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   : n132.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 07:39:38 CST 2018
12.18/12.34	% done 6311 iterations in 12.142s
12.18/12.34	% SZS status Theorem for 'stdin'
12.18/12.34	% SZS output start Refutation
12.18/12.34	tff(zf_stmt_52, axiom,
12.18/12.34	  ((t = one_one_int) =>
12.18/12.34	   (?[X:int,Y:int]:
12.18/12.34	      (app_encode_app(int,int,
12.18/12.34	                      app_encode_app(int,app_encode_fun(int,int),
12.18/12.34	                                     plus_plus_int,
12.18/12.34	                                     app_encode_app(nat,int,
12.18/12.34	                                                    app_encode_app(int,
12.18/12.34	                                                                   app_encode_fun(
12.18/12.34	                                                                   nat,int),
12.18/12.34	                                                                   power_power_int,
12.18/12.34	                                                                   X),
12.18/12.34	                                                    app_encode_app(int,nat,
12.18/12.34	                                                                   number_number_of_nat,
12.18/12.34	                                                                   app_encode_app(
12.18/12.34	                                                                   int,int,
12.18/12.34	                                                                   bit0,
12.18/12.34	                                                                   app_encode_app(
12.18/12.34	                                                                   int,int,
12.18/12.34	                                                                   bit1,pls))))),
12.18/12.34	                      app_encode_app(nat,int,
12.18/12.34	                                     app_encode_app(int,
12.18/12.34	                                                    app_encode_fun(nat,int),
12.18/12.34	                                                    power_power_int,Y),
12.18/12.34	                                     app_encode_app(int,nat,
12.18/12.34	                                                    number_number_of_nat,
12.18/12.34	                                                    app_encode_app(int,int,
12.18/12.34	                                                                   bit0,
12.18/12.34	                                                                   app_encode_app(
12.18/12.34	                                                                   int,int,
12.18/12.34	                                                                   bit1,pls))))) =
12.18/12.34	       app_encode_app(int,int,
12.18/12.34	                      app_encode_app(int,app_encode_fun(int,int),
12.18/12.34	                                     plus_plus_int,
12.18/12.34	                                     app_encode_app(int,int,
12.18/12.34	                                                    app_encode_app(int,
12.18/12.34	                                                                   app_encode_fun(
12.18/12.34	                                                                   int,int),
12.18/12.34	                                                                   times_times_int,
12.18/12.34	                                                                   app_encode_app(
12.18/12.34	                                                                   int,int,
12.18/12.34	                                                                   number_number_of_int,
12.18/12.34	                                                                   app_encode_app(
12.18/12.34	                                                                   int,int,
12.18/12.34	                                                                   bit0,
12.18/12.34	                                                                   app_encode_app(
12.18/12.34	                                                                   int,int,
12.18/12.34	                                                                   bit0,
12.18/12.34	                                                                   app_encode_app(
12.18/12.34	                                                                   int,int,
12.18/12.34	                                                                   bit1,pls))))),
12.18/12.34	                                                    m)),
12.18/12.34	                      one_one_int))))).
12.18/12.34	tff('0', plain,
12.18/12.34	    (app_encode_app(int, int, 
12.18/12.34	       app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.34	         app_encode_app(nat, int, 
12.18/12.34	           app_encode_app(int, app_encode_fun(nat, int), power_power_int, 
12.18/12.34	             sk_X), 
12.18/12.34	           app_encode_app(int, nat, number_number_of_nat, 
12.18/12.34	             app_encode_app(int, int, bit0, 
12.18/12.34	               app_encode_app(int, int, bit1, pls))))), 
12.18/12.34	       app_encode_app(nat, int, 
12.18/12.34	         app_encode_app(int, app_encode_fun(nat, int), power_power_int, sk_Y), 
12.18/12.34	         app_encode_app(int, nat, number_number_of_nat, 
12.18/12.34	           app_encode_app(int, int, bit0, 
12.18/12.34	             app_encode_app(int, int, bit1, pls)))))
12.18/12.34	      = app_encode_app(int, int, 
12.18/12.34	          app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.34	            app_encode_app(int, int, 
12.18/12.34	              app_encode_app(int, app_encode_fun(int, int), times_times_int, 
12.18/12.34	                app_encode_app(int, int, number_number_of_int, 
12.18/12.34	                  app_encode_app(int, int, bit0, 
12.18/12.34	                    app_encode_app(int, int, bit0, 
12.18/12.34	                      app_encode_app(int, int, bit1, pls))))), m)), 
12.18/12.34	          one_one_int)
12.18/12.34	     | t != one_one_int),
12.18/12.34	    inference('cnf', [status(esa)], [zf_stmt_52])).
12.18/12.34	tff(zf_stmt_193, axiom,
12.18/12.34	  (![K:int]: (app_encode_app(int,int,number_number_of_int,K) = K))).
12.18/12.34	tff('1', plain,
12.18/12.34	    ![X320 : int]:
12.18/12.34	      app_encode_app(int, int, number_number_of_int, X320) = X320,
12.18/12.34	    inference('cnf', [status(esa)], [zf_stmt_193])).
12.18/12.34	tff('2', plain,
12.18/12.34	    (app_encode_app(int, int, 
12.18/12.34	       app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.34	         app_encode_app(nat, int, 
12.18/12.34	           app_encode_app(int, app_encode_fun(nat, int), power_power_int, 
12.18/12.34	             sk_X), 
12.18/12.34	           app_encode_app(int, nat, number_number_of_nat, 
12.18/12.34	             app_encode_app(int, int, bit0, 
12.18/12.34	               app_encode_app(int, int, bit1, pls))))), 
12.18/12.34	       app_encode_app(nat, int, 
12.18/12.34	         app_encode_app(int, app_encode_fun(nat, int), power_power_int, sk_Y), 
12.18/12.34	         app_encode_app(int, nat, number_number_of_nat, 
12.18/12.34	           app_encode_app(int, int, bit0, 
12.18/12.34	             app_encode_app(int, int, bit1, pls)))))
12.18/12.34	      = app_encode_app(int, int, 
12.18/12.34	          app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.34	            app_encode_app(int, int, 
12.18/12.34	              app_encode_app(int, app_encode_fun(int, int), times_times_int, 
12.18/12.34	                app_encode_app(int, int, bit0, 
12.18/12.34	                  app_encode_app(int, int, bit0, 
12.18/12.34	                    app_encode_app(int, int, bit1, pls)))), m)), one_one_int)
12.18/12.34	     | t != one_one_int),
12.18/12.34	    inference('demod', [status(thm)], ['0', '1'])).
12.18/12.34	tff(zf_stmt_311, axiom,
12.18/12.34	  (app_encode_app(int,int,number_number_of_int,
12.18/12.34	                  app_encode_app(int,int,bit1,pls)) =
12.18/12.34	   one_one_int)).
12.18/12.34	tff('3', plain,
12.18/12.34	    app_encode_app(int, int, number_number_of_int, 
12.18/12.34	      app_encode_app(int, int, bit1, pls))
12.18/12.34	     = one_one_int,
12.18/12.34	    inference('cnf', [status(esa)], [zf_stmt_311])).
12.18/12.34	tff('4', plain, app_encode_app(int, int, bit1, pls) = one_one_int,
12.18/12.34	    inference('demod', [status(thm)], ['3', '1'])).
12.18/12.34	tff('5', plain,
12.18/12.34	    (app_encode_app(int, int, 
12.18/12.34	       app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.34	         app_encode_app(nat, int, 
12.18/12.34	           app_encode_app(int, app_encode_fun(nat, int), power_power_int, 
12.18/12.34	             sk_X), 
12.18/12.34	           app_encode_app(int, nat, number_number_of_nat, 
12.18/12.34	             app_encode_app(int, int, bit0, one_one_int)))), 
12.18/12.34	       app_encode_app(nat, int, 
12.18/12.34	         app_encode_app(int, app_encode_fun(nat, int), power_power_int, sk_Y), 
12.18/12.34	         app_encode_app(int, nat, number_number_of_nat, 
12.18/12.34	           app_encode_app(int, int, bit0, one_one_int))))
12.18/12.34	      = app_encode_app(int, int, 
12.18/12.34	          app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.34	            app_encode_app(int, int, 
12.18/12.34	              app_encode_app(int, app_encode_fun(int, int), times_times_int, 
12.18/12.34	                app_encode_app(int, int, bit0, 
12.18/12.34	                  app_encode_app(int, int, bit0, one_one_int))), m)), 
12.18/12.34	          one_one_int)
12.18/12.34	     | t != one_one_int),
12.18/12.34	    inference('demod', [status(thm)], ['2', '4', '4', '4'])).
