0.00/0.00	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : app
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : kbo
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n093.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 07:33:53 CST 2018
53.28/53.37	% done 12045 iterations in 53.181s
53.28/53.37	% SZS status Theorem for 'stdin'
53.28/53.37	% SZS output start Refutation
53.28/53.38	tff(zf_stmt_1287, conjecture,
53.28/53.38	  (app_encode_app(nat,int,
53.28/53.38	                  app_encode_app(fun_nat_int,app_encode_fun(nat,int),
53.28/53.38	                                 hAPP_nat_int,
53.28/53.38	                                 app_encode_app(int,fun_nat_int,
53.28/53.38	                                                power_power_int,
53.28/53.38	                                                app_encode_app(int,int,
53.28/53.38	                                                               app_encode_app(
53.28/53.38	                                                               int,
53.28/53.38	                                                               app_encode_fun(
53.28/53.38	                                                               int,int),
53.28/53.38	                                                               plus_plus_int,
53.28/53.38	                                                               one_one_int),
53.28/53.38	                                                               app_encode_app(
53.28/53.38	                                                               nat,int,
53.28/53.38	                                                               app_encode_app(
53.28/53.38	                                                               fun_nat_int,
53.28/53.38	                                                               app_encode_fun(
53.28/53.38	                                                               nat,int),
53.28/53.38	                                                               hAPP_nat_int,
53.28/53.38	                                                               semiri1621563631at_int),
53.28/53.38	                                                               n)))),
53.28/53.38	                  app_encode_app(int,nat,number_number_of_nat,
53.28/53.38	                                 app_encode_app(int,int,bit0,
53.28/53.38	                                                app_encode_app(int,int,bit1,
53.28/53.38	                                                               pls)))) !=
53.28/53.38	   zero_zero_int)).
53.28/53.38	tff(zf_stmt_0, negated_conjecture,
53.28/53.38	  (app_encode_app(nat,int,
53.28/53.38	                  app_encode_app(fun_nat_int,app_encode_fun(nat,int),
53.28/53.38	                                 hAPP_nat_int,
53.28/53.38	                                 app_encode_app(int,fun_nat_int,
53.28/53.38	                                                power_power_int,
53.28/53.38	                                                app_encode_app(int,int,
53.28/53.38	                                                               app_encode_app(
53.28/53.38	                                                               int,
53.28/53.38	                                                               app_encode_fun(
53.28/53.38	                                                               int,int),
53.28/53.38	                                                               plus_plus_int,
53.28/53.38	                                                               one_one_int),
53.28/53.38	                                                               app_encode_app(
53.28/53.38	                                                               nat,int,
53.28/53.38	                                                               app_encode_app(
53.28/53.38	                                                               fun_nat_int,
53.28/53.38	                                                               app_encode_fun(
53.28/53.38	                                                               nat,int),
53.28/53.38	                                                               hAPP_nat_int,
53.28/53.38	                                                               semiri1621563631at_int),
53.28/53.38	                                                               n)))),
53.28/53.38	                  app_encode_app(int,nat,number_number_of_nat,
53.28/53.38	                                 app_encode_app(int,int,bit0,
53.28/53.38	                                                app_encode_app(int,int,bit1,
53.28/53.38	                                                               pls)))) =
53.28/53.38	   zero_zero_int)).
53.28/53.38	tff('0', plain,
53.28/53.38	    app_encode_app(nat, int, 
53.28/53.38	      app_encode_app(fun_nat_int, app_encode_fun(nat, int), hAPP_nat_int, 
53.28/53.38	        app_encode_app(int, fun_nat_int, power_power_int, 
53.28/53.38	          app_encode_app(int, int, 
53.28/53.38	            app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
53.28/53.38	              one_one_int), 
53.28/53.38	            app_encode_app(nat, int, 
53.28/53.38	              app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
53.28/53.38	                hAPP_nat_int, semiri1621563631at_int), n)))), 
53.28/53.38	      app_encode_app(int, nat, number_number_of_nat, 
53.28/53.38	        app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls))))
53.28/53.38	     = zero_zero_int,
53.28/53.38	    inference('cnf', [status(esa)], [zf_stmt_0])).
53.28/53.38	tff(zf_stmt_150, axiom,
53.28/53.38	  (![Z:int,W:int]:
53.28/53.38	     (app_encode_app(int,int,
53.28/53.38	                     app_encode_app(int,app_encode_fun(int,int),
53.28/53.38	                                    plus_plus_int,Z),
53.28/53.38	                     W) =
53.28/53.38	      app_encode_app(int,int,
53.28/53.38	                     app_encode_app(int,app_encode_fun(int,int),
53.28/53.38	                                    plus_plus_int,W),
53.28/53.38	                     Z)))).
53.28/53.38	tff('1', plain,
53.28/53.38	    ![X94 : int, X95 : int]:
53.28/53.38	      app_encode_app(int, int, 
53.28/53.38	        app_encode_app(int, app_encode_fun(int, int), plus_plus_int, X95), 
53.28/53.38	        X94)
53.28/53.38	       = app_encode_app(int, int, 
53.28/53.38	           app_encode_app(int, app_encode_fun(int, int), plus_plus_int, X94), 
53.28/53.38	           X95),
53.28/53.38	    inference('cnf', [status(esa)], [zf_stmt_150])).
53.28/53.38	tff(zf_stmt_897, axiom,
53.28/53.38	  (![K_1:int]:
53.28/53.38	     (app_encode_app(int,int,succ,K_1) =
53.28/53.38	      app_encode_app(int,int,
53.28/53.38	                     app_encode_app(int,app_encode_fun(int,int),
53.28/53.38	                                    plus_plus_int,K_1),
53.28/53.38	                     one_one_int)))).
53.28/53.38	tff('2', plain,
53.28/53.38	    ![X1856 : int]:
53.28/53.38	      app_encode_app(int, int, succ, X1856)
53.28/53.38	       = app_encode_app(int, int, 
53.28/53.38	           app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
53.28/53.38	             X1856), one_one_int),
53.28/53.38	    inference('cnf', [status(esa)], [zf_stmt_897])).
53.28/53.38	tff('3', plain,
53.28/53.38	    ![X0 : int]:
53.28/53.38	      app_encode_app(int, int, succ, X0)
53.28/53.38	       = app_encode_app(int, int, 
53.28/53.38	           app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
53.28/53.38	             one_one_int), X0),
53.28/53.38	    inference('sup+', [status(thm)], ['1', '2'])).
53.28/53.38	tff(zf_stmt_1210, axiom,
53.28/53.38	  (![A:int,B_1:int]:
53.28/53.38	     app_encode_app(bool,$o,hBOOL,
53.28/53.38	                    app_encode_app(int,bool,
53.28/53.38	                                   app_encode_app(fun_int_bool,
53.28/53.38	                                                  app_encode_fun(int,bool),
53.28/53.38	                                                  hAPP_int_bool,
53.28/53.38	                                                  app_encode_app(int,
53.28/53.38	                                                                 fun_int_bool,
53.28/53.38	                                                                 app_encode_app(
53.28/53.38	                                                                 int,
53.28/53.38	                                                                 app_encode_fun(
53.28/53.38	                                                                 int,
53.28/53.38	                                                                 fun_int_bool),
53.28/53.38	                                                                 zcong,A),B_1)),
53.28/53.38	                                   one_one_int)))).
