0.00/0.00	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : appext
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : rpo6
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   : n127.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
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 08:01:54 CST 2018
3.20/3.40	% done 1255 iterations in 3.201s
3.20/3.40	% SZS status Theorem for 'stdin'
3.20/3.40	% SZS output start Refutation
3.24/3.41	tff(zf_stmt_52, axiom,
3.24/3.41	  (app_encode_app(int,int,
3.24/3.41	                  app_encode_app(int,app_encode_fun(int,int),plus_plus(int),
3.24/3.41	                                 app_encode_app(nat,int,
3.24/3.41	                                                app_encode_app(int,
3.24/3.41	                                                               app_encode_fun(
3.24/3.41	                                                               nat,int),
3.24/3.41	                                                               power_power(
3.24/3.41	                                                               int),s),
3.24/3.41	                                                app_encode_app(int,nat,
3.24/3.41	                                                               number_number_of(
3.24/3.41	                                                               nat),
3.24/3.41	                                                               app_encode_app(
3.24/3.41	                                                               int,int,bit0,
3.24/3.41	                                                               app_encode_app(
3.24/3.41	                                                               int,int,bit1,
3.24/3.41	                                                               pls))))),
3.24/3.41	                  one_one(int)) =
3.24/3.41	   app_encode_app(int,int,
3.24/3.41	                  app_encode_app(int,app_encode_fun(int,int),
3.24/3.41	                                 times_times(int),
3.24/3.41	                                 app_encode_app(int,int,
3.24/3.41	                                                app_encode_app(int,
3.24/3.41	                                                               app_encode_fun(
3.24/3.41	                                                               int,int),
3.24/3.41	                                                               plus_plus(int),
3.24/3.41	                                                               app_encode_app(
3.24/3.41	                                                               int,int,
3.24/3.41	                                                               app_encode_app(
3.24/3.41	                                                               int,
3.24/3.41	                                                               app_encode_fun(
3.24/3.41	                                                               int,int),
3.24/3.41	                                                               times_times(
3.24/3.41	                                                               int),
3.24/3.41	                                                               app_encode_app(
3.24/3.41	                                                               int,int,
3.24/3.41	                                                               number_number_of(
3.24/3.41	                                                               int),
3.24/3.41	                                                               app_encode_app(
3.24/3.41	                                                               int,int,bit0,
3.24/3.41	                                                               app_encode_app(
3.24/3.41	                                                               int,int,bit0,
3.24/3.41	                                                               app_encode_app(
3.24/3.41	                                                               int,int,bit1,
3.24/3.41	                                                               pls))))),m)),
3.24/3.41	                                                one_one(int))),
3.24/3.41	                  t))).
3.24/3.41	tff('0', plain,
3.24/3.41	    app_encode_app(int, int, 
3.24/3.41	      app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.24/3.41	        app_encode_app(nat, int, 
3.24/3.41	          app_encode_app(int, app_encode_fun(nat, int), power_power(int), s), 
3.24/3.41	          app_encode_app(int, nat, number_number_of(nat), 
3.24/3.41	            app_encode_app(int, int, bit0, 
3.24/3.41	              app_encode_app(int, int, bit1, pls))))), one_one(int))
3.24/3.41	     = app_encode_app(int, int, 
3.24/3.41	         app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.24/3.41	           app_encode_app(int, int, 
3.24/3.41	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.24/3.41	               app_encode_app(int, int, 
3.24/3.41	                 app_encode_app(int, app_encode_fun(int, int), 
3.24/3.41	                   times_times(int), 
3.24/3.41	                   app_encode_app(int, int, number_number_of(int), 
3.24/3.41	                     app_encode_app(int, int, bit0, 
3.24/3.41	                       app_encode_app(int, int, bit0, 
3.24/3.41	                         app_encode_app(int, int, bit1, pls))))), m)), 
3.24/3.41	             one_one(int))), t),
3.24/3.41	    inference('cnf', [status(esa)], [zf_stmt_52])).
3.24/3.41	tff(zf_stmt_106, axiom,
3.24/3.41	  (one_one(int) =
3.24/3.41	   app_encode_app(int,int,number_number_of(int),
3.24/3.41	                  app_encode_app(int,int,bit1,pls)))).
3.24/3.41	tff('1', plain,
3.24/3.41	    one_one(int)
3.24/3.41	     = app_encode_app(int, int, number_number_of(int), 
3.24/3.41	         app_encode_app(int, int, bit1, pls)),
3.24/3.41	    inference('cnf', [status(esa)], [zf_stmt_106])).
3.24/3.41	tff(zf_stmt_86, axiom,
3.24/3.41	  (![K1:int]: (app_encode_app(int,int,number_number_of(int),K1) = K1))).
3.24/3.41	tff('2', plain,
3.24/3.41	    ![X82 : int]: app_encode_app(int, int, number_number_of(int), X82) = X82,
3.24/3.41	    inference('cnf', [status(esa)], [zf_stmt_86])).
3.24/3.41	tff('3', plain, one_one(int) = app_encode_app(int, int, bit1, pls),
3.24/3.41	    inference('demod', [status(thm)], ['1', '2'])).
3.24/3.41	tff(zf_stmt_67, axiom,
3.24/3.41	  (![L1:int,K1:int]:
3.24/3.41	     (app_encode_app(int,int,
3.24/3.41	                     app_encode_app(int,app_encode_fun(int,int),
3.24/3.41	                                    times_times(int),
3.24/3.41	                                    app_encode_app(int,int,bit0,K1)),
3.24/3.41	                     L1) =
3.24/3.41	      app_encode_app(int,int,bit0,
3.24/3.41	                     app_encode_app(int,int,
3.24/3.41	                                    app_encode_app(int,
3.24/3.41	                                                   app_encode_fun(int,int),
3.24/3.41	                                                   times_times(int),K1),
3.24/3.41	                                    L1))))).
3.24/3.41	tff('4', plain,
3.24/3.41	    ![X43 : int, X44 : int]:
3.24/3.41	      app_encode_app(int, int, 
3.24/3.41	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.24/3.41	          app_encode_app(int, int, bit0, X43)), X44)
3.24/3.41	       = app_encode_app(int, int, bit0, 
3.24/3.41	           app_encode_app(int, int, 
3.24/3.41	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.24/3.41	               X43), X44)),
3.24/3.41	    inference('cnf', [status(esa)], [zf_stmt_67])).
3.24/3.41	tff(zf_stmt_66, axiom,
3.24/3.41	  (![W:int]:
3.24/3.41	     (app_encode_app(int,int,
3.24/3.41	                     app_encode_app(int,app_encode_fun(int,int),
3.24/3.41	                                    times_times(int),pls),
3.24/3.41	                     W) =
3.24/3.41	      pls))).