12.18/12.34	tff(zf_stmt_239, axiom,
12.18/12.34	  (![A_52:int]:
12.18/12.34	     (app_encode_app(int,int,
12.18/12.34	                     app_encode_app(int,app_encode_fun(int,int),
12.18/12.34	                                    times_times_int,one_one_int),
12.18/12.34	                     A_52) =
12.18/12.34	      A_52))).
12.18/12.34	tff('6', plain,
12.18/12.34	    ![X440 : int]:
12.18/12.34	      app_encode_app(int, int, 
12.18/12.34	        app_encode_app(int, app_encode_fun(int, int), times_times_int, 
12.18/12.34	          one_one_int), X440)
12.18/12.34	       = X440,
12.18/12.34	    inference('cnf', [status(esa)], [zf_stmt_239])).
12.18/12.34	tff(zf_stmt_631, axiom,
12.18/12.34	  (![A:int,B_1:int,M:int]:
12.18/12.34	     (app_encode_app(int,$o,
12.18/12.34	                     app_encode_app(int,app_encode_fun(int,$o),
12.18/12.34	                                    app_encode_app(int,
12.18/12.34	                                                   app_encode_fun(int,
12.18/12.34	                                                                  app_encode_fun(
12.18/12.34	                                                                  int,$o)),
12.18/12.34	                                                   zcong,A),
12.18/12.34	                                    B_1),
12.18/12.34	                     M) <=>
12.18/12.34	      (?[K_1:int]:
12.18/12.34	         (B_1 =
12.18/12.34	          app_encode_app(int,int,
12.18/12.34	                         app_encode_app(int,app_encode_fun(int,int),
12.18/12.34	                                        plus_plus_int,A),
12.18/12.34	                         app_encode_app(int,int,
12.18/12.34	                                        app_encode_app(int,
12.18/12.34	                                                       app_encode_fun(
12.18/12.34	                                                       int,int),
12.18/12.34	                                                       times_times_int,M),
12.18/12.34	                                        K_1))))))).
12.18/12.34	tff('7', plain,
12.18/12.34	    ![X1196 : int, X1197 : int, X1198 : int]:
12.18/12.34	      (X1198
12.18/12.34	        = app_encode_app(int, int, 
12.18/12.34	            app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.34	              X1196), 
12.18/12.34	            app_encode_app(int, int, 
12.18/12.34	              app_encode_app(int, app_encode_fun(int, int), times_times_int, 
12.18/12.34	                X1197), sk_K_1(X1197, X1198, X1196)))
12.18/12.34	       | ~ app_encode_app(int, $o, 
12.18/12.34	             app_encode_app(int, app_encode_fun(int, $o), 
12.18/12.34	               app_encode_app(int, 
12.18/12.34	                 app_encode_fun(int, app_encode_fun(int, $o)), zcong, X1196), 
12.18/12.34	               X1198), X1197)),
12.18/12.34	    inference('cnf', [status(esa)], [zf_stmt_631])).
12.18/12.34	tff('8', plain,
12.18/12.34	    ![X0 : int, X1 : int]:
12.18/12.34	      (X1
12.18/12.34	        = app_encode_app(int, int, 
12.18/12.34	            app_encode_app(int, app_encode_fun(int, int), plus_plus_int, X0), 
12.18/12.34	            sk_K_1(one_one_int, X1, X0))
12.18/12.34	       | ~ app_encode_app(int, $o, 
12.18/12.34	             app_encode_app(int, app_encode_fun(int, $o), 
12.18/12.34	               app_encode_app(int, 
12.18/12.34	                 app_encode_fun(int, app_encode_fun(int, $o)), zcong, X0), 
12.18/12.34	               X1), one_one_int)),
12.18/12.34	    inference('sup+', [status(thm)], ['6', '7'])).
12.18/12.34	tff(zf_stmt_619, axiom,
12.18/12.34	  (![A:int,B_1:int]:
12.18/12.34	     app_encode_app(int,$o,
12.18/12.34	                    app_encode_app(int,app_encode_fun(int,$o),
12.18/12.34	                                   app_encode_app(int,
12.18/12.34	                                                  app_encode_fun(int,
12.18/12.34	                                                                 app_encode_fun(
12.18/12.34	                                                                 int,$o)),
12.18/12.34	                                                  zcong,A),
12.18/12.34	                                   B_1),
12.18/12.34	                    one_one_int))).
12.18/12.34	tff('9', plain,
12.18/12.34	    ![X1159 : int, X1160 : int]:
12.18/12.34	      app_encode_app(int, $o, 
12.18/12.34	        app_encode_app(int, app_encode_fun(int, $o), 
12.18/12.34	          app_encode_app(int, app_encode_fun(int, app_encode_fun(int, $o)), 
12.18/12.34	            zcong, X1159), X1160), one_one_int),
12.18/12.34	    inference('cnf', [status(esa)], [zf_stmt_619])).
12.18/12.34	tff('10', plain,
12.18/12.34	    ![X0 : int, X1 : int]:
12.18/12.34	      (X1
12.18/12.34	        = app_encode_app(int, int, 
12.18/12.34	            app_encode_app(int, app_encode_fun(int, int), plus_plus_int, X0), 
12.18/12.34	            sk_K_1(one_one_int, X1, X0))
12.18/12.34	       | ~ $true),
12.18/12.34	    inference('demod', [status(thm)], ['8', '9'])).
12.18/12.34	tff('11', plain,
12.18/12.34	    ![X0 : int, X1 : int]:
12.18/12.34	      X1
12.18/12.34	       = app_encode_app(int, int, 
12.18/12.34	           app_encode_app(int, app_encode_fun(int, int), plus_plus_int, X0), 
12.18/12.34	           sk_K_1(one_one_int, X1, X0)),
12.18/12.34	    inference('simplify', [status(thm)], ['10'])).
12.18/12.34	tff(zf_stmt_566, axiom, (app_encode_app(int,int,bit1,min) = min)).
12.18/12.34	tff('12', plain, app_encode_app(int, int, bit1, min) = min,
12.18/12.34	    inference('cnf', [status(esa)], [zf_stmt_566])).
12.18/12.34	tff(zf_stmt_300, axiom,
12.18/12.34	  (![K:int,L:int]:
12.18/12.34	     (app_encode_app(int,int,
12.18/12.34	                     app_encode_app(int,app_encode_fun(int,int),
12.18/12.34	                                    plus_plus_int,
12.18/12.34	                                    app_encode_app(int,int,bit1,K)),
12.18/12.34	                     app_encode_app(int,int,bit0,L)) =
12.18/12.34	      app_encode_app(int,int,bit1,
12.18/12.34	                     app_encode_app(int,int,
12.18/12.34	                                    app_encode_app(int,
12.18/12.34	                                                   app_encode_fun(int,int),
12.18/12.34	                                                   plus_plus_int,K),
12.18/12.34	                                    L))))).
12.18/12.34	tff('13', plain,
12.18/12.34	    ![X558 : int, X559 : int]:
12.18/12.34	      app_encode_app(int, int, 
12.18/12.34	        app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.34	          app_encode_app(int, int, bit1, X558)), 
12.18/12.34	        app_encode_app(int, int, bit0, X559))
12.18/12.34	       = app_encode_app(int, int, bit1, 
12.18/12.34	           app_encode_app(int, int, 
12.18/12.34	             app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.34	               X558), X559)),
12.18/12.34	    inference('cnf', [status(esa)], [zf_stmt_300])).