53.28/53.38	tff('4', plain,
53.28/53.38	    ![X2554 : int, X2555 : int]:
53.28/53.38	      app_encode_app(bool, $o, hBOOL, 
53.28/53.38	        app_encode_app(int, bool, 
53.28/53.38	          app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
53.28/53.38	            hAPP_int_bool, 
53.28/53.38	            app_encode_app(int, fun_int_bool, 
53.28/53.38	              app_encode_app(int, app_encode_fun(int, fun_int_bool), zcong, 
53.28/53.38	                X2554), X2555)), one_one_int)),
53.28/53.38	    inference('cnf', [status(esa)], [zf_stmt_1210])).
53.28/53.38	tff(zf_stmt_1219, axiom,
53.28/53.38	  (![A_1:int,B:int,Ma:int]:
53.28/53.38	     (app_encode_app(bool,$o,hBOOL,
53.28/53.38	                     app_encode_app(int,bool,
53.28/53.38	                                    app_encode_app(fun_int_bool,
53.28/53.38	                                                   app_encode_fun(int,bool),
53.28/53.38	                                                   hAPP_int_bool,
53.28/53.38	                                                   app_encode_app(int,
53.28/53.38	                                                                  fun_int_bool,
53.28/53.38	                                                                  app_encode_app(
53.28/53.38	                                                                  int,
53.28/53.38	                                                                  app_encode_fun(
53.28/53.38	                                                                  int,
53.28/53.38	                                                                  fun_int_bool),
53.28/53.38	                                                                  zcong,A_1),
53.28/53.38	                                                                  B)),
53.28/53.38	                                    Ma)) <=>
53.28/53.38	      (?[K_2:int]:
53.28/53.38	         (B =
53.28/53.38	          app_encode_app(int,int,
53.28/53.38	                         app_encode_app(int,app_encode_fun(int,int),
53.28/53.38	                                        plus_plus_int,A_1),
53.28/53.38	                         app_encode_app(int,int,
53.28/53.38	                                        app_encode_app(int,
53.28/53.38	                                                       app_encode_fun(
53.28/53.38	                                                       int,int),
53.28/53.38	                                                       times_times_int,Ma),
53.28/53.38	                                        K_2))))))).
53.28/53.38	tff('5', plain,
53.28/53.38	    ![X2592 : int, X2593 : int, X2594 : int]:
53.28/53.38	      (X2594
53.28/53.38	        = app_encode_app(int, int, 
53.28/53.38	            app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
53.28/53.38	              X2592), 
53.28/53.38	            app_encode_app(int, int, 
53.28/53.38	              app_encode_app(int, app_encode_fun(int, int), times_times_int, 
53.28/53.38	                X2593), sk_K_22(X2593, X2594, X2592)))
53.28/53.38	       | ~ app_encode_app(bool, $o, hBOOL, 
53.28/53.38	             app_encode_app(int, bool, 
53.28/53.38	               app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
53.28/53.38	                 hAPP_int_bool, 
53.28/53.38	                 app_encode_app(int, fun_int_bool, 
53.28/53.38	                   app_encode_app(int, app_encode_fun(int, fun_int_bool), 
53.28/53.38	                     zcong, X2592), X2594)), X2593))),
53.28/53.38	    inference('cnf', [status(esa)], [zf_stmt_1219])).
53.28/53.38	tff('6', plain,
53.28/53.38	    ![X0 : int, X1 : int]:
53.28/53.38	      (~ $true
53.28/53.38	       | X0
53.28/53.38	          = app_encode_app(int, int, 
53.28/53.38	              app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
53.28/53.38	                X1), 
53.28/53.38	              app_encode_app(int, int, 
53.28/53.38	                app_encode_app(int, app_encode_fun(int, int), 
53.28/53.38	                  times_times_int, one_one_int), 
53.28/53.38	                sk_K_22(one_one_int, X0, X1)))),
53.28/53.38	    inference('sup-', [status(thm)], ['4', '5'])).
53.28/53.38	tff(zf_stmt_747, axiom,
53.28/53.38	  (![A_16:int]:
53.28/53.38	     (app_encode_app(int,int,
53.28/53.38	                     app_encode_app(int,app_encode_fun(int,int),
53.28/53.38	                                    times_times_int,one_one_int),
53.28/53.38	                     A_16) =
53.28/53.38	      A_16))).
53.28/53.38	tff('7', plain,
53.28/53.38	    ![X1479 : int]:
53.28/53.38	      app_encode_app(int, int, 
53.28/53.38	        app_encode_app(int, app_encode_fun(int, int), times_times_int, 
53.28/53.38	          one_one_int), X1479)
53.28/53.38	       = X1479,
53.28/53.38	    inference('cnf', [status(esa)], [zf_stmt_747])).
53.28/53.38	tff('8', plain,
53.28/53.38	    ![X0 : int, X1 : int]:
53.28/53.38	      (~ $true
53.28/53.38	       | X0
53.28/53.38	          = app_encode_app(int, int, 
53.28/53.38	              app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
53.28/53.38	                X1), sk_K_22(one_one_int, X0, X1))),
53.28/53.38	    inference('demod', [status(thm)], ['6', '7'])).
53.28/53.38	tff('9', plain,
53.28/53.38	    ![X0 : int, X1 : int]:
53.28/53.38	      X0
53.28/53.38	       = app_encode_app(int, int, 
53.28/53.38	           app_encode_app(int, app_encode_fun(int, int), plus_plus_int, X1), 
53.28/53.38	           sk_K_22(one_one_int, X0, X1)),
53.28/53.38	    inference('simplify', [status(thm)], ['8'])).
53.28/53.38	tff(zf_stmt_687, axiom,
53.28/53.38	  (![A_31:int,B_16:int]:
53.28/53.38	     (app_encode_app(int,int,
53.28/53.38	                     app_encode_app(int,app_encode_fun(int,int),
53.28/53.38	                                    minus_minus_int,
53.28/53.38	                                    app_encode_app(int,int,
53.28/53.38	                                                   app_encode_app(int,
53.28/53.38	                                                                  app_encode_fun(
53.28/53.38	                                                                  int,int),
53.28/53.38	                                                                  plus_plus_int,
53.28/53.38	                                                                  A_31),
53.28/53.38	                                                   B_16)),
53.28/53.38	                     B_16) =
53.28/53.38	      A_31))).
53.28/53.38	tff('10', plain,
53.28/53.38	    ![X1348 : int, X1349 : int]:
53.28/53.38	      app_encode_app(int, int, 
53.28/53.38	        app_encode_app(int, app_encode_fun(int, int), minus_minus_int, 
53.28/53.38	          app_encode_app(int, int, 
53.28/53.38	            app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
53.28/53.38	              X1348), X1349)), X1349)
53.28/53.38	       = X1348,
53.28/53.38	    inference('cnf', [status(esa)], [zf_stmt_687])).
