),
69.36/69.47	                                                                  B_2)),
69.36/69.47	                                    Ma)) <=>
69.36/69.47	      (?[K_2:int]:
69.36/69.47	         (B_2 =
69.36/69.47	          app_encode_app(int,int,
69.36/69.47	                         app_encode_app(fun_int_int,app_encode_fun(int,int),
69.36/69.47	                                        hAPP_int_int,
69.36/69.47	                                        app_encode_app(int,fun_int_int,
69.36/69.47	                                                       plus_plus_int,A_2)),
69.36/69.47	                         app_encode_app(int,int,
69.36/69.47	                                        app_encode_app(fun_int_int,
69.36/69.47	                                                       app_encode_fun(
69.36/69.47	                                                       int,int),hAPP_int_int,
69.36/69.47	                                                       app_encode_app(
69.36/69.47	                                                       int,fun_int_int,
69.36/69.47	                                                       times_times_int,Ma)),
69.36/69.47	                                        K_2))))))).
69.36/69.47	tff('16', plain,
69.36/69.47	    ![X1216 : int, X1217 : int, X1218 : int]:
69.36/69.47	      (X1218
69.36/69.47	        = app_encode_app(int, int, 
69.36/69.47	            app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	              hAPP_int_int, 
69.36/69.47	              app_encode_app(int, fun_int_int, plus_plus_int, X1216)), 
69.36/69.47	            app_encode_app(int, int, 
69.36/69.47	              app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	                hAPP_int_int, 
69.36/69.47	                app_encode_app(int, fun_int_int, times_times_int, X1217)), 
69.36/69.47	              sk_K_2(X1217, X1218, X1216)))
69.36/69.47	       | ~ app_encode_app(bool, $o, hBOOL, 
69.36/69.47	             app_encode_app(int, bool, 
69.36/69.47	               app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
69.36/69.47	                 hAPP_int_bool, 
69.36/69.47	                 app_encode_app(int, fun_int_bool, 
69.36/69.47	                   app_encode_app(int, app_encode_fun(int, fun_int_bool), 
69.36/69.47	                     zcong, X1216), X1218)), X1217))),
69.36/69.47	    inference('cnf', [status(esa)], [zf_stmt_687])).
69.36/69.47	tff('17', plain,
69.36/69.47	    ![X0 : int, X1 : int]:
69.36/69.47	      (X1
69.36/69.47	        = app_encode_app(int, int, 
69.36/69.47	            app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	              hAPP_int_int, 
69.36/69.47	              app_encode_app(int, fun_int_int, plus_plus_int, X0)), 
69.36/69.47	            app_encode_app(int, int, number_number_of_int, 
69.36/69.47	              sk_K_2(one_one_int, X1, X0)))
69.36/69.47	       | ~ app_encode_app(bool, $o, hBOOL, 
69.36/69.47	             app_encode_app(int, bool, 
69.36/69.47	               app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
69.36/69.47	                 hAPP_int_bool, 
69.36/69.47	                 app_encode_app(int, fun_int_bool, 
69.36/69.47	                   app_encode_app(int, app_encode_fun(int, fun_int_bool), 
69.36/69.47	                     zcong, X0), X1)), one_one_int))),
69.36/69.47	    inference('sup+', [status(thm)], ['15', '16'])).
69.36/69.47	tff(zf_stmt_671, axiom,
69.36/69.47	  (![A:int,B:int]:
69.36/69.47	     app_encode_app(bool,$o,hBOOL,
69.36/69.47	                    app_encode_app(int,bool,
69.36/69.47	                                   app_encode_app(fun_int_bool,
69.36/69.47	                                                  app_encode_fun(int,bool),
69.36/69.47	                                                  hAPP_int_bool,
69.36/69.47	                                                  app_encode_app(int,
69.36/69.47	                                                                 fun_int_bool,
69.36/69.47	                                                                 app_encode_app(
69.36/69.47	                                                                 int,
69.36/69.47	                                                                 app_encode_fun(
69.36/69.47	                                                                 int,
69.36/69.47	                                                                 fun_int_bool),
69.36/69.47	                                                                 zcong,A),B)),
69.36/69.47	                                   one_one_int)))).
69.36/69.47	tff('18', plain,
69.36/69.47	    ![X1173 : int, X1174 : int]:
69.36/69.47	      app_encode_app(bool, $o, hBOOL, 
69.36/69.47	        app_encode_app(int, bool, 
69.36/69.47	          app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
69.36/69.47	            hAPP_int_bool, 
69.36/69.47	            app_encode_app(int, fun_int_bool, 
69.36/69.47	              app_encode_app(int, app_encode_fun(int, fun_int_bool), zcong, 
69.36/69.47	                X1173), X1174)), one_one_int)),
69.36/69.47	    inference('cnf', [status(esa)], [zf_stmt_671])).
69.36/69.47	tff('19', plain,
69.36/69.47	    ![X0 : int, X1 : int]:
69.36/69.47	      (X1
69.36/69.47	        = app_encode_app(int, int, 
69.36/69.47	            app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	              hAPP_int_int, 
69.36/69.47	              app_encode_app(int, fun_int_int, plus_plus_int, X0)), 
69.36/69.47	            sk_K_2(one_one_int, X1, X0))
69.36/69.47	       | ~ $true),
69.36/69.47	    inference('demod', [status(thm)], ['17', '6', '18'])).
69.36/69.47	tff('20', plain,
69.36/69.47	    ![X0 : int, X1 : int]:
69.36/69.47	      X1
69.36/69.47	       = app_encode_app(int, int, 
69.36/69.47	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	             hAPP_int_int, 
69.36/69.47	             app_encode_app(int, fun_int_int, plus_plus_int, X0)), 
69.36/69.47	           sk_K_2(one_one_int, X1, X0)),
69.36/69.47	    inference('simplify', [status(thm)], ['19'])).
69.36/69.47	tff(zf_stmt_283, axiom,
69.36/69.47	  (![A_100:nat]:
69.36/69.47	     (app_encode_app(nat,nat,
69.36/69.47	                     app_encode_app(fun_nat_nat,app_encode_fun(nat,nat),
69.36/69.47	                                    hAPP_nat_nat,
69.36/69.47	                                    app_encode_app(nat,fun_nat_nat,
69.36/69.47	                                                   times_times_nat,A_100)),
69.36/69.47	                     one_one_nat) =
69.36/69.47	      A_100))).
69.36/69.47	tff('21', plain,
69.36/69.47	    ![X444 : nat]:
69.36/69.47	      app_encode_app(nat, nat, 
69.36/69.47	        app_encode_app(fun_nat_nat, app_encode_fun(nat, nat), hAPP_nat_nat, 
69.36/69.47	          app_encode_app(nat, fun_nat_nat, times_times_nat, X444)), 
69.36/69.47	        one_one_nat)
69.36/69.47	       = X444,
69.36/69.47	    inference('cnf', [status(esa)], [zf_stmt_283])).
69.36/69.47	tff(zf_stmt_677, axiom,
69.36/69.47	  (![N_4:nat]:
69.36/69.47	     (app_encode_app(nat,real,
69.36/69.47	                     app_encode_app(fun_nat_real,app_encode_fun(nat,real),
69.36/69.47	                                    hAPP_nat_real,
69.36/69.47	                                    app_encode_app(real,fun_nat_real,
69.36/69.47	                                                   power_power_real,
69.36/69.47	                                                   app_encode_app(int,real,
69.36/69.47	                                                                  number267125858f_real,
69.36/69.47	                                                                  min))),
69.36/69.47	                     app_encode_app(nat,nat,
69.36/69.47	                                    app_encode_app(fun_nat_nat,
69.36/69.47	                                                   app_encode_fun(nat,nat),
69.36/69.47	                                                   hAPP_nat_nat,
69.36/69.47	                                                   app_encode_app(nat,
69.36/69.47	                                                                  fun_nat_nat,
69.36/69.47	                                                                  times_times_nat,
69.36/69.47	                                                                  app_encode_app(
69.36/69.47	                                                                  int,nat,
69.36/69.47	                                                                  number_number_of_nat,
69.36/69.47	                                                                  app_encode_app(
69.36/69.47	                                                                  int,int,
69.36/69.47	                                                                  bit0,
69.36/69.47	                                                                  app_encode_app(
69.36/69.47	                                                                  int,int,
69.36/69.47	                                                                  bit1,pls))))),
69.36/69.47	                                    N_4)) =
69.36/69.47	      one_one_real))).
69.36/69.47	tff('22', plain,
69.36/69.47	    ![X1196 : nat]:
69.36/69.47	      app_encode_app(nat, real, 
69.36/69.47	        app_encode_app(fun_nat_real, app_encode_fun(nat, real), 
69.36/69.47	          hAPP_nat_real, 
69.36/69.47	          app_encode_app(real, fun_nat_real, power_power_real, 
69.36/69.47	            app_encode_app(int, real, number267125858f_real, min))), 
69.36/69.47	        app_encode_app(nat, nat, 
69.36/69.47	          app_encode_app(fun_nat_nat, app_encode_fun(nat, nat), 
69.36/69.47	            hAPP_nat_nat, 
69.36/69.47	            app_encode_app(nat, fun_nat_nat, times_times_nat, 
69.36/69.47	              app_encode_app(int, nat, number_number_of_nat, 
69.36/69.47	                app_encode_app(int, int, bit0, 
69.36/69.47	                  app_encode_app(int, int, bit1, pls))))), X1196))
69.36/69.47	       = one_one_real,
69.36/69.47	    inference('cnf', [status(esa)], [zf_stmt_677])).
69.36/69.47	tff('23', plain,
69.36/69.47	    ![X1196 : nat]:
69.36/69.47	      app_encode_app(nat, real, 
69.36/69.47	        app_encode_app(fun_nat_real, app_encode_fun(nat, real), 
69.36/69.47	          hAPP_nat_real, 
69.36/69.47	          app_encode_app(real, fun_nat_real, power_power_real, 
69.36/69.47	            app_encode_app(int, real, number267125858f_real, min))), 
69.36/69.47	        app_encode_app(nat, nat, 
69.36/69.47	          app_encode_app(fun_nat_nat, app_encode_fun(nat, nat), 
69.36/69.47	            hAPP_nat_nat, 
69.36/69.47	            app_encode_app(nat, fun_nat_nat, times_times_nat, 
69.36/69.47	              app_encode_app(int, nat, number_number_of_nat, 
69.36/69.47	                app_encode_app(int, int, bit0, one_one_int)))), X1196))
69.36/69.47	       = one_one_real,
69.36/69.47	    inference('demod', [status(thm)], ['22', '5', '9'])).