12.18/12.34	tff('14', plain,
12.18/12.34	    ![X0 : int]:
12.18/12.34	      app_encode_app(int, int, 
12.18/12.34	        app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.34	          one_one_int), app_encode_app(int, int, bit0, X0))
12.18/12.34	       = app_encode_app(int, int, bit1, 
12.18/12.34	           app_encode_app(int, int, 
12.18/12.34	             app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.34	               pls), X0)),
12.18/12.34	    inference('sup+', [status(thm)], ['4', '13'])).
12.18/12.34	tff(zf_stmt_253, axiom,
12.18/12.34	  (![K:int]:
12.18/12.34	     (app_encode_app(int,int,
12.18/12.34	                     app_encode_app(int,app_encode_fun(int,int),
12.18/12.34	                                    plus_plus_int,pls),
12.18/12.34	                     K) =
12.18/12.34	      K))).
12.18/12.34	tff('15', plain,
12.18/12.34	    ![X464 : int]:
12.18/12.34	      app_encode_app(int, int, 
12.18/12.34	        app_encode_app(int, app_encode_fun(int, int), plus_plus_int, pls), 
12.18/12.34	        X464)
12.18/12.34	       = X464,
12.18/12.34	    inference('cnf', [status(esa)], [zf_stmt_253])).
12.18/12.34	tff('16', plain,
12.18/12.34	    ![X0 : int]:
12.18/12.34	      app_encode_app(int, int, 
12.18/12.34	        app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.34	          one_one_int), app_encode_app(int, int, bit0, X0))
12.18/12.34	       = app_encode_app(int, int, bit1, X0),
12.18/12.34	    inference('demod', [status(thm)], ['14', '15'])).
12.18/12.34	tff(zf_stmt_255, axiom,
12.18/12.34	  (![K:int]:
12.18/12.34	     (app_encode_app(int,int,bit0,K) =
12.18/12.34	      app_encode_app(int,int,
12.18/12.34	                     app_encode_app(int,app_encode_fun(int,int),
12.18/12.34	                                    plus_plus_int,K),
12.18/12.34	                     K)))).
12.18/12.34	tff('17', plain,
12.18/12.34	    ![X467 : int]:
12.18/12.34	      app_encode_app(int, int, bit0, X467)
12.18/12.34	       = app_encode_app(int, int, 
12.18/12.34	           app_encode_app(int, app_encode_fun(int, int), plus_plus_int, X467), 
12.18/12.34	           X467),
12.18/12.34	    inference('cnf', [status(esa)], [zf_stmt_255])).
12.18/12.34	tff(zf_stmt_171, axiom,
12.18/12.34	  (![A_62:int,B_18:int,C_9:int]:
12.18/12.34	     (app_encode_app(int,int,
12.18/12.34	                     app_encode_app(int,app_encode_fun(int,int),
12.18/12.34	                                    plus_plus_int,
12.18/12.34	                                    app_encode_app(int,int,
12.18/12.34	                                                   app_encode_app(int,
12.18/12.34	                                                                  app_encode_fun(
12.18/12.34	                                                                  int,int),
12.18/12.34	                                                                  plus_plus_int,
12.18/12.34	                                                                  A_62),
12.18/12.34	                                                   B_18)),
12.18/12.34	                     C_9) =
12.18/12.34	      app_encode_app(int,int,
12.18/12.34	                     app_encode_app(int,app_encode_fun(int,int),
12.18/12.34	                                    plus_plus_int,
12.18/12.34	                                    app_encode_app(int,int,
12.18/12.34	                                                   app_encode_app(int,
12.18/12.34	                                                                  app_encode_fun(
12.18/12.34	                                                                  int,int),
12.18/12.34	                                                                  plus_plus_int,
12.18/12.34	                                                                  A_62),
12.18/12.34	                                                   C_9)),
12.18/12.34	                     B_18)))).
12.18/12.34	tff('18', plain,
12.18/12.34	    ![X258 : int, X259 : int, X260 : int]:
12.18/12.34	      app_encode_app(int, int, 
12.18/12.34	        app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.34	          app_encode_app(int, int, 
12.18/12.34	            app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.34	              X258), X260)), X259)
12.18/12.34	       = app_encode_app(int, int, 
12.18/12.34	           app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.34	             app_encode_app(int, int, 
12.18/12.34	               app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.34	                 X258), X259)), X260),
12.18/12.34	    inference('cnf', [status(esa)], [zf_stmt_171])).
12.18/12.34	tff('19', plain,
12.18/12.34	    ![X0 : int, X1 : int]:
12.18/12.34	      app_encode_app(int, int, 
12.18/12.34	        app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.34	          app_encode_app(int, int, bit0, X0)), X1)
12.18/12.34	       = app_encode_app(int, int, 
12.18/12.34	           app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.34	             app_encode_app(int, int, 
12.18/12.34	               app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.34	                 X0), X1)), X0),
12.18/12.34	    inference('sup+', [status(thm)], ['17', '18'])).
12.18/12.34	tff(zf_stmt_183, axiom,
12.18/12.34	  (![A_58:int,C_5:int]:
12.18/12.34	     (app_encode_app(int,int,
12.18/12.34	                     app_encode_app(int,app_encode_fun(int,int),
12.18/12.34	                                    plus_plus_int,A_58),
12.18/12.34	                     C_5) =
12.18/12.34	      app_encode_app(int,int,
12.18/12.34	                     app_encode_app(int,app_encode_fun(int,int),
12.18/12.34	                                    plus_plus_int,C_5),
12.18/12.34	                     A_58)))).
12.18/12.34	tff('20', plain,
12.18/12.34	    ![X292 : int, X293 : int]:
12.18/12.34	      app_encode_app(int, int, 
12.18/12.34	        app_encode_app(int, app_encode_fun(int, int), plus_plus_int, X293), 
12.18/12.34	        X292)
12.18/12.34	       = app_encode_app(int, int, 
12.18/12.34	           app_encode_app(int, app_encode_fun(int, int), plus_plus_int, X292), 
12.18/12.34	           X293),
12.18/12.34	    inference('cnf', [status(esa)], [zf_stmt_183])).
12.18/12.34	tff('21', plain,
12.18/12.34	    ![X0 : int, X1 : int]:
12.18/12.34	      app_encode_app(int, int, 
12.18/12.34	        app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.34	          app_encode_app(int, int, bit0, X0)), X1)
12.18/12.34	       = app_encode_app(int, int, 
12.18/12.34	           app_encode_app(int, app_encode_fun(int, int), plus_plus_int, X0), 
12.18/12.34	           app_encode_app(int, int, 
12.18/12.34	             app_encode_app(int, app_encode_fun(int, int), plus_plus_int, X0), 
12.18/12.34	             X1)),
12.18/12.34	    inference('demod', [status(thm)], ['19', '20'])).
12.18/12.34	tff('22', plain,
12.18/12.34	    ![X0 : int]:
12.18/12.34	      app_encode_app(int, int, 
12.18/12.34	        app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.34	          app_encode_app(int, int, bit0, one_one_int)), 
12.18/12.34	        app_encode_app(int, int, bit0, X0))
12.18/12.34	       = app_encode_app(int, int, 
12.18/12.34	           app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.34	             one_one_int), app_encode_app(int, int, bit1, X0)),
12.18/12.34	    inference('sup+', [status(thm)], ['16', '21'])).
12.18/12.34	tff(zf_stmt_254, axiom,
12.18/12.34	  (![K:int,L:int]:
12.18/12.34	     (app_encode_app(int,int,
12.18/12.34	                     app_encode_app(int,app_encode_fun(int,int),
12.18/12.34	                                    plus_plus_int,
12.18/12.34	                                    app_encode_app(int,int,bit0,K)),
12.18/12.34	                     app_encode_app(int,int,bit0,L)) =
12.18/12.34	      app_encode_app(int,int,bit0,
12.18/12.34	                     app_encode_app(int,int,
12.18/12.34	                                    app_encode_app(int,
12.18/12.34	                                                   app_encode_fun(int,int),
12.18/12.34	                                                   plus_plus_int,K),
12.18/12.34	                                    L))))).
