0.00/0.00	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : appext
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : kbo
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n083.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 08:01:54 CST 2018
2.87/3.09	% done 1365 iterations in 2.888s
2.87/3.09	% SZS status Theorem for 'stdin'
2.87/3.09	% SZS output start Refutation
2.87/3.09	tff(zf_stmt_86, axiom,
2.87/3.09	  (![K1:int]: (app_encode_app(int,int,number_number_of(int),K1) = K1))).
2.87/3.09	tff('0', plain,
2.87/3.09	    ![X82 : int]: app_encode_app(int, int, number_number_of(int), X82) = X82,
2.87/3.09	    inference('cnf', [status(esa)], [zf_stmt_86])).
2.87/3.09	tff(zf_stmt_52, axiom,
2.87/3.09	  (app_encode_app(int,int,
2.87/3.09	                  app_encode_app(int,app_encode_fun(int,int),plus_plus(int),
2.87/3.09	                                 app_encode_app(nat,int,
2.87/3.09	                                                app_encode_app(int,
2.87/3.09	                                                               app_encode_fun(
2.87/3.09	                                                               nat,int),
2.87/3.09	                                                               power_power(
2.87/3.09	                                                               int),s),
2.87/3.09	                                                app_encode_app(int,nat,
2.87/3.09	                                                               number_number_of(
2.87/3.09	                                                               nat),
2.87/3.09	                                                               app_encode_app(
2.87/3.09	                                                               int,int,bit0,
2.87/3.09	                                                               app_encode_app(
2.87/3.09	                                                               int,int,bit1,
2.87/3.09	                                                               pls))))),
2.87/3.09	                  one_one(int)) =
2.87/3.09	   app_encode_app(int,int,
2.87/3.09	                  app_encode_app(int,app_encode_fun(int,int),
2.87/3.09	                                 times_times(int),
2.87/3.09	                                 app_encode_app(int,int,
2.87/3.09	                                                app_encode_app(int,
2.87/3.09	                                                               app_encode_fun(
2.87/3.09	                                                               int,int),
2.87/3.09	                                                               plus_plus(int),
2.87/3.09	                                                               app_encode_app(
2.87/3.09	                                                               int,int,
2.87/3.09	                                                               app_encode_app(
2.87/3.09	                                                               int,
2.87/3.09	                                                               app_encode_fun(
2.87/3.09	                                                               int,int),
2.87/3.09	                                                               times_times(
2.87/3.09	                                                               int),
2.87/3.09	                                                               app_encode_app(
2.87/3.09	                                                               int,int,
2.87/3.09	                                                               number_number_of(
2.87/3.09	                                                               int),
2.87/3.09	                                                               app_encode_app(
2.87/3.09	                                                               int,int,bit0,
2.87/3.09	                                                               app_encode_app(
2.87/3.09	                                                               int,int,bit0,
2.87/3.09	                                                               app_encode_app(
2.87/3.09	                                                               int,int,bit1,
2.87/3.09	                                                               pls))))),m)),
2.87/3.09	                                                one_one(int))),
2.87/3.09	                  t))).
2.87/3.09	tff('1', plain,
2.87/3.09	    app_encode_app(int, int, 
2.87/3.09	      app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.87/3.09	        app_encode_app(nat, int, 
2.87/3.09	          app_encode_app(int, app_encode_fun(nat, int), power_power(int), s), 
2.87/3.09	          app_encode_app(int, nat, number_number_of(nat), 
2.87/3.09	            app_encode_app(int, int, bit0, 
2.87/3.09	              app_encode_app(int, int, bit1, pls))))), one_one(int))
2.87/3.09	     = app_encode_app(int, int, 
2.87/3.09	         app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.87/3.09	           app_encode_app(int, int, 
2.87/3.09	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.87/3.09	               app_encode_app(int, int, 
2.87/3.09	                 app_encode_app(int, app_encode_fun(int, int), 
2.87/3.09	                   times_times(int), 
2.87/3.09	                   app_encode_app(int, int, number_number_of(int), 
2.87/3.09	                     app_encode_app(int, int, bit0, 
2.87/3.09	                       app_encode_app(int, int, bit0, 
2.87/3.09	                         app_encode_app(int, int, bit1, pls))))), m)), 
2.87/3.09	             one_one(int))), t),
2.87/3.09	    inference('cnf', [status(esa)], [zf_stmt_52])).
2.87/3.09	tff(zf_stmt_106, axiom,
2.87/3.09	  (one_one(int) =
2.87/3.09	   app_encode_app(int,int,number_number_of(int),
2.87/3.09	                  app_encode_app(int,int,bit1,pls)))).
2.87/3.09	tff('2', plain,
2.87/3.09	    one_one(int)
2.87/3.09	     = app_encode_app(int, int, number_number_of(int), 
2.87/3.09	         app_encode_app(int, int, bit1, pls)),
2.87/3.09	    inference('cnf', [status(esa)], [zf_stmt_106])).
2.87/3.09	tff(zf_stmt_41, axiom, (t = one_one(int))).
2.87/3.09	tff('3', plain, t = one_one(int),
2.87/3.09	    inference('cnf', [status(esa)], [zf_stmt_41])).
2.87/3.09	tff('4', plain, t = app_encode_app(int, int, bit1, pls),
2.87/3.09	    inference('demod', [status(thm)], ['2', '3', '0'])).