69.36/69.47	tff('24', plain,
69.36/69.47	    app_encode_app(nat, real, 
69.36/69.47	      app_encode_app(fun_nat_real, app_encode_fun(nat, real), hAPP_nat_real, 
69.36/69.47	        app_encode_app(real, fun_nat_real, power_power_real, 
69.36/69.47	          app_encode_app(int, real, number267125858f_real, min))), 
69.36/69.47	      app_encode_app(int, nat, number_number_of_nat, 
69.36/69.47	        app_encode_app(int, int, bit0, one_one_int)))
69.36/69.47	     = one_one_real,
69.36/69.47	    inference('sup+', [status(thm)], ['21', '23'])).
69.36/69.47	tff(zf_stmt_117, axiom,
69.36/69.47	  (![X_26:real]:
69.36/69.47	     (app_encode_app(real,real,
69.36/69.47	                     app_encode_app(fun_real_real,app_encode_fun(real,real),
69.36/69.47	                                    hAPP_real_real,
69.36/69.47	                                    app_encode_app(real,fun_real_real,
69.36/69.47	                                                   times_times_real,X_26)),
69.36/69.47	                     X_26) =
69.36/69.47	      app_encode_app(nat,real,
69.36/69.47	                     app_encode_app(fun_nat_real,app_encode_fun(nat,real),
69.36/69.47	                                    hAPP_nat_real,
69.36/69.47	                                    app_encode_app(real,fun_nat_real,
69.36/69.47	                                                   power_power_real,X_26)),
69.36/69.47	                     app_encode_app(int,nat,number_number_of_nat,
69.36/69.47	                                    app_encode_app(int,int,bit0,
69.36/69.47	                                                   app_encode_app(int,int,
69.36/69.47	                                                                  bit1,pls))))))).
69.36/69.47	tff('25', plain,
69.36/69.47	    ![X19 : real]:
69.36/69.47	      app_encode_app(real, real, 
69.36/69.47	        app_encode_app(fun_real_real, app_encode_fun(real, real), 
69.36/69.47	          hAPP_real_real, 
69.36/69.47	          app_encode_app(real, fun_real_real, times_times_real, X19)), X19)
69.36/69.47	       = app_encode_app(nat, real, 
69.36/69.47	           app_encode_app(fun_nat_real, app_encode_fun(nat, real), 
69.36/69.47	             hAPP_nat_real, 
69.36/69.47	             app_encode_app(real, fun_nat_real, power_power_real, X19)), 
69.36/69.47	           app_encode_app(int, nat, number_number_of_nat, 
69.36/69.47	             app_encode_app(int, int, bit0, 
69.36/69.47	               app_encode_app(int, int, bit1, pls)))),
69.36/69.47	    inference('cnf', [status(esa)], [zf_stmt_117])).
69.36/69.47	tff('26', plain,
69.36/69.47	    ![X19 : real]:
69.36/69.47	      app_encode_app(real, real, 
69.36/69.47	        app_encode_app(fun_real_real, app_encode_fun(real, real), 
69.36/69.47	          hAPP_real_real, 
69.36/69.47	          app_encode_app(real, fun_real_real, times_times_real, X19)), X19)
69.36/69.47	       = app_encode_app(nat, real, 
69.36/69.47	           app_encode_app(fun_nat_real, app_encode_fun(nat, real), 
69.36/69.47	             hAPP_nat_real, 
69.36/69.47	             app_encode_app(real, fun_nat_real, power_power_real, X19)), 
69.36/69.47	           app_encode_app(int, nat, number_number_of_nat, 
69.36/69.47	             app_encode_app(int, int, bit0, one_one_int))),
69.36/69.47	    inference('demod', [status(thm)], ['25', '5', '9'])).
69.36/69.47	tff(zf_stmt_339, axiom,
69.36/69.47	  (![V_13:int,W_12:int]:
69.36/69.47	     (app_encode_app(real,real,
69.36/69.47	                     app_encode_app(fun_real_real,app_encode_fun(real,real),
69.36/69.47	                                    hAPP_real_real,
69.36/69.47	                                    app_encode_app(real,fun_real_real,
69.36/69.47	                                                   times_times_real,
69.36/69.47	                                                   app_encode_app(int,real,
69.36/69.47	                                                                  number267125858f_real,
69.36/69.47	                                                                  V_13))),
69.36/69.47	                     app_encode_app(int,real,number267125858f_real,W_12)) =
69.36/69.47	      app_encode_app(int,real,number267125858f_real,
69.36/69.47	                     app_encode_app(int,int,
69.36/69.47	                                    app_encode_app(fun_int_int,
69.36/69.47	                                                   app_encode_fun(int,int),
69.36/69.47	                                                   hAPP_int_int,
69.36/69.47	                                                   app_encode_app(int,
69.36/69.47	                                                                  fun_int_int,
69.36/69.47	                                                                  times_times_int,
69.36/69.47	                                                                  V_13)),
69.36/69.47	                                    W_12))))).
69.36/69.47	tff('27', plain,
69.36/69.47	    ![X546 : int, X547 : int]:
69.36/69.47	      app_encode_app(real, real, 
69.36/69.47	        app_encode_app(fun_real_real, app_encode_fun(real, real), 
69.36/69.47	          hAPP_real_real, 
69.36/69.47	          app_encode_app(real, fun_real_real, times_times_real, 
69.36/69.47	            app_encode_app(int, real, number267125858f_real, X546))), 
69.36/69.47	        app_encode_app(int, real, number267125858f_real, X547))
69.36/69.47	       = app_encode_app(int, real, number267125858f_real, 
69.36/69.47	           app_encode_app(int, int, 
69.36/69.47	             app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	               hAPP_int_int, 
69.36/69.47	               app_encode_app(int, fun_int_int, times_times_int, X546)), 
69.36/69.47	             X547)),
69.36/69.47	    inference('cnf', [status(esa)], [zf_stmt_339])).
69.36/69.47	tff('28', plain,
69.36/69.47	    app_encode_app(int, real, number267125858f_real, 
69.36/69.47	      app_encode_app(int, int, 
69.36/69.47	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
69.36/69.47	          app_encode_app(int, fun_int_int, times_times_int, min)), min))
69.36/69.47	     = one_one_real,
69.36/69.47	    inference('demod', [status(thm)], ['24', '26', '27'])).
69.36/69.47	tff(zf_stmt_359, axiom,
69.36/69.47	  (app_encode_app(int,real,number267125858f_real,
69.36/69.47	                  app_encode_app(int,int,bit1,pls)) =
69.36/69.47	   one_one_real)).
69.36/69.47	tff('29', plain,
69.36/69.47	    app_encode_app(int, real, number267125858f_real, 
69.36/69.47	      app_encode_app(int, int, bit1, pls))
69.36/69.47	     = one_one_real,
69.36/69.47	    inference('cnf', [status(esa)], [zf_stmt_359])).
69.36/69.47	tff('30', plain,
69.36/69.47	    app_encode_app(int, real, number267125858f_real, one_one_int)
69.36/69.47	     = one_one_real,
69.36/69.47	    inference('demod', [status(thm)], ['29', '5', '9'])).
69.36/69.47	tff(zf_stmt_233, axiom,
69.36/69.47	  (![X_2:int,Y_2:int]:
69.36/69.47	     ((app_encode_app(int,real,number267125858f_real,X_2) =
69.36/69.47	       app_encode_app(int,real,number267125858f_real,Y_2)) <=>
69.36/69.47	      (X_2 = Y_2)))).
69.36/69.47	tff('31', plain,
69.36/69.47	    ![X305 : int, X306 : int]:
69.36/69.47	      (X306 = X305
69.36/69.47	       | app_encode_app(int, real, number267125858f_real, X306)
69.36/69.47	          != app_encode_app(int, real, number267125858f_real, X305)),
69.36/69.47	    inference('cnf', [status(esa)], [zf_stmt_233])).
69.36/69.47	tff('32', plain,
69.36/69.47	    ![X0 : int]:
69.36/69.47	      (one_one_real != app_encode_app(int, real, number267125858f_real, X0)
69.36/69.47	       | one_one_int = X0),
69.36/69.47	    inference('sup-', [status(thm)], ['30', '31'])).
69.36/69.47	tff('33', plain,
69.36/69.47	    (one_one_real != one_one_real
69.36/69.47	     | one_one_int
69.36/69.47	        = app_encode_app(int, int, 
69.36/69.47	            app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	              hAPP_int_int, 
69.36/69.47	              app_encode_app(int, fun_int_int, times_times_int, min)), min)),
69.36/69.47	    inference('sup-', [status(thm)], ['28', '32'])).
69.36/69.47	tff('34', plain,
69.36/69.47	    one_one_int
69.36/69.47	     = app_encode_app(int, int, 
69.36/69.47	         app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
69.36/69.47	           app_encode_app(int, fun_int_int, times_times_int, min)), min),
69.36/69.47	    inference('simplify', [status(thm)], ['33'])).
69.36/69.47	tff(zf_stmt_365, axiom,
69.36/69.47	  (![K_1:int,L:int]:
69.36/69.47	     (app_encode_app(int,int,
69.36/69.47	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
69.36/69.47	                                    hAPP_int_int,
69.36/69.47	                                    app_encode_app(int,fun_int_int,
69.36/69.47	                                                   times_times_int,
69.36/69.47	                                                   app_encode_app(int,int,
69.36/69.47	                                                                  bit1,K_1))),
69.36/69.47	                     L) =
69.36/69.47	      app_encode_app(int,int,
69.36/69.47	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
69.36/69.47	                                    hAPP_int_int,
69.36/69.47	                                    app_encode_app(int,fun_int_int,
69.36/69.47	                                                   plus_plus_int,
69.36/69.47	                                                   app_encode_app(int,int,
69.36/69.47	                                                                  bit0,
69.36/69.47	                                                                  app_encode_app(
69.36/69.47	                                                                  int,int,
69.36/69.47	                                                                  app_encode_app(
69.36/69.47	                                                                  fun_int_int,
69.36/69.47	                                                                  app_encode_fun(
69.36/69.47	                                                                  int,int),
69.36/69.47	                                                                  hAPP_int_int,
69.36/69.47	                                                                  app_encode_app(
69.36/69.47	                                                                  int,
69.36/69.47	                                                                  fun_int_int,
69.36/69.47	                                                                  times_times_int,
69.36/69.47	                                                                  K_1)),L)))),
69.36/69.47	                     L)))).