3.24/3.41	tff('5', plain,
3.24/3.41	    ![X42 : int]:
3.24/3.41	      app_encode_app(int, int, 
3.24/3.41	        app_encode_app(int, app_encode_fun(int, int), times_times(int), pls), 
3.24/3.41	        X42)
3.24/3.41	       = pls,
3.24/3.41	    inference('cnf', [status(esa)], [zf_stmt_66])).
3.24/3.41	tff(zf_stmt_50, axiom,
3.24/3.41	  (![L1:int,K1:int]:
3.24/3.41	     (app_encode_app(int,int,
3.24/3.41	                     app_encode_app(int,app_encode_fun(int,int),
3.24/3.41	                                    times_times(int),
3.24/3.41	                                    app_encode_app(int,int,bit1,K1)),
3.24/3.41	                     L1) =
3.24/3.41	      app_encode_app(int,int,
3.24/3.41	                     app_encode_app(int,app_encode_fun(int,int),
3.24/3.41	                                    plus_plus(int),
3.24/3.41	                                    app_encode_app(int,int,bit0,
3.24/3.41	                                                   app_encode_app(int,int,
3.24/3.41	                                                                  app_encode_app(
3.24/3.41	                                                                  int,
3.24/3.41	                                                                  app_encode_fun(
3.24/3.41	                                                                  int,int),
3.24/3.41	                                                                  times_times(
3.24/3.41	                                                                  int),K1),L1))),
3.24/3.41	                     L1)))).
3.24/3.41	tff('6', plain,
3.24/3.41	    ![X12 : int, X13 : int]:
3.24/3.41	      app_encode_app(int, int, 
3.24/3.41	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.24/3.41	          app_encode_app(int, int, bit1, X12)), X13)
3.24/3.41	       = app_encode_app(int, int, 
3.24/3.41	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.24/3.41	             app_encode_app(int, int, bit0, 
3.24/3.41	               app_encode_app(int, int, 
3.24/3.41	                 app_encode_app(int, app_encode_fun(int, int), 
3.24/3.41	                   times_times(int), X12), X13))), X13),
3.24/3.41	    inference('cnf', [status(esa)], [zf_stmt_50])).
3.24/3.41	tff('7', plain,
3.24/3.41	    ![X0 : int]:
3.24/3.41	      app_encode_app(int, int, 
3.24/3.41	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.24/3.41	          app_encode_app(int, int, bit1, pls)), X0)
3.24/3.41	       = app_encode_app(int, int, 
3.24/3.41	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.24/3.41	             app_encode_app(int, int, bit0, pls)), X0),
3.24/3.41	    inference('sup+', [status(thm)], ['5', '6'])).
3.24/3.41	tff(zf_stmt_65, axiom, (app_encode_app(int,int,bit0,pls) = pls)).
3.24/3.41	tff('8', plain, app_encode_app(int, int, bit0, pls) = pls,
3.24/3.41	    inference('cnf', [status(esa)], [zf_stmt_65])).
3.24/3.41	tff(zf_stmt_89, axiom,
3.24/3.41	  (![K1:int]:
3.24/3.41	     (app_encode_app(int,int,
3.24/3.41	                     app_encode_app(int,app_encode_fun(int,int),
3.24/3.41	                                    plus_plus(int),pls),
3.24/3.41	                     K1) =
3.24/3.41	      K1))).
3.24/3.41	tff('9', plain,
3.24/3.41	    ![X87 : int]:
3.24/3.41	      app_encode_app(int, int, 
3.24/3.41	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
3.24/3.41	        X87)
3.24/3.41	       = X87,
3.24/3.41	    inference('cnf', [status(esa)], [zf_stmt_89])).
3.24/3.41	tff('10', plain,
3.24/3.41	    ![X0 : int]:
3.24/3.41	      app_encode_app(int, int, 
3.24/3.41	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.24/3.41	          app_encode_app(int, int, bit1, pls)), X0)
3.24/3.41	       = X0,
3.24/3.41	    inference('demod', [status(thm)], ['7', '8', '9'])).
3.24/3.41	tff(zf_stmt_41, axiom, (t = one_one(int))).
3.24/3.41	tff('11', plain, t = one_one(int),
3.24/3.41	    inference('cnf', [status(esa)], [zf_stmt_41])).
3.24/3.41	tff('12', plain, t = app_encode_app(int, int, bit1, pls),
3.24/3.41	    inference('demod', [status(thm)], ['11', '3'])).
3.24/3.41	tff('13', plain,
3.24/3.41	    app_encode_app(int, int, 
3.24/3.41	      app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.24/3.41	        app_encode_app(nat, int, 
3.24/3.41	          app_encode_app(int, app_encode_fun(nat, int), power_power(int), s), 
3.24/3.41	          app_encode_app(int, nat, number_number_of(nat), 
3.24/3.41	            app_encode_app(int, int, bit0, 
3.24/3.41	              app_encode_app(int, int, bit1, pls))))), 
3.24/3.41	      app_encode_app(int, int, bit1, pls))
3.24/3.41	     = app_encode_app(int, int, 
3.24/3.41	         app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.24/3.41	           app_encode_app(int, int, 
3.24/3.41	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.24/3.41	               app_encode_app(int, int, bit0, 
3.24/3.41	                 app_encode_app(int, int, bit0, m))), 
3.24/3.41	             app_encode_app(int, int, bit1, pls))), 
3.24/3.41	         app_encode_app(int, int, bit1, pls)),
3.24/3.41	    inference('demod', [status(thm)],
3.24/3.41	              ['0', '3', '2', '4', '4', '10', '3', '12'])).
3.24/3.41	tff(zf_stmt_77, axiom,
3.24/3.41	  (![L1:int,K1:int]:
3.24/3.41	     (app_encode_app(int,int,
3.24/3.41	                     app_encode_app(int,app_encode_fun(int,int),
3.24/3.41	                                    plus_plus(int),
3.24/3.41	                                    app_encode_app(int,int,bit0,K1)),
3.24/3.41	                     app_encode_app(int,int,bit1,L1)) =
3.24/3.41	      app_encode_app(int,int,bit1,
3.24/3.41	                     app_encode_app(int,int,
3.24/3.41	                                    app_encode_app(int,
3.24/3.41	                                                   app_encode_fun(int,int),
3.24/3.41	                                                   plus_plus(int),K1),
3.24/3.41	                                    L1))))).
3.24/3.41	tff('14', plain,
3.24/3.41	    ![X71 : int, X72 : int]:
3.24/3.41	      app_encode_app(int, int, 
3.24/3.41	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.24/3.41	          app_encode_app(int, int, bit0, X71)), 
3.24/3.41	        app_encode_app(int, int, bit1, X72))
3.24/3.41	       = app_encode_app(int, int, bit1, 
3.24/3.41	           app_encode_app(int, int, 
3.24/3.41	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.24/3.41	               X71), X72)),
3.24/3.41	    inference('cnf', [status(esa)], [zf_stmt_77])).
