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
0.00/0.20	% Computer   : n035.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 07:33:53 CST 2018
54.32/54.43	% done 12052 iterations in 54.222s
54.32/54.43	% SZS status Theorem for 'stdin'
54.32/54.43	% SZS output start Refutation
54.32/54.43	tff(zf_stmt_1288, conjecture,
54.32/54.43	  (app_encode_app(nat,int,
54.32/54.43	                  app_encode_app(fun_nat_int,app_encode_fun(nat,int),
54.32/54.43	                                 hAPP_nat_int,
54.32/54.43	                                 app_encode_app(int,fun_nat_int,
54.32/54.43	                                                power_power_int,
54.32/54.43	                                                app_encode_app(int,int,
54.32/54.43	                                                               app_encode_app(
54.32/54.43	                                                               int,
54.32/54.43	                                                               app_encode_fun(
54.32/54.43	                                                               int,int),
54.32/54.43	                                                               plus_plus_int,
54.32/54.43	                                                               one_one_int),
54.32/54.43	                                                               app_encode_app(
54.32/54.43	                                                               nat,int,
54.32/54.43	                                                               app_encode_app(
54.32/54.43	                                                               fun_nat_int,
54.32/54.43	                                                               app_encode_fun(
54.32/54.43	                                                               nat,int),
54.32/54.43	                                                               hAPP_nat_int,
54.32/54.43	                                                               semiri1621563631at_int),
54.32/54.43	                                                               n)))),
54.32/54.43	                  app_encode_app(int,nat,number_number_of_nat,
54.32/54.43	                                 app_encode_app(int,int,bit0,
54.32/54.43	                                                app_encode_app(int,int,bit1,
54.32/54.43	                                                               pls)))) !=
54.32/54.43	   zero_zero_int)).
54.32/54.43	tff(zf_stmt_0, negated_conjecture,
54.32/54.43	  (app_encode_app(nat,int,
54.32/54.43	                  app_encode_app(fun_nat_int,app_encode_fun(nat,int),
54.32/54.43	                                 hAPP_nat_int,
54.32/54.43	                                 app_encode_app(int,fun_nat_int,
54.32/54.43	                                                power_power_int,
54.32/54.43	                                                app_encode_app(int,int,
54.32/54.43	                                                               app_encode_app(
54.32/54.43	                                                               int,
54.32/54.43	                                                               app_encode_fun(
54.32/54.43	                                                               int,int),
54.32/54.43	                                                               plus_plus_int,
54.32/54.43	                                                               one_one_int),
54.32/54.43	                                                               app_encode_app(
54.32/54.43	                                                               nat,int,
54.32/54.43	                                                               app_encode_app(
54.32/54.43	                                                               fun_nat_int,
54.32/54.43	                                                               app_encode_fun(
54.32/54.43	                                                               nat,int),
54.32/54.43	                                                               hAPP_nat_int,
54.32/54.43	                                                               semiri1621563631at_int),
54.32/54.43	                                                               n)))),
54.32/54.43	                  app_encode_app(int,nat,number_number_of_nat,
54.32/54.43	                                 app_encode_app(int,int,bit0,
54.32/54.43	                                                app_encode_app(int,int,bit1,
54.32/54.43	                                                               pls)))) =
54.32/54.43	   zero_zero_int)).
54.32/54.43	tff('0', plain,
54.32/54.43	    app_encode_app(nat, int, 
54.32/54.43	      app_encode_app(fun_nat_int, app_encode_fun(nat, int), hAPP_nat_int, 
54.32/54.43	        app_encode_app(int, fun_nat_int, power_power_int, 
54.32/54.43	          app_encode_app(int, int, 
54.32/54.43	            app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
54.32/54.43	              one_one_int), 
54.32/54.43	            app_encode_app(nat, int, 
54.32/54.43	              app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
54.32/54.43	                hAPP_nat_int, semiri1621563631at_int), n)))), 
54.32/54.43	      app_encode_app(int, nat, number_number_of_nat, 
54.32/54.43	        app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls))))
54.32/54.43	     = zero_zero_int,
54.32/54.43	    inference('cnf', [status(esa)], [zf_stmt_0])).
54.32/54.43	tff(zf_stmt_151, axiom,
54.32/54.43	  (![Z:int,W:int]:
54.32/54.43	     (app_encode_app(int,int,
54.32/54.43	                     app_encode_app(int,app_encode_fun(int,int),
54.32/54.43	                                    plus_plus_int,Z),
54.32/54.43	                     W) =
54.32/54.43	      app_encode_app(int,int,
54.32/54.43	                     app_encode_app(int,app_encode_fun(int,int),
54.32/54.43	                                    plus_plus_int,W),
54.32/54.43	                     Z)))).
54.32/54.43	tff('1', plain,
54.32/54.43	    ![X98 : int, X99 : int]:
54.32/54.43	      app_encode_app(int, int, 
54.32/54.43	        app_encode_app(int, app_encode_fun(int, int), plus_plus_int, X99), 
54.32/54.43	        X98)
54.32/54.43	       = app_encode_app(int, int, 
54.32/54.43	           app_encode_app(int, app_encode_fun(int, int), plus_plus_int, X98), 
54.32/54.43	           X99),
54.32/54.43	    inference('cnf', [status(esa)], [zf_stmt_151])).
54.32/54.43	tff(zf_stmt_898, axiom,
54.32/54.43	  (![K_1:int]:
54.32/54.43	     (app_encode_app(int,int,succ,K_1) =
54.32/54.43	      app_encode_app(int,int,
54.32/54.43	                     app_encode_app(int,app_encode_fun(int,int),
54.32/54.43	                                    plus_plus_int,K_1),
54.32/54.43	                     one_one_int)))).
54.32/54.43	tff('2', plain,
54.32/54.43	    ![X1860 : int]:
54.32/54.43	      app_encode_app(int, int, succ, X1860)
54.32/54.43	       = app_encode_app(int, int, 
54.32/54.43	           app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
54.32/54.43	             X1860), one_one_int),
54.32/54.43	    inference('cnf', [status(esa)], [zf_stmt_898])).
54.32/54.43	tff('3', plain,
54.32/54.43	    ![X0 : int]:
54.32/54.43	      app_encode_app(int, int, succ, X0)
54.32/54.43	       = app_encode_app(int, int, 
54.32/54.43	           app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
54.32/54.43	             one_one_int), X0),
54.32/54.43	    inference('sup+', [status(thm)], ['1', '2'])).
54.32/54.43	tff(zf_stmt_1211, axiom,
54.32/54.43	  (![A:int,B_1:int]:
54.32/54.43	     app_encode_app(bool,$o,hBOOL,
54.32/54.43	                    app_encode_app(int,bool,
54.32/54.43	                                   app_encode_app(fun_int_bool,
54.32/54.43	                                                  app_encode_fun(int,bool),
54.32/54.43	                                                  hAPP_int_bool,
54.32/54.43	                                                  app_encode_app(int,
54.32/54.43	                                                                 fun_int_bool,
54.32/54.43	                                                                 app_encode_app(
54.32/54.43	                                                                 int,
54.32/54.43	                                                                 app_encode_fun(
54.32/54.43	                                                                 int,
54.32/54.43	                                                                 fun_int_bool),
54.32/54.43	                                                                 zcong,A),B_1)),
54.32/54.43	                                   one_one_int)))).