69.36/69.47	tff('35', plain,
69.36/69.47	    ![X577 : int, X578 : int]:
69.36/69.47	      app_encode_app(int, int, 
69.36/69.47	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
69.36/69.47	          app_encode_app(int, fun_int_int, times_times_int, 
69.36/69.47	            app_encode_app(int, int, bit1, X577))), X578)
69.36/69.47	       = app_encode_app(int, int, 
69.36/69.47	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	             hAPP_int_int, 
69.36/69.47	             app_encode_app(int, fun_int_int, plus_plus_int, 
69.36/69.47	               app_encode_app(int, int, bit0, 
69.36/69.47	                 app_encode_app(int, int, 
69.36/69.47	                   app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	                     hAPP_int_int, 
69.36/69.47	                     app_encode_app(int, fun_int_int, times_times_int, X577)), 
69.36/69.47	                   X578)))), X578),
69.36/69.47	    inference('cnf', [status(esa)], [zf_stmt_365])).
69.36/69.47	tff(zf_stmt_229, axiom,
69.36/69.47	  (![A_104:int,C_30:int]:
69.36/69.47	     (app_encode_app(int,int,
69.36/69.47	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
69.36/69.47	                                    hAPP_int_int,
69.36/69.47	                                    app_encode_app(int,fun_int_int,
69.36/69.47	                                                   plus_plus_int,A_104)),
69.36/69.47	                     C_30) =
69.36/69.47	      app_encode_app(int,int,
69.36/69.47	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
69.36/69.47	                                    hAPP_int_int,
69.36/69.47	                                    app_encode_app(int,fun_int_int,
69.36/69.47	                                                   plus_plus_int,C_30)),
69.36/69.47	                     A_104)))).
69.36/69.47	tff('36', plain,
69.36/69.47	    ![X296 : int, X297 : int]:
69.36/69.47	      app_encode_app(int, int, 
69.36/69.47	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
69.36/69.47	          app_encode_app(int, fun_int_int, plus_plus_int, X297)), X296)
69.36/69.47	       = app_encode_app(int, int, 
69.36/69.47	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	             hAPP_int_int, 
69.36/69.47	             app_encode_app(int, fun_int_int, plus_plus_int, X296)), X297),
69.36/69.47	    inference('cnf', [status(esa)], [zf_stmt_229])).
69.36/69.47	tff('37', plain,
69.36/69.47	    ![X577 : int, X578 : int]:
69.36/69.47	      app_encode_app(int, int, 
69.36/69.47	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
69.36/69.47	          app_encode_app(int, fun_int_int, times_times_int, 
69.36/69.47	            app_encode_app(int, int, bit1, X577))), X578)
69.36/69.47	       = app_encode_app(int, int, 
69.36/69.47	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	             hAPP_int_int, 
69.36/69.47	             app_encode_app(int, fun_int_int, plus_plus_int, X578)), 
69.36/69.47	           app_encode_app(int, int, bit0, 
69.36/69.47	             app_encode_app(int, int, 
69.36/69.47	               app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	                 hAPP_int_int, 
69.36/69.47	                 app_encode_app(int, fun_int_int, times_times_int, X577)), 
69.36/69.47	               X578))),
69.36/69.47	    inference('demod', [status(thm)], ['35', '36'])).
69.36/69.47	tff('38', plain,
69.36/69.47	    app_encode_app(int, int, 
69.36/69.47	      app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
69.36/69.47	        app_encode_app(int, fun_int_int, times_times_int, 
69.36/69.47	          app_encode_app(int, int, bit1, min))), min)
69.36/69.47	     = app_encode_app(int, int, 
69.36/69.47	         app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
69.36/69.47	           app_encode_app(int, fun_int_int, plus_plus_int, min)), 
69.36/69.47	         app_encode_app(int, int, bit0, one_one_int)),
69.36/69.47	    inference('sup+', [status(thm)], ['34', '37'])).
69.36/69.47	tff(zf_stmt_617, axiom, (app_encode_app(int,int,bit1,min) = min)).
69.36/69.47	tff('39', plain, app_encode_app(int, int, bit1, min) = min,
69.36/69.47	    inference('cnf', [status(esa)], [zf_stmt_617])).
69.36/69.47	tff(zf_stmt_349, axiom,
69.36/69.47	  (![K_1:int,L:int]:
69.36/69.47	     (app_encode_app(int,int,
69.36/69.47	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
69.36/69.47	                                    hAPP_int_int,
69.36/69.47	                                    app_encode_app(int,fun_int_int,
69.36/69.47	                                                   plus_plus_int,
69.36/69.47	                                                   app_encode_app(int,int,
69.36/69.47	                                                                  bit0,K_1))),
69.36/69.47	                     app_encode_app(int,int,bit1,L)) =
69.36/69.47	      app_encode_app(int,int,bit1,
69.36/69.47	                     app_encode_app(int,int,
69.36/69.47	                                    app_encode_app(fun_int_int,
69.36/69.47	                                                   app_encode_fun(int,int),
69.36/69.47	                                                   hAPP_int_int,
69.36/69.47	                                                   app_encode_app(int,
69.36/69.47	                                                                  fun_int_int,
69.36/69.47	                                                                  plus_plus_int,
69.36/69.47	                                                                  K_1)),
69.36/69.47	                                    L))))).
69.36/69.47	tff('40', plain,
69.36/69.47	    ![X568 : int, X569 : int]:
69.36/69.47	      app_encode_app(int, int, 
69.36/69.47	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
69.36/69.47	          app_encode_app(int, fun_int_int, plus_plus_int, 
69.36/69.47	            app_encode_app(int, int, bit0, X568))), 
69.36/69.47	        app_encode_app(int, int, bit1, X569))
69.36/69.47	       = app_encode_app(int, int, bit1, 
69.36/69.47	           app_encode_app(int, int, 
69.36/69.47	             app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	               hAPP_int_int, 
69.36/69.47	               app_encode_app(int, fun_int_int, plus_plus_int, X568)), X569)),
69.36/69.47	    inference('cnf', [status(esa)], [zf_stmt_349])).
69.36/69.47	tff('41', plain,
69.36/69.47	    ![X0 : int]:
69.36/69.47	      app_encode_app(int, int, 
69.36/69.47	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
69.36/69.47	          app_encode_app(int, fun_int_int, plus_plus_int, 
69.36/69.47	            app_encode_app(int, int, bit0, X0))), min)
69.36/69.47	       = app_encode_app(int, int, bit1, 
69.36/69.47	           app_encode_app(int, int, 
69.36/69.47	             app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	               hAPP_int_int, 
69.36/69.47	               app_encode_app(int, fun_int_int, plus_plus_int, X0)), min)),
69.36/69.47	    inference('sup+', [status(thm)], ['39', '40'])).
69.36/69.47	tff('42', plain,
69.36/69.47	    ![X0 : int]:
69.36/69.47	      app_encode_app(int, int, 
69.36/69.47	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
69.36/69.47	          app_encode_app(int, fun_int_int, plus_plus_int, min)), 
69.36/69.47	        app_encode_app(int, int, bit0, X0))
69.36/69.47	       = app_encode_app(int, int, bit1, 
69.36/69.47	           app_encode_app(int, int, 
69.36/69.47	             app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	               hAPP_int_int, 
69.36/69.47	               app_encode_app(int, fun_int_int, plus_plus_int, X0)), min)),
69.36/69.47	    inference('demod', [status(thm)], ['41', '36'])).
69.36/69.47	tff('43', plain,
69.36/69.47	    app_encode_app(int, int, 
69.36/69.47	      app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
69.36/69.47	        app_encode_app(int, fun_int_int, times_times_int, min)), min)
69.36/69.47	     = app_encode_app(int, int, bit1, 
69.36/69.47	         app_encode_app(int, int, 
69.36/69.47	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	             hAPP_int_int, 
69.36/69.47	             app_encode_app(int, fun_int_int, plus_plus_int, one_one_int)), 
69.36/69.47	           min)),
69.36/69.47	    inference('demod', [status(thm)], ['38', '39', '42'])).
69.36/69.47	tff('44', plain,
69.36/69.47	    one_one_int
69.36/69.47	     = app_encode_app(int, int, bit1, 
69.36/69.47	         app_encode_app(int, int, 
69.36/69.47	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	             hAPP_int_int, 
69.36/69.47	             app_encode_app(int, fun_int_int, plus_plus_int, one_one_int)), 
69.36/69.47	           min)),
69.36/69.47	    inference('demod', [status(thm)], ['43', '34'])).
69.36/69.47	tff(zf_stmt_237, axiom,
69.36/69.47	  (![K:int,L_1:int]:
69.36/69.47	     ((app_encode_app(int,int,bit1,K) = app_encode_app(int,int,bit1,L_1)) <=>
69.36/69.47	      (K = L_1)))).
69.36/69.47	tff('45', plain,
69.36/69.47	    ![X317 : int, X318 : int]:
69.36/69.47	      (X318 = X317
69.36/69.47	       | app_encode_app(int, int, bit1, X318)
69.36/69.47	          != app_encode_app(int, int, bit1, X317)),
69.36/69.47	    inference('cnf', [status(esa)], [zf_stmt_237])).
69.36/69.47	tff('46', plain,
69.36/69.47	    ![X0 : int]:
69.36/69.47	      (one_one_int != app_encode_app(int, int, bit1, X0) | zero_zero_int = X0),
69.36/69.47	    inference('sup-', [status(thm)], ['9', '45'])).
69.36/69.47	tff('47', plain,
69.36/69.47	    (one_one_int != one_one_int
69.36/69.47	     | zero_zero_int
69.36/69.47	        = app_encode_app(int, int, 
69.36/69.47	            app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	              hAPP_int_int, 
69.36/69.47	              app_encode_app(int, fun_int_int, plus_plus_int, one_one_int)), 
69.36/69.47	            min)),
69.36/69.47	    inference('sup-', [status(thm)], ['44', '46'])).