3.24/3.41	tff(zf_stmt_88, axiom,
3.24/3.41	  (![K1:int]:
3.24/3.41	     (app_encode_app(int,int,
3.24/3.41	                     app_encode_app(int,app_encode_fun(int,int),
3.24/3.41	                                    plus_plus(int),K1),
3.24/3.41	                     pls) =
3.24/3.41	      K1))).
3.24/3.41	tff('15', plain,
3.24/3.41	    ![X86 : int]:
3.24/3.41	      app_encode_app(int, int, 
3.24/3.41	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X86), 
3.24/3.41	        pls)
3.24/3.41	       = X86,
3.24/3.41	    inference('cnf', [status(esa)], [zf_stmt_88])).
3.24/3.41	tff('16', plain,
3.24/3.41	    app_encode_app(int, int, 
3.24/3.41	      app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.24/3.41	        app_encode_app(nat, int, 
3.24/3.41	          app_encode_app(int, app_encode_fun(nat, int), power_power(int), s), 
3.24/3.41	          app_encode_app(int, nat, number_number_of(nat), 
3.24/3.41	            app_encode_app(int, int, bit0, 
3.24/3.41	              app_encode_app(int, int, bit1, pls))))), 
3.24/3.41	      app_encode_app(int, int, bit1, pls))
3.24/3.41	     = app_encode_app(int, int, bit1, 
3.24/3.41	         app_encode_app(int, int, bit0, 
3.24/3.41	           app_encode_app(int, int, 
3.24/3.41	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.24/3.41	               m), app_encode_app(int, int, bit1, pls)))),
3.24/3.41	    inference('demod', [status(thm)],
3.24/3.41	              ['13', '14', '15', '6', '4', '14', '15'])).
3.24/3.41	tff(zf_stmt_148, axiom, (number(int))).
3.24/3.41	tff('17', plain, number(int), inference('cnf', [status(esa)], [zf_stmt_148])).
3.24/3.41	tff(zf_stmt_44, axiom,
3.24/3.41	  (![B1:$tType]:
3.24/3.41	     ((monoid_mult(B1) & number(B1)) =>
3.24/3.41	      (![W:int]:
3.24/3.41	         (app_encode_app(nat,B1,
3.24/3.41	                         app_encode_app(B1,app_encode_fun(nat,B1),
3.24/3.41	                                        power_power(B1),
3.24/3.41	                                        app_encode_app(int,B1,
3.24/3.41	                                                       number_number_of(B1),W)),
3.24/3.41	                         app_encode_app(int,nat,number_number_of(nat),
3.24/3.41	                                        app_encode_app(int,int,bit0,
3.24/3.41	                                                       app_encode_app(
3.24/3.41	                                                       int,int,bit1,pls)))) =
3.24/3.41	          app_encode_app(B1,B1,
3.24/3.41	                         app_encode_app(B1,app_encode_fun(B1,B1),
3.24/3.41	                                        times_times(B1),
3.24/3.41	                                        app_encode_app(int,B1,
3.24/3.41	                                                       number_number_of(B1),W)),
3.24/3.41	                         app_encode_app(int,B1,number_number_of(B1),W))))))).
3.24/3.41	tff('18', plain,
3.24/3.41	    ![X4 : $tType, X5 : int]:
3.24/3.41	      (app_encode_app(nat, X4, 
3.24/3.41	         app_encode_app(X4, app_encode_fun(nat, X4), power_power(X4), 
3.24/3.41	           app_encode_app(int, X4, number_number_of(X4), X5)), 
3.24/3.41	         app_encode_app(int, nat, number_number_of(nat), 
3.24/3.41	           app_encode_app(int, int, bit0, 
3.24/3.41	             app_encode_app(int, int, bit1, pls))))
3.24/3.41	        = app_encode_app(X4, X4, 
3.24/3.41	            app_encode_app(X4, app_encode_fun(X4, X4), times_times(X4), 
3.24/3.41	              app_encode_app(int, X4, number_number_of(X4), X5)), 
3.24/3.41	            app_encode_app(int, X4, number_number_of(X4), X5))
3.24/3.41	       | ~ number(X4)
3.24/3.41	       | ~ monoid_mult(X4)),
3.24/3.41	    inference('cnf', [status(esa)], [zf_stmt_44])).
3.24/3.41	tff('19', plain,
3.24/3.41	    ![X0 : int]:
3.24/3.41	      (~ $true
3.24/3.41	       | ~ monoid_mult(int)
3.24/3.41	       | app_encode_app(nat, int, 
3.24/3.41	           app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
3.24/3.41	             app_encode_app(int, int, number_number_of(int), X0)), 
3.24/3.41	           app_encode_app(int, nat, number_number_of(nat), 
3.24/3.41	             app_encode_app(int, int, bit0, 
3.24/3.41	               app_encode_app(int, int, bit1, pls))))
3.24/3.41	          = app_encode_app(int, int, 
3.24/3.41	              app_encode_app(int, app_encode_fun(int, int), 
3.24/3.41	                times_times(int), 
3.24/3.41	                app_encode_app(int, int, number_number_of(int), X0)), 
3.24/3.41	              app_encode_app(int, int, number_number_of(int), X0))),
3.24/3.41	    inference('sup-', [status(thm)], ['17', '18'])).
3.24/3.41	tff(zf_stmt_143, axiom, (monoid_mult(int))).
3.24/3.41	tff('20', plain, monoid_mult(int),
3.24/3.41	    inference('cnf', [status(esa)], [zf_stmt_143])).
3.24/3.41	tff('21', plain,
3.24/3.41	    ![X0 : int]:
3.24/3.41	      (~ $true
3.24/3.41	       | ~ $true
3.24/3.41	       | app_encode_app(nat, int, 
3.24/3.41	           app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
3.24/3.41	             app_encode_app(int, int, number_number_of(int), X0)), 
3.24/3.41	           app_encode_app(int, nat, number_number_of(nat), 
3.24/3.41	             app_encode_app(int, int, bit0, 
3.24/3.41	               app_encode_app(int, int, bit1, pls))))
3.24/3.41	          = app_encode_app(int, int, 
3.24/3.41	              app_encode_app(int, app_encode_fun(int, int), 
3.24/3.41	                times_times(int), 
3.24/3.41	                app_encode_app(int, int, number_number_of(int), X0)), 
3.24/3.41	              app_encode_app(int, int, number_number_of(int), X0))),
3.24/3.41	    inference('demod', [status(thm)], ['19', '20'])).