2.87/3.09	tff(zf_stmt_67, axiom,
2.87/3.09	  (![L1:int,K1:int]:
2.87/3.09	     (app_encode_app(int,int,
2.87/3.09	                     app_encode_app(int,app_encode_fun(int,int),
2.87/3.09	                                    times_times(int),
2.87/3.09	                                    app_encode_app(int,int,bit0,K1)),
2.87/3.09	                     L1) =
2.87/3.09	      app_encode_app(int,int,bit0,
2.87/3.09	                     app_encode_app(int,int,
2.87/3.09	                                    app_encode_app(int,
2.87/3.09	                                                   app_encode_fun(int,int),
2.87/3.09	                                                   times_times(int),K1),
2.87/3.09	                                    L1))))).
2.87/3.09	tff('5', plain,
2.87/3.09	    ![X43 : int, X44 : int]:
2.87/3.09	      app_encode_app(int, int, 
2.87/3.09	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.87/3.09	          app_encode_app(int, int, bit0, X43)), X44)
2.87/3.09	       = app_encode_app(int, int, bit0, 
2.87/3.09	           app_encode_app(int, int, 
2.87/3.09	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.87/3.09	               X43), X44)),
2.87/3.09	    inference('cnf', [status(esa)], [zf_stmt_67])).
2.87/3.09	tff(zf_stmt_66, axiom,
2.87/3.09	  (![W:int]:
2.87/3.09	     (app_encode_app(int,int,
2.87/3.09	                     app_encode_app(int,app_encode_fun(int,int),
2.87/3.09	                                    times_times(int),pls),
2.87/3.09	                     W) =
2.87/3.09	      pls))).
2.87/3.09	tff('6', plain,
2.87/3.09	    ![X42 : int]:
2.87/3.09	      app_encode_app(int, int, 
2.87/3.09	        app_encode_app(int, app_encode_fun(int, int), times_times(int), pls), 
2.87/3.09	        X42)
2.87/3.09	       = pls,
2.87/3.09	    inference('cnf', [status(esa)], [zf_stmt_66])).
2.87/3.09	tff(zf_stmt_50, axiom,
2.87/3.09	  (![L1:int,K1:int]:
2.87/3.09	     (app_encode_app(int,int,
2.87/3.09	                     app_encode_app(int,app_encode_fun(int,int),
2.87/3.09	                                    times_times(int),
2.87/3.09	                                    app_encode_app(int,int,bit1,K1)),
2.87/3.09	                     L1) =
2.87/3.09	      app_encode_app(int,int,
2.87/3.09	                     app_encode_app(int,app_encode_fun(int,int),
2.87/3.09	                                    plus_plus(int),
2.87/3.09	                                    app_encode_app(int,int,bit0,
2.87/3.09	                                                   app_encode_app(int,int,
2.87/3.09	                                                                  app_encode_app(
2.87/3.09	                                                                  int,
2.87/3.09	                                                                  app_encode_fun(
2.87/3.09	                                                                  int,int),
2.87/3.09	                                                                  times_times(
2.87/3.09	                                                                  int),K1),L1))),
2.87/3.09	                     L1)))).
2.87/3.09	tff('7', plain,
2.87/3.09	    ![X12 : int, X13 : int]:
2.87/3.09	      app_encode_app(int, int, 
2.87/3.09	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.87/3.09	          app_encode_app(int, int, bit1, X12)), X13)
2.87/3.09	       = app_encode_app(int, int, 
2.87/3.09	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.87/3.09	             app_encode_app(int, int, bit0, 
2.87/3.09	               app_encode_app(int, int, 
2.87/3.09	                 app_encode_app(int, app_encode_fun(int, int), 
2.87/3.09	                   times_times(int), X12), X13))), X13),
2.87/3.09	    inference('cnf', [status(esa)], [zf_stmt_50])).
2.87/3.09	tff('8', plain,
2.87/3.09	    ![X0 : int]:
2.87/3.09	      app_encode_app(int, int, 
2.87/3.09	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.87/3.09	          app_encode_app(int, int, bit1, pls)), X0)
2.87/3.09	       = app_encode_app(int, int, 
2.87/3.09	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.87/3.09	             app_encode_app(int, int, bit0, pls)), X0),
2.87/3.09	    inference('sup+', [status(thm)], ['6', '7'])).
2.87/3.09	tff(zf_stmt_65, axiom, (app_encode_app(int,int,bit0,pls) = pls)).
2.87/3.09	tff('9', plain, app_encode_app(int, int, bit0, pls) = pls,
2.87/3.09	    inference('cnf', [status(esa)], [zf_stmt_65])).
2.87/3.09	tff(zf_stmt_89, axiom,
2.87/3.09	  (![K1:int]:
2.87/3.09	     (app_encode_app(int,int,
2.87/3.09	                     app_encode_app(int,app_encode_fun(int,int),
2.87/3.09	                                    plus_plus(int),pls),
2.87/3.09	                     K1) =
2.87/3.09	      K1))).
2.87/3.09	tff('10', plain,
2.87/3.09	    ![X87 : int]:
2.87/3.09	      app_encode_app(int, int, 
2.87/3.09	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
2.87/3.09	        X87)
2.87/3.09	       = X87,
2.87/3.09	    inference('cnf', [status(esa)], [zf_stmt_89])).
2.87/3.09	tff('11', plain,
2.87/3.09	    ![X0 : int]:
2.87/3.09	      app_encode_app(int, int, 
2.87/3.09	        app_encode_app(int, app_encode_fun(int, int), times_times(int), t), 
2.87/3.09	        X0)
2.87/3.09	       = X0,
2.87/3.09	    inference('demod', [status(thm)], ['8', '4', '9', '10'])).