69.36/69.47	tff('48', plain,
69.36/69.47	    zero_zero_int
69.36/69.47	     = app_encode_app(int, int, 
69.36/69.47	         app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
69.36/69.47	           app_encode_app(int, fun_int_int, plus_plus_int, one_one_int)), 
69.36/69.47	         min),
69.36/69.47	    inference('simplify', [status(thm)], ['47'])).
69.36/69.47	tff(zf_stmt_220, axiom,
69.36/69.47	  (![A_107:int,B_60:int,C_33:int]:
69.36/69.47	     (app_encode_app(int,int,
69.36/69.47	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
69.36/69.47	                                    hAPP_int_int,
69.36/69.47	                                    app_encode_app(int,fun_int_int,
69.36/69.47	                                                   plus_plus_int,
69.36/69.47	                                                   app_encode_app(int,int,
69.36/69.47	                                                                  app_encode_app(
69.36/69.47	                                                                  fun_int_int,
69.36/69.47	                                                                  app_encode_fun(
69.36/69.47	                                                                  int,int),
69.36/69.47	                                                                  hAPP_int_int,
69.36/69.47	                                                                  app_encode_app(
69.36/69.47	                                                                  int,
69.36/69.47	                                                                  fun_int_int,
69.36/69.47	                                                                  plus_plus_int,
69.36/69.47	                                                                  A_107)),
69.36/69.47	                                                                  B_60))),
69.36/69.47	                     C_33) =
69.36/69.47	      app_encode_app(int,int,
69.36/69.47	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
69.36/69.47	                                    hAPP_int_int,
69.36/69.47	                                    app_encode_app(int,fun_int_int,
69.36/69.47	                                                   plus_plus_int,A_107)),
69.36/69.47	                     app_encode_app(int,int,
69.36/69.47	                                    app_encode_app(fun_int_int,
69.36/69.47	                                                   app_encode_fun(int,int),
69.36/69.47	                                                   hAPP_int_int,
69.36/69.47	                                                   app_encode_app(int,
69.36/69.47	                                                                  fun_int_int,
69.36/69.47	                                                                  plus_plus_int,
69.36/69.47	                                                                  B_60)),
69.36/69.47	                                    C_33))))).
69.36/69.47	tff('49', plain,
69.36/69.47	    ![X269 : int, X270 : int, X271 : int]:
69.36/69.47	      app_encode_app(int, int, 
69.36/69.47	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
69.36/69.47	          app_encode_app(int, fun_int_int, plus_plus_int, 
69.36/69.47	            app_encode_app(int, int, 
69.36/69.47	              app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	                hAPP_int_int, 
69.36/69.47	                app_encode_app(int, fun_int_int, plus_plus_int, X269)), X270))), 
69.36/69.47	        X271)
69.36/69.47	       = app_encode_app(int, int, 
69.36/69.47	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	             hAPP_int_int, 
69.36/69.47	             app_encode_app(int, fun_int_int, plus_plus_int, X269)), 
69.36/69.47	           app_encode_app(int, int, 
69.36/69.47	             app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	               hAPP_int_int, 
69.36/69.47	               app_encode_app(int, fun_int_int, plus_plus_int, X270)), X271)),
69.36/69.47	    inference('cnf', [status(esa)], [zf_stmt_220])).
69.36/69.47	tff('50', plain,
69.36/69.47	    ![X0 : int]:
69.36/69.47	      app_encode_app(int, int, 
69.36/69.47	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
69.36/69.47	          app_encode_app(int, fun_int_int, plus_plus_int, zero_zero_int)), 
69.36/69.47	        X0)
69.36/69.47	       = app_encode_app(int, int, 
69.36/69.47	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	             hAPP_int_int, 
69.36/69.47	             app_encode_app(int, fun_int_int, plus_plus_int, one_one_int)), 
69.36/69.47	           app_encode_app(int, int, 
69.36/69.47	             app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	               hAPP_int_int, 
69.36/69.47	               app_encode_app(int, fun_int_int, plus_plus_int, min)), X0)),
69.36/69.47	    inference('sup+', [status(thm)], ['48', '49'])).
69.36/69.47	tff(zf_stmt_301, axiom,
69.36/69.47	  (![K_1:int]:
69.36/69.47	     (app_encode_app(int,int,
69.36/69.47	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
69.36/69.47	                                    hAPP_int_int,
69.36/69.47	                                    app_encode_app(int,fun_int_int,
69.36/69.47	                                                   plus_plus_int,pls)),
69.36/69.47	                     K_1) =
69.36/69.47	      K_1))).
69.36/69.47	tff('51', plain,
69.36/69.47	    ![X472 : int]:
69.36/69.47	      app_encode_app(int, int, 
69.36/69.47	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
69.36/69.47	          app_encode_app(int, fun_int_int, plus_plus_int, pls)), X472)
69.36/69.47	       = X472,
69.36/69.47	    inference('cnf', [status(esa)], [zf_stmt_301])).
69.36/69.47	tff('52', plain,
69.36/69.47	    ![X472 : int]:
69.36/69.47	      app_encode_app(int, int, 
69.36/69.47	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
69.36/69.47	          app_encode_app(int, fun_int_int, plus_plus_int, zero_zero_int)), 
69.36/69.47	        X472)
69.36/69.47	       = X472,
69.36/69.47	    inference('demod', [status(thm)], ['51', '5'])).
69.36/69.47	tff('53', plain,
69.36/69.47	    (sk_Z(int, int, number_number_of_int, 
69.36/69.47	       app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
69.36/69.47	         app_encode_app(int, fun_int_int, plus_plus_int, zero_zero_int)))
69.36/69.47	      != sk_Z(int, int, number_number_of_int, 
69.36/69.47	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	             hAPP_int_int, 
69.36/69.47	             app_encode_app(int, fun_int_int, plus_plus_int, zero_zero_int)))
69.36/69.47	     | app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
69.36/69.47	         app_encode_app(int, fun_int_int, plus_plus_int, zero_zero_int))
69.36/69.47	        = number_number_of_int),
69.36/69.47	    inference('sup-', [status(thm)], ['52', '13'])).
69.36/69.47	tff('54', plain,
69.36/69.47	    app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
69.36/69.47	      app_encode_app(int, fun_int_int, plus_plus_int, zero_zero_int))
69.36/69.47	     = number_number_of_int,
69.36/69.47	    inference('simplify', [status(thm)], ['53'])).
69.36/69.47	tff('55', plain,
69.36/69.47	    ![X0 : int]:
69.36/69.47	      X0
69.36/69.47	       = app_encode_app(int, int, 
69.36/69.47	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	             hAPP_int_int, 
69.36/69.47	             app_encode_app(int, fun_int_int, plus_plus_int, one_one_int)), 
69.36/69.47	           app_encode_app(int, int, 
69.36/69.47	             app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	               hAPP_int_int, 
69.36/69.47	               app_encode_app(int, fun_int_int, plus_plus_int, min)), X0)),
69.36/69.47	    inference('demod', [status(thm)], ['50', '54', '6'])).
69.36/69.47	tff('56', plain,
69.36/69.47	    ![X0 : int]:
69.36/69.47	      sk_K_2(one_one_int, X0, min)
69.36/69.47	       = app_encode_app(int, int, 
69.36/69.47	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	             hAPP_int_int, 
69.36/69.47	             app_encode_app(int, fun_int_int, plus_plus_int, one_one_int)), 
69.36/69.47	           X0),
69.36/69.47	    inference('sup+', [status(thm)], ['20', '55'])).
69.36/69.47	tff(zf_stmt_303, axiom,
69.36/69.47	  (![K_1:int]:
69.36/69.47	     (app_encode_app(int,int,bit0,K_1) =
69.36/69.47	      app_encode_app(int,int,
69.36/69.47	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
69.36/69.47	                                    hAPP_int_int,
69.36/69.47	                                    app_encode_app(int,fun_int_int,
69.36/69.47	                                                   plus_plus_int,K_1)),
69.36/69.47	                     K_1)))).
69.36/69.47	tff('57', plain,
69.36/69.47	    ![X475 : int]:
69.36/69.47	      app_encode_app(int, int, bit0, X475)
69.36/69.47	       = app_encode_app(int, int, 
69.36/69.47	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	             hAPP_int_int, 
69.36/69.47	             app_encode_app(int, fun_int_int, plus_plus_int, X475)), X475),
69.36/69.47	    inference('cnf', [status(esa)], [zf_stmt_303])).
69.36/69.47	tff('58', plain,
69.36/69.47	    app_encode_app(int, int, bit0, one_one_int)
69.36/69.47	     = sk_K_2(one_one_int, one_one_int, min),
69.36/69.47	    inference('sup+', [status(thm)], ['56', '57'])).
69.36/69.47	tff(zf_stmt_299, axiom,
69.36/69.47	  (![K_1:int,L:int]:
69.36/69.47	     (app_encode_app(int,int,
69.36/69.47	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
69.36/69.47	                                    hAPP_int_int,
69.36/69.47	                                    app_encode_app(int,fun_int_int,
69.36/69.47	                                                   times_times_int,
69.36/69.47	                                                   app_encode_app(int,int,
69.36/69.47	                                                                  bit0,K_1))),
69.36/69.47	                     L) =
69.36/69.47	      app_encode_app(int,int,bit0,
69.36/69.47	                     app_encode_app(int,int,
69.36/69.47	                                    app_encode_app(fun_int_int,
69.36/69.47	                                                   app_encode_fun(int,int),
69.36/69.47	                                                   hAPP_int_int,
69.36/69.47	                                                   app_encode_app(int,
69.36/69.47	                                                                  fun_int_int,
69.36/69.47	                                                                  times_times_int,
69.36/69.47	                                                                  K_1)),
69.36/69.47	                                    L))))).
69.36/69.47	tff('59', plain,
69.36/69.47	    ![X469 : int, X470 : int]:
69.36/69.47	      app_encode_app(int, int, 
69.36/69.47	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
69.36/69.47	          app_encode_app(int, fun_int_int, times_times_int, 
69.36/69.47	            app_encode_app(int, int, bit0, X469))), X470)
69.36/69.47	       = app_encode_app(int, int, bit0, 
69.36/69.47	           app_encode_app(int, int, 
69.36/69.47	             app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	               hAPP_int_int, 
69.36/69.47	               app_encode_app(int, fun_int_int, times_times_int, X469)), 
69.36/69.47	             X470)),
69.36/69.47	    inference('cnf', [status(esa)], [zf_stmt_299])).