3.24/3.41	tff('22', plain,
3.24/3.41	    ![X0 : int]:
3.24/3.41	      app_encode_app(nat, int, 
3.24/3.41	        app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
3.24/3.41	          app_encode_app(int, int, number_number_of(int), X0)), 
3.24/3.41	        app_encode_app(int, nat, number_number_of(nat), 
3.24/3.41	          app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls))))
3.24/3.41	       = app_encode_app(int, int, 
3.24/3.41	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.24/3.41	             app_encode_app(int, int, number_number_of(int), X0)), 
3.24/3.41	           app_encode_app(int, int, number_number_of(int), X0)),
3.24/3.41	    inference('simplify', [status(thm)], ['21'])).
3.24/3.41	tff('23', plain,
3.24/3.41	    ![X0 : int]:
3.24/3.41	      app_encode_app(nat, int, 
3.24/3.41	        app_encode_app(int, app_encode_fun(nat, int), power_power(int), X0), 
3.24/3.41	        app_encode_app(int, nat, number_number_of(nat), 
3.24/3.41	          app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls))))
3.24/3.41	       = app_encode_app(int, int, 
3.24/3.41	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.24/3.41	             X0), X0),
3.24/3.41	    inference('demod', [status(thm)], ['22', '2', '2', '2'])).
3.24/3.41	tff(zf_stmt_76, axiom,
3.24/3.41	  (![L1:int,K1:int]:
3.24/3.41	     (app_encode_app(int,int,
3.24/3.41	                     app_encode_app(int,app_encode_fun(int,int),
3.24/3.41	                                    plus_plus(int),
3.24/3.41	                                    app_encode_app(int,int,bit1,K1)),
3.24/3.41	                     app_encode_app(int,int,bit0,L1)) =
3.24/3.41	      app_encode_app(int,int,bit1,
3.24/3.41	                     app_encode_app(int,int,
3.24/3.41	                                    app_encode_app(int,
3.24/3.41	                                                   app_encode_fun(int,int),
3.24/3.41	                                                   plus_plus(int),K1),
3.24/3.41	                                    L1))))).
3.24/3.41	tff('24', plain,
3.24/3.41	    ![X69 : int, X70 : int]:
3.24/3.41	      app_encode_app(int, int, 
3.24/3.41	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.24/3.41	          app_encode_app(int, int, bit1, X69)), 
3.24/3.41	        app_encode_app(int, int, bit0, X70))
3.24/3.41	       = app_encode_app(int, int, bit1, 
3.24/3.41	           app_encode_app(int, int, 
3.24/3.41	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.24/3.41	               X69), X70)),
3.24/3.41	    inference('cnf', [status(esa)], [zf_stmt_76])).
3.24/3.41	tff(zf_stmt_146, axiom, (number_ring(int))).
3.24/3.41	tff('25', plain, number_ring(int),
3.24/3.41	    inference('cnf', [status(esa)], [zf_stmt_146])).
3.24/3.41	tff(zf_stmt_103, axiom,
3.24/3.41	  (![A:$tType]:
3.24/3.41	     (number_ring(A) =>
3.24/3.41	      (![A1:A]:
3.24/3.41	         (app_encode_app(A,A,
3.24/3.41	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
3.24/3.41	                                        A1),
3.24/3.41	                         app_encode_app(int,A,number_number_of(A),
3.24/3.41	                                        app_encode_app(int,int,bit1,pls))) =
3.24/3.41	          A1))))).
3.24/3.41	tff('26', plain,
3.24/3.41	    ![X116 : $tType, X117 : X116]:
3.24/3.41	      (app_encode_app(X116, X116, 
3.24/3.41	         app_encode_app(X116, app_encode_fun(X116, X116), times_times(X116), 
3.24/3.41	           X117), 
3.24/3.41	         app_encode_app(int, X116, number_number_of(X116), 
3.24/3.41	           app_encode_app(int, int, bit1, pls)))
3.24/3.41	        = X117
3.24/3.41	       | ~ number_ring(X116)),
3.24/3.41	    inference('cnf', [status(esa)], [zf_stmt_103])).
3.24/3.41	tff('27', plain,
3.24/3.41	    ![X0 : int]:
3.24/3.41	      (~ $true
3.24/3.41	       | app_encode_app(int, int, 
3.24/3.41	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.24/3.41	             X0), 
3.24/3.41	           app_encode_app(int, int, number_number_of(int), 
3.24/3.41	             app_encode_app(int, int, bit1, pls)))
3.24/3.41	          = X0),
3.24/3.41	    inference('sup-', [status(thm)], ['25', '26'])).
3.24/3.41	tff('28', plain,
3.24/3.41	    ![X0 : int]:
3.24/3.41	      (~ $true
3.24/3.41	       | app_encode_app(int, int, 
3.24/3.41	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.24/3.41	             X0), app_encode_app(int, int, bit1, pls))
3.24/3.41	          = X0),
3.24/3.41	    inference('demod', [status(thm)], ['27', '2'])).
3.24/3.41	tff('29', plain,
3.24/3.41	    ![X0 : int]:
3.24/3.41	      app_encode_app(int, int, 
3.24/3.41	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X0), 
3.24/3.41	        app_encode_app(int, int, bit1, pls))
3.24/3.41	       = X0,
3.24/3.41	    inference('simplify', [status(thm)], ['28'])).
3.24/3.41	tff(zf_stmt_93, axiom,
3.24/3.41	  (![Z2:int,Z1:int,W:int]:
3.24/3.41	     (app_encode_app(int,int,
3.24/3.41	                     app_encode_app(int,app_encode_fun(int,int),
3.24/3.41	                                    times_times(int),W),
3.24/3.41	                     app_encode_app(int,int,
3.24/3.41	                                    app_encode_app(int,
3.24/3.41	                                                   app_encode_fun(int,int),
3.24/3.41	                                                   plus_plus(int),Z1),
3.24/3.41	                                    Z2)) =
3.24/3.41	      app_encode_app(int,int,
3.24/3.41	                     app_encode_app(int,app_encode_fun(int,int),
3.24/3.41	                                    plus_plus(int),
3.24/3.41	                                    app_encode_app(int,int,
3.24/3.41	                                                   app_encode_app(int,
3.24/3.41	                                                                  app_encode_fun(
3.24/3.41	                                                                  int,int),
3.24/3.41	                                                                  times_times(
3.24/3.41	                                                                  int),W),
3.24/3.41	                                                   Z1)),
3.24/3.41	                     app_encode_app(int,int,
3.24/3.41	                                    app_encode_app(int,
3.24/3.41	                                                   app_encode_fun(int,int),
3.24/3.41	                                                   times_times(int),W),
3.24/3.41	                                    Z2))))).