12.18/12.34	tff('23', plain,
12.18/12.34	    ![X465 : int, X466 : int]:
12.18/12.34	      app_encode_app(int, int, 
12.18/12.34	        app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.34	          app_encode_app(int, int, bit0, X465)), 
12.18/12.34	        app_encode_app(int, int, bit0, X466))
12.18/12.34	       = app_encode_app(int, int, bit0, 
12.18/12.34	           app_encode_app(int, int, 
12.18/12.34	             app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.34	               X465), X466)),
12.18/12.34	    inference('cnf', [status(esa)], [zf_stmt_254])).
12.18/12.34	tff('24', plain,
12.18/12.34	    ![X0 : int, X1 : int]:
12.18/12.34	      app_encode_app(int, int, 
12.18/12.34	        app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.34	          app_encode_app(int, int, bit0, X0)), 
12.18/12.34	        app_encode_app(int, int, bit0, X1))
12.18/12.34	       = app_encode_app(int, int, bit0, 
12.18/12.34	           app_encode_app(int, int, 
12.18/12.34	             app_encode_app(int, app_encode_fun(int, int), plus_plus_int, X1), 
12.18/12.34	             X0)),
12.18/12.34	    inference('sup+', [status(thm)], ['23', '20'])).
12.18/12.34	tff('25', plain,
12.18/12.34	    ![X0 : int]:
12.18/12.34	      app_encode_app(int, int, bit0, 
12.18/12.34	        app_encode_app(int, int, 
12.18/12.34	          app_encode_app(int, app_encode_fun(int, int), plus_plus_int, X0), 
12.18/12.34	          one_one_int))
12.18/12.34	       = app_encode_app(int, int, 
12.18/12.34	           app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.34	             one_one_int), app_encode_app(int, int, bit1, X0)),
12.18/12.34	    inference('demod', [status(thm)], ['22', '24'])).
12.18/12.34	tff('26', plain,
12.18/12.34	    app_encode_app(int, int, bit0, 
12.18/12.34	      app_encode_app(int, int, 
12.18/12.34	        app_encode_app(int, app_encode_fun(int, int), plus_plus_int, min), 
12.18/12.34	        one_one_int))
12.18/12.34	     = app_encode_app(int, int, 
12.18/12.34	         app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.34	           one_one_int), min),
12.18/12.34	    inference('sup+', [status(thm)], ['12', '25'])).
12.18/12.34	tff('27', plain,
12.18/12.34	    app_encode_app(int, int, bit0, 
12.18/12.34	      app_encode_app(int, int, 
12.18/12.34	        app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.34	          one_one_int), min))
12.18/12.34	     = app_encode_app(int, int, 
12.18/12.34	         app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.34	           one_one_int), min),
12.18/12.34	    inference('demod', [status(thm)], ['26', '20'])).
12.18/12.34	tff(zf_stmt_404, axiom,
12.18/12.34	  (![B_7:int,A_30:int]:
12.18/12.34	     ((B_7 =
12.18/12.34	       app_encode_app(int,int,
12.18/12.34	                      app_encode_app(int,app_encode_fun(int,int),
12.18/12.34	                                     plus_plus_int,B_7),
12.18/12.34	                      A_30)) <=>
12.18/12.34	      (A_30 = zero_zero_int)))).
12.18/12.34	tff('28', plain,
12.18/12.34	    ![X728 : int, X729 : int]:
12.18/12.34	      (X728 = zero_zero_int
12.18/12.34	       | X729
12.18/12.34	          != app_encode_app(int, int, 
12.18/12.34	               app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.34	                 X729), X728)),
12.18/12.34	    inference('cnf', [status(esa)], [zf_stmt_404])).
12.18/12.34	tff(zf_stmt_407, axiom, (pls = zero_zero_int)).
12.18/12.34	tff('29', plain, pls = zero_zero_int,
12.18/12.34	    inference('cnf', [status(esa)], [zf_stmt_407])).
12.18/12.34	tff('30', plain,
12.18/12.34	    ![X728 : int, X729 : int]:
12.18/12.34	      (X728 = pls
12.18/12.34	       | X729
12.18/12.34	          != app_encode_app(int, int, 
12.18/12.34	               app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.34	                 X729), X728)),
12.18/12.34	    inference('demod', [status(thm)], ['28', '29'])).
12.18/12.34	tff('31', plain,
12.18/12.34	    ![X0 : int]: (X0 != app_encode_app(int, int, bit0, X0) | X0 = pls),
12.18/12.34	    inference('sup-', [status(thm)], ['17', '30'])).
12.18/12.34	tff('32', plain,
12.18/12.34	    (app_encode_app(int, int, 
12.18/12.34	       app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.34	         one_one_int), min)
12.18/12.34	      != app_encode_app(int, int, 
12.18/12.34	           app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.34	             one_one_int), min)
12.18/12.34	     | app_encode_app(int, int, 
12.18/12.34	         app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.34	           one_one_int), min)
12.18/12.34	        = pls),
12.18/12.34	    inference('sup-', [status(thm)], ['27', '31'])).
12.18/12.34	tff('33', plain,
12.18/12.34	    app_encode_app(int, int, 
12.18/12.34	      app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.34	        one_one_int), min)
12.18/12.34	     = pls,
12.18/12.34	    inference('simplify', [status(thm)], ['32'])).
12.18/12.34	tff(zf_stmt_174, axiom,
12.18/12.34	  (![A_61:int,B_17:int,C_8:int]:
12.18/12.34	     (app_encode_app(int,int,
12.18/12.34	                     app_encode_app(int,app_encode_fun(int,int),
12.18/12.34	                                    plus_plus_int,
12.18/12.34	                                    app_encode_app(int,int,
12.18/12.34	                                                   app_encode_app(int,
12.18/12.34	                                                                  app_encode_fun(
12.18/12.34	                                                                  int,int),
12.18/12.34	                                                                  plus_plus_int,
12.18/12.34	                                                                  A_61),
12.18/12.34	                                                   B_17)),
12.18/12.34	                     C_8) =
12.18/12.34	      app_encode_app(int,int,
12.18/12.34	                     app_encode_app(int,app_encode_fun(int,int),
12.18/12.34	                                    plus_plus_int,A_61),
12.18/12.34	                     app_encode_app(int,int,
12.18/12.34	                                    app_encode_app(int,
12.18/12.34	                                                   app_encode_fun(int,int),
12.18/12.34	                                                   plus_plus_int,B_17),
12.18/12.34	                                    C_8))))).
12.18/12.34	tff('34', plain,
12.18/12.34	    ![X267 : int, X268 : int, X269 : int]:
12.18/12.34	      app_encode_app(int, int, 
12.18/12.34	        app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.34	          app_encode_app(int, int, 
12.18/12.34	            app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.34	              X267), X268)), X269)
12.18/12.34	       = app_encode_app(int, int, 
12.18/12.34	           app_encode_app(int, app_encode_fun(int, int), plus_plus_int, X267), 
12.18/12.34	           app_encode_app(int, int, 
12.18/12.34	             app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.34	               X268), X269)),
12.18/12.34	    inference('cnf', [status(esa)], [zf_stmt_174])).
12.18/12.34	tff('35', plain,
12.18/12.34	    ![X0 : int]:
12.18/12.34	      app_encode_app(int, int, 
12.18/12.34	        app_encode_app(int, app_encode_fun(int, int), plus_plus_int, pls), 
12.18/12.34	        X0)
12.18/12.34	       = app_encode_app(int, int, 
12.18/12.34	           app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.34	             one_one_int), 
12.18/12.34	           app_encode_app(int, int, 
12.18/12.34	             app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.34	               min), X0)),
12.18/12.34	    inference('sup+', [status(thm)], ['33', '34'])).
12.18/12.34	tff('36', plain,
12.18/12.34	    ![X0 : int]:
12.18/12.34	      X0
12.18/12.34	       = app_encode_app(int, int, 
12.18/12.34	           app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.34	             one_one_int), 
12.18/12.34	           app_encode_app(int, int, 
12.18/12.34	             app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.34	               min), X0)),
12.18/12.34	    inference('demod', [status(thm)], ['35', '15'])).