69.36/69.47	tff(zf_stmt_323, axiom,
69.36/69.47	  (![A_97:int,M_12:int]:
69.36/69.47	     (app_encode_app(int,int,
69.36/69.47	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
69.36/69.47	                                    hAPP_int_int,
69.36/69.47	                                    app_encode_app(int,fun_int_int,
69.36/69.47	                                                   plus_plus_int,
69.36/69.47	                                                   app_encode_app(int,int,
69.36/69.47	                                                                  app_encode_app(
69.36/69.47	                                                                  fun_int_int,
69.36/69.47	                                                                  app_encode_fun(
69.36/69.47	                                                                  int,int),
69.36/69.47	                                                                  hAPP_int_int,
69.36/69.47	                                                                  app_encode_app(
69.36/69.47	                                                                  int,
69.36/69.47	                                                                  fun_int_int,
69.36/69.47	                                                                  times_times_int,
69.36/69.47	                                                                  A_97)),M_12))),
69.36/69.47	                     M_12) =
69.36/69.47	      app_encode_app(int,int,
69.36/69.47	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
69.36/69.47	                                    hAPP_int_int,
69.36/69.47	                                    app_encode_app(int,fun_int_int,
69.36/69.47	                                                   times_times_int,
69.36/69.47	                                                   app_encode_app(int,int,
69.36/69.47	                                                                  app_encode_app(
69.36/69.47	                                                                  fun_int_int,
69.36/69.47	                                                                  app_encode_fun(
69.36/69.47	                                                                  int,int),
69.36/69.47	                                                                  hAPP_int_int,
69.36/69.47	                                                                  app_encode_app(
69.36/69.47	                                                                  int,
69.36/69.47	                                                                  fun_int_int,
69.36/69.47	                                                                  plus_plus_int,
69.36/69.47	                                                                  A_97)),
69.36/69.47	                                                                  one_one_int))),
69.36/69.47	                     M_12)))).
69.36/69.47	tff('60', plain,
69.36/69.47	    ![X519 : int, X520 : int]:
69.36/69.47	      app_encode_app(int, int, 
69.36/69.47	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
69.36/69.47	          app_encode_app(int, fun_int_int, plus_plus_int, 
69.36/69.47	            app_encode_app(int, int, 
69.36/69.47	              app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	                hAPP_int_int, 
69.36/69.47	                app_encode_app(int, fun_int_int, times_times_int, X519)), 
69.36/69.47	              X520))), X520)
69.36/69.47	       = app_encode_app(int, int, 
69.36/69.47	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	             hAPP_int_int, 
69.36/69.47	             app_encode_app(int, fun_int_int, times_times_int, 
69.36/69.47	               app_encode_app(int, int, 
69.36/69.47	                 app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	                   hAPP_int_int, 
69.36/69.47	                   app_encode_app(int, fun_int_int, plus_plus_int, X519)), 
69.36/69.47	                 one_one_int))), X520),
69.36/69.47	    inference('cnf', [status(esa)], [zf_stmt_323])).
69.36/69.47	tff('61', plain,
69.36/69.47	    ![X519 : int, X520 : int]:
69.36/69.47	      app_encode_app(int, int, 
69.36/69.47	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
69.36/69.47	          app_encode_app(int, fun_int_int, plus_plus_int, X520)), 
69.36/69.47	        app_encode_app(int, int, 
69.36/69.47	          app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	            hAPP_int_int, 
69.36/69.47	            app_encode_app(int, fun_int_int, times_times_int, X519)), X520))
69.36/69.47	       = app_encode_app(int, int, 
69.36/69.47	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	             hAPP_int_int, 
69.36/69.47	             app_encode_app(int, fun_int_int, times_times_int, 
69.36/69.47	               app_encode_app(int, int, 
69.36/69.47	                 app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	                   hAPP_int_int, 
69.36/69.47	                   app_encode_app(int, fun_int_int, plus_plus_int, X519)), 
69.36/69.47	                 one_one_int))), X520),
69.36/69.47	    inference('demod', [status(thm)], ['60', '36'])).
69.36/69.47	tff('62', plain,
69.36/69.47	    ![X0 : int]:
69.36/69.47	      app_encode_app(int, int, 
69.36/69.47	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
69.36/69.47	          app_encode_app(int, fun_int_int, plus_plus_int, X0)), 
69.36/69.47	        app_encode_app(int, int, 
69.36/69.47	          app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	            hAPP_int_int, 
69.36/69.47	            app_encode_app(int, fun_int_int, times_times_int, one_one_int)), 
69.36/69.47	          X0))
69.36/69.47	       = app_encode_app(int, int, 
69.36/69.47	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	             hAPP_int_int, 
69.36/69.47	             app_encode_app(int, fun_int_int, times_times_int, 
69.36/69.47	               sk_K_2(one_one_int, one_one_int, min))), X0),
69.36/69.47	    inference('sup+', [status(thm)], ['56', '61'])).
69.36/69.47	tff('63', plain,
69.36/69.47	    ![X0 : int]:
69.36/69.47	      app_encode_app(int, int, 
69.36/69.47	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
69.36/69.47	          app_encode_app(int, fun_int_int, plus_plus_int, X0)), X0)
69.36/69.47	       = app_encode_app(int, int, 
69.36/69.47	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	             hAPP_int_int, 
69.36/69.47	             app_encode_app(int, fun_int_int, times_times_int, 
69.36/69.47	               sk_K_2(one_one_int, one_one_int, min))), X0),
69.36/69.47	    inference('demod', [status(thm)], ['62', '15', '6'])).
69.36/69.47	tff('64', plain,
69.36/69.47	    ![X0 : int]:
69.36/69.47	      app_encode_app(int, int, bit0, X0)
69.36/69.47	       = app_encode_app(int, int, 
69.36/69.47	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	             hAPP_int_int, 
69.36/69.47	             app_encode_app(int, fun_int_int, times_times_int, 
69.36/69.47	               sk_K_2(one_one_int, one_one_int, min))), X0),
69.36/69.47	    inference('demod', [status(thm)], ['63', '57'])).
69.36/69.47	tff('65', plain,
69.36/69.47	    ![X0 : int]:
69.36/69.47	      app_encode_app(int, int, 
69.36/69.47	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
69.36/69.47	          app_encode_app(int, fun_int_int, plus_plus_int, X0)), one_one_int)
69.36/69.47	       = sk_K_2(one_one_int, X0, min),
69.36/69.47	    inference('sup+', [status(thm)], ['56', '36'])).
69.36/69.47	tff(zf_stmt_350, axiom,
69.36/69.47	  (![K_1:int]:
69.36/69.47	     (app_encode_app(int,int,bit1,K_1) =
69.36/69.47	      app_encode_app(int,int,
69.36/69.47	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
69.36/69.47	                                    hAPP_int_int,
69.36/69.47	                                    app_encode_app(int,fun_int_int,
69.36/69.47	                                                   plus_plus_int,
69.36/69.47	                                                   app_encode_app(int,int,
69.36/69.47	                                                                  app_encode_app(
69.36/69.47	                                                                  fun_int_int,
69.36/69.47	                                                                  app_encode_fun(
69.36/69.47	                                                                  int,int),
69.36/69.47	                                                                  hAPP_int_int,
69.36/69.47	                                                                  app_encode_app(
69.36/69.47	                                                                  int,
69.36/69.47	                                                                  fun_int_int,
69.36/69.47	                                                                  plus_plus_int,
69.36/69.47	                                                                  one_one_int)),
69.36/69.47	                                                                  K_1))),
69.36/69.47	                     K_1)))).
69.36/69.47	tff('66', plain,
69.36/69.47	    ![X570 : int]:
69.36/69.47	      app_encode_app(int, int, bit1, X570)
69.36/69.47	       = app_encode_app(int, int, 
69.36/69.47	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	             hAPP_int_int, 
69.36/69.47	             app_encode_app(int, fun_int_int, plus_plus_int, 
69.36/69.47	               app_encode_app(int, int, 
69.36/69.47	                 app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	                   hAPP_int_int, 
69.36/69.47	                   app_encode_app(int, fun_int_int, plus_plus_int, 
69.36/69.47	                     one_one_int)), X570))), X570),
69.36/69.47	    inference('cnf', [status(esa)], [zf_stmt_350])).
69.36/69.47	tff('67', plain,
69.36/69.47	    ![X570 : int]:
69.36/69.47	      app_encode_app(int, int, bit1, X570)
69.36/69.47	       = app_encode_app(int, int, 
69.36/69.47	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	             hAPP_int_int, 
69.36/69.47	             app_encode_app(int, fun_int_int, plus_plus_int, X570)), 
69.36/69.47	           app_encode_app(int, int, 
69.36/69.47	             app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	               hAPP_int_int, 
69.36/69.47	               app_encode_app(int, fun_int_int, plus_plus_int, one_one_int)), 
69.36/69.47	             X570)),
69.36/69.47	    inference('demod', [status(thm)], ['66', '36'])).
69.36/69.47	tff(zf_stmt_226, axiom,
69.36/69.47	  (![A_105:int,C_31:int,D_9:int]:
69.36/69.47	     (app_encode_app(int,int,
69.36/69.47	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
69.36/69.47	                                    hAPP_int_int,
69.36/69.47	                                    app_encode_app(int,fun_int_int,
69.36/69.47	                                                   plus_plus_int,A_105)),
69.36/69.47	                     app_encode_app(int,int,
69.36/69.47	                                    app_encode_app(fun_int_int,
69.36/69.47	                                                   app_encode_fun(int,int),
69.36/69.47	                                                   hAPP_int_int,
69.36/69.47	                                                   app_encode_app(int,
69.36/69.47	                                                                  fun_int_int,
69.36/69.47	                                                                  plus_plus_int,
69.36/69.47	                                                                  C_31)),
69.36/69.47	                                    D_9)) =
69.36/69.47	      app_encode_app(int,int,
69.36/69.47	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
69.36/69.47	                                    hAPP_int_int,
69.36/69.47	                                    app_encode_app(int,fun_int_int,
69.36/69.47	                                                   plus_plus_int,C_31)),
69.36/69.47	                     app_encode_app(int,int,
69.36/69.47	                                    app_encode_app(fun_int_int,
69.36/69.47	                                                   app_encode_fun(int,int),
69.36/69.47	                                                   hAPP_int_int,
69.36/69.47	                                                   app_encode_app(int,
69.36/69.47	                                                                  fun_int_int,
69.36/69.47	                                                                  plus_plus_int,
69.36/69.47	                                                                  A_105)),
69.36/69.47	                                    D_9))))).