2.87/3.09	tff('12', plain,
2.87/3.09	    app_encode_app(int, int, 
2.87/3.09	      app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.87/3.09	        app_encode_app(nat, int, 
2.87/3.09	          app_encode_app(int, app_encode_fun(nat, int), power_power(int), s), 
2.87/3.09	          app_encode_app(int, nat, number_number_of(nat), 
2.87/3.09	            app_encode_app(int, int, bit0, t)))), t)
2.87/3.09	     = app_encode_app(int, int, 
2.87/3.09	         app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.87/3.09	           app_encode_app(int, int, 
2.87/3.09	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.87/3.09	               app_encode_app(int, int, bit0, 
2.87/3.09	                 app_encode_app(int, int, bit0, m))), t)), t),
2.87/3.09	    inference('demod', [status(thm)],
2.87/3.09	              ['1', '4', '3', '4', '0', '5', '5', '11', '3'])).
2.87/3.09	tff(zf_stmt_48, axiom,
2.87/3.09	  (![A:$tType]:
2.87/3.09	     (number_ring(A) =>
2.87/3.09	      (![V:int]:
2.87/3.09	         (app_encode_app(A,A,
2.87/3.09	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
2.87/3.09	                                        app_encode_app(int,A,
2.87/3.09	                                                       number_number_of(A),V)),
2.87/3.09	                         one_one(A)) =
2.87/3.09	          app_encode_app(int,A,number_number_of(A),
2.87/3.09	                         app_encode_app(int,int,
2.87/3.09	                                        app_encode_app(int,
2.87/3.09	                                                       app_encode_fun(
2.87/3.09	                                                       int,int),
2.87/3.09	                                                       plus_plus(int),V),
2.87/3.09	                                        app_encode_app(int,int,bit1,pls)))))))).
2.87/3.09	tff('13', plain,
2.87/3.09	    ![X9 : $tType, X10 : int]:
2.87/3.09	      (app_encode_app(X9, X9, 
2.87/3.09	         app_encode_app(X9, app_encode_fun(X9, X9), plus_plus(X9), 
2.87/3.09	           app_encode_app(int, X9, number_number_of(X9), X10)), one_one(X9))
2.87/3.09	        = app_encode_app(int, X9, number_number_of(X9), 
2.87/3.09	            app_encode_app(int, int, 
2.87/3.09	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.87/3.09	                X10), app_encode_app(int, int, bit1, pls)))
2.87/3.09	       | ~ number_ring(X9)),
2.87/3.09	    inference('cnf', [status(esa)], [zf_stmt_48])).
2.87/3.09	tff('14', plain,
2.87/3.09	    ![X9 : $tType, X10 : int]:
2.87/3.09	      (app_encode_app(X9, X9, 
2.87/3.09	         app_encode_app(X9, app_encode_fun(X9, X9), plus_plus(X9), 
2.87/3.09	           app_encode_app(int, X9, number_number_of(X9), X10)), one_one(X9))
2.87/3.09	        = app_encode_app(int, X9, number_number_of(X9), 
2.87/3.09	            app_encode_app(int, int, 
2.87/3.09	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.87/3.09	                X10), t))
2.87/3.09	       | ~ number_ring(X9)),
2.87/3.09	    inference('demod', [status(thm)], ['13', '4'])).
2.87/3.09	tff('15', plain,
2.87/3.09	    ![X0 : $tType]:
2.87/3.09	      (app_encode_app(X0, X0, 
2.87/3.09	         app_encode_app(X0, app_encode_fun(X0, X0), plus_plus(X0), 
2.87/3.09	           app_encode_app(int, X0, number_number_of(X0), 
2.87/3.09	             app_encode_app(nat, int, 
2.87/3.09	               app_encode_app(int, app_encode_fun(nat, int), 
2.87/3.09	                 power_power(int), s), 
2.87/3.09	               app_encode_app(int, nat, number_number_of(nat), 
2.87/3.09	                 app_encode_app(int, int, bit0, t))))), one_one(X0))
2.87/3.09	        = app_encode_app(int, X0, number_number_of(X0), 
2.87/3.09	            app_encode_app(int, int, 
2.87/3.09	              app_encode_app(int, app_encode_fun(int, int), 
2.87/3.09	                times_times(int), 
2.87/3.09	                app_encode_app(int, int, 
2.87/3.09	                  app_encode_app(int, app_encode_fun(int, int), 
2.87/3.09	                    plus_plus(int), 
2.87/3.09	                    app_encode_app(int, int, bit0, 
2.87/3.09	                      app_encode_app(int, int, bit0, m))), t)), t))
2.87/3.09	       | ~ number_ring(X0)),
2.87/3.09	    inference('sup+', [status(thm)], ['12', '14'])).
2.87/3.09	tff(zf_stmt_44, axiom,
2.87/3.09	  (![B1:$tType]:
2.87/3.09	     ((monoid_mult(B1) & number(B1)) =>
2.87/3.09	      (![W:int]:
2.87/3.09	         (app_encode_app(nat,B1,
2.87/3.09	                         app_encode_app(B1,app_encode_fun(nat,B1),
2.87/3.09	                                        power_power(B1),
2.87/3.09	                                        app_encode_app(int,B1,
2.87/3.09	                                                       number_number_of(B1),W)),
2.87/3.09	                         app_encode_app(int,nat,number_number_of(nat),
2.87/3.09	                                        app_encode_app(int,int,bit0,
2.87/3.09	                                                       app_encode_app(
2.87/3.09	                                                       int,int,bit1,pls)))) =
2.87/3.09	          app_encode_app(B1,B1,
2.87/3.09	                         app_encode_app(B1,app_encode_fun(B1,B1),
2.87/3.09	                                        times_times(B1),
2.87/3.09	                                        app_encode_app(int,B1,
2.87/3.09	                                                       number_number_of(B1),W)),
2.87/3.09	                         app_encode_app(int,B1,number_number_of(B1),W))))))).