54.32/54.43	tff('4', plain,
54.32/54.43	    ![X2558 : int, X2559 : int]:
54.32/54.43	      app_encode_app(bool, $o, hBOOL, 
54.32/54.43	        app_encode_app(int, bool, 
54.32/54.43	          app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
54.32/54.43	            hAPP_int_bool, 
54.32/54.43	            app_encode_app(int, fun_int_bool, 
54.32/54.43	              app_encode_app(int, app_encode_fun(int, fun_int_bool), zcong, 
54.32/54.43	                X2558), X2559)), one_one_int)),
54.32/54.43	    inference('cnf', [status(esa)], [zf_stmt_1211])).
54.32/54.43	tff(zf_stmt_1220, axiom,
54.32/54.43	  (![A_1:int,B:int,Ma:int]:
54.32/54.43	     (app_encode_app(bool,$o,hBOOL,
54.32/54.43	                     app_encode_app(int,bool,
54.32/54.43	                                    app_encode_app(fun_int_bool,
54.32/54.43	                                                   app_encode_fun(int,bool),
54.32/54.43	                                                   hAPP_int_bool,
54.32/54.43	                                                   app_encode_app(int,
54.32/54.43	                                                                  fun_int_bool,
54.32/54.43	                                                                  app_encode_app(
54.32/54.43	                                                                  int,
54.32/54.43	                                                                  app_encode_fun(
54.32/54.43	                                                                  int,
54.32/54.43	                                                                  fun_int_bool),
54.32/54.43	                                                                  zcong,A_1),
54.32/54.43	                                                                  B)),
54.32/54.43	                                    Ma)) <=>
54.32/54.43	      (?[K_2:int]:
54.32/54.43	         (B =
54.32/54.43	          app_encode_app(int,int,
54.32/54.43	                         app_encode_app(int,app_encode_fun(int,int),
54.32/54.43	                                        plus_plus_int,A_1),
54.32/54.43	                         app_encode_app(int,int,
54.32/54.43	                                        app_encode_app(int,
54.32/54.43	                                                       app_encode_fun(
54.32/54.43	                                                       int,int),
54.32/54.43	                                                       times_times_int,Ma),
54.32/54.43	                                        K_2))))))).
54.32/54.43	tff('5', plain,
54.32/54.43	    ![X2596 : int, X2597 : int, X2598 : int]:
54.32/54.43	      (X2598
54.32/54.43	        = app_encode_app(int, int, 
54.32/54.43	            app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
54.32/54.43	              X2596), 
54.32/54.43	            app_encode_app(int, int, 
54.32/54.43	              app_encode_app(int, app_encode_fun(int, int), times_times_int, 
54.32/54.43	                X2597), sk_K_22(X2597, X2598, X2596)))
54.32/54.43	       | ~ app_encode_app(bool, $o, hBOOL, 
54.32/54.43	             app_encode_app(int, bool, 
54.32/54.43	               app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
54.32/54.43	                 hAPP_int_bool, 
54.32/54.43	                 app_encode_app(int, fun_int_bool, 
54.32/54.43	                   app_encode_app(int, app_encode_fun(int, fun_int_bool), 
54.32/54.43	                     zcong, X2596), X2598)), X2597))),
54.32/54.43	    inference('cnf', [status(esa)], [zf_stmt_1220])).
54.32/54.43	tff('6', plain,
54.32/54.43	    ![X0 : int, X1 : int]:
54.32/54.43	      (~ $true
54.32/54.43	       | X0
54.32/54.43	          = app_encode_app(int, int, 
54.32/54.43	              app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
54.32/54.43	                X1), 
54.32/54.43	              app_encode_app(int, int, 
54.32/54.43	                app_encode_app(int, app_encode_fun(int, int), 
54.32/54.43	                  times_times_int, one_one_int), 
54.32/54.43	                sk_K_22(one_one_int, X0, X1)))),
54.32/54.43	    inference('sup-', [status(thm)], ['4', '5'])).
54.32/54.43	tff(zf_stmt_748, axiom,
54.32/54.43	  (![A_16:int]:
54.32/54.43	     (app_encode_app(int,int,
54.32/54.43	                     app_encode_app(int,app_encode_fun(int,int),
54.32/54.43	                                    times_times_int,one_one_int),
54.32/54.43	                     A_16) =
54.32/54.43	      A_16))).
54.32/54.43	tff('7', plain,
54.32/54.43	    ![X1483 : int]:
54.32/54.43	      app_encode_app(int, int, 
54.32/54.43	        app_encode_app(int, app_encode_fun(int, int), times_times_int, 
54.32/54.43	          one_one_int), X1483)
54.32/54.43	       = X1483,
54.32/54.43	    inference('cnf', [status(esa)], [zf_stmt_748])).
54.32/54.43	tff('8', plain,
54.32/54.43	    ![X0 : int, X1 : int]:
54.32/54.43	      (~ $true
54.32/54.43	       | X0
54.32/54.43	          = app_encode_app(int, int, 
54.32/54.43	              app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
54.32/54.43	                X1), sk_K_22(one_one_int, X0, X1))),
54.32/54.43	    inference('demod', [status(thm)], ['6', '7'])).
54.32/54.43	tff('9', plain,
54.32/54.43	    ![X0 : int, X1 : int]:
54.32/54.43	      X0
54.32/54.43	       = app_encode_app(int, int, 
54.32/54.43	           app_encode_app(int, app_encode_fun(int, int), plus_plus_int, X1), 
54.32/54.43	           sk_K_22(one_one_int, X0, X1)),
54.32/54.43	    inference('simplify', [status(thm)], ['8'])).
54.32/54.43	tff(zf_stmt_688, axiom,
54.32/54.43	  (![A_31:int,B_16:int]:
54.32/54.43	     (app_encode_app(int,int,
54.32/54.43	                     app_encode_app(int,app_encode_fun(int,int),
54.32/54.43	                                    minus_minus_int,
54.32/54.43	                                    app_encode_app(int,int,
54.32/54.43	                                                   app_encode_app(int,
54.32/54.43	                                                                  app_encode_fun(
54.32/54.43	                                                                  int,int),
54.32/54.43	                                                                  plus_plus_int,
54.32/54.43	                                                                  A_31),
54.32/54.43	                                                   B_16)),
54.32/54.43	                     B_16) =
54.32/54.43	      A_31))).
54.32/54.43	tff('10', plain,
54.32/54.43	    ![X1352 : int, X1353 : int]:
54.32/54.43	      app_encode_app(int, int, 
54.32/54.43	        app_encode_app(int, app_encode_fun(int, int), minus_minus_int, 
54.32/54.43	          app_encode_app(int, int, 
54.32/54.43	            app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
54.32/54.43	              X1352), X1353)), X1353)
54.32/54.43	       = X1352,
54.32/54.43	    inference('cnf', [status(esa)], [zf_stmt_688])).