69.36/69.47	tff('68', plain,
69.36/69.47	    ![X287 : int, X288 : int, X289 : int]:
69.36/69.47	      app_encode_app(int, int, 
69.36/69.47	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
69.36/69.47	          app_encode_app(int, fun_int_int, plus_plus_int, X288)), 
69.36/69.47	        app_encode_app(int, int, 
69.36/69.47	          app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	            hAPP_int_int, 
69.36/69.47	            app_encode_app(int, fun_int_int, plus_plus_int, X287)), X289))
69.36/69.47	       = app_encode_app(int, int, 
69.36/69.47	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	             hAPP_int_int, 
69.36/69.47	             app_encode_app(int, fun_int_int, plus_plus_int, X287)), 
69.36/69.47	           app_encode_app(int, int, 
69.36/69.47	             app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	               hAPP_int_int, 
69.36/69.47	               app_encode_app(int, fun_int_int, plus_plus_int, X288)), X289)),
69.36/69.47	    inference('cnf', [status(esa)], [zf_stmt_226])).
69.36/69.47	tff('69', plain,
69.36/69.47	    ![X0 : int]:
69.36/69.47	      app_encode_app(int, int, bit1, X0)
69.36/69.47	       = app_encode_app(int, int, 
69.36/69.47	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	             hAPP_int_int, 
69.36/69.47	             app_encode_app(int, fun_int_int, plus_plus_int, one_one_int)), 
69.36/69.47	           app_encode_app(int, int, 
69.36/69.47	             app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	               hAPP_int_int, 
69.36/69.47	               app_encode_app(int, fun_int_int, plus_plus_int, X0)), X0)),
69.36/69.47	    inference('sup+', [status(thm)], ['67', '68'])).
69.36/69.47	tff('70', plain,
69.36/69.47	    ![X0 : int]:
69.36/69.47	      app_encode_app(int, int, bit1, X0)
69.36/69.47	       = app_encode_app(int, int, 
69.36/69.47	           app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	             hAPP_int_int, 
69.36/69.47	             app_encode_app(int, fun_int_int, plus_plus_int, one_one_int)), 
69.36/69.47	           app_encode_app(int, int, bit0, X0)),
69.36/69.47	    inference('demod', [status(thm)], ['69', '57'])).
69.36/69.47	tff('71', plain,
69.36/69.47	    ![X0 : int]:
69.36/69.47	      app_encode_app(int, int, bit1, X0)
69.36/69.47	       = sk_K_2(one_one_int, app_encode_app(int, int, bit0, X0), min),
69.36/69.47	    inference('demod', [status(thm)], ['70', '56'])).
69.36/69.47	tff('72', plain,
69.36/69.47	    (app_encode_app(int, int, 
69.36/69.47	       app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
69.36/69.47	         app_encode_app(int, fun_int_int, plus_plus_int, 
69.36/69.47	           app_encode_app(nat, int, 
69.36/69.47	             app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
69.36/69.47	               hAPP_nat_int, 
69.36/69.47	               app_encode_app(int, fun_nat_int, power_power_int, sk_X)), 
69.36/69.47	             app_encode_app(int, nat, number_number_of_nat, 
69.36/69.47	               sk_K_2(one_one_int, one_one_int, min))))), 
69.36/69.47	       app_encode_app(nat, int, 
69.36/69.47	         app_encode_app(fun_nat_int, app_encode_fun(nat, int), hAPP_nat_int, 
69.36/69.47	           app_encode_app(int, fun_nat_int, power_power_int, sk_Y)), 
69.36/69.47	         app_encode_app(int, nat, number_number_of_nat, 
69.36/69.47	           sk_K_2(one_one_int, one_one_int, min))))
69.36/69.47	      = app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m))
69.36/69.47	     | t != one_one_int),
69.36/69.47	    inference('demod', [status(thm)],
69.36/69.47	              ['10', '58', '58', '58', '59', '64', '65', '71'])).
69.36/69.47	tff(zf_stmt_1301, conjecture,
69.36/69.47	  (?[X:int,Y:int]:
69.36/69.47	     (app_encode_app(int,int,
69.36/69.47	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
69.36/69.47	                                    hAPP_int_int,
69.36/69.47	                                    app_encode_app(int,fun_int_int,
69.36/69.47	                                                   plus_plus_int,
69.36/69.47	                                                   app_encode_app(nat,int,
69.36/69.47	                                                                  app_encode_app(
69.36/69.47	                                                                  fun_nat_int,
69.36/69.47	                                                                  app_encode_fun(
69.36/69.47	                                                                  nat,int),
69.36/69.47	                                                                  hAPP_nat_int,
69.36/69.47	                                                                  app_encode_app(
69.36/69.47	                                                                  int,
69.36/69.47	                                                                  fun_nat_int,
69.36/69.47	                                                                  power_power_int,
69.36/69.47	                                                                  X)),
69.36/69.47	                                                                  app_encode_app(
69.36/69.47	                                                                  int,nat,
69.36/69.47	                                                                  number_number_of_nat,
69.36/69.47	                                                                  app_encode_app(
69.36/69.47	                                                                  int,int,
69.36/69.47	                                                                  bit0,
69.36/69.47	                                                                  app_encode_app(
69.36/69.47	                                                                  int,int,
69.36/69.47	                                                                  bit1,pls)))))),
69.36/69.47	                     app_encode_app(nat,int,
69.36/69.47	                                    app_encode_app(fun_nat_int,
69.36/69.47	                                                   app_encode_fun(nat,int),
69.36/69.47	                                                   hAPP_nat_int,
69.36/69.47	                                                   app_encode_app(int,
69.36/69.47	                                                                  fun_nat_int,
69.36/69.47	                                                                  power_power_int,
69.36/69.47	                                                                  Y)),
69.36/69.47	                                    app_encode_app(int,nat,
69.36/69.47	                                                   number_number_of_nat,
69.36/69.47	                                                   app_encode_app(int,int,
69.36/69.47	                                                                  bit0,
69.36/69.47	                                                                  app_encode_app(
69.36/69.47	                                                                  int,int,
69.36/69.47	                                                                  bit1,pls))))) =
69.36/69.47	      app_encode_app(int,int,
69.36/69.47	                     app_encode_app(fun_int_int,app_encode_fun(int,int),
69.36/69.47	                                    hAPP_int_int,
69.36/69.47	                                    app_encode_app(int,fun_int_int,
69.36/69.47	                                                   plus_plus_int,
69.36/69.47	                                                   app_encode_app(int,int,
69.36/69.47	                                                                  app_encode_app(
69.36/69.47	                                                                  fun_int_int,
69.36/69.47	                                                                  app_encode_fun(
69.36/69.47	                                                                  int,int),
69.36/69.47	                                                                  hAPP_int_int,
69.36/69.47	                                                                  app_encode_app(
69.36/69.47	                                                                  int,
69.36/69.47	                                                                  fun_int_int,
69.36/69.47	                                                                  times_times_int,
69.36/69.47	                                                                  app_encode_app(
69.36/69.47	                                                                  int,int,
69.36/69.47	                                                                  number_number_of_int,
69.36/69.47	                                                                  app_encode_app(
69.36/69.47	                                                                  int,int,
69.36/69.47	                                                                  bit0,
69.36/69.47	                                                                  app_encode_app(
69.36/69.47	                                                                  int,int,
69.36/69.47	                                                                  bit0,
69.36/69.47	                                                                  app_encode_app(
69.36/69.47	                                                                  int,int,
69.36/69.47	                                                                  bit1,pls)))))),
69.36/69.47	                                                                  m))),
69.36/69.47	                     one_one_int)))).
69.36/69.47	tff(zf_stmt_0, negated_conjecture,
69.36/69.47	  (~
69.36/69.47	    (?[X:int,Y:int]:
69.36/69.47	       (app_encode_app(int,int,
69.36/69.47	                       app_encode_app(fun_int_int,app_encode_fun(int,int),
69.36/69.47	                                      hAPP_int_int,
69.36/69.47	                                      app_encode_app(int,fun_int_int,
69.36/69.47	                                                     plus_plus_int,
69.36/69.47	                                                     app_encode_app(nat,int,
69.36/69.47	                                                                    app_encode_app(
69.36/69.47	                                                                    fun_nat_int,
69.36/69.47	                                                                    app_encode_fun(
69.36/69.47	                                                                    nat,int),
69.36/69.47	                                                                    hAPP_nat_int,
69.36/69.47	                                                                    app_encode_app(
69.36/69.47	                                                                    int,
69.36/69.47	                                                                    fun_nat_int,
69.36/69.47	                                                                    power_power_int,
69.36/69.47	                                                                    X)),
69.36/69.47	                                                                    app_encode_app(
69.36/69.47	                                                                    int,nat,
69.36/69.47	                                                                    number_number_of_nat,
69.36/69.47	                                                                    app_encode_app(
69.36/69.47	                                                                    int,int,
69.36/69.47	                                                                    bit0,
69.36/69.47	                                                                    app_encode_app(
69.36/69.47	                                                                    int,int,
69.36/69.47	                                                                    bit1,pls)))))),
69.36/69.47	                       app_encode_app(nat,int,
69.36/69.47	                                      app_encode_app(fun_nat_int,
69.36/69.47	                                                     app_encode_fun(nat,int),
69.36/69.47	                                                     hAPP_nat_int,
69.36/69.47	                                                     app_encode_app(int,
69.36/69.47	                                                                    fun_nat_int,
69.36/69.47	                                                                    power_power_int,
69.36/69.47	                                                                    Y)),
69.36/69.47	                                      app_encode_app(int,nat,
69.36/69.47	                                                     number_number_of_nat,
69.36/69.47	                                                     app_encode_app(int,int,
69.36/69.47	                                                                    bit0,
69.36/69.47	                                                                    app_encode_app(
69.36/69.47	                                                                    int,int,
69.36/69.47	                                                                    bit1,pls))))) =
69.36/69.47	        app_encode_app(int,int,
69.36/69.47	                       app_encode_app(fun_int_int,app_encode_fun(int,int),
69.36/69.47	                                      hAPP_int_int,
69.36/69.47	                                      app_encode_app(int,fun_int_int,
69.36/69.47	                                                     plus_plus_int,
69.36/69.47	                                                     app_encode_app(int,int,
69.36/69.47	                                                                    app_encode_app(
69.36/69.47	                                                                    fun_int_int,
69.36/69.47	                                                                    app_encode_fun(
69.36/69.47	                                                                    int,int),
69.36/69.47	                                                                    hAPP_int_int,
69.36/69.47	                                                                    app_encode_app(
69.36/69.47	                                                                    int,
69.36/69.47	                                                                    fun_int_int,
69.36/69.47	                                                                    times_times_int,
69.36/69.47	                                                                    app_encode_app(
69.36/69.47	                                                                    int,int,
69.36/69.47	                                                                    number_number_of_int,
69.36/69.47	                                                                    app_encode_app(
69.36/69.47	                                                                    int,int,
69.36/69.47	                                                                    bit0,
69.36/69.47	                                                                    app_encode_app(
69.36/69.47	                                                                    int,int,
69.36/69.47	                                                                    bit0,
69.36/69.47	                                                                    app_encode_app(
69.36/69.47	                                                                    int,int,
69.36/69.47	                                                                    bit1,pls)))))),
69.36/69.47	                                                                    m))),
69.36/69.47	                       one_one_int))))).