2.87/3.09	tff('16', plain,
2.87/3.09	    ![X4 : $tType, X5 : int]:
2.87/3.09	      (app_encode_app(nat, X4, 
2.87/3.09	         app_encode_app(X4, app_encode_fun(nat, X4), power_power(X4), 
2.87/3.09	           app_encode_app(int, X4, number_number_of(X4), X5)), 
2.87/3.09	         app_encode_app(int, nat, number_number_of(nat), 
2.87/3.09	           app_encode_app(int, int, bit0, 
2.87/3.09	             app_encode_app(int, int, bit1, pls))))
2.87/3.09	        = app_encode_app(X4, X4, 
2.87/3.09	            app_encode_app(X4, app_encode_fun(X4, X4), times_times(X4), 
2.87/3.09	              app_encode_app(int, X4, number_number_of(X4), X5)), 
2.87/3.09	            app_encode_app(int, X4, number_number_of(X4), X5))
2.87/3.09	       | ~ number(X4)
2.87/3.09	       | ~ monoid_mult(X4)),
2.87/3.09	    inference('cnf', [status(esa)], [zf_stmt_44])).
2.87/3.09	tff('17', plain,
2.87/3.09	    ![X0 : int]:
2.87/3.09	      (app_encode_app(nat, int, 
2.87/3.09	         app_encode_app(int, app_encode_fun(nat, int), power_power(int), X0), 
2.87/3.09	         app_encode_app(int, nat, number_number_of(nat), 
2.87/3.09	           app_encode_app(int, int, bit0, 
2.87/3.09	             app_encode_app(int, int, bit1, pls))))
2.87/3.09	        = app_encode_app(int, int, 
2.87/3.09	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.87/3.09	              app_encode_app(int, int, number_number_of(int), X0)), 
2.87/3.09	            app_encode_app(int, int, number_number_of(int), X0))
2.87/3.09	       | ~ monoid_mult(int)
2.87/3.09	       | ~ number(int)),
2.87/3.09	    inference('sup+', [status(thm)], ['0', '16'])).
2.87/3.09	tff(zf_stmt_143, axiom, (monoid_mult(int))).
2.87/3.09	tff('18', plain, monoid_mult(int),
2.87/3.09	    inference('cnf', [status(esa)], [zf_stmt_143])).
2.87/3.09	tff(zf_stmt_148, axiom, (number(int))).
2.87/3.09	tff('19', plain, number(int), inference('cnf', [status(esa)], [zf_stmt_148])).
2.87/3.09	tff('20', plain,
2.87/3.09	    ![X0 : int]:
2.87/3.09	      (app_encode_app(nat, int, 
2.87/3.09	         app_encode_app(int, app_encode_fun(nat, int), power_power(int), X0), 
2.87/3.09	         app_encode_app(int, nat, number_number_of(nat), 
2.87/3.09	           app_encode_app(int, int, bit0, 
2.87/3.09	             app_encode_app(int, int, bit1, pls))))
2.87/3.09	        = app_encode_app(int, int, 
2.87/3.09	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.87/3.09	              X0), X0)
2.87/3.09	       | ~ $true
2.87/3.09	       | ~ $true),
2.87/3.09	    inference('demod', [status(thm)], ['17', '0', '0', '18', '19'])).
2.87/3.09	tff('21', plain,
2.87/3.09	    ![X0 : int]:
2.87/3.09	      app_encode_app(nat, int, 
2.87/3.09	        app_encode_app(int, app_encode_fun(nat, int), power_power(int), X0), 
2.87/3.09	        app_encode_app(int, nat, number_number_of(nat), 
2.87/3.09	          app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls))))
2.87/3.09	       = app_encode_app(int, int, 
2.87/3.09	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.87/3.09	             X0), X0),
2.87/3.09	    inference('simplify', [status(thm)], ['20'])).
2.87/3.09	tff('22', plain,
2.87/3.09	    ![X0 : int]:
2.87/3.09	      app_encode_app(nat, int, 
2.87/3.09	        app_encode_app(int, app_encode_fun(nat, int), power_power(int), X0), 
2.87/3.09	        app_encode_app(int, nat, number_number_of(nat), 
2.87/3.09	          app_encode_app(int, int, bit0, t)))
2.87/3.09	       = app_encode_app(int, int, 
2.87/3.09	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.87/3.09	             X0), X0),
2.87/3.09	    inference('demod', [status(thm)], ['21', '4'])).
2.87/3.09	tff(zf_stmt_77, axiom,
2.87/3.09	  (![L1:int,K1:int]:
2.87/3.09	     (app_encode_app(int,int,
2.87/3.09	                     app_encode_app(int,app_encode_fun(int,int),
2.87/3.09	                                    plus_plus(int),
2.87/3.09	                                    app_encode_app(int,int,bit0,K1)),
2.87/3.09	                     app_encode_app(int,int,bit1,L1)) =
2.87/3.09	      app_encode_app(int,int,bit1,
2.87/3.09	                     app_encode_app(int,int,
2.87/3.09	                                    app_encode_app(int,
2.87/3.09	                                                   app_encode_fun(int,int),
2.87/3.09	                                                   plus_plus(int),K1),
2.87/3.09	                                    L1))))).