53.28/53.38	tff(zf_stmt_1104, axiom,
53.28/53.38	  (![K_1:int]:
53.28/53.38	     (app_encode_app(int,int,
53.28/53.38	                     app_encode_app(int,app_encode_fun(int,int),
53.28/53.38	                                    minus_minus_int,K_1),
53.28/53.38	                     min) =
53.28/53.38	      app_encode_app(int,int,succ,K_1)))).
53.28/53.38	tff('11', plain,
53.28/53.38	    ![X2300 : int]:
53.28/53.38	      app_encode_app(int, int, 
53.28/53.38	        app_encode_app(int, app_encode_fun(int, int), minus_minus_int, X2300), 
53.28/53.38	        min)
53.28/53.38	       = app_encode_app(int, int, succ, X2300),
53.28/53.38	    inference('cnf', [status(esa)], [zf_stmt_1104])).
53.28/53.38	tff('12', plain,
53.28/53.38	    ![X0 : int]:
53.28/53.38	      X0
53.28/53.38	       = app_encode_app(int, int, succ, 
53.28/53.38	           app_encode_app(int, int, 
53.28/53.38	             app_encode_app(int, app_encode_fun(int, int), plus_plus_int, X0), 
53.28/53.38	             min)),
53.28/53.38	    inference('sup+', [status(thm)], ['10', '11'])).
53.28/53.38	tff('13', plain,
53.28/53.38	    ![X0 : int]:
53.28/53.38	      X0
53.28/53.38	       = app_encode_app(int, int, succ, 
53.28/53.38	           app_encode_app(int, int, 
53.28/53.38	             app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
53.28/53.38	               min), X0)),
53.28/53.38	    inference('sup+', [status(thm)], ['1', '12'])).
53.28/53.38	tff('14', plain,
53.28/53.38	    ![X0 : int]:
53.28/53.38	      sk_K_22(one_one_int, X0, min) = app_encode_app(int, int, succ, X0),
53.28/53.38	    inference('sup+', [status(thm)], ['9', '13'])).
53.28/53.38	tff('15', plain,
53.28/53.38	    ![X0 : int]:
53.28/53.38	      sk_K_22(one_one_int, X0, min)
53.28/53.38	       = app_encode_app(int, int, 
53.28/53.38	           app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
53.28/53.38	             one_one_int), X0),
53.28/53.38	    inference('demod', [status(thm)], ['3', '14'])).
53.28/53.38	tff(zf_stmt_181, axiom, (pls = zero_zero_int)).
53.28/53.38	tff('16', plain, pls = zero_zero_int,
53.28/53.38	    inference('cnf', [status(esa)], [zf_stmt_181])).
53.28/53.38	tff(zf_stmt_108, axiom,
53.28/53.38	  (one_one_int =
53.28/53.38	   app_encode_app(int,int,number_number_of_int,
53.28/53.38	                  app_encode_app(int,int,bit1,pls)))).
53.28/53.38	tff('17', plain,
53.28/53.38	    one_one_int
53.28/53.38	     = app_encode_app(int, int, number_number_of_int, 
53.28/53.38	         app_encode_app(int, int, bit1, pls)),
53.28/53.38	    inference('cnf', [status(esa)], [zf_stmt_108])).
53.28/53.38	tff(zf_stmt_260, axiom,
53.28/53.38	  (![K_1:int]: (app_encode_app(int,int,number_number_of_int,K_1) = K_1))).
53.28/53.38	tff('18', plain,
53.28/53.38	    ![X255 : int]:
53.28/53.38	      app_encode_app(int, int, number_number_of_int, X255) = X255,
53.28/53.38	    inference('cnf', [status(esa)], [zf_stmt_260])).
53.28/53.38	tff('19', plain, one_one_int = app_encode_app(int, int, bit1, zero_zero_int),
53.28/53.38	    inference('demod', [status(thm)], ['17', '16', '18'])).
53.28/53.38	tff(zf_stmt_186, axiom,
53.28/53.38	  (![K_1:int]:
53.28/53.38	     (app_encode_app(int,int,bit0,K_1) =
53.28/53.38	      app_encode_app(int,int,
53.28/53.38	                     app_encode_app(int,app_encode_fun(int,int),
53.28/53.38	                                    plus_plus_int,K_1),
53.28/53.38	                     K_1)))).
53.28/53.38	tff('20', plain,
53.28/53.38	    ![X155 : int]:
53.28/53.38	      app_encode_app(int, int, bit0, X155)
53.28/53.38	       = app_encode_app(int, int, 
53.28/53.38	           app_encode_app(int, app_encode_fun(int, int), plus_plus_int, X155), 
53.28/53.38	           X155),
53.28/53.38	    inference('cnf', [status(esa)], [zf_stmt_186])).
53.28/53.38	tff('21', plain,
53.28/53.38	    app_encode_app(int, int, bit0, one_one_int)
53.28/53.38	     = app_encode_app(int, int, succ, one_one_int),
53.28/53.38	    inference('sup+', [status(thm)], ['2', '20'])).
53.28/53.38	tff('22', plain,
53.28/53.38	    app_encode_app(int, int, bit0, one_one_int)
53.28/53.38	     = sk_K_22(one_one_int, one_one_int, min),
53.28/53.38	    inference('demod', [status(thm)], ['21', '14'])).
53.28/53.38	tff(zf_stmt_113, axiom,
53.28/53.38	  (![X:int,Y:int]:
53.28/53.38	     (app_encode_app(bool,$o,hBOOL,
53.28/53.38	                     app_encode_app(int,bool,
53.28/53.38	                                    app_encode_app(fun_int_bool,
53.28/53.38	                                                   app_encode_fun(int,bool),
53.28/53.38	                                                   hAPP_int_bool,
53.28/53.38	                                                   app_encode_app(int,
53.28/53.38	                                                                  fun_int_bool,
53.28/53.38	                                                                  app_encode_app(
53.28/53.38	                                                                  fun_int_fun_int_bool,
53.28/53.38	                                                                  app_encode_fun(
53.28/53.38	                                                                  int,
53.28/53.38	                                                                  fun_int_bool),
53.28/53.38	                                                                  hAPP_i1948725293t_bool,
53.28/53.38	                                                                  ord_less_int),
53.28/53.38	                                                                  X)),
53.28/53.38	                                    Y)) | 
53.28/53.38	      (X = Y) | 
53.28/53.38	      app_encode_app(bool,$o,hBOOL,
53.28/53.38	                     app_encode_app(int,bool,
53.28/53.38	                                    app_encode_app(fun_int_bool,
53.28/53.38	                                                   app_encode_fun(int,bool),
53.28/53.38	                                                   hAPP_int_bool,
53.28/53.38	                                                   app_encode_app(int,
53.28/53.38	                                                                  fun_int_bool,
53.28/53.38	                                                                  app_encode_app(
53.28/53.38	                                                                  fun_int_fun_int_bool,
53.28/53.38	                                                                  app_encode_fun(
53.28/53.38	                                                                  int,
53.28/53.38	                                                                  fun_int_bool),
53.28/53.38	                                                                  hAPP_i1948725293t_bool,
53.28/53.38	                                                                  ord_less_int),
53.28/53.38	                                                                  Y)),
53.28/53.38	                                    X))))).