54.32/54.43	tff(zf_stmt_1105, axiom,
54.32/54.43	  (![K_1:int]:
54.32/54.43	     (app_encode_app(int,int,
54.32/54.43	                     app_encode_app(int,app_encode_fun(int,int),
54.32/54.43	                                    minus_minus_int,K_1),
54.32/54.43	                     min) =
54.32/54.43	      app_encode_app(int,int,succ,K_1)))).
54.32/54.43	tff('11', plain,
54.32/54.43	    ![X2304 : int]:
54.32/54.43	      app_encode_app(int, int, 
54.32/54.43	        app_encode_app(int, app_encode_fun(int, int), minus_minus_int, X2304), 
54.32/54.43	        min)
54.32/54.43	       = app_encode_app(int, int, succ, X2304),
54.32/54.43	    inference('cnf', [status(esa)], [zf_stmt_1105])).
54.32/54.43	tff('12', plain,
54.32/54.43	    ![X0 : int]:
54.32/54.43	      X0
54.32/54.43	       = app_encode_app(int, int, succ, 
54.32/54.43	           app_encode_app(int, int, 
54.32/54.43	             app_encode_app(int, app_encode_fun(int, int), plus_plus_int, X0), 
54.32/54.43	             min)),
54.32/54.43	    inference('sup+', [status(thm)], ['10', '11'])).
54.32/54.43	tff('13', plain,
54.32/54.43	    ![X0 : int]:
54.32/54.43	      X0
54.32/54.43	       = app_encode_app(int, int, succ, 
54.32/54.43	           app_encode_app(int, int, 
54.32/54.43	             app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
54.32/54.43	               min), X0)),
54.32/54.43	    inference('sup+', [status(thm)], ['1', '12'])).
54.32/54.43	tff('14', plain,
54.32/54.43	    ![X0 : int]:
54.32/54.43	      sk_K_22(one_one_int, X0, min) = app_encode_app(int, int, succ, X0),
54.32/54.43	    inference('sup+', [status(thm)], ['9', '13'])).
54.32/54.43	tff('15', plain,
54.32/54.43	    ![X0 : int]:
54.32/54.43	      sk_K_22(one_one_int, X0, min)
54.32/54.43	       = app_encode_app(int, int, 
54.32/54.43	           app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
54.32/54.43	             one_one_int), X0),
54.32/54.43	    inference('demod', [status(thm)], ['3', '14'])).
54.32/54.43	tff(zf_stmt_182, axiom, (pls = zero_zero_int)).
54.32/54.43	tff('16', plain, pls = zero_zero_int,
54.32/54.43	    inference('cnf', [status(esa)], [zf_stmt_182])).
54.32/54.43	tff(zf_stmt_109, axiom,
54.32/54.43	  (one_one_int =
54.32/54.43	   app_encode_app(int,int,number_number_of_int,
54.32/54.43	                  app_encode_app(int,int,bit1,pls)))).
54.32/54.43	tff('17', plain,
54.32/54.43	    one_one_int
54.32/54.43	     = app_encode_app(int, int, number_number_of_int, 
54.32/54.43	         app_encode_app(int, int, bit1, pls)),
54.32/54.43	    inference('cnf', [status(esa)], [zf_stmt_109])).
54.32/54.43	tff(zf_stmt_261, axiom,
54.32/54.43	  (![K_1:int]: (app_encode_app(int,int,number_number_of_int,K_1) = K_1))).
54.32/54.43	tff('18', plain,
54.32/54.43	    ![X259 : int]:
54.32/54.43	      app_encode_app(int, int, number_number_of_int, X259) = X259,
54.32/54.43	    inference('cnf', [status(esa)], [zf_stmt_261])).
54.32/54.43	tff('19', plain, one_one_int = app_encode_app(int, int, bit1, zero_zero_int),
54.32/54.43	    inference('demod', [status(thm)], ['17', '16', '18'])).
54.32/54.43	tff(zf_stmt_187, axiom,
54.32/54.43	  (![K_1:int]:
54.32/54.43	     (app_encode_app(int,int,bit0,K_1) =
54.32/54.43	      app_encode_app(int,int,
54.32/54.43	                     app_encode_app(int,app_encode_fun(int,int),
54.32/54.43	                                    plus_plus_int,K_1),
54.32/54.43	                     K_1)))).
54.32/54.43	tff('20', plain,
54.32/54.43	    ![X159 : int]:
54.32/54.43	      app_encode_app(int, int, bit0, X159)
54.32/54.43	       = app_encode_app(int, int, 
54.32/54.43	           app_encode_app(int, app_encode_fun(int, int), plus_plus_int, X159), 
54.32/54.43	           X159),
54.32/54.43	    inference('cnf', [status(esa)], [zf_stmt_187])).
54.32/54.43	tff('21', plain,
54.32/54.43	    app_encode_app(int, int, bit0, one_one_int)
54.32/54.43	     = app_encode_app(int, int, succ, one_one_int),
54.32/54.43	    inference('sup+', [status(thm)], ['2', '20'])).
54.32/54.43	tff('22', plain,
54.32/54.43	    app_encode_app(int, int, bit0, one_one_int)
54.32/54.43	     = sk_K_22(one_one_int, one_one_int, min),
54.32/54.43	    inference('demod', [status(thm)], ['21', '14'])).
54.32/54.43	tff(zf_stmt_114, axiom,
54.32/54.43	  (![X:int,Y:int]:
54.32/54.43	     (app_encode_app(bool,$o,hBOOL,
54.32/54.43	                     app_encode_app(int,bool,
54.32/54.43	                                    app_encode_app(fun_int_bool,
54.32/54.43	                                                   app_encode_fun(int,bool),
54.32/54.43	                                                   hAPP_int_bool,
54.32/54.43	                                                   app_encode_app(int,
54.32/54.43	                                                                  fun_int_bool,
54.32/54.43	                                                                  app_encode_app(
54.32/54.43	                                                                  fun_int_fun_int_bool,
54.32/54.43	                                                                  app_encode_fun(
54.32/54.43	                                                                  int,
54.32/54.43	                                                                  fun_int_bool),
54.32/54.43	                                                                  hAPP_i1948725293t_bool,
54.32/54.43	                                                                  ord_less_int),
54.32/54.43	                                                                  X)),
54.32/54.43	                                    Y)) | 
54.32/54.43	      (X = Y) | 
54.32/54.43	      app_encode_app(bool,$o,hBOOL,
54.32/54.43	                     app_encode_app(int,bool,
54.32/54.43	                                    app_encode_app(fun_int_bool,
54.32/54.43	                                                   app_encode_fun(int,bool),
54.32/54.43	                                                   hAPP_int_bool,
54.32/54.43	                                                   app_encode_app(int,
54.32/54.43	                                                                  fun_int_bool,
54.32/54.43	                                                                  app_encode_app(
54.32/54.43	                                                                  fun_int_fun_int_bool,
54.32/54.43	                                                                  app_encode_fun(
54.32/54.43	                                                                  int,
54.32/54.43	                                                                  fun_int_bool),
54.32/54.43	                                                                  hAPP_i1948725293t_bool,
54.32/54.43	                                                                  ord_less_int),
54.32/54.43	                                                                  Y)),
54.32/54.43	                                    X))))).