3.24/3.41	tff('30', plain,
3.24/3.41	    ![X94 : int, X95 : int, X96 : int]:
3.24/3.41	      app_encode_app(int, int, 
3.24/3.41	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X94), 
3.24/3.41	        app_encode_app(int, int, 
3.24/3.41	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X95), 
3.24/3.41	          X96))
3.24/3.41	       = app_encode_app(int, int, 
3.24/3.41	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.24/3.41	             app_encode_app(int, int, 
3.24/3.41	               app_encode_app(int, app_encode_fun(int, int), 
3.24/3.41	                 times_times(int), X94), X95)), 
3.24/3.41	           app_encode_app(int, int, 
3.24/3.41	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.24/3.41	               X94), X96)),
3.24/3.41	    inference('cnf', [status(esa)], [zf_stmt_93])).
3.24/3.41	tff('31', plain,
3.24/3.41	    ![X0 : int, X1 : int]:
3.24/3.41	      app_encode_app(int, int, 
3.24/3.41	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X0), 
3.24/3.41	        app_encode_app(int, int, 
3.24/3.41	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.24/3.41	            app_encode_app(int, int, bit1, pls)), X1))
3.24/3.41	       = app_encode_app(int, int, 
3.24/3.41	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
3.24/3.41	           app_encode_app(int, int, 
3.24/3.41	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.24/3.41	               X0), X1)),
3.24/3.41	    inference('sup+', [status(thm)], ['29', '30'])).
3.24/3.41	tff('32', plain,
3.24/3.41	    ![X0 : int, X1 : int]:
3.24/3.41	      app_encode_app(int, int, 
3.24/3.41	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X1), 
3.24/3.41	        app_encode_app(int, int, bit1, 
3.24/3.41	          app_encode_app(int, int, 
3.24/3.41	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.24/3.41	              pls), X0)))
3.24/3.41	       = app_encode_app(int, int, 
3.24/3.41	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X1), 
3.24/3.41	           app_encode_app(int, int, 
3.24/3.41	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.24/3.41	               X1), app_encode_app(int, int, bit0, X0))),
3.24/3.41	    inference('sup+', [status(thm)], ['24', '31'])).
3.24/3.41	tff(zf_stmt_2, axiom,
3.24/3.41	  (![X:app_encode_fun(Alpha,Beta),Y:app_encode_fun(Alpha,Beta)]:
3.24/3.41	     ((![Z:Alpha]:
3.24/3.41	         (app_encode_app(Alpha,Beta,X,Z) = app_encode_app(Alpha,Beta,Y,Z))) =>
3.24/3.41	      (X = Y)))).
3.24/3.41	tff('33', plain,
3.24/3.41	    ![X0 : $tType, X1 : $tType, X2 : app_encode_fun(X0, X1), 
3.24/3.41	      X3 : app_encode_fun(X0, X1)]:
3.24/3.41	      (X3 = X2
3.24/3.41	       | app_encode_app(X0, X1, X3, sk_Z(X1, X0, X2, X3))
3.24/3.41	          != app_encode_app(X0, X1, X2, sk_Z(X1, X0, X2, X3))),
3.24/3.41	    inference('cnf', [status(esa)], [zf_stmt_2])).
3.24/3.41	tff('34', plain,
3.24/3.41	    ![X0 : app_encode_fun(int, int)]:
3.24/3.41	      (app_encode_app(int, int, X0, 
3.24/3.41	         sk_Z(int, int, number_number_of(int), X0))
3.24/3.41	        != sk_Z(int, int, number_number_of(int), X0)
3.24/3.41	       | X0 = number_number_of(int)),
3.24/3.41	    inference('sup-', [status(thm)], ['2', '33'])).
3.24/3.41	tff('35', plain,
3.24/3.41	    (sk_Z(int, int, number_number_of(int), 
3.24/3.41	       app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls))
3.24/3.41	      != sk_Z(int, int, number_number_of(int), 
3.24/3.41	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls))
3.24/3.41	     | app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls)
3.24/3.41	        = number_number_of(int)),
3.24/3.41	    inference('sup-', [status(thm)], ['9', '34'])).
3.24/3.41	tff('36', plain,
3.24/3.41	    app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls)
3.24/3.41	     = number_number_of(int),
3.24/3.41	    inference('simplify', [status(thm)], ['35'])).
3.24/3.41	tff(zf_stmt_92, axiom,
3.24/3.41	  (![W:int,Z2:int,Z1:int]:
3.24/3.41	     (app_encode_app(int,int,
3.24/3.41	                     app_encode_app(int,app_encode_fun(int,int),
3.24/3.41	                                    times_times(int),
3.24/3.41	                                    app_encode_app(int,int,
3.24/3.41	                                                   app_encode_app(int,
3.24/3.41	                                                                  app_encode_fun(
3.24/3.41	                                                                  int,int),
3.24/3.41	                                                                  plus_plus(
3.24/3.41	                                                                  int),Z1),
3.24/3.41	                                                   Z2)),
3.24/3.41	                     W) =
3.24/3.41	      app_encode_app(int,int,
3.24/3.41	                     app_encode_app(int,app_encode_fun(int,int),
3.24/3.41	                                    plus_plus(int),
3.24/3.41	                                    app_encode_app(int,int,
3.24/3.41	                                                   app_encode_app(int,
3.24/3.41	                                                                  app_encode_fun(
3.24/3.41	                                                                  int,int),
3.24/3.41	                                                                  times_times(
3.24/3.41	                                                                  int),Z1),
3.24/3.41	                                                   W)),
3.24/3.41	                     app_encode_app(int,int,
3.24/3.41	                                    app_encode_app(int,
3.24/3.41	                                                   app_encode_fun(int,int),
3.24/3.41	                                                   times_times(int),Z2),
3.24/3.41	                                    W))))).
3.24/3.41	tff('37', plain,
3.24/3.41	    ![X91 : int, X92 : int, X93 : int]:
3.24/3.41	      app_encode_app(int, int, 
3.24/3.41	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.24/3.41	          app_encode_app(int, int, 
3.24/3.41	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.24/3.41	              X91), X93)), X92)
3.24/3.41	       = app_encode_app(int, int, 
3.24/3.41	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.24/3.41	             app_encode_app(int, int, 
3.24/3.41	               app_encode_app(int, app_encode_fun(int, int), 
3.24/3.41	                 times_times(int), X91), X92)), 
3.24/3.41	           app_encode_app(int, int, 
3.24/3.41	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.24/3.41	               X93), X92)),
3.24/3.41	    inference('cnf', [status(esa)], [zf_stmt_92])).
3.24/3.41	tff('38', plain,
3.24/3.41	    ![X0 : int, X1 : int]:
3.24/3.41	      app_encode_app(int, int, 
3.24/3.41	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X1), 
3.24/3.41	        app_encode_app(int, int, 
3.24/3.41	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
3.24/3.41	          X0))
3.24/3.41	       = app_encode_app(int, int, 
3.24/3.41	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.24/3.41	             app_encode_app(int, int, 
3.24/3.41	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.24/3.41	                 X1), X1)), X0),
3.24/3.41	    inference('sup+', [status(thm)], ['37', '30'])).