69.36/69.47	tff('73', plain,
69.36/69.47	    ![X2825 : int, X2826 : int]:
69.36/69.47	      app_encode_app(int, int, 
69.36/69.47	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
69.36/69.47	          app_encode_app(int, fun_int_int, plus_plus_int, 
69.36/69.47	            app_encode_app(nat, int, 
69.36/69.47	              app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
69.36/69.47	                hAPP_nat_int, 
69.36/69.47	                app_encode_app(int, fun_nat_int, power_power_int, X2825)), 
69.36/69.47	              app_encode_app(int, nat, number_number_of_nat, 
69.36/69.47	                app_encode_app(int, int, bit0, 
69.36/69.47	                  app_encode_app(int, int, bit1, pls)))))), 
69.36/69.47	        app_encode_app(nat, int, 
69.36/69.47	          app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
69.36/69.47	            hAPP_nat_int, 
69.36/69.47	            app_encode_app(int, fun_nat_int, power_power_int, X2826)), 
69.36/69.47	          app_encode_app(int, nat, number_number_of_nat, 
69.36/69.47	            app_encode_app(int, int, bit0, 
69.36/69.47	              app_encode_app(int, int, bit1, pls)))))
69.36/69.47	       != app_encode_app(int, int, 
69.36/69.47	            app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	              hAPP_int_int, 
69.36/69.47	              app_encode_app(int, fun_int_int, plus_plus_int, 
69.36/69.47	                app_encode_app(int, int, 
69.36/69.47	                  app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	                    hAPP_int_int, 
69.36/69.47	                    app_encode_app(int, fun_int_int, times_times_int, 
69.36/69.47	                      app_encode_app(int, int, number_number_of_int, 
69.36/69.47	                        app_encode_app(int, int, bit0, 
69.36/69.47	                          app_encode_app(int, int, bit0, 
69.36/69.47	                            app_encode_app(int, int, bit1, pls)))))), m))), 
69.36/69.47	            one_one_int),
69.36/69.47	    inference('cnf', [status(esa)], [zf_stmt_0])).
69.36/69.47	tff('74', plain,
69.36/69.47	    ![X2825 : int, X2826 : int]:
69.36/69.47	      app_encode_app(int, int, 
69.36/69.47	        app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
69.36/69.47	          app_encode_app(int, fun_int_int, plus_plus_int, 
69.36/69.47	            app_encode_app(nat, int, 
69.36/69.47	              app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
69.36/69.47	                hAPP_nat_int, 
69.36/69.47	                app_encode_app(int, fun_nat_int, power_power_int, X2825)), 
69.36/69.47	              app_encode_app(int, nat, number_number_of_nat, 
69.36/69.47	                sk_K_2(one_one_int, one_one_int, min))))), 
69.36/69.47	        app_encode_app(nat, int, 
69.36/69.47	          app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
69.36/69.47	            hAPP_nat_int, 
69.36/69.47	            app_encode_app(int, fun_nat_int, power_power_int, X2826)), 
69.36/69.47	          app_encode_app(int, nat, number_number_of_nat, 
69.36/69.47	            sk_K_2(one_one_int, one_one_int, min))))
69.36/69.47	       != app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m)),
69.36/69.47	    inference('demod', [status(thm)],
69.36/69.47	              ['73', '5', '9', '58', '5', '9', '58', '5', '9', '58', '6', 
69.36/69.47	               '59', '64', '65', '71'])).
69.36/69.47	tff('75', plain, t != one_one_int,
69.36/69.47	    inference('simplify_reflect-', [status(thm)], ['72', '74'])).
69.36/69.47	tff('76', plain,
69.36/69.47	    app_encode_app(bool, $o, hBOOL, 
69.36/69.47	      app_encode_app(int, bool, 
69.36/69.47	        app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
69.36/69.47	          hAPP_int_bool, 
69.36/69.47	          app_encode_app(int, fun_int_bool, 
69.36/69.47	            app_encode_app(fun_int_fun_int_bool, 
69.36/69.47	              app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
69.36/69.47	              ord_less_int), one_one_int)), t)),
69.36/69.47	    inference('simplify_reflect-', [status(thm)], ['3', '75'])).
69.36/69.47	tff(zf_stmt_99, axiom,
69.36/69.47	  (app_encode_app(bool,$o,hBOOL,
69.36/69.47	                  app_encode_app(int,bool,
69.36/69.47	                                 app_encode_app(fun_int_bool,
69.36/69.47	                                                app_encode_fun(int,bool),
69.36/69.47	                                                hAPP_int_bool,
69.36/69.47	                                                app_encode_app(int,
69.36/69.47	                                                               fun_int_bool,
69.36/69.47	                                                               app_encode_app(
69.36/69.47	                                                               fun_int_fun_int_bool,
69.36/69.47	                                                               app_encode_fun(
69.36/69.47	                                                               int,
69.36/69.47	                                                               fun_int_bool),
69.36/69.47	                                                               hAPP_i1948725293t_bool,
69.36/69.47	                                                               ord_less_int),
69.36/69.47	                                                               one_one_int)),
69.36/69.47	                                 t)) =>
69.36/69.47	   (?[X:int,Y:int]:
69.36/69.47	      (app_encode_app(int,int,
69.36/69.47	                      app_encode_app(fun_int_int,app_encode_fun(int,int),
69.36/69.47	                                     hAPP_int_int,
69.36/69.47	                                     app_encode_app(int,fun_int_int,
69.36/69.47	                                                    plus_plus_int,
69.36/69.47	                                                    app_encode_app(nat,int,
69.36/69.47	                                                                   app_encode_app(
69.36/69.47	                                                                   fun_nat_int,
69.36/69.47	                                                                   app_encode_fun(
69.36/69.47	                                                                   nat,int),
69.36/69.47	                                                                   hAPP_nat_int,
69.36/69.47	                                                                   app_encode_app(
69.36/69.47	                                                                   int,
69.36/69.47	                                                                   fun_nat_int,
69.36/69.47	                                                                   power_power_int,
69.36/69.47	                                                                   X)),
69.36/69.47	                                                                   app_encode_app(
69.36/69.47	                                                                   int,nat,
69.36/69.47	                                                                   number_number_of_nat,
69.36/69.47	                                                                   app_encode_app(
69.36/69.47	                                                                   int,int,
69.36/69.47	                                                                   bit0,
69.36/69.47	                                                                   app_encode_app(
69.36/69.47	                                                                   int,int,
69.36/69.47	                                                                   bit1,pls)))))),
69.36/69.47	                      app_encode_app(nat,int,
69.36/69.47	                                     app_encode_app(fun_nat_int,
69.36/69.47	                                                    app_encode_fun(nat,int),
69.36/69.47	                                                    hAPP_nat_int,
69.36/69.47	                                                    app_encode_app(int,
69.36/69.47	                                                                   fun_nat_int,
69.36/69.47	                                                                   power_power_int,
69.36/69.47	                                                                   Y)),
69.36/69.47	                                     app_encode_app(int,nat,
69.36/69.47	                                                    number_number_of_nat,
69.36/69.47	                                                    app_encode_app(int,int,
69.36/69.47	                                                                   bit0,
69.36/69.47	                                                                   app_encode_app(
69.36/69.47	                                                                   int,int,
69.36/69.47	                                                                   bit1,pls))))) =
69.36/69.47	       app_encode_app(int,int,
69.36/69.47	                      app_encode_app(fun_int_int,app_encode_fun(int,int),
69.36/69.47	                                     hAPP_int_int,
69.36/69.47	                                     app_encode_app(int,fun_int_int,
69.36/69.47	                                                    plus_plus_int,
69.36/69.47	                                                    app_encode_app(int,int,
69.36/69.47	                                                                   app_encode_app(
69.36/69.47	                                                                   fun_int_int,
69.36/69.47	                                                                   app_encode_fun(
69.36/69.47	                                                                   int,int),
69.36/69.47	                                                                   hAPP_int_int,
69.36/69.47	                                                                   app_encode_app(
69.36/69.47	                                                                   int,
69.36/69.47	                                                                   fun_int_int,
69.36/69.47	                                                                   times_times_int,
69.36/69.47	                                                                   app_encode_app(
69.36/69.47	                                                                   int,int,
69.36/69.47	                                                                   number_number_of_int,
69.36/69.47	                                                                   app_encode_app(
69.36/69.47	                                                                   int,int,
69.36/69.47	                                                                   bit0,
69.36/69.47	                                                                   app_encode_app(
69.36/69.47	                                                                   int,int,
69.36/69.47	                                                                   bit0,
69.36/69.47	                                                                   app_encode_app(
69.36/69.47	                                                                   int,int,
69.36/69.47	                                                                   bit1,pls)))))),
69.36/69.47	                                                                   m))),
69.36/69.47	                      one_one_int))))).