54.32/54.43	tff('23', plain,
54.32/54.43	    ![X25 : int, X26 : int]:
54.32/54.43	      (app_encode_app(bool, $o, hBOOL, 
54.32/54.43	         app_encode_app(int, bool, 
54.32/54.43	           app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
54.32/54.43	             hAPP_int_bool, 
54.32/54.43	             app_encode_app(int, fun_int_bool, 
54.32/54.43	               app_encode_app(fun_int_fun_int_bool, 
54.32/54.43	                 app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
54.32/54.43	                 ord_less_int), X25)), X26))
54.32/54.43	       | X25 = X26
54.32/54.43	       | app_encode_app(bool, $o, hBOOL, 
54.32/54.43	           app_encode_app(int, bool, 
54.32/54.43	             app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
54.32/54.43	               hAPP_int_bool, 
54.32/54.43	               app_encode_app(int, fun_int_bool, 
54.32/54.43	                 app_encode_app(fun_int_fun_int_bool, 
54.32/54.43	                   app_encode_fun(int, fun_int_bool), 
54.32/54.43	                   hAPP_i1948725293t_bool, ord_less_int), X26)), X25))),
54.32/54.43	    inference('cnf', [status(esa)], [zf_stmt_114])).
54.32/54.43	tff(zf_stmt_235, axiom,
54.32/54.43	  (app_encode_app(int,int,number_number_of_int,
54.32/54.43	                  app_encode_app(int,int,bit0,
54.32/54.43	                                 app_encode_app(int,int,bit1,pls))) =
54.32/54.43	   app_encode_app(nat,int,
54.32/54.43	                  app_encode_app(fun_nat_int,app_encode_fun(nat,int),
54.32/54.43	                                 hAPP_nat_int,semiri1621563631at_int),
54.32/54.43	                  app_encode_app(int,nat,number_number_of_nat,
54.32/54.43	                                 app_encode_app(int,int,bit0,
54.32/54.43	                                                app_encode_app(int,int,bit1,
54.32/54.43	                                                               pls)))))).
54.32/54.43	tff('24', plain,
54.32/54.43	    app_encode_app(int, int, number_number_of_int, 
54.32/54.43	      app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls)))
54.32/54.43	     = app_encode_app(nat, int, 
54.32/54.43	         app_encode_app(fun_nat_int, app_encode_fun(nat, int), hAPP_nat_int, 
54.32/54.43	           semiri1621563631at_int), 
54.32/54.43	         app_encode_app(int, nat, number_number_of_nat, 
54.32/54.43	           app_encode_app(int, int, bit0, 
54.32/54.43	             app_encode_app(int, int, bit1, pls)))),
54.32/54.43	    inference('cnf', [status(esa)], [zf_stmt_235])).
54.32/54.43	tff('25', plain,
54.32/54.43	    app_encode_app(int, int, bit0, one_one_int)
54.32/54.43	     = app_encode_app(nat, int, 
54.32/54.43	         app_encode_app(fun_nat_int, app_encode_fun(nat, int), hAPP_nat_int, 
54.32/54.43	           semiri1621563631at_int), 
54.32/54.43	         app_encode_app(int, nat, number_number_of_nat, 
54.32/54.43	           app_encode_app(int, int, bit0, one_one_int))),
54.32/54.43	    inference('demod', [status(thm)], ['24', '16', '19', '18', '16', '19'])).
54.32/54.43	tff(zf_stmt_167, axiom,
54.32/54.43	  (![K_1:nat]:
54.32/54.43	     (~
54.32/54.43	       app_encode_app(bool,$o,hBOOL,
54.32/54.43	                      app_encode_app(int,bool,
54.32/54.43	                                     app_encode_app(fun_int_bool,
54.32/54.43	                                                    app_encode_fun(int,bool),
54.32/54.43	                                                    hAPP_int_bool,
54.32/54.43	                                                    app_encode_app(int,
54.32/54.43	                                                                   fun_int_bool,
54.32/54.43	                                                                   app_encode_app(
54.32/54.43	                                                                   fun_int_fun_int_bool,
54.32/54.43	                                                                   app_encode_fun(
54.32/54.43	                                                                   int,
54.32/54.43	                                                                   fun_int_bool),
54.32/54.43	                                                                   hAPP_i1948725293t_bool,
54.32/54.43	                                                                   ord_less_int),
54.32/54.43	                                                                   app_encode_app(
54.32/54.43	                                                                   nat,int,
54.32/54.43	                                                                   app_encode_app(
54.32/54.43	                                                                   fun_nat_int,
54.32/54.43	                                                                   app_encode_fun(
54.32/54.43	                                                                   nat,int),
54.32/54.43	                                                                   hAPP_nat_int,
54.32/54.43	                                                                   semiri1621563631at_int),
54.32/54.43	                                                                   K_1))),
54.32/54.43	                                     zero_zero_int))))).
54.32/54.43	tff('26', plain,
54.32/54.43	    ![X130 : nat]:
54.32/54.43	      ~ app_encode_app(bool, $o, hBOOL, 
54.32/54.43	          app_encode_app(int, bool, 
54.32/54.43	            app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
54.32/54.43	              hAPP_int_bool, 
54.32/54.43	              app_encode_app(int, fun_int_bool, 
54.32/54.43	                app_encode_app(fun_int_fun_int_bool, 
54.32/54.43	                  app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
54.32/54.43	                  ord_less_int), 
54.32/54.43	                app_encode_app(nat, int, 
54.32/54.43	                  app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
54.32/54.43	                    hAPP_nat_int, semiri1621563631at_int), X130))), 
54.32/54.43	            zero_zero_int)),
54.32/54.43	    inference('cnf', [status(esa)], [zf_stmt_167])).
54.32/54.43	tff('27', plain,
54.32/54.43	    ~ app_encode_app(bool, $o, hBOOL, 
54.32/54.43	        app_encode_app(int, bool, 
54.32/54.43	          app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
54.32/54.43	            hAPP_int_bool, 
54.32/54.43	            app_encode_app(int, fun_int_bool, 
54.32/54.43	              app_encode_app(fun_int_fun_int_bool, 
54.32/54.43	                app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
54.32/54.43	                ord_less_int), app_encode_app(int, int, bit0, one_one_int))), 
54.32/54.43	          zero_zero_int)),
54.32/54.43	    inference('sup-', [status(thm)], ['25', '26'])).