3.24/3.41	tff(zf_stmt_90, axiom,
3.24/3.41	  (![K1:int]:
3.24/3.41	     (app_encode_app(int,int,bit0,K1) =
3.24/3.41	      app_encode_app(int,int,
3.24/3.41	                     app_encode_app(int,app_encode_fun(int,int),
3.24/3.41	                                    plus_plus(int),K1),
3.24/3.41	                     K1)))).
3.24/3.41	tff('39', plain,
3.24/3.41	    ![X88 : int]:
3.24/3.41	      app_encode_app(int, int, bit0, X88)
3.24/3.41	       = app_encode_app(int, int, 
3.24/3.41	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X88), 
3.24/3.41	           X88),
3.24/3.41	    inference('cnf', [status(esa)], [zf_stmt_90])).
3.24/3.41	tff('40', plain,
3.24/3.41	    ![X0 : int, X1 : int]:
3.24/3.41	      app_encode_app(int, int, 
3.24/3.41	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X1), 
3.24/3.41	        app_encode_app(int, int, bit0, X0))
3.24/3.41	       = app_encode_app(int, int, bit0, 
3.24/3.41	           app_encode_app(int, int, 
3.24/3.41	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.24/3.41	               X1), X0)),
3.24/3.41	    inference('demod', [status(thm)], ['38', '39', '39', '4'])).
3.24/3.41	tff('41', plain,
3.24/3.41	    ![X0 : int, X1 : int]:
3.24/3.41	      app_encode_app(int, int, 
3.24/3.41	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X1), 
3.24/3.41	        app_encode_app(int, int, bit1, X0))
3.24/3.41	       = app_encode_app(int, int, 
3.24/3.41	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X1), 
3.24/3.41	           app_encode_app(int, int, bit0, 
3.24/3.41	             app_encode_app(int, int, 
3.24/3.41	               app_encode_app(int, app_encode_fun(int, int), 
3.24/3.41	                 times_times(int), X1), X0))),
3.24/3.41	    inference('demod', [status(thm)], ['32', '36', '2', '40'])).
3.24/3.41	tff('42', plain,
3.24/3.41	    ![X0 : int]:
3.24/3.41	      app_encode_app(int, int, 
3.24/3.41	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X0), 
3.24/3.41	        pls)
3.24/3.41	       = app_encode_app(int, int, bit0, 
3.24/3.41	           app_encode_app(int, int, 
3.24/3.41	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.24/3.41	               X0), pls)),
3.24/3.41	    inference('sup+', [status(thm)], ['8', '40'])).
3.24/3.41	tff('43', plain,
3.24/3.41	    ![X0 : int]:
3.24/3.41	      app_encode_app(int, int, 
3.24/3.41	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X0), 
3.24/3.41	        app_encode_app(int, int, bit1, pls))
3.24/3.41	       = app_encode_app(int, int, 
3.24/3.41	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
3.24/3.41	           app_encode_app(int, int, 
3.24/3.41	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.24/3.41	               X0), pls)),
3.24/3.41	    inference('sup+', [status(thm)], ['15', '31'])).
3.24/3.41	tff('44', plain,
3.24/3.41	    ![X0 : int]:
3.24/3.41	      app_encode_app(int, int, 
3.24/3.41	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
3.24/3.41	        app_encode_app(int, int, 
3.24/3.41	          app_encode_app(int, app_encode_fun(int, int), times_times(int), X0), 
3.24/3.41	          pls))
3.24/3.41	       = X0,
3.24/3.41	    inference('sup+', [status(thm)], ['43', '29'])).
3.24/3.41	tff('45', plain,
3.24/3.41	    app_encode_app(int, int, 
3.24/3.41	      app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.24/3.41	        app_encode_app(int, int, 
3.24/3.41	          app_encode_app(int, app_encode_fun(int, int), times_times(int), s), 
3.24/3.41	          s)), app_encode_app(int, int, bit1, pls))
3.24/3.41	     = app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m)),
3.24/3.41	    inference('demod', [status(thm)], ['16', '23', '41', '42', '44'])).
3.24/3.41	tff('46', plain,
3.24/3.41	    (sk_Z(int, int, number_number_of(int), 
3.24/3.41	       app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.24/3.41	         app_encode_app(int, int, bit1, pls)))
3.24/3.41	      != sk_Z(int, int, number_number_of(int), 
3.24/3.41	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.24/3.41	             app_encode_app(int, int, bit1, pls)))
3.24/3.41	     | app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.24/3.41	         app_encode_app(int, int, bit1, pls))
3.24/3.41	        = number_number_of(int)),
3.24/3.41	    inference('sup-', [status(thm)], ['10', '34'])).
3.24/3.41	tff('47', plain,
3.24/3.41	    app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.24/3.41	      app_encode_app(int, int, bit1, pls))
3.24/3.41	     = number_number_of(int),
3.24/3.41	    inference('simplify', [status(thm)], ['46'])).
3.24/3.41	tff(zf_stmt_168, conjecture,
3.24/3.41	  (?[X:int,Y:int]:
3.24/3.41	     (app_encode_app(int,int,
3.24/3.41	                     app_encode_app(int,app_encode_fun(int,int),
3.24/3.41	                                    plus_plus(int),
3.24/3.41	                                    app_encode_app(nat,int,
3.24/3.41	                                                   app_encode_app(int,
3.24/3.41	                                                                  app_encode_fun(
3.24/3.41	                                                                  nat,int),
3.24/3.41	                                                                  power_power(
3.24/3.41	                                                                  int),X),
3.24/3.41	                                                   app_encode_app(int,nat,
3.24/3.41	                                                                  number_number_of(
3.24/3.41	                                                                  nat),
3.24/3.41	                                                                  app_encode_app(
3.24/3.41	                                                                  int,int,
3.24/3.41	                                                                  bit0,
3.24/3.41	                                                                  app_encode_app(
3.24/3.41	                                                                  int,int,
3.24/3.41	                                                                  bit1,pls))))),
3.24/3.41	                     app_encode_app(nat,int,
3.24/3.41	                                    app_encode_app(int,
3.24/3.41	                                                   app_encode_fun(nat,int),
3.24/3.41	                                                   power_power(int),Y),
3.24/3.41	                                    app_encode_app(int,nat,
3.24/3.41	                                                   number_number_of(nat),
3.24/3.41	                                                   app_encode_app(int,int,
3.24/3.41	                                                                  bit0,
3.24/3.41	                                                                  app_encode_app(
3.24/3.41	                                                                  int,int,
3.24/3.41	                                                                  bit1,pls))))) =
3.24/3.41	      app_encode_app(int,int,
3.24/3.41	                     app_encode_app(int,app_encode_fun(int,int),
3.24/3.41	                                    plus_plus(int),
3.24/3.41	                                    app_encode_app(int,int,
3.24/3.41	                                                   app_encode_app(int,
3.24/3.41	                                                                  app_encode_fun(
3.24/3.41	                                                                  int,int),
3.24/3.41	                                                                  times_times(
3.24/3.41	                                                                  int),
3.24/3.41	                                                                  app_encode_app(
3.24/3.41	                                                                  int,int,
3.24/3.41	                                                                  number_number_of(
3.24/3.41	                                                                  int),
3.24/3.41	                                                                  app_encode_app(
3.24/3.41	                                                                  int,int,
3.24/3.41	                                                                  bit0,
3.24/3.41	                                                                  app_encode_app(
3.24/3.41	                                                                  int,int,
3.24/3.41	                                                                  bit0,
3.24/3.41	                                                                  app_encode_app(
3.24/3.41	                                                                  int,int,
3.24/3.41	                                                                  bit1,pls))))),
3.24/3.41	                                                   m)),
3.24/3.41	                     one_one(int))))).