69.36/69.47	tff('77', plain,
69.36/69.47	    (app_encode_app(int, int, 
69.36/69.47	       app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
69.36/69.47	         app_encode_app(int, fun_int_int, plus_plus_int, 
69.36/69.47	           app_encode_app(nat, int, 
69.36/69.47	             app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
69.36/69.47	               hAPP_nat_int, 
69.36/69.47	               app_encode_app(int, fun_nat_int, power_power_int, sk_X1)), 
69.36/69.47	             app_encode_app(int, nat, number_number_of_nat, 
69.36/69.47	               app_encode_app(int, int, bit0, 
69.36/69.47	                 app_encode_app(int, int, bit1, pls)))))), 
69.36/69.47	       app_encode_app(nat, int, 
69.36/69.47	         app_encode_app(fun_nat_int, app_encode_fun(nat, int), hAPP_nat_int, 
69.36/69.47	           app_encode_app(int, fun_nat_int, power_power_int, sk_Y1)), 
69.36/69.47	         app_encode_app(int, nat, number_number_of_nat, 
69.36/69.47	           app_encode_app(int, int, bit0, 
69.36/69.47	             app_encode_app(int, int, bit1, pls)))))
69.36/69.47	      = app_encode_app(int, int, 
69.36/69.47	          app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	            hAPP_int_int, 
69.36/69.47	            app_encode_app(int, fun_int_int, plus_plus_int, 
69.36/69.47	              app_encode_app(int, int, 
69.36/69.47	                app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	                  hAPP_int_int, 
69.36/69.47	                  app_encode_app(int, fun_int_int, times_times_int, 
69.36/69.47	                    app_encode_app(int, int, number_number_of_int, 
69.36/69.47	                      app_encode_app(int, int, bit0, 
69.36/69.47	                        app_encode_app(int, int, bit0, 
69.36/69.47	                          app_encode_app(int, int, bit1, pls)))))), m))), 
69.36/69.47	          one_one_int)
69.36/69.47	     | ~ app_encode_app(bool, $o, hBOOL, 
69.36/69.47	           app_encode_app(int, bool, 
69.36/69.47	             app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
69.36/69.47	               hAPP_int_bool, 
69.36/69.47	               app_encode_app(int, fun_int_bool, 
69.36/69.47	                 app_encode_app(fun_int_fun_int_bool, 
69.36/69.47	                   app_encode_fun(int, fun_int_bool), 
69.36/69.47	                   hAPP_i1948725293t_bool, ord_less_int), one_one_int)), t))),
69.36/69.47	    inference('cnf', [status(esa)], [zf_stmt_99])).
69.36/69.47	tff('78', plain,
69.36/69.47	    (app_encode_app(int, int, 
69.36/69.47	       app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
69.36/69.47	         app_encode_app(int, fun_int_int, plus_plus_int, 
69.36/69.47	           app_encode_app(nat, int, 
69.36/69.47	             app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
69.36/69.47	               hAPP_nat_int, 
69.36/69.47	               app_encode_app(int, fun_nat_int, power_power_int, sk_X1)), 
69.36/69.47	             app_encode_app(int, nat, number_number_of_nat, 
69.36/69.47	               app_encode_app(int, int, bit0, 
69.36/69.47	                 app_encode_app(int, int, bit1, zero_zero_int)))))), 
69.36/69.47	       app_encode_app(nat, int, 
69.36/69.47	         app_encode_app(fun_nat_int, app_encode_fun(nat, int), hAPP_nat_int, 
69.36/69.47	           app_encode_app(int, fun_nat_int, power_power_int, sk_Y1)), 
69.36/69.47	         app_encode_app(int, nat, number_number_of_nat, 
69.36/69.47	           app_encode_app(int, int, bit0, 
69.36/69.47	             app_encode_app(int, int, bit1, zero_zero_int)))))
69.36/69.47	      = app_encode_app(int, int, 
69.36/69.47	          app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	            hAPP_int_int, 
69.36/69.47	            app_encode_app(int, fun_int_int, plus_plus_int, 
69.36/69.47	              app_encode_app(int, int, 
69.36/69.47	                app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.47	                  hAPP_int_int, 
69.36/69.47	                  app_encode_app(int, fun_int_int, times_times_int, 
69.36/69.47	                    app_encode_app(int, int, bit0, 
69.36/69.47	                      app_encode_app(int, int, bit0, 
69.36/69.47	                        app_encode_app(int, int, bit1, zero_zero_int))))), m))), 
69.36/69.47	          one_one_int)
69.36/69.47	     | ~ app_encode_app(bool, $o, hBOOL, 
69.36/69.47	           app_encode_app(int, bool, 
69.36/69.47	             app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
69.36/69.47	               hAPP_int_bool, 
69.36/69.47	               app_encode_app(int, fun_int_bool, 
69.36/69.47	                 app_encode_app(fun_int_fun_int_bool, 
69.36/69.47	                   app_encode_fun(int, fun_int_bool), 
69.36/69.47	                   hAPP_i1948725293t_bool, ord_less_int), one_one_int)), t))),
69.36/69.47	    inference('demod', [status(thm)], ['77', '5', '5', '5', '6'])).
69.36/69.47	tff('79', plain,
69.36/69.47	    (app_encode_app(int, int, 
69.36/69.47	       app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
69.36/69.48	         app_encode_app(int, fun_int_int, plus_plus_int, 
69.36/69.48	           app_encode_app(nat, int, 
69.36/69.48	             app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
69.36/69.48	               hAPP_nat_int, 
69.36/69.48	               app_encode_app(int, fun_nat_int, power_power_int, sk_X1)), 
69.36/69.48	             app_encode_app(int, nat, number_number_of_nat, 
69.36/69.48	               app_encode_app(int, int, bit0, one_one_int))))), 
69.36/69.48	       app_encode_app(nat, int, 
69.36/69.48	         app_encode_app(fun_nat_int, app_encode_fun(nat, int), hAPP_nat_int, 
69.36/69.48	           app_encode_app(int, fun_nat_int, power_power_int, sk_Y1)), 
69.36/69.48	         app_encode_app(int, nat, number_number_of_nat, 
69.36/69.48	           app_encode_app(int, int, bit0, one_one_int))))
69.36/69.48	      = app_encode_app(int, int, 
69.36/69.48	          app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.48	            hAPP_int_int, 
69.36/69.48	            app_encode_app(int, fun_int_int, plus_plus_int, 
69.36/69.48	              app_encode_app(int, int, 
69.36/69.48	                app_encode_app(fun_int_int, app_encode_fun(int, int), 
69.36/69.48	                  hAPP_int_int, 
69.36/69.48	                  app_encode_app(int, fun_int_int, times_times_int, 
69.36/69.48	                    app_encode_app(int, int, bit0, 
69.36/69.48	                      app_encode_app(int, int, bit0, one_one_int)))), m))), 
69.36/69.48	          one_one_int)
69.36/69.48	     | ~ app_encode_app(bool, $o, hBOOL, 
69.36/69.48	           app_encode_app(int, bool, 
69.36/69.48	             app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
69.36/69.48	               hAPP_int_bool, 
69.36/69.48	               app_encode_app(int, fun_int_bool, 
69.36/69.48	                 app_encode_app(fun_int_fun_int_bool, 
69.36/69.48	                   app_encode_fun(int, fun_int_bool), 
69.36/69.48	                   hAPP_i1948725293t_bool, ord_less_int), one_one_int)), t))),
69.36/69.48	    inference('demod', [status(thm)], ['78', '9', '9', '9'])).
69.36/69.48	tff('80', plain,
69.36/69.48	    (app_encode_app(int, int, 
69.36/69.48	       app_encode_app(fun_int_int, app_encode_fun(int, int), hAPP_int_int, 
69.36/69.48	         app_encode_app(int, fun_int_int, plus_plus_int, 
69.36/69.48	           app_encode_app(nat, int, 
69.36/69.48	             app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
69.36/69.48	               hAPP_nat_int, 
69.36/69.48	               app_encode_app(int, fun_nat_int, power_power_int, sk_X1)), 
69.36/69.48	             app_encode_app(int, nat, number_number_of_nat, 
69.36/69.48	               sk_K_2(one_one_int, one_one_int, min))))), 
69.36/69.48	       app_encode_app(nat, int, 
69.36/69.48	         app_encode_app(fun_nat_int, app_encode_fun(nat, int), hAPP_nat_int, 
69.36/69.48	           app_encode_app(int, fun_nat_int, power_power_int, sk_Y1)), 
69.36/69.48	         app_encode_app(int, nat, number_number_of_nat, 
69.36/69.48	           sk_K_2(one_one_int, one_one_int, min))))
69.36/69.48	      = app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m))
69.36/69.48	     | ~ app_encode_app(bool, $o, hBOOL, 
69.36/69.48	           app_encode_app(int, bool, 
69.36/69.48	             app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
69.36/69.48	               hAPP_int_bool, 
69.36/69.48	               app_encode_app(int, fun_int_bool, 
69.36/69.48	                 app_encode_app(fun_int_fun_int_bool, 
69.36/69.48	                   app_encode_fun(int, fun_int_bool), 
69.36/69.48	                   hAPP_i1948725293t_bool, ord_less_int), one_one_int)), t))),
69.36/69.48	    inference('demod', [status(thm)],
69.36/69.48	              ['79', '58', '58', '58', '59', '64', '65', '71'])).
69.36/69.48	tff('81', plain,
69.36/69.48	    ~ app_encode_app(bool, $o, hBOOL, 
69.36/69.48	        app_encode_app(int, bool, 
69.36/69.48	          app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
69.36/69.48	            hAPP_int_bool, 
69.36/69.48	            app_encode_app(int, fun_int_bool, 
69.36/69.48	              app_encode_app(fun_int_fun_int_bool, 
69.36/69.48	                app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
69.36/69.48	                ord_less_int), one_one_int)), t)),
69.36/69.48	    inference('simplify_reflect-', [status(thm)], ['80', '74'])).
69.36/69.48	tff('82', plain, ~ $true, inference('sup-', [status(thm)], ['76', '81'])).
69.36/69.48	tff('83', plain, $false, inference('simplify', [status(thm)], ['82'])).
69.36/69.48	
69.36/69.48	% SZS output end Refutation
69.36/69.48	EOF