12.18/12.34	tff('37', plain,
12.18/12.34	    ![X0 : int]:
12.18/12.34	      sk_K_1(one_one_int, X0, min)
12.18/12.34	       = app_encode_app(int, int, 
12.18/12.34	           app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.35	             one_one_int), X0),
12.18/12.35	    inference('sup+', [status(thm)], ['11', '36'])).
12.18/12.35	tff('38', plain,
12.18/12.35	    app_encode_app(int, int, bit0, one_one_int)
12.18/12.35	     = sk_K_1(one_one_int, one_one_int, min),
12.18/12.35	    inference('sup+', [status(thm)], ['37', '17'])).
12.18/12.35	tff(zf_stmt_233, axiom,
12.18/12.35	  (![X_25:int,Y_23:int,Z_7:int]:
12.18/12.35	     (app_encode_app(int,int,
12.18/12.35	                     app_encode_app(int,app_encode_fun(int,int),
12.18/12.35	                                    times_times_int,X_25),
12.18/12.35	                     app_encode_app(int,int,
12.18/12.35	                                    app_encode_app(int,
12.18/12.35	                                                   app_encode_fun(int,int),
12.18/12.35	                                                   plus_plus_int,Y_23),
12.18/12.35	                                    Z_7)) =
12.18/12.35	      app_encode_app(int,int,
12.18/12.35	                     app_encode_app(int,app_encode_fun(int,int),
12.18/12.35	                                    plus_plus_int,
12.18/12.35	                                    app_encode_app(int,int,
12.18/12.35	                                                   app_encode_app(int,
12.18/12.35	                                                                  app_encode_fun(
12.18/12.35	                                                                  int,int),
12.18/12.35	                                                                  times_times_int,
12.18/12.35	                                                                  X_25),
12.18/12.35	                                                   Y_23)),
12.18/12.35	                     app_encode_app(int,int,
12.18/12.35	                                    app_encode_app(int,
12.18/12.35	                                                   app_encode_fun(int,int),
12.18/12.35	                                                   times_times_int,X_25),
12.18/12.35	                                    Z_7))))).
12.18/12.35	tff('39', plain,
12.18/12.35	    ![X432 : int, X433 : int, X434 : int]:
12.18/12.35	      app_encode_app(int, int, 
12.18/12.35	        app_encode_app(int, app_encode_fun(int, int), times_times_int, X432), 
12.18/12.35	        app_encode_app(int, int, 
12.18/12.35	          app_encode_app(int, app_encode_fun(int, int), plus_plus_int, X433), 
12.18/12.35	          X434))
12.18/12.35	       = app_encode_app(int, int, 
12.18/12.35	           app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.35	             app_encode_app(int, int, 
12.18/12.35	               app_encode_app(int, app_encode_fun(int, int), 
12.18/12.35	                 times_times_int, X432), X433)), 
12.18/12.35	           app_encode_app(int, int, 
12.18/12.35	             app_encode_app(int, app_encode_fun(int, int), times_times_int, 
12.18/12.35	               X432), X434)),
12.18/12.35	    inference('cnf', [status(esa)], [zf_stmt_233])).
12.18/12.35	tff('40', plain,
12.18/12.35	    ![X0 : int, X1 : int]:
12.18/12.35	      app_encode_app(int, int, 
12.18/12.35	        app_encode_app(int, app_encode_fun(int, int), times_times_int, X1), 
12.18/12.35	        app_encode_app(int, int, 
12.18/12.35	          app_encode_app(int, app_encode_fun(int, int), plus_plus_int, X0), 
12.18/12.35	          X0))
12.18/12.35	       = app_encode_app(int, int, bit0, 
12.18/12.35	           app_encode_app(int, int, 
12.18/12.35	             app_encode_app(int, app_encode_fun(int, int), times_times_int, 
12.18/12.35	               X1), X0)),
12.18/12.35	    inference('sup+', [status(thm)], ['17', '39'])).
12.18/12.35	tff('41', plain,
12.18/12.35	    ![X0 : int, X1 : int]:
12.18/12.35	      app_encode_app(int, int, 
12.18/12.35	        app_encode_app(int, app_encode_fun(int, int), times_times_int, X1), 
12.18/12.35	        app_encode_app(int, int, bit0, X0))
12.18/12.35	       = app_encode_app(int, int, bit0, 
12.18/12.35	           app_encode_app(int, int, 
12.18/12.35	             app_encode_app(int, app_encode_fun(int, int), times_times_int, 
12.18/12.35	               X1), X0)),
12.18/12.35	    inference('demod', [status(thm)], ['40', '17'])).
12.18/12.35	tff(zf_stmt_165, axiom,
12.18/12.35	  (![A_64:int,B_20:int]:
12.18/12.35	     (app_encode_app(int,int,
12.18/12.35	                     app_encode_app(int,app_encode_fun(int,int),
12.18/12.35	                                    times_times_int,A_64),
12.18/12.35	                     B_20) =
12.18/12.35	      app_encode_app(int,int,
12.18/12.35	                     app_encode_app(int,app_encode_fun(int,int),
12.18/12.35	                                    times_times_int,B_20),
12.18/12.35	                     A_64)))).
12.18/12.35	tff('42', plain,
12.18/12.35	    ![X238 : int, X239 : int]:
12.18/12.35	      app_encode_app(int, int, 
12.18/12.35	        app_encode_app(int, app_encode_fun(int, int), times_times_int, X239), 
12.18/12.35	        X238)
12.18/12.35	       = app_encode_app(int, int, 
12.18/12.35	           app_encode_app(int, app_encode_fun(int, int), times_times_int, 
12.18/12.35	             X238), X239),
12.18/12.35	    inference('cnf', [status(esa)], [zf_stmt_165])).
12.18/12.35	tff('43', plain,
12.18/12.35	    ![X0 : int, X1 : int]:
12.18/12.35	      app_encode_app(int, int, 
12.18/12.35	        app_encode_app(int, app_encode_fun(int, int), times_times_int, 
12.18/12.35	          app_encode_app(int, int, bit0, X0)), X1)
12.18/12.35	       = app_encode_app(int, int, bit0, 
12.18/12.35	           app_encode_app(int, int, 
12.18/12.35	             app_encode_app(int, app_encode_fun(int, int), times_times_int, 
12.18/12.35	               X1), X0)),
12.18/12.35	    inference('sup+', [status(thm)], ['41', '42'])).
12.18/12.35	tff('44', plain,
12.18/12.35	    ![X0 : int]:
12.18/12.35	      app_encode_app(int, int, 
12.18/12.35	        app_encode_app(int, app_encode_fun(int, int), times_times_int, X0), 
12.18/12.35	        sk_K_1(one_one_int, one_one_int, min))
12.18/12.35	       = app_encode_app(int, int, bit0, 
12.18/12.35	           app_encode_app(int, int, 
12.18/12.35	             app_encode_app(int, app_encode_fun(int, int), times_times_int, 
12.18/12.35	               X0), one_one_int)),
12.18/12.35	    inference('sup+', [status(thm)], ['38', '41'])).
12.18/12.35	tff(zf_stmt_236, axiom,
12.18/12.35	  (![A_53:int]:
12.18/12.35	     (app_encode_app(int,int,
12.18/12.35	                     app_encode_app(int,app_encode_fun(int,int),
12.18/12.35	                                    times_times_int,A_53),
12.18/12.35	                     one_one_int) =
12.18/12.35	      A_53))).
12.18/12.35	tff('45', plain,
12.18/12.35	    ![X437 : int]:
12.18/12.35	      app_encode_app(int, int, 
12.18/12.35	        app_encode_app(int, app_encode_fun(int, int), times_times_int, X437), 
12.18/12.35	        one_one_int)
12.18/12.35	       = X437,
12.18/12.35	    inference('cnf', [status(esa)], [zf_stmt_236])).