54.32/54.43	tff('28', plain,
54.32/54.43	    (~ $true
54.32/54.43	     | app_encode_app(bool, $o, hBOOL, 
54.32/54.43	         app_encode_app(int, bool, 
54.32/54.43	           app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
54.32/54.43	             hAPP_int_bool, 
54.32/54.43	             app_encode_app(int, fun_int_bool, 
54.32/54.43	               app_encode_app(fun_int_fun_int_bool, 
54.32/54.43	                 app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
54.32/54.43	                 ord_less_int), zero_zero_int)), 
54.32/54.43	           app_encode_app(int, int, bit0, one_one_int)))
54.32/54.43	     | app_encode_app(int, int, bit0, one_one_int) = zero_zero_int),
54.32/54.43	    inference('sup-', [status(thm)], ['23', '27'])).
54.32/54.43	tff('29', plain,
54.32/54.43	    (app_encode_app(int, int, bit0, one_one_int) = zero_zero_int
54.32/54.43	     | app_encode_app(bool, $o, hBOOL, 
54.32/54.43	         app_encode_app(int, bool, 
54.32/54.43	           app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
54.32/54.43	             hAPP_int_bool, 
54.32/54.43	             app_encode_app(int, fun_int_bool, 
54.32/54.43	               app_encode_app(fun_int_fun_int_bool, 
54.32/54.43	                 app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
54.32/54.43	                 ord_less_int), zero_zero_int)), 
54.32/54.43	           app_encode_app(int, int, bit0, one_one_int)))),
54.32/54.43	    inference('simplify', [status(thm)], ['28'])).
54.32/54.43	tff(zf_stmt_127, axiom,
54.32/54.43	  (![Na:nat]:
54.32/54.43	     ((app_encode_app(nat,int,
54.32/54.43	                      app_encode_app(fun_nat_int,app_encode_fun(nat,int),
54.32/54.43	                                     hAPP_nat_int,semiri1621563631at_int),
54.32/54.43	                      Na) =
54.32/54.43	       zero_zero_int) <=>
54.32/54.43	      (Na = zero_zero_nat)))).
54.32/54.43	tff('30', plain,
54.32/54.43	    ![X47 : nat]:
54.32/54.43	      (X47 = zero_zero_nat
54.32/54.43	       | app_encode_app(nat, int, 
54.32/54.43	           app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
54.32/54.43	             hAPP_nat_int, semiri1621563631at_int), X47)
54.32/54.43	          != zero_zero_int),
54.32/54.43	    inference('cnf', [status(esa)], [zf_stmt_127])).
54.32/54.43	tff('31', plain,
54.32/54.43	    (app_encode_app(int, int, bit0, one_one_int) != zero_zero_int
54.32/54.43	     | app_encode_app(int, nat, number_number_of_nat, 
54.32/54.43	         app_encode_app(int, int, bit0, one_one_int))
54.32/54.43	        = zero_zero_nat),
54.32/54.43	    inference('sup-', [status(thm)], ['25', '30'])).
54.32/54.43	tff(zf_stmt_91, axiom,
54.32/54.43	  (app_encode_app(nat,int,
54.32/54.43	                  app_encode_app(fun_nat_int,app_encode_fun(nat,int),
54.32/54.43	                                 hAPP_nat_int,
54.32/54.43	                                 app_encode_app(int,fun_nat_int,
54.32/54.43	                                                power_power_int,zero_zero_int)),
54.32/54.43	                  app_encode_app(int,nat,number_number_of_nat,
54.32/54.43	                                 app_encode_app(int,int,bit0,
54.32/54.43	                                                app_encode_app(int,int,bit1,
54.32/54.43	                                                               pls)))) =
54.32/54.43	   zero_zero_int)).
54.32/54.43	tff('32', plain,
54.32/54.43	    app_encode_app(nat, int, 
54.32/54.43	      app_encode_app(fun_nat_int, app_encode_fun(nat, int), hAPP_nat_int, 
54.32/54.43	        app_encode_app(int, fun_nat_int, power_power_int, zero_zero_int)), 
54.32/54.43	      app_encode_app(int, nat, number_number_of_nat, 
54.32/54.43	        app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls))))
54.32/54.43	     = zero_zero_int,
54.32/54.43	    inference('cnf', [status(esa)], [zf_stmt_91])).
54.32/54.43	tff('33', plain,
54.32/54.43	    app_encode_app(nat, int, 
54.32/54.43	      app_encode_app(fun_nat_int, app_encode_fun(nat, int), hAPP_nat_int, 
54.32/54.43	        app_encode_app(int, fun_nat_int, power_power_int, zero_zero_int)), 
54.32/54.43	      app_encode_app(int, nat, number_number_of_nat, 
54.32/54.43	        app_encode_app(int, int, bit0, one_one_int)))
54.32/54.43	     = zero_zero_int,
54.32/54.43	    inference('demod', [status(thm)], ['32', '16', '19'])).
54.32/54.43	tff(zf_stmt_106, axiom,
54.32/54.43	  (![W_12:int]:
54.32/54.43	     (((app_encode_app(int,nat,number_number_of_nat,W_12) = zero_zero_nat) =>
54.32/54.43	       (app_encode_app(nat,int,
54.32/54.43	                       app_encode_app(fun_nat_int,app_encode_fun(nat,int),
54.32/54.43	                                      hAPP_nat_int,
54.32/54.43	                                      app_encode_app(int,fun_nat_int,
54.32/54.43	                                                     power_power_int,
54.32/54.43	                                                     zero_zero_int)),
54.32/54.43	                       app_encode_app(int,nat,number_number_of_nat,W_12)) =
54.32/54.43	        one_one_int)) & 
54.32/54.43	      ((app_encode_app(int,nat,number_number_of_nat,W_12) != zero_zero_nat) =>
54.32/54.43	       (app_encode_app(nat,int,
54.32/54.43	                       app_encode_app(fun_nat_int,app_encode_fun(nat,int),
54.32/54.43	                                      hAPP_nat_int,
54.32/54.43	                                      app_encode_app(int,fun_nat_int,
54.32/54.43	                                                     power_power_int,
54.32/54.43	                                                     zero_zero_int)),
54.32/54.43	                       app_encode_app(int,nat,number_number_of_nat,W_12)) =
54.32/54.43	        zero_zero_int))))).
54.32/54.43	tff('34', plain,
54.32/54.43	    ![X20 : int]:
54.32/54.43	      (app_encode_app(nat, int, 
54.32/54.43	         app_encode_app(fun_nat_int, app_encode_fun(nat, int), hAPP_nat_int, 
54.32/54.43	           app_encode_app(int, fun_nat_int, power_power_int, zero_zero_int)), 
54.32/54.43	         app_encode_app(int, nat, number_number_of_nat, X20))
54.32/54.43	        = one_one_int
54.32/54.43	       | app_encode_app(int, nat, number_number_of_nat, X20) != zero_zero_nat),
54.32/54.43	    inference('cnf', [status(esa)], [zf_stmt_106])).
54.32/54.43	tff('35', plain,
54.32/54.43	    (zero_zero_int = one_one_int
54.32/54.43	     | app_encode_app(int, nat, number_number_of_nat, 
54.32/54.43	         app_encode_app(int, int, bit0, one_one_int))
54.32/54.43	        != zero_zero_nat),
54.32/54.43	    inference('sup+', [status(thm)], ['33', '34'])).