53.28/53.38	tff('23', plain,
53.28/53.38	    ![X21 : int, X22 : int]:
53.28/53.38	      (app_encode_app(bool, $o, hBOOL, 
53.28/53.38	         app_encode_app(int, bool, 
53.28/53.38	           app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
53.28/53.38	             hAPP_int_bool, 
53.28/53.38	             app_encode_app(int, fun_int_bool, 
53.28/53.38	               app_encode_app(fun_int_fun_int_bool, 
53.28/53.38	                 app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
53.28/53.38	                 ord_less_int), X21)), X22))
53.28/53.38	       | X21 = X22
53.28/53.38	       | app_encode_app(bool, $o, hBOOL, 
53.28/53.38	           app_encode_app(int, bool, 
53.28/53.38	             app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
53.28/53.38	               hAPP_int_bool, 
53.28/53.38	               app_encode_app(int, fun_int_bool, 
53.28/53.38	                 app_encode_app(fun_int_fun_int_bool, 
53.28/53.38	                   app_encode_fun(int, fun_int_bool), 
53.28/53.38	                   hAPP_i1948725293t_bool, ord_less_int), X22)), X21))),
53.28/53.38	    inference('cnf', [status(esa)], [zf_stmt_113])).
53.28/53.38	tff(zf_stmt_234, axiom,
53.28/53.38	  (app_encode_app(int,int,number_number_of_int,
53.28/53.38	                  app_encode_app(int,int,bit0,
53.28/53.38	                                 app_encode_app(int,int,bit1,pls))) =
53.28/53.38	   app_encode_app(nat,int,
53.28/53.38	                  app_encode_app(fun_nat_int,app_encode_fun(nat,int),
53.28/53.38	                                 hAPP_nat_int,semiri1621563631at_int),
53.28/53.38	                  app_encode_app(int,nat,number_number_of_nat,
53.28/53.38	                                 app_encode_app(int,int,bit0,
53.28/53.38	                                                app_encode_app(int,int,bit1,
53.28/53.38	                                                               pls)))))).
53.28/53.38	tff('24', plain,
53.28/53.38	    app_encode_app(int, int, number_number_of_int, 
53.28/53.38	      app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls)))
53.28/53.38	     = app_encode_app(nat, int, 
53.28/53.38	         app_encode_app(fun_nat_int, app_encode_fun(nat, int), hAPP_nat_int, 
53.28/53.38	           semiri1621563631at_int), 
53.28/53.38	         app_encode_app(int, nat, number_number_of_nat, 
53.28/53.38	           app_encode_app(int, int, bit0, 
53.28/53.38	             app_encode_app(int, int, bit1, pls)))),
53.28/53.38	    inference('cnf', [status(esa)], [zf_stmt_234])).
53.28/53.38	tff('25', plain,
53.28/53.38	    app_encode_app(int, int, bit0, one_one_int)
53.28/53.38	     = app_encode_app(nat, int, 
53.28/53.38	         app_encode_app(fun_nat_int, app_encode_fun(nat, int), hAPP_nat_int, 
53.28/53.38	           semiri1621563631at_int), 
53.28/53.38	         app_encode_app(int, nat, number_number_of_nat, 
53.28/53.38	           app_encode_app(int, int, bit0, one_one_int))),
53.28/53.38	    inference('demod', [status(thm)], ['24', '16', '19', '18', '16', '19'])).
53.28/53.38	tff(zf_stmt_166, axiom,
53.28/53.38	  (![K_1:nat]:
53.28/53.38	     (~
53.28/53.38	       app_encode_app(bool,$o,hBOOL,
53.28/53.38	                      app_encode_app(int,bool,
53.28/53.38	                                     app_encode_app(fun_int_bool,
53.28/53.38	                                                    app_encode_fun(int,bool),
53.28/53.38	                                                    hAPP_int_bool,
53.28/53.38	                                                    app_encode_app(int,
53.28/53.38	                                                                   fun_int_bool,
53.28/53.38	                                                                   app_encode_app(
53.28/53.38	                                                                   fun_int_fun_int_bool,
53.28/53.38	                                                                   app_encode_fun(
53.28/53.38	                                                                   int,
53.28/53.38	                                                                   fun_int_bool),
53.28/53.38	                                                                   hAPP_i1948725293t_bool,
53.28/53.38	                                                                   ord_less_int),
53.28/53.38	                                                                   app_encode_app(
53.28/53.38	                                                                   nat,int,
53.28/53.38	                                                                   app_encode_app(
53.28/53.38	                                                                   fun_nat_int,
53.28/53.38	                                                                   app_encode_fun(
53.28/53.38	                                                                   nat,int),
53.28/53.38	                                                                   hAPP_nat_int,
53.28/53.38	                                                                   semiri1621563631at_int),
53.28/53.38	                                                                   K_1))),
53.28/53.38	                                     zero_zero_int))))).
53.28/53.38	tff('26', plain,
53.28/53.38	    ![X126 : nat]:
53.28/53.38	      ~ app_encode_app(bool, $o, hBOOL, 
53.28/53.38	          app_encode_app(int, bool, 
53.28/53.38	            app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
53.28/53.38	              hAPP_int_bool, 
53.28/53.38	              app_encode_app(int, fun_int_bool, 
53.28/53.38	                app_encode_app(fun_int_fun_int_bool, 
53.28/53.38	                  app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
53.28/53.38	                  ord_less_int), 
53.28/53.38	                app_encode_app(nat, int, 
53.28/53.38	                  app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
53.28/53.38	                    hAPP_nat_int, semiri1621563631at_int), X126))), 
53.28/53.38	            zero_zero_int)),
53.28/53.38	    inference('cnf', [status(esa)], [zf_stmt_166])).
53.28/53.38	tff('27', plain,
53.28/53.38	    ~ app_encode_app(bool, $o, hBOOL, 
53.28/53.38	        app_encode_app(int, bool, 
53.28/53.38	          app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
53.28/53.38	            hAPP_int_bool, 
53.28/53.38	            app_encode_app(int, fun_int_bool, 
53.28/53.38	              app_encode_app(fun_int_fun_int_bool, 
53.28/53.38	                app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
53.28/53.38	                ord_less_int), app_encode_app(int, int, bit0, one_one_int))), 
53.28/53.38	          zero_zero_int)),
53.28/53.38	    inference('sup-', [status(thm)], ['25', '26'])).