2.87/3.09	tff('23', plain,
2.87/3.09	    ![X71 : int, X72 : int]:
2.87/3.09	      app_encode_app(int, int, 
2.87/3.09	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.87/3.09	          app_encode_app(int, int, bit0, X71)), 
2.87/3.09	        app_encode_app(int, int, bit1, X72))
2.87/3.09	       = app_encode_app(int, int, bit1, 
2.87/3.09	           app_encode_app(int, int, 
2.87/3.09	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.87/3.09	               X71), X72)),
2.87/3.09	    inference('cnf', [status(esa)], [zf_stmt_77])).
2.87/3.09	tff('24', plain,
2.87/3.09	    ![X0 : int]:
2.87/3.09	      app_encode_app(int, int, 
2.87/3.09	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.87/3.09	          app_encode_app(int, int, bit0, X0)), t)
2.87/3.09	       = app_encode_app(int, int, bit1, 
2.87/3.09	           app_encode_app(int, int, 
2.87/3.09	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.87/3.09	               X0), pls)),
2.87/3.09	    inference('sup+', [status(thm)], ['4', '23'])).
2.87/3.09	tff(zf_stmt_88, axiom,
2.87/3.09	  (![K1:int]:
2.87/3.09	     (app_encode_app(int,int,
2.87/3.09	                     app_encode_app(int,app_encode_fun(int,int),
2.87/3.09	                                    plus_plus(int),K1),
2.87/3.09	                     pls) =
2.87/3.09	      K1))).
2.87/3.09	tff('25', plain,
2.87/3.09	    ![X86 : int]:
2.87/3.09	      app_encode_app(int, int, 
2.87/3.09	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X86), 
2.87/3.09	        pls)
2.87/3.09	       = X86,
2.87/3.09	    inference('cnf', [status(esa)], [zf_stmt_88])).
2.87/3.09	tff('26', plain,
2.87/3.09	    ![X0 : int]:
2.87/3.09	      app_encode_app(int, int, 
2.87/3.09	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.87/3.09	          app_encode_app(int, int, bit0, X0)), t)
2.87/3.09	       = app_encode_app(int, int, bit1, X0),
2.87/3.09	    inference('demod', [status(thm)], ['24', '25'])).
2.87/3.09	tff(zf_stmt_103, axiom,
2.87/3.09	  (![A:$tType]:
2.87/3.09	     (number_ring(A) =>
2.87/3.09	      (![A1:A]:
2.87/3.09	         (app_encode_app(A,A,
2.87/3.09	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
2.87/3.09	                                        A1),
2.87/3.09	                         app_encode_app(int,A,number_number_of(A),
2.87/3.09	                                        app_encode_app(int,int,bit1,pls))) =
2.87/3.09	          A1))))).
2.87/3.09	tff('27', plain,
2.87/3.09	    ![X116 : $tType, X117 : X116]:
2.87/3.09	      (app_encode_app(X116, X116, 
2.87/3.09	         app_encode_app(X116, app_encode_fun(X116, X116), times_times(X116), 
2.87/3.09	           X117), 
2.87/3.09	         app_encode_app(int, X116, number_number_of(X116), 
2.87/3.09	           app_encode_app(int, int, bit1, pls)))
2.87/3.09	        = X117
2.87/3.09	       | ~ number_ring(X116)),
2.87/3.09	    inference('cnf', [status(esa)], [zf_stmt_103])).
2.87/3.09	tff('28', plain,
2.87/3.09	    ![X116 : $tType, X117 : X116]:
2.87/3.09	      (app_encode_app(X116, X116, 
2.87/3.09	         app_encode_app(X116, app_encode_fun(X116, X116), times_times(X116), 
2.87/3.09	           X117), app_encode_app(int, X116, number_number_of(X116), t))
2.87/3.09	        = X117
2.87/3.09	       | ~ number_ring(X116)),
2.87/3.09	    inference('demod', [status(thm)], ['27', '4'])).
2.87/3.09	tff('29', plain,
2.87/3.09	    ![X0 : int]:
2.87/3.09	      (app_encode_app(int, int, 
2.87/3.09	         app_encode_app(int, app_encode_fun(int, int), times_times(int), X0), 
2.87/3.09	         t)
2.87/3.09	        = X0
2.87/3.09	       | ~ number_ring(int)),
2.87/3.09	    inference('sup+', [status(thm)], ['0', '28'])).
2.87/3.09	tff(zf_stmt_146, axiom, (number_ring(int))).
2.87/3.09	tff('30', plain, number_ring(int),
2.87/3.09	    inference('cnf', [status(esa)], [zf_stmt_146])).
2.87/3.09	tff('31', plain,
2.87/3.09	    ![X0 : int]:
2.87/3.09	      (app_encode_app(int, int, 
2.87/3.09	         app_encode_app(int, app_encode_fun(int, int), times_times(int), X0), 
2.87/3.09	         t)
2.87/3.09	        = X0
2.87/3.09	       | ~ $true),
2.87/3.09	    inference('demod', [status(thm)], ['29', '30'])).
2.87/3.09	tff('32', plain,
2.87/3.09	    ![X0 : int]:
2.87/3.09	      app_encode_app(int, int, 
2.87/3.09	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X0), 
2.87/3.09	        t)
2.87/3.09	       = X0,
2.87/3.09	    inference('simplify', [status(thm)], ['31'])).