54.32/54.43	tff(zf_stmt_183, axiom, (zero_zero_int != one_one_int)).
54.32/54.43	tff('36', plain, zero_zero_int != one_one_int,
54.32/54.43	    inference('cnf', [status(esa)], [zf_stmt_183])).
54.32/54.43	tff('37', plain,
54.32/54.43	    app_encode_app(int, nat, number_number_of_nat, 
54.32/54.43	      app_encode_app(int, int, bit0, one_one_int))
54.32/54.43	     != zero_zero_nat,
54.32/54.43	    inference('simplify_reflect-', [status(thm)], ['35', '36'])).
54.32/54.43	tff('38', plain,
54.32/54.43	    app_encode_app(int, int, bit0, one_one_int) != zero_zero_int,
54.32/54.43	    inference('simplify_reflect-', [status(thm)], ['31', '37'])).
54.32/54.43	tff('39', plain,
54.32/54.43	    app_encode_app(bool, $o, hBOOL, 
54.32/54.43	      app_encode_app(int, bool, 
54.32/54.43	        app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
54.32/54.43	          hAPP_int_bool, 
54.32/54.43	          app_encode_app(int, fun_int_bool, 
54.32/54.43	            app_encode_app(fun_int_fun_int_bool, 
54.32/54.43	              app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
54.32/54.43	              ord_less_int), zero_zero_int)), 
54.32/54.43	        app_encode_app(int, int, bit0, one_one_int))),
54.32/54.43	    inference('simplify_reflect-', [status(thm)], ['29', '38'])).
54.32/54.43	tff(zf_stmt_381, axiom,
54.32/54.43	  (![K_1:int]:
54.32/54.43	     (app_encode_app(bool,$o,hBOOL,
54.32/54.43	                     app_encode_app(int,bool,
54.32/54.43	                                    app_encode_app(fun_int_bool,
54.32/54.43	                                                   app_encode_fun(int,bool),
54.32/54.43	                                                   hAPP_int_bool,
54.32/54.43	                                                   app_encode_app(int,
54.32/54.43	                                                                  fun_int_bool,
54.32/54.43	                                                                  app_encode_app(
54.32/54.43	                                                                  fun_int_fun_int_bool,
54.32/54.43	                                                                  app_encode_fun(
54.32/54.43	                                                                  int,
54.32/54.43	                                                                  fun_int_bool),
54.32/54.43	                                                                  hAPP_i1948725293t_bool,
54.32/54.43	                                                                  ord_less_int),
54.32/54.43	                                                                  zero_zero_int)),
54.32/54.43	                                    K_1)) =>
54.32/54.43	      (?[N_1:nat]:
54.32/54.43	         (app_encode_app(bool,$o,hBOOL,
54.32/54.43	                         app_encode_app(nat,bool,
54.32/54.43	                                        app_encode_app(fun_nat_bool,
54.32/54.43	                                                       app_encode_fun(
54.32/54.43	                                                       nat,bool),
54.32/54.43	                                                       hAPP_nat_bool,
54.32/54.43	                                                       app_encode_app(
54.32/54.43	                                                       nat,fun_nat_bool,
54.32/54.43	                                                       app_encode_app(
54.32/54.43	                                                       fun_nat_fun_nat_bool,
54.32/54.43	                                                       app_encode_fun(
54.32/54.43	                                                       nat,fun_nat_bool),
54.32/54.43	                                                       hAPP_n1699378549t_bool,
54.32/54.43	                                                       ord_less_nat),
54.32/54.43	                                                       zero_zero_nat)),
54.32/54.43	                                        N_1)) & 
54.32/54.43	          (K_1 =
54.32/54.43	           app_encode_app(nat,int,
54.32/54.43	                          app_encode_app(fun_nat_int,app_encode_fun(nat,int),
54.32/54.43	                                         hAPP_nat_int,semiri1621563631at_int),
54.32/54.43	                          N_1))))))).
54.32/54.43	tff('40', plain,
54.32/54.43	    ![X494 : int]:
54.32/54.43	      (X494
54.32/54.43	        = app_encode_app(nat, int, 
54.32/54.43	            app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
54.32/54.43	              hAPP_nat_int, semiri1621563631at_int), sk_N_1(X494))
54.32/54.43	       | ~ app_encode_app(bool, $o, hBOOL, 
54.32/54.43	             app_encode_app(int, bool, 
54.32/54.43	               app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
54.32/54.43	                 hAPP_int_bool, 
54.32/54.43	                 app_encode_app(int, fun_int_bool, 
54.32/54.43	                   app_encode_app(fun_int_fun_int_bool, 
54.32/54.43	                     app_encode_fun(int, fun_int_bool), 
54.32/54.43	                     hAPP_i1948725293t_bool, ord_less_int), zero_zero_int)), 
54.32/54.43	               X494))),
54.32/54.43	    inference('cnf', [status(esa)], [zf_stmt_381])).
54.32/54.43	tff('41', plain,
54.32/54.43	    (~ $true
54.32/54.43	     | app_encode_app(int, int, bit0, one_one_int)
54.32/54.43	        = app_encode_app(nat, int, 
54.32/54.43	            app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
54.32/54.43	              hAPP_nat_int, semiri1621563631at_int), 
54.32/54.43	            sk_N_1(app_encode_app(int, int, bit0, one_one_int)))),
54.32/54.43	    inference('sup-', [status(thm)], ['39', '40'])).
54.32/54.43	tff('42', plain,
54.32/54.43	    app_encode_app(int, int, bit0, one_one_int)
54.32/54.43	     = app_encode_app(nat, int, 
54.32/54.43	         app_encode_app(fun_nat_int, app_encode_fun(nat, int), hAPP_nat_int, 
54.32/54.43	           semiri1621563631at_int), 
54.32/54.43	         sk_N_1(app_encode_app(int, int, bit0, one_one_int))),
54.32/54.43	    inference('simplify', [status(thm)], ['41'])).
54.32/54.43	tff(zf_stmt_736, axiom,
54.32/54.43	  (![N:nat]:
54.32/54.43	     (app_encode_app(int,nat,nat_1,
54.32/54.43	                     app_encode_app(nat,int,
54.32/54.43	                                    app_encode_app(fun_nat_int,
54.32/54.43	                                                   app_encode_fun(nat,int),
54.32/54.43	                                                   hAPP_nat_int,
54.32/54.43	                                                   semiri1621563631at_int),
54.32/54.43	                                    N)) =
54.32/54.43	      N))).
54.32/54.43	tff('43', plain,
54.32/54.43	    ![X1471 : nat]:
54.32/54.43	      app_encode_app(int, nat, nat_1, 
54.32/54.43	        app_encode_app(nat, int, 
54.32/54.43	          app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
54.32/54.43	            hAPP_nat_int, semiri1621563631at_int), X1471))
54.32/54.43	       = X1471,
54.32/54.43	    inference('cnf', [status(esa)], [zf_stmt_736])).