53.28/53.38	tff('28', plain,
53.28/53.38	    (~ $true
53.28/53.38	     | app_encode_app(bool, $o, hBOOL, 
53.28/53.38	         app_encode_app(int, bool, 
53.28/53.38	           app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
53.28/53.38	             hAPP_int_bool, 
53.28/53.38	             app_encode_app(int, fun_int_bool, 
53.28/53.38	               app_encode_app(fun_int_fun_int_bool, 
53.28/53.38	                 app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
53.28/53.38	                 ord_less_int), zero_zero_int)), 
53.28/53.38	           app_encode_app(int, int, bit0, one_one_int)))
53.28/53.38	     | app_encode_app(int, int, bit0, one_one_int) = zero_zero_int),
53.28/53.38	    inference('sup-', [status(thm)], ['23', '27'])).
53.28/53.38	tff('29', plain,
53.28/53.38	    (app_encode_app(int, int, bit0, one_one_int) = zero_zero_int
53.28/53.38	     | app_encode_app(bool, $o, hBOOL, 
53.28/53.38	         app_encode_app(int, bool, 
53.28/53.38	           app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
53.28/53.38	             hAPP_int_bool, 
53.28/53.38	             app_encode_app(int, fun_int_bool, 
53.28/53.38	               app_encode_app(fun_int_fun_int_bool, 
53.28/53.38	                 app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
53.28/53.38	                 ord_less_int), zero_zero_int)), 
53.28/53.38	           app_encode_app(int, int, bit0, one_one_int)))),
53.28/53.38	    inference('simplify', [status(thm)], ['28'])).
53.28/53.38	tff(zf_stmt_126, axiom,
53.28/53.38	  (![Na:nat]:
53.28/53.38	     ((app_encode_app(nat,int,
53.28/53.38	                      app_encode_app(fun_nat_int,app_encode_fun(nat,int),
53.28/53.38	                                     hAPP_nat_int,semiri1621563631at_int),
53.28/53.38	                      Na) =
53.28/53.38	       zero_zero_int) <=>
53.28/53.38	      (Na = zero_zero_nat)))).
53.28/53.38	tff('30', plain,
53.28/53.38	    ![X43 : nat]:
53.28/53.38	      (X43 = zero_zero_nat
53.28/53.38	       | app_encode_app(nat, int, 
53.28/53.38	           app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
53.28/53.38	             hAPP_nat_int, semiri1621563631at_int), X43)
53.28/53.38	          != zero_zero_int),
53.28/53.38	    inference('cnf', [status(esa)], [zf_stmt_126])).
53.28/53.38	tff('31', plain,
53.28/53.38	    (app_encode_app(int, int, bit0, one_one_int) != zero_zero_int
53.28/53.38	     | app_encode_app(int, nat, number_number_of_nat, 
53.28/53.38	         app_encode_app(int, int, bit0, one_one_int))
53.28/53.38	        = zero_zero_nat),
53.28/53.38	    inference('sup-', [status(thm)], ['25', '30'])).
53.28/53.38	tff(zf_stmt_90, axiom,
53.28/53.38	  (app_encode_app(nat,int,
53.28/53.38	                  app_encode_app(fun_nat_int,app_encode_fun(nat,int),
53.28/53.38	                                 hAPP_nat_int,
53.28/53.38	                                 app_encode_app(int,fun_nat_int,
53.28/53.38	                                                power_power_int,zero_zero_int)),
53.28/53.38	                  app_encode_app(int,nat,number_number_of_nat,
53.28/53.38	                                 app_encode_app(int,int,bit0,
53.28/53.38	                                                app_encode_app(int,int,bit1,
53.28/53.38	                                                               pls)))) =
53.28/53.38	   zero_zero_int)).
53.28/53.38	tff('32', plain,
53.28/53.38	    app_encode_app(nat, int, 
53.28/53.38	      app_encode_app(fun_nat_int, app_encode_fun(nat, int), hAPP_nat_int, 
53.28/53.38	        app_encode_app(int, fun_nat_int, power_power_int, zero_zero_int)), 
53.28/53.38	      app_encode_app(int, nat, number_number_of_nat, 
53.28/53.38	        app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls))))
53.28/53.38	     = zero_zero_int,
53.28/53.38	    inference('cnf', [status(esa)], [zf_stmt_90])).
53.28/53.38	tff('33', plain,
53.28/53.38	    app_encode_app(nat, int, 
53.28/53.38	      app_encode_app(fun_nat_int, app_encode_fun(nat, int), hAPP_nat_int, 
53.28/53.38	        app_encode_app(int, fun_nat_int, power_power_int, zero_zero_int)), 
53.28/53.38	      app_encode_app(int, nat, number_number_of_nat, 
53.28/53.38	        app_encode_app(int, int, bit0, one_one_int)))
53.28/53.38	     = zero_zero_int,
53.28/53.38	    inference('demod', [status(thm)], ['32', '16', '19'])).
53.28/53.38	tff(zf_stmt_105, axiom,
53.28/53.38	  (![W_12:int]:
53.28/53.38	     (((app_encode_app(int,nat,number_number_of_nat,W_12) = zero_zero_nat) =>
53.28/53.38	       (app_encode_app(nat,int,
53.28/53.38	                       app_encode_app(fun_nat_int,app_encode_fun(nat,int),
53.28/53.38	                                      hAPP_nat_int,
53.28/53.38	                                      app_encode_app(int,fun_nat_int,
53.28/53.38	                                                     power_power_int,
53.28/53.38	                                                     zero_zero_int)),
53.28/53.38	                       app_encode_app(int,nat,number_number_of_nat,W_12)) =
53.28/53.38	        one_one_int)) & 
53.28/53.38	      ((app_encode_app(int,nat,number_number_of_nat,W_12) != zero_zero_nat) =>
53.28/53.38	       (app_encode_app(nat,int,
53.28/53.38	                       app_encode_app(fun_nat_int,app_encode_fun(nat,int),
53.28/53.38	                                      hAPP_nat_int,
53.28/53.38	                                      app_encode_app(int,fun_nat_int,
53.28/53.38	                                                     power_power_int,
53.28/53.38	                                                     zero_zero_int)),
53.28/53.38	                       app_encode_app(int,nat,number_number_of_nat,W_12)) =
53.28/53.38	        zero_zero_int))))).
53.28/53.38	tff('34', plain,
53.28/53.38	    ![X16 : int]:
53.28/53.38	      (app_encode_app(nat, int, 
53.28/53.38	         app_encode_app(fun_nat_int, app_encode_fun(nat, int), hAPP_nat_int, 
53.28/53.38	           app_encode_app(int, fun_nat_int, power_power_int, zero_zero_int)), 
53.28/53.38	         app_encode_app(int, nat, number_number_of_nat, X16))
53.28/53.38	        = one_one_int
53.28/53.38	       | app_encode_app(int, nat, number_number_of_nat, X16) != zero_zero_nat),
53.28/53.38	    inference('cnf', [status(esa)], [zf_stmt_105])).