12.18/12.35	tff('46', plain,
12.18/12.35	    ![X0 : int]:
12.18/12.35	      app_encode_app(int, int, 
12.18/12.35	        app_encode_app(int, app_encode_fun(int, int), times_times_int, X0), 
12.18/12.35	        sk_K_1(one_one_int, one_one_int, min))
12.18/12.35	       = app_encode_app(int, int, bit0, X0),
12.18/12.35	    inference('demod', [status(thm)], ['44', '45'])).
12.18/12.35	tff('47', plain,
12.18/12.35	    ![X0 : int]:
12.18/12.35	      app_encode_app(int, int, 
12.18/12.35	        app_encode_app(int, app_encode_fun(int, int), plus_plus_int, X0), 
12.18/12.35	        one_one_int)
12.18/12.35	       = sk_K_1(one_one_int, X0, min),
12.18/12.35	    inference('sup+', [status(thm)], ['37', '20'])).
12.18/12.35	tff('48', plain,
12.18/12.35	    ![X0 : int]:
12.18/12.35	      sk_K_1(one_one_int, app_encode_app(int, int, bit0, X0), min)
12.18/12.35	       = app_encode_app(int, int, bit1, X0),
12.18/12.35	    inference('demod', [status(thm)], ['16', '37'])).
12.18/12.35	tff(zf_stmt_51, axiom,
12.18/12.35	  (app_encode_app(int,$o,
12.18/12.35	                  app_encode_app(int,app_encode_fun(int,$o),ord_less_eq_int,
12.18/12.35	                                 one_one_int),
12.18/12.35	                  t))).
12.18/12.35	tff('49', plain,
12.18/12.35	    app_encode_app(int, $o, 
12.18/12.35	      app_encode_app(int, app_encode_fun(int, $o), ord_less_eq_int, 
12.18/12.35	        one_one_int), t),
12.18/12.35	    inference('cnf', [status(esa)], [zf_stmt_51])).
12.18/12.35	tff(zf_stmt_88, axiom,
12.18/12.35	  (![Z:int,W:int]:
12.18/12.35	     (app_encode_app(int,$o,
12.18/12.35	                     app_encode_app(int,app_encode_fun(int,$o),ord_less_int,Z),
12.18/12.35	                     W) <=>
12.18/12.35	      (app_encode_app(int,$o,
12.18/12.35	                      app_encode_app(int,app_encode_fun(int,$o),
12.18/12.35	                                     ord_less_eq_int,Z),
12.18/12.35	                      W) & 
12.18/12.35	       (Z != W))))).
12.18/12.35	tff('50', plain,
12.18/12.35	    ![X33 : int, X35 : int]:
12.18/12.35	      (app_encode_app(int, $o, 
12.18/12.35	         app_encode_app(int, app_encode_fun(int, $o), ord_less_int, X33), 
12.18/12.35	         X35)
12.18/12.35	       | X33 = X35
12.18/12.35	       | ~ app_encode_app(int, $o, 
12.18/12.35	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq_int, 
12.18/12.35	               X33), X35)),
12.18/12.35	    inference('cnf', [status(esa)], [zf_stmt_88])).
12.18/12.35	tff('51', plain,
12.18/12.35	    (~ $true
12.18/12.35	     | one_one_int = t
12.18/12.35	     | app_encode_app(int, $o, 
12.18/12.35	         app_encode_app(int, app_encode_fun(int, $o), ord_less_int, 
12.18/12.35	           one_one_int), t)),
12.18/12.35	    inference('sup-', [status(thm)], ['49', '50'])).
12.18/12.35	tff('52', plain,
12.18/12.35	    (app_encode_app(int, $o, 
12.18/12.35	       app_encode_app(int, app_encode_fun(int, $o), ord_less_int, 
12.18/12.35	         one_one_int), t)
12.18/12.35	     | one_one_int = t),
12.18/12.35	    inference('simplify', [status(thm)], ['51'])).
12.18/12.35	tff(zf_stmt_53, axiom,
12.18/12.35	  (app_encode_app(int,$o,
12.18/12.35	                  app_encode_app(int,app_encode_fun(int,$o),ord_less_int,
12.18/12.35	                                 one_one_int),
12.18/12.35	                  t) =>
12.18/12.35	   (?[X:int,Y:int]:
12.18/12.35	      (app_encode_app(int,int,
12.18/12.35	                      app_encode_app(int,app_encode_fun(int,int),
12.18/12.35	                                     plus_plus_int,
12.18/12.35	                                     app_encode_app(nat,int,
12.18/12.35	                                                    app_encode_app(int,
12.18/12.35	                                                                   app_encode_fun(
12.18/12.35	                                                                   nat,int),
12.18/12.35	                                                                   power_power_int,
12.18/12.35	                                                                   X),
12.18/12.35	                                                    app_encode_app(int,nat,
12.18/12.35	                                                                   number_number_of_nat,
12.18/12.35	                                                                   app_encode_app(
12.18/12.35	                                                                   int,int,
12.18/12.35	                                                                   bit0,
12.18/12.35	                                                                   app_encode_app(
12.18/12.35	                                                                   int,int,
12.18/12.35	                                                                   bit1,pls))))),
12.18/12.35	                      app_encode_app(nat,int,
12.18/12.35	                                     app_encode_app(int,
12.18/12.35	                                                    app_encode_fun(nat,int),
12.18/12.35	                                                    power_power_int,Y),
12.18/12.35	                                     app_encode_app(int,nat,
12.18/12.35	                                                    number_number_of_nat,
12.18/12.35	                                                    app_encode_app(int,int,
12.18/12.35	                                                                   bit0,
12.18/12.35	                                                                   app_encode_app(
12.18/12.35	                                                                   int,int,
12.18/12.35	                                                                   bit1,pls))))) =
12.18/12.35	       app_encode_app(int,int,
12.18/12.35	                      app_encode_app(int,app_encode_fun(int,int),
12.18/12.35	                                     plus_plus_int,
12.18/12.35	                                     app_encode_app(int,int,
12.18/12.35	                                                    app_encode_app(int,
12.18/12.35	                                                                   app_encode_fun(
12.18/12.35	                                                                   int,int),
12.18/12.35	                                                                   times_times_int,
12.18/12.35	                                                                   app_encode_app(
12.18/12.35	                                                                   int,int,
12.18/12.35	                                                                   number_number_of_int,
12.18/12.35	                                                                   app_encode_app(
12.18/12.35	                                                                   int,int,
12.18/12.35	                                                                   bit0,
12.18/12.35	                                                                   app_encode_app(
12.18/12.35	                                                                   int,int,
12.18/12.35	                                                                   bit0,
12.18/12.35	                                                                   app_encode_app(
12.18/12.35	                                                                   int,int,
12.18/12.35	                                                                   bit1,pls))))),
12.18/12.35	                                                    m)),
12.18/12.35	                      one_one_int))))).
12.18/12.35	tff('53', plain,
12.18/12.35	    (app_encode_app(int, int, 
12.18/12.35	       app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.35	         app_encode_app(nat, int, 
12.18/12.35	           app_encode_app(int, app_encode_fun(nat, int), power_power_int, 
12.18/12.35	             sk_X1), 
12.18/12.35	           app_encode_app(int, nat, number_number_of_nat, 
12.18/12.35	             app_encode_app(int, int, bit0, 
12.18/12.35	               app_encode_app(int, int, bit1, pls))))), 
12.18/12.35	       app_encode_app(nat, int, 
12.18/12.35	         app_encode_app(int, app_encode_fun(nat, int), power_power_int, 
12.18/12.35	           sk_Y1), 
12.18/12.35	         app_encode_app(int, nat, number_number_of_nat, 
12.18/12.35	           app_encode_app(int, int, bit0, 
12.18/12.35	             app_encode_app(int, int, bit1, pls)))))
12.18/12.35	      = app_encode_app(int, int, 
12.18/12.35	          app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.35	            app_encode_app(int, int, 
12.18/12.35	              app_encode_app(int, app_encode_fun(int, int), times_times_int, 
12.18/12.35	                app_encode_app(int, int, number_number_of_int, 
12.18/12.35	                  app_encode_app(int, int, bit0, 
12.18/12.35	                    app_encode_app(int, int, bit0, 
12.18/12.35	                      app_encode_app(int, int, bit1, pls))))), m)), 
12.18/12.35	          one_one_int)
12.18/12.35	     | ~ app_encode_app(int, $o, 
12.18/12.35	           app_encode_app(int, app_encode_fun(int, $o), ord_less_int, 
12.18/12.35	             one_one_int), t)),
12.18/12.35	    inference('cnf', [status(esa)], [zf_stmt_53])).