54.32/54.43	tff(zf_stmt_850, axiom,
54.32/54.43	  (![W:int]:
54.32/54.43	     (app_encode_app(int,nat,nat_1,
54.32/54.43	                     app_encode_app(int,int,number_number_of_int,W)) =
54.32/54.43	      app_encode_app(int,nat,number_number_of_nat,W)))).
54.32/54.43	tff('44', plain,
54.32/54.43	    ![X1747 : int]:
54.32/54.43	      app_encode_app(int, nat, nat_1, 
54.32/54.43	        app_encode_app(int, int, number_number_of_int, X1747))
54.32/54.43	       = app_encode_app(int, nat, number_number_of_nat, X1747),
54.32/54.43	    inference('cnf', [status(esa)], [zf_stmt_850])).
54.32/54.43	tff('45', plain,
54.32/54.43	    ![X1747 : int]:
54.32/54.43	      app_encode_app(int, nat, nat_1, X1747)
54.32/54.43	       = app_encode_app(int, nat, number_number_of_nat, X1747),
54.32/54.43	    inference('demod', [status(thm)], ['44', '18'])).
54.32/54.43	tff('46', plain,
54.32/54.43	    ![X1471 : nat]:
54.32/54.43	      app_encode_app(int, nat, number_number_of_nat, 
54.32/54.43	        app_encode_app(nat, int, 
54.32/54.43	          app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
54.32/54.43	            hAPP_nat_int, semiri1621563631at_int), X1471))
54.32/54.43	       = X1471,
54.32/54.43	    inference('demod', [status(thm)], ['43', '45'])).
54.32/54.43	tff('47', plain,
54.32/54.43	    app_encode_app(int, nat, number_number_of_nat, 
54.32/54.43	      app_encode_app(int, int, bit0, one_one_int))
54.32/54.43	     = sk_N_1(app_encode_app(int, int, bit0, one_one_int)),
54.32/54.43	    inference('sup+', [status(thm)], ['42', '46'])).
54.32/54.43	tff('48', plain,
54.32/54.43	    app_encode_app(int, nat, number_number_of_nat, 
54.32/54.43	      sk_K_22(one_one_int, one_one_int, min))
54.32/54.43	     = sk_N_1(sk_K_22(one_one_int, one_one_int, min)),
54.32/54.43	    inference('demod', [status(thm)], ['47', '22', '22'])).
54.32/54.43	tff('49', plain,
54.32/54.43	    app_encode_app(nat, int, 
54.32/54.43	      app_encode_app(fun_nat_int, app_encode_fun(nat, int), hAPP_nat_int, 
54.32/54.43	        app_encode_app(int, fun_nat_int, power_power_int, 
54.32/54.43	          sk_K_22(one_one_int, 
54.32/54.43	            app_encode_app(nat, int, 
54.32/54.43	              app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
54.32/54.43	                hAPP_nat_int, semiri1621563631at_int), n), min))), 
54.32/54.43	      sk_N_1(sk_K_22(one_one_int, one_one_int, min)))
54.32/54.43	     = zero_zero_int,
54.32/54.43	    inference('demod', [status(thm)], ['0', '15', '16', '19', '22', '48'])).
54.32/54.43	tff(zf_stmt_315, axiom,
54.32/54.43	  (![N_20:nat,A_94:int]:
54.32/54.43	     ((A_94 != zero_zero_int) =>
54.32/54.43	      (app_encode_app(nat,int,
54.32/54.43	                      app_encode_app(fun_nat_int,app_encode_fun(nat,int),
54.32/54.43	                                     hAPP_nat_int,
54.32/54.43	                                     app_encode_app(int,fun_nat_int,
54.32/54.43	                                                    power_power_int,A_94)),
54.32/54.43	                      N_20) !=
54.32/54.43	       zero_zero_int)))).
54.32/54.43	tff('50', plain,
54.32/54.43	    ![X381 : int, X382 : nat]:
54.32/54.43	      (app_encode_app(nat, int, 
54.32/54.43	         app_encode_app(fun_nat_int, app_encode_fun(nat, int), hAPP_nat_int, 
54.32/54.43	           app_encode_app(int, fun_nat_int, power_power_int, X381)), X382)
54.32/54.43	        != zero_zero_int
54.32/54.43	       | X381 = zero_zero_int),
54.32/54.43	    inference('cnf', [status(esa)], [zf_stmt_315])).
54.32/54.43	tff('51', plain,
54.32/54.43	    (zero_zero_int != zero_zero_int
54.32/54.43	     | sk_K_22(one_one_int, 
54.32/54.43	         app_encode_app(nat, int, 
54.32/54.43	           app_encode_app(fun_nat_int, app_encode_fun(nat, int), 
54.32/54.43	             hAPP_nat_int, semiri1621563631at_int), n), min)
54.32/54.43	        = zero_zero_int),
54.32/54.43	    inference('sup-', [status(thm)], ['49', '50'])).
54.32/54.43	tff('52', plain,
54.32/54.43	    sk_K_22(one_one_int, 
54.32/54.43	      app_encode_app(nat, int, 
54.32/54.43	        app_encode_app(fun_nat_int, app_encode_fun(nat, int), hAPP_nat_int, 
54.32/54.43	          semiri1621563631at_int), n), min)
54.32/54.43	     = zero_zero_int,
54.32/54.43	    inference('simplify', [status(thm)], ['51'])).
54.32/54.43	tff('53', plain,
54.32/54.43	    ![X0 : int]:
54.32/54.43	      app_encode_app(int, int, succ, sk_K_22(one_one_int, X0, one_one_int))
54.32/54.43	       = X0,
54.32/54.43	    inference('sup+', [status(thm)], ['9', '3'])).
54.32/54.43	tff(zf_stmt_400, axiom,
54.32/54.43	  (![B_58:int,A_85:int,C_44:int]:
54.32/54.43	     ((app_encode_app(int,int,
54.32/54.43	                      app_encode_app(int,app_encode_fun(int,int),
54.32/54.43	                                     plus_plus_int,B_58),
54.32/54.43	                      A_85) =
54.32/54.43	       app_encode_app(int,int,
54.32/54.43	                      app_encode_app(int,app_encode_fun(int,int),
54.32/54.43	                                     plus_plus_int,C_44),
54.32/54.43	                      A_85)) =>
54.32/54.43	      (B_58 = C_44)))).
54.32/54.43	tff('54', plain,
54.32/54.43	    ![X529 : int, X530 : int, X531 : int]:
54.32/54.43	      (X530 = X529
54.32/54.43	       | app_encode_app(int, int, 
54.32/54.43	           app_encode_app(int, app_encode_fun(int, int), plus_plus_int, X530), 
54.32/54.43	           X531)
54.32/54.43	          != app_encode_app(int, int, 
54.32/54.43	               app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
54.32/54.43	                 X529), X531)),
54.32/54.43	    inference('cnf', [status(esa)], [zf_stmt_400])).
