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    : rpo6
0.00/0.00	% Command    : 
0.00/0.01	#!/bin/sh
0.00/0.01	
0.00/0.01	./zipperposition.native ${1:+"$1"} \
0.00/0.01	  -i tptp \
0.00/0.01	  -o tptp \
0.00/0.01	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.01	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.01	  --no-ho \
0.00/0.01	  --no-avatar \
0.00/0.01	  --no-induction \
0.00/0.01	  --no-unif-pattern \
0.00/0.01	  --ord $2 \
0.00/0.01	  --simultaneous-sup false \
0.00/0.01	  --no-max-vars \
0.00/0.01	  --no-fool
0.00/0.20	% Computer   : n132.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 09:46:09 CST 2018
2.82/3.07	% done 1195 iterations in 2.869s
2.82/3.07	% SZS status Theorem for 'stdin'
2.82/3.07	% SZS output start Refutation
2.82/3.08	tff(zf_stmt_190, conjecture,
2.82/3.08	  (app_encode_app(real,real,
2.82/3.08	                  app_encode_app(fun(real,real),app_encode_fun(real,real),
2.82/3.08	                                 aa(real,real),sqrt),
2.82/3.08	                  app_encode_app(int,real,number_number_of(real),
2.82/3.08	                                 app_encode_app(int,int,bit0,
2.82/3.08	                                                app_encode_app(int,int,bit0,
2.82/3.08	                                                               app_encode_app(
2.82/3.08	                                                               int,int,bit1,
2.82/3.08	                                                               pls))))) =
2.82/3.08	   app_encode_app(real,real,
2.82/3.08	                  app_encode_app(fun(real,real),app_encode_fun(real,real),
2.82/3.08	                                 aa(real,real),sqrt),
2.82/3.08	                  app_encode_app(nat,real,
2.82/3.08	                                 app_encode_app(real,
2.82/3.08	                                                app_encode_fun(nat,real),
2.82/3.08	                                                power_power(real),
2.82/3.08	                                                app_encode_app(int,real,
2.82/3.08	                                                               number_number_of(
2.82/3.08	                                                               real),
2.82/3.08	                                                               app_encode_app(
2.82/3.08	                                                               int,int,bit0,
2.82/3.08	                                                               app_encode_app(
2.82/3.08	                                                               int,int,bit1,
2.82/3.08	                                                               pls)))),
2.82/3.08	                                 app_encode_app(int,nat,
2.82/3.08	                                                number_number_of(nat),
2.82/3.08	                                                app_encode_app(int,int,bit0,
2.82/3.08	                                                               app_encode_app(
2.82/3.08	                                                               int,int,bit1,
2.82/3.08	                                                               pls))))))).
2.82/3.08	tff(zf_stmt_0, negated_conjecture,
2.82/3.08	  (app_encode_app(real,real,
2.82/3.08	                  app_encode_app(fun(real,real),app_encode_fun(real,real),
2.82/3.08	                                 aa(real,real),sqrt),
2.82/3.08	                  app_encode_app(int,real,number_number_of(real),
2.82/3.08	                                 app_encode_app(int,int,bit0,
2.82/3.08	                                                app_encode_app(int,int,bit0,
2.82/3.08	                                                               app_encode_app(
2.82/3.08	                                                               int,int,bit1,
2.82/3.08	                                                               pls))))) !=
2.82/3.08	   app_encode_app(real,real,
2.82/3.08	                  app_encode_app(fun(real,real),app_encode_fun(real,real),
2.82/3.08	                                 aa(real,real),sqrt),
2.82/3.08	                  app_encode_app(nat,real,
2.82/3.08	                                 app_encode_app(real,
2.82/3.08	                                                app_encode_fun(nat,real),
2.82/3.08	                                                power_power(real),
2.82/3.08	                                                app_encode_app(int,real,
2.82/3.08	                                                               number_number_of(
2.82/3.08	                                                               real),
2.82/3.08	                                                               app_encode_app(
2.82/3.08	                                                               int,int,bit0,
2.82/3.08	                                                               app_encode_app(
2.82/3.08	                                                               int,int,bit1,
2.82/3.08	                                                               pls)))),
2.82/3.08	                                 app_encode_app(int,nat,
2.82/3.08	                                                number_number_of(nat),
2.82/3.08	                                                app_encode_app(int,int,bit0,
2.82/3.08	                                                               app_encode_app(
2.82/3.08	                                                               int,int,bit1,
2.82/3.08	                                                               pls))))))).