3.24/3.41	tff(zf_stmt_0, negated_conjecture,
3.24/3.41	  (~
3.24/3.41	    (?[X:int,Y:int]:
3.24/3.41	       (app_encode_app(int,int,
3.24/3.41	                       app_encode_app(int,app_encode_fun(int,int),
3.24/3.41	                                      plus_plus(int),
3.24/3.41	                                      app_encode_app(nat,int,
3.24/3.41	                                                     app_encode_app(int,
3.24/3.41	                                                                    app_encode_fun(
3.24/3.41	                                                                    nat,int),
3.24/3.41	                                                                    power_power(
3.24/3.41	                                                                    int),X),
3.24/3.41	                                                     app_encode_app(int,nat,
3.24/3.41	                                                                    number_number_of(
3.24/3.41	                                                                    nat),
3.24/3.41	                                                                    app_encode_app(
3.24/3.41	                                                                    int,int,
3.24/3.41	                                                                    bit0,
3.24/3.41	                                                                    app_encode_app(
3.24/3.41	                                                                    int,int,
3.24/3.41	                                                                    bit1,pls))))),
3.24/3.41	                       app_encode_app(nat,int,
3.24/3.41	                                      app_encode_app(int,
3.24/3.41	                                                     app_encode_fun(nat,int),
3.24/3.41	                                                     power_power(int),Y),
3.24/3.41	                                      app_encode_app(int,nat,
3.24/3.41	                                                     number_number_of(nat),
3.24/3.41	                                                     app_encode_app(int,int,
3.24/3.41	                                                                    bit0,
3.24/3.41	                                                                    app_encode_app(
3.24/3.41	                                                                    int,int,
3.24/3.41	                                                                    bit1,pls))))) =
3.24/3.41	        app_encode_app(int,int,
3.24/3.41	                       app_encode_app(int,app_encode_fun(int,int),
3.24/3.41	                                      plus_plus(int),
3.24/3.41	                                      app_encode_app(int,int,
3.24/3.41	                                                     app_encode_app(int,
3.24/3.41	                                                                    app_encode_fun(
3.24/3.41	                                                                    int,int),
3.24/3.41	                                                                    times_times(
3.24/3.41	                                                                    int),
3.24/3.41	                                                                    app_encode_app(
3.24/3.41	                                                                    int,int,
3.24/3.41	                                                                    number_number_of(
3.24/3.41	                                                                    int),
3.24/3.41	                                                                    app_encode_app(
3.24/3.41	                                                                    int,int,
3.24/3.41	                                                                    bit0,
3.24/3.41	                                                                    app_encode_app(
3.24/3.41	                                                                    int,int,
3.24/3.41	                                                                    bit0,
3.24/3.41	                                                                    app_encode_app(
3.24/3.41	                                                                    int,int,
3.24/3.41	                                                                    bit1,pls))))),
3.24/3.41	                                                     m)),
3.24/3.41	                       one_one(int)))))).
3.24/3.41	tff('48', plain,
3.24/3.41	    ![X181 : int, X182 : int]:
3.24/3.41	      app_encode_app(int, int, 
3.24/3.41	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.24/3.41	          app_encode_app(nat, int, 
3.24/3.41	            app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
3.24/3.41	              X181), 
3.24/3.41	            app_encode_app(int, nat, number_number_of(nat), 
3.24/3.41	              app_encode_app(int, int, bit0, 
3.24/3.41	                app_encode_app(int, int, bit1, pls))))), 
3.24/3.41	        app_encode_app(nat, int, 
3.24/3.41	          app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
3.24/3.41	            X182), 
3.24/3.41	          app_encode_app(int, nat, number_number_of(nat), 
3.24/3.41	            app_encode_app(int, int, bit0, 
3.24/3.41	              app_encode_app(int, int, bit1, pls)))))
3.24/3.41	       != app_encode_app(int, int, 
3.24/3.41	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.24/3.41	              app_encode_app(int, int, 
3.24/3.41	                app_encode_app(int, app_encode_fun(int, int), 
3.24/3.41	                  times_times(int), 
3.24/3.41	                  app_encode_app(int, int, number_number_of(int), 
3.24/3.41	                    app_encode_app(int, int, bit0, 
3.24/3.41	                      app_encode_app(int, int, bit0, 
3.24/3.41	                        app_encode_app(int, int, bit1, pls))))), m)), 
3.24/3.41	            one_one(int)),
3.24/3.41	    inference('cnf', [status(esa)], [zf_stmt_0])).
3.24/3.41	tff(zf_stmt_73, axiom,
3.24/3.41	  (![A:$tType]:
3.24/3.41	     (number_ring(A) =>
3.24/3.41	      (![Z:A,W:int,V:int]:
3.24/3.41	         (app_encode_app(A,A,
3.24/3.41	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
3.24/3.41	                                        app_encode_app(int,A,
3.24/3.41	                                                       number_number_of(A),V)),
3.24/3.41	                         app_encode_app(A,A,
3.24/3.41	                                        app_encode_app(A,app_encode_fun(A,A),
3.24/3.41	                                                       plus_plus(A),
3.24/3.41	                                                       app_encode_app(
3.24/3.41	                                                       int,A,
3.24/3.41	                                                       number_number_of(A),W)),
3.24/3.41	                                        Z)) =
3.24/3.41	          app_encode_app(A,A,
3.24/3.41	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
3.24/3.41	                                        app_encode_app(int,A,
3.24/3.41	                                                       number_number_of(A),
3.24/3.41	                                                       app_encode_app(
3.24/3.41	                                                       int,int,
3.24/3.41	                                                       app_encode_app(
3.24/3.41	                                                       int,
3.24/3.41	                                                       app_encode_fun(
3.24/3.41	                                                       int,int),
3.24/3.41	                                                       plus_plus(int),V),W))),
3.24/3.41	                         Z)))))).