54.32/54.43	tff('55', plain,
54.32/54.43	    ![X0 : int, X1 : int]:
54.32/54.43	      (app_encode_app(int, int, succ, X0)
54.32/54.43	        != app_encode_app(int, int, 
54.32/54.43	             app_encode_app(int, app_encode_fun(int, int), plus_plus_int, X1), 
54.32/54.43	             one_one_int)
54.32/54.43	       | X0 = X1),
54.32/54.43	    inference('sup-', [status(thm)], ['2', '54'])).
54.32/54.43	tff('56', plain,
54.32/54.43	    ![X0 : int, X1 : int]:
54.32/54.43	      (app_encode_app(int, int, succ, X0)
54.32/54.43	        != app_encode_app(int, int, succ, X1)
54.32/54.43	       | X0 = X1),
54.32/54.43	    inference('demod', [status(thm)], ['55', '2'])).
54.32/54.43	tff('57', plain,
54.32/54.43	    ![X0 : int, X1 : int]:
54.32/54.43	      (X0 != app_encode_app(int, int, succ, X1)
54.32/54.43	       | sk_K_22(one_one_int, X0, one_one_int) = X1),
54.32/54.43	    inference('sup-', [status(thm)], ['53', '56'])).
54.32/54.43	tff('58', plain,
54.32/54.43	    ![X1 : int]:
54.32/54.43	      sk_K_22(one_one_int, app_encode_app(int, int, succ, X1), one_one_int)
54.32/54.43	       = X1,
54.32/54.43	    inference('simplify', [status(thm)], ['57'])).
54.32/54.43	tff('59', plain,
54.32/54.43	    ![X1 : int]:
54.32/54.43	      sk_K_22(one_one_int, sk_K_22(one_one_int, X1, min), one_one_int) = X1,
54.32/54.43	    inference('demod', [status(thm)], ['58', '14'])).
54.32/54.43	tff('60', plain,
54.32/54.43	    sk_K_22(one_one_int, zero_zero_int, one_one_int)
54.32/54.43	     = app_encode_app(nat, int, 
54.32/54.43	         app_encode_app(fun_nat_int, app_encode_fun(nat, int), hAPP_nat_int, 
54.32/54.43	           semiri1621563631at_int), n),
54.32/54.43	    inference('sup+', [status(thm)], ['52', '59'])).
54.32/54.43	tff(zf_stmt_1104, axiom, (app_encode_app(int,int,succ,min) = pls)).
54.32/54.43	tff('61', plain, app_encode_app(int, int, succ, min) = pls,
54.32/54.43	    inference('cnf', [status(esa)], [zf_stmt_1104])).
54.32/54.43	tff('62', plain, app_encode_app(int, int, succ, min) = zero_zero_int,
54.32/54.43	    inference('demod', [status(thm)], ['61', '16'])).
54.32/54.43	tff('63', plain,
54.32/54.43	    ![X0 : int]:
54.32/54.43	      (zero_zero_int != app_encode_app(int, int, succ, X0) | min = X0),
54.32/54.43	    inference('sup-', [status(thm)], ['62', '56'])).
54.32/54.43	tff('64', plain,
54.32/54.43	    ![X0 : int]:
54.32/54.43	      (zero_zero_int != X0 | min = sk_K_22(one_one_int, X0, one_one_int)),
54.32/54.43	    inference('sup-', [status(thm)], ['53', '63'])).
54.32/54.43	tff('65', plain, min = sk_K_22(one_one_int, zero_zero_int, one_one_int),
54.32/54.43	    inference('simplify', [status(thm)], ['64'])).
54.32/54.43	tff('66', plain,
54.32/54.43	    min
54.32/54.43	     = app_encode_app(nat, int, 
54.32/54.43	         app_encode_app(fun_nat_int, app_encode_fun(nat, int), hAPP_nat_int, 
54.32/54.43	           semiri1621563631at_int), n),
54.32/54.43	    inference('demod', [status(thm)], ['60', '65'])).
54.32/54.43	tff('67', plain,
54.32/54.43	    ~ app_encode_app(bool, $o, hBOOL, 
54.32/54.43	        app_encode_app(int, bool, 
54.32/54.43	          app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
54.32/54.43	            hAPP_int_bool, 
54.32/54.43	            app_encode_app(int, fun_int_bool, 
54.32/54.43	              app_encode_app(fun_int_fun_int_bool, 
54.32/54.43	                app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
54.32/54.43	                ord_less_int), min)), zero_zero_int)),
54.32/54.43	    inference('sup-', [status(thm)], ['66', '26'])).
54.32/54.43	tff(zf_stmt_1086, axiom,
54.32/54.43	  (app_encode_app(bool,$o,hBOOL,
54.32/54.43	                  app_encode_app(int,bool,
54.32/54.43	                                 app_encode_app(fun_int_bool,
54.32/54.43	                                                app_encode_fun(int,bool),
54.32/54.43	                                                hAPP_int_bool,
54.32/54.43	                                                app_encode_app(int,
54.32/54.43	                                                               fun_int_bool,
54.32/54.43	                                                               app_encode_app(
54.32/54.43	                                                               fun_int_fun_int_bool,
54.32/54.43	                                                               app_encode_fun(
54.32/54.43	                                                               int,
54.32/54.43	                                                               fun_int_bool),
54.32/54.43	                                                               hAPP_i1948725293t_bool,
54.32/54.43	                                                               ord_less_int),
54.32/54.43	                                                               min)),
54.32/54.43	                                 pls)))).
54.32/54.43	tff('68', plain,
54.32/54.43	    app_encode_app(bool, $o, hBOOL, 
54.32/54.43	      app_encode_app(int, bool, 
54.32/54.43	        app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
54.32/54.43	          hAPP_int_bool, 
54.32/54.43	          app_encode_app(int, fun_int_bool, 
54.32/54.43	            app_encode_app(fun_int_fun_int_bool, 
54.32/54.43	              app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
54.32/54.43	              ord_less_int), min)), pls)),
54.32/54.43	    inference('cnf', [status(esa)], [zf_stmt_1086])).
54.32/54.43	tff('69', plain,
54.32/54.43	    app_encode_app(bool, $o, hBOOL, 
54.32/54.43	      app_encode_app(int, bool, 
54.32/54.43	        app_encode_app(fun_int_bool, app_encode_fun(int, bool), 
54.32/54.43	          hAPP_int_bool, 
54.32/54.43	          app_encode_app(int, fun_int_bool, 
54.32/54.43	            app_encode_app(fun_int_fun_int_bool, 
54.32/54.43	              app_encode_fun(int, fun_int_bool), hAPP_i1948725293t_bool, 
54.32/54.43	              ord_less_int), min)), zero_zero_int)),
54.32/54.43	    inference('demod', [status(thm)], ['68', '16'])).
54.32/54.43	tff('70', plain, ~ $true, inference('demod', [status(thm)], ['67', '69'])).
54.32/54.43	tff('71', plain, $false, inference('simplify', [status(thm)], ['70'])).
54.32/54.43	
54.32/54.43	% SZS output end Refutation
54.32/54.43	EOF