2.87/3.09	tff('33', plain,
2.87/3.09	    ![X0 : $tType]:
2.87/3.09	      (app_encode_app(X0, X0, 
2.87/3.09	         app_encode_app(X0, app_encode_fun(X0, X0), plus_plus(X0), 
2.87/3.09	           app_encode_app(int, X0, number_number_of(X0), 
2.87/3.09	             app_encode_app(int, int, 
2.87/3.09	               app_encode_app(int, app_encode_fun(int, int), 
2.87/3.09	                 times_times(int), s), s))), one_one(X0))
2.87/3.09	        = app_encode_app(int, X0, number_number_of(X0), 
2.87/3.09	            app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m)))
2.87/3.09	       | ~ number_ring(X0)),
2.87/3.09	    inference('demod', [status(thm)], ['15', '22', '26', '32'])).
2.87/3.09	tff('34', plain,
2.87/3.09	    (app_encode_app(int, int, 
2.87/3.09	       app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.87/3.09	         app_encode_app(int, int, 
2.87/3.09	           app_encode_app(int, app_encode_fun(int, int), times_times(int), s), 
2.87/3.09	           s)), one_one(int))
2.87/3.09	      = app_encode_app(int, int, number_number_of(int), 
2.87/3.09	          app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m)))
2.87/3.09	     | ~ number_ring(int)),
2.87/3.09	    inference('sup+', [status(thm)], ['0', '33'])).
2.87/3.09	tff('35', plain,
2.87/3.09	    (app_encode_app(int, int, 
2.87/3.09	       app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.87/3.09	         app_encode_app(int, int, 
2.87/3.09	           app_encode_app(int, app_encode_fun(int, int), times_times(int), s), 
2.87/3.09	           s)), t)
2.87/3.09	      = app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m))
2.87/3.09	     | ~ $true),
2.87/3.09	    inference('demod', [status(thm)], ['34', '3', '0', '30'])).
2.87/3.09	tff('36', plain,
2.87/3.09	    app_encode_app(int, int, 
2.87/3.09	      app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.87/3.09	        app_encode_app(int, int, 
2.87/3.09	          app_encode_app(int, app_encode_fun(int, int), times_times(int), s), 
2.87/3.09	          s)), t)
2.87/3.09	     = app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m)),
2.87/3.09	    inference('simplify', [status(thm)], ['35'])).
2.87/3.09	tff(zf_stmt_121, axiom,
2.87/3.09	  (![A:$tType]:
2.87/3.09	     (monoid_mult(A) =>
2.87/3.09	      (![N:nat]:
2.87/3.09	         (app_encode_app(nat,A,
2.87/3.09	                         app_encode_app(A,app_encode_fun(nat,A),
2.87/3.09	                                        power_power(A),one_one(A)),
2.87/3.09	                         N) =
2.87/3.09	          one_one(A)))))).
2.87/3.09	tff('37', plain,
2.87/3.09	    ![X142 : $tType, X143 : nat]:
2.87/3.09	      (app_encode_app(nat, X142, 
2.87/3.09	         app_encode_app(X142, app_encode_fun(nat, X142), power_power(X142), 
2.87/3.09	           one_one(X142)), X143)
2.87/3.09	        = one_one(X142)
2.87/3.09	       | ~ monoid_mult(X142)),
2.87/3.09	    inference('cnf', [status(esa)], [zf_stmt_121])).
2.87/3.09	tff('38', plain,
2.87/3.09	    ![X0 : nat]:
2.87/3.09	      (app_encode_app(nat, int, 
2.87/3.09	         app_encode_app(int, app_encode_fun(nat, int), power_power(int), t), 
2.87/3.09	         X0)
2.87/3.09	        = one_one(int)
2.87/3.09	       | ~ monoid_mult(int)),
2.87/3.09	    inference('sup+', [status(thm)], ['3', '37'])).
2.87/3.09	tff('39', plain,
2.87/3.09	    ![X0 : nat]:
2.87/3.09	      (app_encode_app(nat, int, 
2.87/3.09	         app_encode_app(int, app_encode_fun(nat, int), power_power(int), t), 
2.87/3.09	         X0)
2.87/3.09	        = t
2.87/3.09	       | ~ $true),
2.87/3.09	    inference('demod', [status(thm)], ['38', '3', '18'])).
2.87/3.09	tff('40', plain,
2.87/3.09	    ![X0 : nat]:
2.87/3.09	      app_encode_app(nat, int, 
2.87/3.09	        app_encode_app(int, app_encode_fun(nat, int), power_power(int), t), 
2.87/3.09	        X0)
2.87/3.09	       = t,
2.87/3.09	    inference('simplify', [status(thm)], ['39'])).