53.28/53.38	tff('35', plain,
53.28/53.38	    (zero_zero_int = one_one_int
53.28/53.38	     | app_encode_app(int, nat, number_number_of_nat, 
53.28/53.38	         app_encode_app(int, int, bit0, one_one_int))
53.28/53.38	        != zero_zero_nat),
53.28/53.38	    inference('sup+', [status(thm)], ['33', '34'])).
53.28/53.38	tff(zf_stmt_182, axiom, (zero_zero_int != one_one_int)).
53.28/53.38	tff('36', plain, zero_zero_int != one_one_int,
53.28/53.38	    inference('cnf', [status(esa)], [zf_stmt_182])).
53.28/53.38	tff('37', plain,
53.28/53.38	    app_encode_app(int, nat, number_number_of_nat, 
53.28/53.38	      app_encode_app(int, int, bit0, one_one_int))
53.28/53.38	     != zero_zero_nat,
53.28/53.38	    inference('simplify_reflect-', [status(thm)], ['35', '36'])).
53.28/53.38	tff('38', plain,
53.28/53.38	    app_encode_app(int, int, bit0, one_one_int) != zero_zero_int,
53.28/53.38	    inference('simplify_reflect-', [status(thm)], ['31', '37'])).
53.28/53.38	tff('39', plain,
53.28/53.38	    app_encode_app(bool, $o, hBOOL, 
53.28/53.38	      app_encode_app(int, bool, 
53.28/53.38	        app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
53.28/53.38	          hAPP_int_bool, 
53.28/53.38	          app_encode_app(int, fun_int_bool, 
53.28/53.38	            app_encode_app(fun_int_fun_int_bool, 
53.28/53.38	              app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
53.28/53.38	              ord_less_int), zero_zero_int)), 
53.28/53.38	        app_encode_app(int, int, bit0, one_one_int))),
53.28/53.38	    inference('simplify_reflect-', [status(thm)], ['29', '38'])).
53.28/53.38	tff(zf_stmt_380, axiom,
53.28/53.38	  (![K_1:int]:
53.28/53.38	     (app_encode_app(bool,$o,hBOOL,
53.28/53.38	                     app_encode_app(int,bool,
53.28/53.38	                                    app_encode_app(fun_int_bool,
53.28/53.38	                                                   app_encode_fun(int,bool),
53.28/53.38	                                                   hAPP_int_bool,
53.28/53.38	                                                   app_encode_app(int,
53.28/53.38	                                                                  fun_int_bool,
53.28/53.38	                                                                  app_encode_app(
53.28/53.38	                                                                  fun_int_fun_int_bool,
53.28/53.38	                                                                  app_encode_fun(
53.28/53.38	                                                                  int,
53.28/53.38	                                                                  fun_int_bool),
53.28/53.38	                                                                  hAPP_i1948725293t_bool,
53.28/53.38	                                                                  ord_less_int),
53.28/53.38	                                                                  zero_zero_int)),
53.28/53.38	                                    K_1)) =>
53.28/53.38	      (?[N_1:nat]:
53.28/53.38	         (app_encode_app(bool,$o,hBOOL,
53.28/53.38	                         app_encode_app(nat,bool,
53.28/53.38	                                        app_encode_app(fun_nat_bool,
53.28/53.38	                                                       app_encode_fun(
53.28/53.38	                                                       nat,bool),
53.28/53.38	                                                       hAPP_nat_bool,
53.28/53.38	                                                       app_encode_app(
53.28/53.38	                                                       nat,fun_nat_bool,
53.28/53.38	                                                       app_encode_app(
53.28/53.38	                                                       fun_nat_fun_nat_bool,
53.28/53.38	                                                       app_encode_fun(
53.28/53.38	                                                       nat,fun_nat_bool),
53.28/53.38	                                                       hAPP_n1699378549t_bool,
53.28/53.38	                                                       ord_less_nat),
53.28/53.38	                                                       zero_zero_nat)),
53.28/53.38	                                        N_1)) & 
53.28/53.38	          (K_1 =
53.28/53.38	           app_encode_app(nat,int,
53.28/53.38	                          app_encode_app(fun_nat_int,app_encode_fun(nat,int),
53.28/53.38	                                         hAPP_nat_int,semiri1621563631at_int),
53.28/53.38	                          N_1))))))).
53.28/53.38	tff('40', plain,
53.28/53.38	    ![X490 : int]:
53.28/53.38	      (X490
53.28/53.38	        = app_encode_app(nat, int, 
53.28/53.38	            app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
53.28/53.38	              hAPP_nat_int, semiri1621563631at_int), sk_N_1(X490))
53.28/53.38	       | ~ app_encode_app(bool, $o, hBOOL, 
53.28/53.38	             app_encode_app(int, bool, 
53.28/53.38	               app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
53.28/53.38	                 hAPP_int_bool, 
53.28/53.38	                 app_encode_app(int, fun_int_bool, 
53.28/53.38	                   app_encode_app(fun_int_fun_int_bool, 
53.28/53.38	                     app_encode_fun(int, fun_int_bool), 
53.28/53.38	                     hAPP_i1948725293t_bool, ord_less_int), zero_zero_int)), 
53.28/53.38	               X490))),
53.28/53.38	    inference('cnf', [status(esa)], [zf_stmt_380])).
53.28/53.38	tff('41', plain,
53.28/53.38	    (~ $true
53.28/53.38	     | app_encode_app(int, int, bit0, one_one_int)
53.28/53.38	        = app_encode_app(nat, int, 
53.28/53.38	            app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
53.28/53.38	              hAPP_nat_int, semiri1621563631at_int), 
53.28/53.38	            sk_N_1(app_encode_app(int, int, bit0, one_one_int)))),
53.28/53.38	    inference('sup-', [status(thm)], ['39', '40'])).
53.28/53.38	tff('42', plain,
53.28/53.38	    app_encode_app(int, int, bit0, one_one_int)
53.28/53.38	     = app_encode_app(nat, int, 
53.28/53.38	         app_encode_app(fun_nat_int, app_encode_fun(nat, int), hAPP_nat_int, 
53.28/53.38	           semiri1621563631at_int), 
53.28/53.38	         sk_N_1(app_encode_app(int, int, bit0, one_one_int))),
53.28/53.38	    inference('simplify', [status(thm)], ['41'])).
53.28/53.38	tff(zf_stmt_735, axiom,
53.28/53.38	  (![N:nat]:
53.28/53.38	     (app_encode_app(int,nat,nat_1,
53.28/53.38	                     app_encode_app(nat,int,
53.28/53.38	                                    app_encode_app(fun_nat_int,
53.28/53.38	                                                   app_encode_fun(nat,int),
53.28/53.38	                                                   hAPP_nat_int,
53.28/53.38	                                                   semiri1621563631at_int),
53.28/53.38	                                    N)) =
53.28/53.38	      N))).
53.28/53.38	tff('43', plain,
53.28/53.38	    ![X1467 : nat]:
53.28/53.38	      app_encode_app(int, nat, nat_1, 
53.28/53.38	        app_encode_app(nat, int, 
53.28/53.38	          app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
53.28/53.38	            hAPP_nat_int, semiri1621563631at_int), X1467))
53.28/53.38	       = X1467,
53.28/53.38	    inference('cnf', [status(esa)], [zf_stmt_735])).