12.18/12.35	tff('54', plain,
12.18/12.35	    (app_encode_app(int, int, 
12.18/12.35	       app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.35	         app_encode_app(nat, int, 
12.18/12.35	           app_encode_app(int, app_encode_fun(nat, int), power_power_int, 
12.18/12.35	             sk_X1), 
12.18/12.35	           app_encode_app(int, nat, number_number_of_nat, 
12.18/12.35	             app_encode_app(int, int, bit0, 
12.18/12.35	               app_encode_app(int, int, bit1, pls))))), 
12.18/12.35	       app_encode_app(nat, int, 
12.18/12.35	         app_encode_app(int, app_encode_fun(nat, int), power_power_int, 
12.18/12.35	           sk_Y1), 
12.18/12.35	         app_encode_app(int, nat, number_number_of_nat, 
12.18/12.35	           app_encode_app(int, int, bit0, 
12.18/12.35	             app_encode_app(int, int, bit1, pls)))))
12.18/12.35	      = app_encode_app(int, int, 
12.18/12.35	          app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.35	            app_encode_app(int, int, 
12.18/12.35	              app_encode_app(int, app_encode_fun(int, int), times_times_int, 
12.18/12.35	                app_encode_app(int, int, bit0, 
12.18/12.35	                  app_encode_app(int, int, bit0, 
12.18/12.35	                    app_encode_app(int, int, bit1, pls)))), m)), one_one_int)
12.18/12.35	     | ~ app_encode_app(int, $o, 
12.18/12.35	           app_encode_app(int, app_encode_fun(int, $o), ord_less_int, 
12.18/12.35	             one_one_int), t)),
12.18/12.35	    inference('demod', [status(thm)], ['53', '1'])).
12.18/12.35	tff('55', plain,
12.18/12.35	    (app_encode_app(int, int, 
12.18/12.35	       app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.35	         app_encode_app(nat, int, 
12.18/12.35	           app_encode_app(int, app_encode_fun(nat, int), power_power_int, 
12.18/12.35	             sk_X1), 
12.18/12.35	           app_encode_app(int, nat, number_number_of_nat, 
12.18/12.35	             app_encode_app(int, int, bit0, one_one_int)))), 
12.18/12.35	       app_encode_app(nat, int, 
12.18/12.35	         app_encode_app(int, app_encode_fun(nat, int), power_power_int, 
12.18/12.35	           sk_Y1), 
12.18/12.35	         app_encode_app(int, nat, number_number_of_nat, 
12.18/12.35	           app_encode_app(int, int, bit0, one_one_int))))
12.18/12.35	      = app_encode_app(int, int, 
12.18/12.35	          app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.35	            app_encode_app(int, int, 
12.18/12.35	              app_encode_app(int, app_encode_fun(int, int), times_times_int, 
12.18/12.35	                app_encode_app(int, int, bit0, 
12.18/12.35	                  app_encode_app(int, int, bit0, one_one_int))), m)), 
12.18/12.35	          one_one_int)
12.18/12.35	     | ~ app_encode_app(int, $o, 
12.18/12.35	           app_encode_app(int, app_encode_fun(int, $o), ord_less_int, 
12.18/12.35	             one_one_int), t)),
12.18/12.35	    inference('demod', [status(thm)], ['54', '4', '4', '4'])).
12.18/12.35	tff('56', plain,
12.18/12.35	    (app_encode_app(int, int, 
12.18/12.35	       app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.35	         app_encode_app(nat, int, 
12.18/12.35	           app_encode_app(int, app_encode_fun(nat, int), power_power_int, 
12.18/12.35	             sk_X1), 
12.18/12.35	           app_encode_app(int, nat, number_number_of_nat, 
12.18/12.35	             sk_K_1(one_one_int, one_one_int, min)))), 
12.18/12.35	       app_encode_app(nat, int, 
12.18/12.35	         app_encode_app(int, app_encode_fun(nat, int), power_power_int, 
12.18/12.35	           sk_Y1), 
12.18/12.35	         app_encode_app(int, nat, number_number_of_nat, 
12.18/12.35	           sk_K_1(one_one_int, one_one_int, min))))
12.18/12.35	      = app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m))
12.18/12.35	     | ~ app_encode_app(int, $o, 
12.18/12.35	           app_encode_app(int, app_encode_fun(int, $o), ord_less_int, 
12.18/12.35	             one_one_int), t)),
12.18/12.35	    inference('demod', [status(thm)],
12.18/12.35	              ['55', '38', '38', '38', '43', '46', '47', '48'])).
12.18/12.35	tff(zf_stmt_749, conjecture,
12.18/12.35	  (?[X:int,Y:int]:
12.18/12.35	     (app_encode_app(int,int,
12.18/12.35	                     app_encode_app(int,app_encode_fun(int,int),
12.18/12.35	                                    plus_plus_int,
12.18/12.35	                                    app_encode_app(nat,int,
12.18/12.35	                                                   app_encode_app(int,
12.18/12.35	                                                                  app_encode_fun(
12.18/12.35	                                                                  nat,int),
12.18/12.35	                                                                  power_power_int,
12.18/12.35	                                                                  X),
12.18/12.35	                                                   app_encode_app(int,nat,
12.18/12.35	                                                                  number_number_of_nat,
12.18/12.35	                                                                  app_encode_app(
12.18/12.35	                                                                  int,int,
12.18/12.35	                                                                  bit0,
12.18/12.35	                                                                  app_encode_app(
12.18/12.35	                                                                  int,int,
12.18/12.35	                                                                  bit1,pls))))),
12.18/12.35	                     app_encode_app(nat,int,
12.18/12.35	                                    app_encode_app(int,
12.18/12.35	                                                   app_encode_fun(nat,int),
12.18/12.35	                                                   power_power_int,Y),
12.18/12.35	                                    app_encode_app(int,nat,
12.18/12.35	                                                   number_number_of_nat,
12.18/12.35	                                                   app_encode_app(int,int,
12.18/12.35	                                                                  bit0,
12.18/12.35	                                                                  app_encode_app(
12.18/12.35	                                                                  int,int,
12.18/12.35	                                                                  bit1,pls))))) =
12.18/12.35	      app_encode_app(int,int,
12.18/12.35	                     app_encode_app(int,app_encode_fun(int,int),
12.18/12.35	                                    plus_plus_int,
12.18/12.35	                                    app_encode_app(int,int,
12.18/12.35	                                                   app_encode_app(int,
12.18/12.35	                                                                  app_encode_fun(
12.18/12.35	                                                                  int,int),
12.18/12.35	                                                                  times_times_int,
12.18/12.35	                                                                  app_encode_app(
12.18/12.35	                                                                  int,int,
12.18/12.35	                                                                  number_number_of_int,
12.18/12.35	                                                                  app_encode_app(
12.18/12.35	                                                                  int,int,
12.18/12.35	                                                                  bit0,
12.18/12.35	                                                                  app_encode_app(
12.18/12.35	                                                                  int,int,
12.18/12.35	                                                                  bit0,
12.18/12.35	                                                                  app_encode_app(
12.18/12.35	                                                                  int,int,
12.18/12.35	                                                                  bit1,pls))))),
12.18/12.35	                                                   m)),
12.18/12.35	                     one_one_int)))).