2.87/3.09	tff(zf_stmt_168, conjecture,
2.87/3.09	  (?[X:int,Y:int]:
2.87/3.09	     (app_encode_app(int,int,
2.87/3.09	                     app_encode_app(int,app_encode_fun(int,int),
2.87/3.09	                                    plus_plus(int),
2.87/3.09	                                    app_encode_app(nat,int,
2.87/3.09	                                                   app_encode_app(int,
2.87/3.09	                                                                  app_encode_fun(
2.87/3.09	                                                                  nat,int),
2.87/3.09	                                                                  power_power(
2.87/3.09	                                                                  int),X),
2.87/3.09	                                                   app_encode_app(int,nat,
2.87/3.09	                                                                  number_number_of(
2.87/3.09	                                                                  nat),
2.87/3.09	                                                                  app_encode_app(
2.87/3.09	                                                                  int,int,
2.87/3.09	                                                                  bit0,
2.87/3.09	                                                                  app_encode_app(
2.87/3.09	                                                                  int,int,
2.87/3.09	                                                                  bit1,pls))))),
2.87/3.09	                     app_encode_app(nat,int,
2.87/3.09	                                    app_encode_app(int,
2.87/3.09	                                                   app_encode_fun(nat,int),
2.87/3.09	                                                   power_power(int),Y),
2.87/3.09	                                    app_encode_app(int,nat,
2.87/3.09	                                                   number_number_of(nat),
2.87/3.09	                                                   app_encode_app(int,int,
2.87/3.09	                                                                  bit0,
2.87/3.09	                                                                  app_encode_app(
2.87/3.09	                                                                  int,int,
2.87/3.09	                                                                  bit1,pls))))) =
2.87/3.09	      app_encode_app(int,int,
2.87/3.09	                     app_encode_app(int,app_encode_fun(int,int),
2.87/3.09	                                    plus_plus(int),
2.87/3.09	                                    app_encode_app(int,int,
2.87/3.09	                                                   app_encode_app(int,
2.87/3.09	                                                                  app_encode_fun(
2.87/3.09	                                                                  int,int),
2.87/3.09	                                                                  times_times(
2.87/3.09	                                                                  int),
2.87/3.09	                                                                  app_encode_app(
2.87/3.09	                                                                  int,int,
2.87/3.09	                                                                  number_number_of(
2.87/3.09	                                                                  int),
2.87/3.09	                                                                  app_encode_app(
2.87/3.09	                                                                  int,int,
2.87/3.09	                                                                  bit0,
2.87/3.09	                                                                  app_encode_app(
2.87/3.09	                                                                  int,int,
2.87/3.09	                                                                  bit0,
2.87/3.09	                                                                  app_encode_app(
2.87/3.09	                                                                  int,int,
2.87/3.09	                                                                  bit1,pls))))),
2.87/3.09	                                                   m)),
2.87/3.09	                     one_one(int))))).
2.87/3.09	tff(zf_stmt_0, negated_conjecture,
2.87/3.09	  (~
2.87/3.09	    (?[X:int,Y:int]:
2.87/3.09	       (app_encode_app(int,int,
2.87/3.09	                       app_encode_app(int,app_encode_fun(int,int),
2.87/3.09	                                      plus_plus(int),
2.87/3.09	                                      app_encode_app(nat,int,
2.87/3.09	                                                     app_encode_app(int,
2.87/3.09	                                                                    app_encode_fun(
2.87/3.09	                                                                    nat,int),
2.87/3.09	                                                                    power_power(
2.87/3.09	                                                                    int),X),
2.87/3.09	                                                     app_encode_app(int,nat,
2.87/3.09	                                                                    number_number_of(
2.87/3.09	                                                                    nat),
2.87/3.09	                                                                    app_encode_app(
2.87/3.09	                                                                    int,int,
2.87/3.09	                                                                    bit0,
2.87/3.09	                                                                    app_encode_app(
2.87/3.09	                                                                    int,int,
2.87/3.09	                                                                    bit1,pls))))),
2.87/3.09	                       app_encode_app(nat,int,
2.87/3.09	                                      app_encode_app(int,
2.87/3.09	                                                     app_encode_fun(nat,int),
2.87/3.09	                                                     power_power(int),Y),
2.87/3.09	                                      app_encode_app(int,nat,
2.87/3.09	                                                     number_number_of(nat),
2.87/3.09	                                                     app_encode_app(int,int,
2.87/3.09	                                                                    bit0,
2.87/3.09	                                                                    app_encode_app(
2.87/3.09	                                                                    int,int,
2.87/3.09	                                                                    bit1,pls))))) =
2.87/3.09	        app_encode_app(int,int,
2.87/3.09	                       app_encode_app(int,app_encode_fun(int,int),
2.87/3.09	                                      plus_plus(int),
2.87/3.09	                                      app_encode_app(int,int,
2.87/3.09	                                                     app_encode_app(int,
2.87/3.09	                                                                    app_encode_fun(
2.87/3.09	                                                                    int,int),
2.87/3.09	                                                                    times_times(
2.87/3.09	                                                                    int),
2.87/3.09	                                                                    app_encode_app(
2.87/3.09	                                                                    int,int,
2.87/3.09	                                                                    number_number_of(
2.87/3.09	                                                                    int),
2.87/3.09	                                                                    app_encode_app(
2.87/3.09	                                                                    int,int,
2.87/3.09	                                                                    bit0,
2.87/3.09	                                                                    app_encode_app(
2.87/3.09	                                                                    int,int,
2.87/3.09	                                                                    bit0,
2.87/3.09	                                                                    app_encode_app(
2.87/3.09	                                                                    int,int,
2.87/3.09	                                                                    bit1,pls))))),
2.87/3.09	                                                     m)),
2.87/3.09	                       one_one(int)))))).