53.28/53.38	tff(zf_stmt_849, axiom,
53.28/53.38	  (![W:int]:
53.28/53.38	     (app_encode_app(int,nat,nat_1,
53.28/53.38	                     app_encode_app(int,int,number_number_of_int,W)) =
53.28/53.38	      app_encode_app(int,nat,number_number_of_nat,W)))).
53.28/53.38	tff('44', plain,
53.28/53.38	    ![X1743 : int]:
53.28/53.38	      app_encode_app(int, nat, nat_1, 
53.28/53.38	        app_encode_app(int, int, number_number_of_int, X1743))
53.28/53.38	       = app_encode_app(int, nat, number_number_of_nat, X1743),
53.28/53.38	    inference('cnf', [status(esa)], [zf_stmt_849])).
53.28/53.38	tff('45', plain,
53.28/53.38	    ![X1743 : int]:
53.28/53.38	      app_encode_app(int, nat, nat_1, X1743)
53.28/53.38	       = app_encode_app(int, nat, number_number_of_nat, X1743),
53.28/53.38	    inference('demod', [status(thm)], ['44', '18'])).
53.28/53.38	tff('46', plain,
53.28/53.38	    ![X1467 : nat]:
53.28/53.38	      app_encode_app(int, nat, number_number_of_nat, 
53.28/53.38	        app_encode_app(nat, int, 
53.28/53.38	          app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
53.28/53.38	            hAPP_nat_int, semiri1621563631at_int), X1467))
53.28/53.38	       = X1467,
53.28/53.38	    inference('demod', [status(thm)], ['43', '45'])).
53.28/53.38	tff('47', plain,
53.28/53.38	    app_encode_app(int, nat, number_number_of_nat, 
53.28/53.38	      app_encode_app(int, int, bit0, one_one_int))
53.28/53.38	     = sk_N_1(app_encode_app(int, int, bit0, one_one_int)),
53.28/53.38	    inference('sup+', [status(thm)], ['42', '46'])).
53.28/53.38	tff('48', plain,
53.28/53.38	    app_encode_app(int, nat, number_number_of_nat, 
53.28/53.38	      sk_K_22(one_one_int, one_one_int, min))
53.28/53.38	     = sk_N_1(sk_K_22(one_one_int, one_one_int, min)),
53.28/53.38	    inference('demod', [status(thm)], ['47', '22', '22'])).
53.28/53.38	tff('49', plain,
53.28/53.38	    app_encode_app(nat, int, 
53.28/53.38	      app_encode_app(fun_nat_int, app_encode_fun(nat, int), hAPP_nat_int, 
53.28/53.38	        app_encode_app(int, fun_nat_int, power_power_int, 
53.28/53.38	          sk_K_22(one_one_int, 
53.28/53.38	            app_encode_app(nat, int, 
53.28/53.38	              app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
53.28/53.38	                hAPP_nat_int, semiri1621563631at_int), n), min))), 
53.28/53.38	      sk_N_1(sk_K_22(one_one_int, one_one_int, min)))
53.28/53.38	     = zero_zero_int,
53.28/53.38	    inference('demod', [status(thm)], ['0', '15', '16', '19', '22', '48'])).
53.28/53.38	tff(zf_stmt_314, axiom,
53.28/53.38	  (![N_20:nat,A_94:int]:
53.28/53.38	     ((A_94 != zero_zero_int) =>
53.28/53.38	      (app_encode_app(nat,int,
53.28/53.38	                      app_encode_app(fun_nat_int,app_encode_fun(nat,int),
53.28/53.38	                                     hAPP_nat_int,
53.28/53.38	                                     app_encode_app(int,fun_nat_int,
53.28/53.38	                                                    power_power_int,A_94)),
53.28/53.38	                      N_20) !=
53.28/53.38	       zero_zero_int)))).
53.28/53.38	tff('50', plain,
53.28/53.38	    ![X377 : int, X378 : nat]:
53.28/53.38	      (app_encode_app(nat, int, 
53.28/53.38	         app_encode_app(fun_nat_int, app_encode_fun(nat, int), hAPP_nat_int, 
53.28/53.38	           app_encode_app(int, fun_nat_int, power_power_int, X377)), X378)
53.28/53.38	        != zero_zero_int
53.28/53.38	       | X377 = zero_zero_int),
53.28/53.38	    inference('cnf', [status(esa)], [zf_stmt_314])).
53.28/53.38	tff('51', plain,
53.28/53.38	    (zero_zero_int != zero_zero_int
53.28/53.38	     | sk_K_22(one_one_int, 
53.28/53.38	         app_encode_app(nat, int, 
53.28/53.38	           app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
53.28/53.38	             hAPP_nat_int, semiri1621563631at_int), n), min)
53.28/53.38	        = zero_zero_int),
53.28/53.38	    inference('sup-', [status(thm)], ['49', '50'])).
53.28/53.38	tff('52', plain,
53.28/53.38	    sk_K_22(one_one_int, 
53.28/53.38	      app_encode_app(nat, int, 
53.28/53.38	        app_encode_app(fun_nat_int, app_encode_fun(nat, int), hAPP_nat_int, 
53.28/53.38	          semiri1621563631at_int), n), min)
53.28/53.38	     = zero_zero_int,
53.28/53.38	    inference('simplify', [status(thm)], ['51'])).
53.28/53.38	tff('53', plain,
53.28/53.38	    ![X0 : int]:
53.28/53.38	      app_encode_app(int, int, succ, sk_K_22(one_one_int, X0, one_one_int))
53.28/53.38	       = X0,
53.28/53.38	    inference('sup+', [status(thm)], ['9', '3'])).
53.28/53.38	tff(zf_stmt_399, axiom,
53.28/53.38	  (![B_58:int,A_85:int,C_44:int]:
53.28/53.38	     ((app_encode_app(int,int,
53.28/53.38	                      app_encode_app(int,app_encode_fun(int,int),
53.28/53.38	                                     plus_plus_int,B_58),
53.28/53.38	                      A_85) =
53.28/53.38	       app_encode_app(int,int,
53.28/53.38	                      app_encode_app(int,app_encode_fun(int,int),
53.28/53.38	                                     plus_plus_int,C_44),
53.28/53.38	                      A_85)) =>
53.28/53.38	      (B_58 = C_44)))).
53.28/53.38	tff('54', plain,
53.28/53.38	    ![X525 : int, X526 : int, X527 : int]:
53.28/53.38	      (X526 = X525
53.28/53.38	       | app_encode_app(int, int, 
53.28/53.38	           app_encode_app(int, app_encode_fun(int, int), plus_plus_int, X526), 
53.28/53.38	           X527)
53.28/53.38	          != app_encode_app(int, int, 
53.28/53.38	               app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
53.28/53.38	                 X525), X527)),
53.28/53.38	    inference('cnf', [status(esa)], [zf_stmt_399])).