12.18/12.35	tff(zf_stmt_0, negated_conjecture,
12.18/12.35	  (~
12.18/12.35	    (?[X:int,Y:int]:
12.18/12.35	       (app_encode_app(int,int,
12.18/12.35	                       app_encode_app(int,app_encode_fun(int,int),
12.18/12.35	                                      plus_plus_int,
12.18/12.35	                                      app_encode_app(nat,int,
12.18/12.35	                                                     app_encode_app(int,
12.18/12.35	                                                                    app_encode_fun(
12.18/12.35	                                                                    nat,int),
12.18/12.35	                                                                    power_power_int,
12.18/12.35	                                                                    X),
12.18/12.35	                                                     app_encode_app(int,nat,
12.18/12.35	                                                                    number_number_of_nat,
12.18/12.35	                                                                    app_encode_app(
12.18/12.35	                                                                    int,int,
12.18/12.35	                                                                    bit0,
12.18/12.35	                                                                    app_encode_app(
12.18/12.35	                                                                    int,int,
12.18/12.35	                                                                    bit1,pls))))),
12.18/12.35	                       app_encode_app(nat,int,
12.18/12.35	                                      app_encode_app(int,
12.18/12.35	                                                     app_encode_fun(nat,int),
12.18/12.35	                                                     power_power_int,Y),
12.18/12.35	                                      app_encode_app(int,nat,
12.18/12.35	                                                     number_number_of_nat,
12.18/12.35	                                                     app_encode_app(int,int,
12.18/12.35	                                                                    bit0,
12.18/12.35	                                                                    app_encode_app(
12.18/12.35	                                                                    int,int,
12.18/12.35	                                                                    bit1,pls))))) =
12.18/12.35	        app_encode_app(int,int,
12.18/12.35	                       app_encode_app(int,app_encode_fun(int,int),
12.18/12.35	                                      plus_plus_int,
12.18/12.35	                                      app_encode_app(int,int,
12.18/12.35	                                                     app_encode_app(int,
12.18/12.35	                                                                    app_encode_fun(
12.18/12.35	                                                                    int,int),
12.18/12.35	                                                                    times_times_int,
12.18/12.35	                                                                    app_encode_app(
12.18/12.35	                                                                    int,int,
12.18/12.35	                                                                    number_number_of_int,
12.18/12.35	                                                                    app_encode_app(
12.18/12.35	                                                                    int,int,
12.18/12.35	                                                                    bit0,
12.18/12.35	                                                                    app_encode_app(
12.18/12.35	                                                                    int,int,
12.18/12.35	                                                                    bit0,
12.18/12.35	                                                                    app_encode_app(
12.18/12.35	                                                                    int,int,
12.18/12.35	                                                                    bit1,pls))))),
12.18/12.35	                                                     m)),
12.18/12.35	                       one_one_int))))).
12.18/12.35	tff('57', plain,
12.18/12.35	    ![X1501 : int, X1502 : int]:
12.18/12.35	      app_encode_app(int, int, 
12.18/12.35	        app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.35	          app_encode_app(nat, int, 
12.18/12.35	            app_encode_app(int, app_encode_fun(nat, int), power_power_int, 
12.18/12.35	              X1501), 
12.18/12.35	            app_encode_app(int, nat, number_number_of_nat, 
12.18/12.35	              app_encode_app(int, int, bit0, 
12.18/12.35	                app_encode_app(int, int, bit1, pls))))), 
12.18/12.35	        app_encode_app(nat, int, 
12.18/12.35	          app_encode_app(int, app_encode_fun(nat, int), power_power_int, 
12.18/12.35	            X1502), 
12.18/12.35	          app_encode_app(int, nat, number_number_of_nat, 
12.18/12.35	            app_encode_app(int, int, bit0, 
12.18/12.35	              app_encode_app(int, int, bit1, pls)))))
12.18/12.35	       != app_encode_app(int, int, 
12.18/12.35	            app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.35	              app_encode_app(int, int, 
12.18/12.35	                app_encode_app(int, app_encode_fun(int, int), 
12.18/12.35	                  times_times_int, 
12.18/12.35	                  app_encode_app(int, int, number_number_of_int, 
12.18/12.35	                    app_encode_app(int, int, bit0, 
12.18/12.35	                      app_encode_app(int, int, bit0, 
12.18/12.35	                        app_encode_app(int, int, bit1, pls))))), m)), 
12.18/12.35	            one_one_int),
12.18/12.35	    inference('cnf', [status(esa)], [zf_stmt_0])).
12.18/12.35	tff('58', plain,
12.18/12.35	    ![X1501 : int, X1502 : int]:
12.18/12.35	      app_encode_app(int, int, 
12.18/12.35	        app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.35	          app_encode_app(nat, int, 
12.18/12.35	            app_encode_app(int, app_encode_fun(nat, int), power_power_int, 
12.18/12.35	              X1501), 
12.18/12.35	            app_encode_app(int, nat, number_number_of_nat, 
12.18/12.35	              sk_K_1(one_one_int, one_one_int, min)))), 
12.18/12.35	        app_encode_app(nat, int, 
12.18/12.35	          app_encode_app(int, app_encode_fun(nat, int), power_power_int, 
12.18/12.35	            X1502), 
12.18/12.35	          app_encode_app(int, nat, number_number_of_nat, 
12.18/12.35	            sk_K_1(one_one_int, one_one_int, min))))
12.18/12.35	       != app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m)),
12.18/12.35	    inference('demod', [status(thm)],
12.18/12.35	              ['57', '4', '38', '4', '38', '4', '38', '1', '43', '46', '47', 
12.18/12.35	               '48'])).
12.18/12.35	tff('59', plain,
12.18/12.35	    ~ app_encode_app(int, $o, 
12.18/12.35	        app_encode_app(int, app_encode_fun(int, $o), ord_less_int, 
12.18/12.35	          one_one_int), t),
12.18/12.35	    inference('simplify_reflect-', [status(thm)], ['56', '58'])).
12.18/12.35	tff('60', plain, (~ $true | one_one_int = t),
12.18/12.35	    inference('sup-', [status(thm)], ['52', '59'])).
12.18/12.35	tff('61', plain, one_one_int = t,
12.18/12.35	    inference('simplify', [status(thm)], ['60'])).
12.18/12.35	tff('62', plain,
12.18/12.35	    (app_encode_app(int, int, 
12.18/12.35	       app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.35	         app_encode_app(nat, int, 
12.18/12.35	           app_encode_app(int, app_encode_fun(nat, int), power_power_int, 
12.18/12.35	             sk_X), 
12.18/12.35	           app_encode_app(int, nat, number_number_of_nat, 
12.18/12.35	             sk_K_1(one_one_int, one_one_int, min)))), 
12.18/12.35	       app_encode_app(nat, int, 
12.18/12.35	         app_encode_app(int, app_encode_fun(nat, int), power_power_int, sk_Y), 
12.18/12.35	         app_encode_app(int, nat, number_number_of_nat, 
12.18/12.35	           sk_K_1(one_one_int, one_one_int, min))))
12.18/12.35	      = app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m))
12.18/12.35	     | one_one_int != one_one_int),
12.18/12.35	    inference('demod', [status(thm)],
12.18/12.35	              ['5', '38', '38', '38', '43', '46', '47', '48', '61'])).
12.18/12.35	tff('63', plain,
12.18/12.35	    app_encode_app(int, int, 
12.18/12.35	      app_encode_app(int, app_encode_fun(int, int), plus_plus_int, 
12.18/12.35	        app_encode_app(nat, int, 
12.18/12.35	          app_encode_app(int, app_encode_fun(nat, int), power_power_int, 
12.18/12.35	            sk_X), 
12.18/12.35	          app_encode_app(int, nat, number_number_of_nat, 
12.18/12.35	            sk_K_1(one_one_int, one_one_int, min)))), 
12.18/12.35	      app_encode_app(nat, int, 
12.18/12.35	        app_encode_app(int, app_encode_fun(nat, int), power_power_int, sk_Y), 
12.18/12.35	        app_encode_app(int, nat, number_number_of_nat, 
12.18/12.35	          sk_K_1(one_one_int, one_one_int, min))))
12.18/12.35	     = app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m)),
12.18/12.35	    inference('simplify', [status(thm)], ['62'])).
12.18/12.35	tff('64', plain, $false,
12.18/12.35	    inference('simplify_reflect-', [status(thm)], ['63', '58'])).
12.18/12.35	
12.18/12.35	% SZS output end Refutation
12.18/12.35	EOF