2.87/3.09	tff('41', plain,
2.87/3.09	    ![X181 : int, X182 : int]:
2.87/3.09	      app_encode_app(int, int, 
2.87/3.09	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.87/3.09	          app_encode_app(nat, int, 
2.87/3.09	            app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
2.87/3.09	              X181), 
2.87/3.09	            app_encode_app(int, nat, number_number_of(nat), 
2.87/3.09	              app_encode_app(int, int, bit0, 
2.87/3.09	                app_encode_app(int, int, bit1, pls))))), 
2.87/3.09	        app_encode_app(nat, int, 
2.87/3.09	          app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
2.87/3.09	            X182), 
2.87/3.09	          app_encode_app(int, nat, number_number_of(nat), 
2.87/3.09	            app_encode_app(int, int, bit0, 
2.87/3.09	              app_encode_app(int, int, bit1, pls)))))
2.87/3.09	       != app_encode_app(int, int, 
2.87/3.09	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.87/3.09	              app_encode_app(int, int, 
2.87/3.09	                app_encode_app(int, app_encode_fun(int, int), 
2.87/3.09	                  times_times(int), 
2.87/3.09	                  app_encode_app(int, int, number_number_of(int), 
2.87/3.09	                    app_encode_app(int, int, bit0, 
2.87/3.09	                      app_encode_app(int, int, bit0, 
2.87/3.09	                        app_encode_app(int, int, bit1, pls))))), m)), 
2.87/3.09	            one_one(int)),
2.87/3.09	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.87/3.09	tff(zf_stmt_2, axiom,
2.87/3.09	  (![X:app_encode_fun(Alpha,Beta),Y:app_encode_fun(Alpha,Beta)]:
2.87/3.09	     ((![Z:Alpha]:
2.87/3.09	         (app_encode_app(Alpha,Beta,X,Z) = app_encode_app(Alpha,Beta,Y,Z))) =>
2.87/3.09	      (X = Y)))).
2.87/3.09	tff('42', plain,
2.87/3.09	    ![X0 : $tType, X1 : $tType, X2 : app_encode_fun(X0, X1), 
2.87/3.09	      X3 : app_encode_fun(X0, X1)]:
2.87/3.09	      (X3 = X2
2.87/3.09	       | app_encode_app(X0, X1, X3, sk_Z(X1, X0, X2, X3))
2.87/3.09	          != app_encode_app(X0, X1, X2, sk_Z(X1, X0, X2, X3))),
2.87/3.09	    inference('cnf', [status(esa)], [zf_stmt_2])).
2.87/3.09	tff('43', plain,
2.87/3.09	    ![X0 : app_encode_fun(int, int)]:
2.87/3.09	      (app_encode_app(int, int, X0, 
2.87/3.09	         sk_Z(int, int, number_number_of(int), X0))
2.87/3.09	        != sk_Z(int, int, number_number_of(int), X0)
2.87/3.09	       | X0 = number_number_of(int)),
2.87/3.09	    inference('sup-', [status(thm)], ['0', '42'])).
2.87/3.09	tff('44', plain,
2.87/3.09	    (sk_Z(int, int, number_number_of(int), 
2.87/3.09	       app_encode_app(int, app_encode_fun(int, int), times_times(int), t))
2.87/3.09	      != sk_Z(int, int, number_number_of(int), 
2.87/3.09	           app_encode_app(int, app_encode_fun(int, int), times_times(int), t))
2.87/3.09	     | app_encode_app(int, app_encode_fun(int, int), times_times(int), t)
2.87/3.09	        = number_number_of(int)),
2.87/3.09	    inference('sup-', [status(thm)], ['11', '43'])).
2.87/3.09	tff('45', plain,
2.87/3.09	    app_encode_app(int, app_encode_fun(int, int), times_times(int), t)
2.87/3.09	     = number_number_of(int),
2.87/3.09	    inference('simplify', [status(thm)], ['44'])).
2.87/3.09	tff('46', plain,
2.87/3.09	    ![X181 : int, X182 : int]:
2.87/3.09	      app_encode_app(int, int, 
2.87/3.09	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.87/3.09	          app_encode_app(nat, int, 
2.87/3.09	            app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
2.87/3.09	              X181), 
2.87/3.09	            app_encode_app(int, nat, number_number_of(nat), 
2.87/3.09	              app_encode_app(int, int, bit0, t)))), 
2.87/3.09	        app_encode_app(nat, int, 
2.87/3.09	          app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
2.87/3.09	            X182), 
2.87/3.09	          app_encode_app(int, nat, number_number_of(nat), 
2.87/3.09	            app_encode_app(int, int, bit0, t))))
2.87/3.09	       != app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m)),
2.87/3.09	    inference('demod', [status(thm)],
2.87/3.09	              ['41', '4', '4', '4', '0', '5', '5', '45', '0', '3', '26'])).
2.87/3.09	tff('47', plain,
2.87/3.09	    ![X0 : int]:
2.87/3.09	      app_encode_app(int, int, 
2.87/3.09	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.87/3.09	          app_encode_app(nat, int, 
2.87/3.09	            app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
2.87/3.09	              X0), 
2.87/3.09	            app_encode_app(int, nat, number_number_of(nat), 
2.87/3.09	              app_encode_app(int, int, bit0, t)))), t)
2.87/3.09	       != app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m)),
2.87/3.09	    inference('sup-', [status(thm)], ['40', '46'])).
2.87/3.09	tff('48', plain,
2.87/3.09	    ![X0 : int]:
2.87/3.09	      app_encode_app(int, int, 
2.87/3.09	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
2.87/3.09	          app_encode_app(int, int, 
2.87/3.09	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.87/3.09	              X0), X0)), t)
2.87/3.09	       != app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m)),
2.87/3.09	    inference('sup-', [status(thm)], ['22', '47'])).
2.87/3.09	tff('49', plain, $false,
2.87/3.09	    inference('simplify_reflect-', [status(thm)], ['36', '48'])).
2.87/3.09	
2.87/3.09	% SZS output end Refutation
2.87/3.09	EOF