53.28/53.38	tff('55', plain,
53.28/53.38	    ![X0 : int, X1 : int]:
53.28/53.38	      (app_encode_app(int, int, succ, X0)
53.28/53.38	        != app_encode_app(int, int, 
53.28/53.38	             app_encode_app(int, app_encode_fun(int, int), plus_plus_int, X1), 
53.28/53.38	             one_one_int)
53.28/53.38	       | X0 = X1),
53.28/53.38	    inference('sup-', [status(thm)], ['2', '54'])).
53.28/53.38	tff('56', plain,
53.28/53.38	    ![X0 : int, X1 : int]:
53.28/53.38	      (app_encode_app(int, int, succ, X0)
53.28/53.38	        != app_encode_app(int, int, succ, X1)
53.28/53.38	       | X0 = X1),
53.28/53.38	    inference('demod', [status(thm)], ['55', '2'])).
53.28/53.38	tff('57', plain,
53.28/53.38	    ![X0 : int, X1 : int]:
53.28/53.38	      (X0 != app_encode_app(int, int, succ, X1)
53.28/53.38	       | sk_K_22(one_one_int, X0, one_one_int) = X1),
53.28/53.38	    inference('sup-', [status(thm)], ['53', '56'])).
53.28/53.38	tff('58', plain,
53.28/53.38	    ![X1 : int]:
53.28/53.38	      sk_K_22(one_one_int, app_encode_app(int, int, succ, X1), one_one_int)
53.28/53.38	       = X1,
53.28/53.38	    inference('simplify', [status(thm)], ['57'])).
53.28/53.38	tff('59', plain,
53.28/53.38	    ![X1 : int]:
53.28/53.38	      sk_K_22(one_one_int, sk_K_22(one_one_int, X1, min), one_one_int) = X1,
53.28/53.38	    inference('demod', [status(thm)], ['58', '14'])).
53.28/53.38	tff('60', plain,
53.28/53.38	    sk_K_22(one_one_int, zero_zero_int, one_one_int)
53.28/53.38	     = app_encode_app(nat, int, 
53.28/53.38	         app_encode_app(fun_nat_int, app_encode_fun(nat, int), hAPP_nat_int, 
53.28/53.38	           semiri1621563631at_int), n),
53.28/53.38	    inference('sup+', [status(thm)], ['52', '59'])).
53.28/53.38	tff(zf_stmt_1103, axiom, (app_encode_app(int,int,succ,min) = pls)).
53.28/53.38	tff('61', plain, app_encode_app(int, int, succ, min) = pls,
53.28/53.38	    inference('cnf', [status(esa)], [zf_stmt_1103])).
53.28/53.38	tff('62', plain, app_encode_app(int, int, succ, min) = zero_zero_int,
53.28/53.38	    inference('demod', [status(thm)], ['61', '16'])).
53.28/53.38	tff('63', plain,
53.28/53.38	    ![X0 : int]:
53.28/53.38	      (zero_zero_int != app_encode_app(int, int, succ, X0) | min = X0),
53.28/53.38	    inference('sup-', [status(thm)], ['62', '56'])).
53.28/53.38	tff('64', plain,
53.28/53.38	    ![X0 : int]:
53.28/53.38	      (zero_zero_int != X0 | min = sk_K_22(one_one_int, X0, one_one_int)),
53.28/53.38	    inference('sup-', [status(thm)], ['53', '63'])).
53.28/53.38	tff('65', plain, min = sk_K_22(one_one_int, zero_zero_int, one_one_int),
53.28/53.38	    inference('simplify', [status(thm)], ['64'])).
53.28/53.38	tff('66', plain,
53.28/53.38	    min
53.28/53.38	     = app_encode_app(nat, int, 
53.28/53.38	         app_encode_app(fun_nat_int, app_encode_fun(nat, int), hAPP_nat_int, 
53.28/53.38	           semiri1621563631at_int), n),
53.28/53.38	    inference('demod', [status(thm)], ['60', '65'])).
53.28/53.38	tff('67', plain,
53.28/53.38	    ~ app_encode_app(bool, $o, hBOOL, 
53.28/53.38	        app_encode_app(int, bool, 
53.28/53.38	          app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
53.28/53.38	            hAPP_int_bool, 
53.28/53.38	            app_encode_app(int, fun_int_bool, 
53.28/53.38	              app_encode_app(fun_int_fun_int_bool, 
53.28/53.38	                app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
53.28/53.38	                ord_less_int), min)), zero_zero_int)),
53.28/53.38	    inference('sup-', [status(thm)], ['66', '26'])).
53.28/53.38	tff(zf_stmt_1085, axiom,
53.28/53.38	  (app_encode_app(bool,$o,hBOOL,
53.28/53.38	                  app_encode_app(int,bool,
53.28/53.38	                                 app_encode_app(fun_int_bool,
53.28/53.38	                                                app_encode_fun(int,bool),
53.28/53.38	                                                hAPP_int_bool,
53.28/53.38	                                                app_encode_app(int,
53.28/53.38	                                                               fun_int_bool,
53.28/53.38	                                                               app_encode_app(
53.28/53.38	                                                               fun_int_fun_int_bool,
53.28/53.38	                                                               app_encode_fun(
53.28/53.38	                                                               int,
53.28/53.38	                                                               fun_int_bool),
53.28/53.38	                                                               hAPP_i1948725293t_bool,
53.28/53.38	                                                               ord_less_int),
53.28/53.38	                                                               min)),
53.28/53.38	                                 pls)))).
53.28/53.38	tff('68', plain,
53.28/53.38	    app_encode_app(bool, $o, hBOOL, 
53.28/53.38	      app_encode_app(int, bool, 
53.28/53.38	        app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
53.28/53.38	          hAPP_int_bool, 
53.28/53.38	          app_encode_app(int, fun_int_bool, 
53.28/53.38	            app_encode_app(fun_int_fun_int_bool, 
53.28/53.38	              app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
53.28/53.38	              ord_less_int), min)), pls)),
53.28/53.38	    inference('cnf', [status(esa)], [zf_stmt_1085])).
53.28/53.38	tff('69', plain,
53.28/53.38	    app_encode_app(bool, $o, hBOOL, 
53.28/53.38	      app_encode_app(int, bool, 
53.28/53.38	        app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
53.28/53.38	          hAPP_int_bool, 
53.28/53.38	          app_encode_app(int, fun_int_bool, 
53.28/53.38	            app_encode_app(fun_int_fun_int_bool, 
53.28/53.38	              app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
53.28/53.38	              ord_less_int), min)), zero_zero_int)),
53.28/53.38	    inference('demod', [status(thm)], ['68', '16'])).
53.28/53.38	tff('70', plain, ~ $true, inference('demod', [status(thm)], ['67', '69'])).
53.28/53.38	tff('71', plain, $false, inference('simplify', [status(thm)], ['70'])).
53.28/53.38	
53.28/53.38	% SZS output end Refutation
53.28/53.38	EOF