3.24/3.41	tff('49', plain,
3.24/3.41	    ![X62 : $tType, X63 : int, X64 : int, X65 : X62]:
3.24/3.41	      (app_encode_app(X62, X62, 
3.24/3.41	         app_encode_app(X62, app_encode_fun(X62, X62), plus_plus(X62), 
3.24/3.41	           app_encode_app(int, X62, number_number_of(X62), X63)), 
3.24/3.41	         app_encode_app(X62, X62, 
3.24/3.41	           app_encode_app(X62, app_encode_fun(X62, X62), plus_plus(X62), 
3.24/3.41	             app_encode_app(int, X62, number_number_of(X62), X64)), X65))
3.24/3.41	        = app_encode_app(X62, X62, 
3.24/3.41	            app_encode_app(X62, app_encode_fun(X62, X62), plus_plus(X62), 
3.24/3.41	              app_encode_app(int, X62, number_number_of(X62), 
3.24/3.41	                app_encode_app(int, int, 
3.24/3.41	                  app_encode_app(int, app_encode_fun(int, int), 
3.24/3.41	                    plus_plus(int), X63), X64))), X65)
3.24/3.41	       | ~ number_ring(X62)),
3.24/3.41	    inference('cnf', [status(esa)], [zf_stmt_73])).
3.24/3.41	tff('50', plain,
3.24/3.41	    ![X0 : int, X1 : int, X2 : int]:
3.24/3.41	      (~ $true
3.24/3.41	       | app_encode_app(int, int, 
3.24/3.41	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.24/3.41	             app_encode_app(int, int, number_number_of(int), X2)), 
3.24/3.41	           app_encode_app(int, int, 
3.24/3.41	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.24/3.41	               app_encode_app(int, int, number_number_of(int), X1)), X0))
3.24/3.41	          = app_encode_app(int, int, 
3.24/3.41	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.24/3.41	                app_encode_app(int, int, number_number_of(int), 
3.24/3.41	                  app_encode_app(int, int, 
3.24/3.41	                    app_encode_app(int, app_encode_fun(int, int), 
3.24/3.41	                      plus_plus(int), X2), X1))), X0)),
3.24/3.41	    inference('sup-', [status(thm)], ['25', '49'])).
3.24/3.41	tff('51', plain,
3.24/3.41	    ![X0 : int, X1 : int, X2 : int]:
3.24/3.41	      (~ $true
3.24/3.41	       | app_encode_app(int, int, 
3.24/3.41	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X2), 
3.24/3.41	           app_encode_app(int, int, 
3.24/3.41	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.24/3.41	               X1), X0))
3.24/3.41	          = app_encode_app(int, int, 
3.24/3.41	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.24/3.41	                app_encode_app(int, int, 
3.24/3.41	                  app_encode_app(int, app_encode_fun(int, int), 
3.24/3.41	                    plus_plus(int), X2), X1)), X0)),
3.24/3.41	    inference('demod', [status(thm)], ['50', '2', '2', '2'])).
3.24/3.41	tff('52', plain,
3.24/3.41	    ![X0 : int, X1 : int, X2 : int]:
3.24/3.41	      app_encode_app(int, int, 
3.24/3.41	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X2), 
3.24/3.41	        app_encode_app(int, int, 
3.24/3.41	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X1), 
3.24/3.41	          X0))
3.24/3.41	       = app_encode_app(int, int, 
3.24/3.41	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.24/3.41	             app_encode_app(int, int, 
3.24/3.41	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.24/3.41	                 X2), X1)), X0),
3.24/3.41	    inference('simplify', [status(thm)], ['51'])).
3.24/3.41	tff('53', plain,
3.24/3.41	    ![X0 : int, X1 : int]:
3.24/3.41	      app_encode_app(int, int, 
3.24/3.41	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
3.24/3.41	        app_encode_app(int, int, 
3.24/3.41	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
3.24/3.41	          X1))
3.24/3.41	       = app_encode_app(int, int, 
3.24/3.41	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.24/3.41	             app_encode_app(int, int, bit0, X0)), X1),
3.24/3.41	    inference('sup+', [status(thm)], ['39', '52'])).
3.24/3.41	tff('54', plain,
3.24/3.41	    ![X71 : int, X72 : int]:
3.24/3.41	      app_encode_app(int, int, 
3.24/3.41	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X71), 
3.24/3.41	        app_encode_app(int, int, 
3.24/3.41	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X71), 
3.24/3.41	          app_encode_app(int, int, bit1, X72)))
3.24/3.41	       = app_encode_app(int, int, bit1, 
3.24/3.41	           app_encode_app(int, int, 
3.24/3.41	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.24/3.41	               X71), X72)),
3.24/3.41	    inference('demod', [status(thm)], ['14', '53'])).
3.24/3.41	tff('55', plain,
3.24/3.41	    ![X181 : int, X182 : int]:
3.24/3.41	      app_encode_app(int, int, 
3.24/3.41	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.24/3.41	          app_encode_app(int, int, 
3.24/3.41	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.24/3.41	              X181), X181)), 
3.24/3.41	        app_encode_app(int, int, 
3.24/3.41	          app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.24/3.41	            X182), X182))
3.24/3.41	       != app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m)),
3.24/3.41	    inference('demod', [status(thm)],
3.24/3.41	              ['48', '23', '23', '2', '4', '4', '47', '2', '3', '53', '53', 
3.24/3.41	               '54', '15', '53', '54', '39'])).
3.24/3.41	tff('56', plain,
3.24/3.41	    ![X0 : int]:
3.24/3.41	      app_encode_app(int, int, 
3.24/3.41	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.24/3.41	          app_encode_app(int, int, 
3.24/3.41	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.24/3.41	              X0), X0)), 
3.24/3.41	        app_encode_app(int, int, number_number_of(int), 
3.24/3.41	          app_encode_app(int, int, bit1, pls)))
3.24/3.41	       != app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m)),
3.24/3.41	    inference('sup-', [status(thm)], ['47', '55'])).
3.24/3.41	tff('57', plain,
3.24/3.41	    ![X0 : int]:
3.24/3.41	      app_encode_app(int, int, 
3.24/3.41	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
3.24/3.41	          app_encode_app(int, int, 
3.24/3.41	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
3.24/3.41	              X0), X0)), app_encode_app(int, int, bit1, pls))
3.24/3.41	       != app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m)),
3.24/3.41	    inference('demod', [status(thm)], ['56', '2'])).
3.24/3.41	tff('58', plain, $false,
3.24/3.41	    inference('simplify_reflect-', [status(thm)], ['45', '57'])).
3.24/3.41	
3.24/3.41	% SZS output end Refutation
3.24/3.41	EOF