2.82/3.08	tff('0', plain,
2.82/3.08	    app_encode_app(real, real, 
2.82/3.08	      app_encode_app(fun(real, real), app_encode_fun(real, real), 
2.82/3.08	        aa(real, real), sqrt), 
2.82/3.08	      app_encode_app(int, real, number_number_of(real), 
2.82/3.08	        app_encode_app(int, int, bit0, 
2.82/3.08	          app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls)))))
2.82/3.08	     != app_encode_app(real, real, 
2.82/3.08	          app_encode_app(fun(real, real), app_encode_fun(real, real), 
2.82/3.08	            aa(real, real), sqrt), 
2.82/3.08	          app_encode_app(nat, real, 
2.82/3.08	            app_encode_app(real, app_encode_fun(nat, real), 
2.82/3.08	              power_power(real), 
2.82/3.08	              app_encode_app(int, real, number_number_of(real), 
2.82/3.08	                app_encode_app(int, int, bit0, 
2.82/3.08	                  app_encode_app(int, int, bit1, pls)))), 
2.82/3.08	            app_encode_app(int, nat, number_number_of(nat), 
2.82/3.08	              app_encode_app(int, int, bit0, 
2.82/3.08	                app_encode_app(int, int, bit1, pls))))),
2.82/3.08	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.82/3.08	tff(zf_stmt_100, axiom, (pls = zero_zero(int))).
2.82/3.08	tff('1', plain, pls = zero_zero(int),
2.82/3.08	    inference('cnf', [status(esa)], [zf_stmt_100])).
2.82/3.08	tff(zf_stmt_180, axiom, (monoid_mult(real))).
2.82/3.08	tff('2', plain, monoid_mult(real),
2.82/3.08	    inference('cnf', [status(esa)], [zf_stmt_180])).
2.82/3.08	tff(zf_stmt_111, axiom,
2.82/3.08	  (![A:$tType]:
2.82/3.08	     (monoid_mult(A) =>
2.82/3.08	      (![A1:A]:
2.82/3.08	         (app_encode_app(nat,A,
2.82/3.08	                         app_encode_app(A,app_encode_fun(nat,A),
2.82/3.08	                                        power_power(A),A1),
2.82/3.08	                         app_encode_app(int,nat,number_number_of(nat),
2.82/3.08	                                        app_encode_app(int,int,bit0,
2.82/3.08	                                                       app_encode_app(
2.82/3.08	                                                       int,int,bit1,pls)))) =
2.82/3.08	          app_encode_app(A,A,
2.82/3.08	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
2.82/3.08	                                        A1),
2.82/3.08	                         A1)))))).
2.82/3.08	tff('3', plain,
2.82/3.08	    ![X144 : $tType, X145 : X144]:
2.82/3.08	      (app_encode_app(nat, X144, 
2.82/3.08	         app_encode_app(X144, app_encode_fun(nat, X144), power_power(X144), 
2.82/3.08	           X145), 
2.82/3.08	         app_encode_app(int, nat, number_number_of(nat), 
2.82/3.08	           app_encode_app(int, int, bit0, 
2.82/3.08	             app_encode_app(int, int, bit1, pls))))
2.82/3.08	        = app_encode_app(X144, X144, 
2.82/3.08	            app_encode_app(X144, app_encode_fun(X144, X144), 
2.82/3.08	              times_times(X144), X145), X145)
2.82/3.08	       | ~ monoid_mult(X144)),
2.82/3.08	    inference('cnf', [status(esa)], [zf_stmt_111])).
2.82/3.08	tff('4', plain,
2.82/3.08	    ![X144 : $tType, X145 : X144]:
2.82/3.08	      (app_encode_app(nat, X144, 
2.82/3.08	         app_encode_app(X144, app_encode_fun(nat, X144), power_power(X144), 
2.82/3.08	           X145), 
2.82/3.08	         app_encode_app(int, nat, number_number_of(nat), 
2.82/3.08	           app_encode_app(int, int, bit0, 
2.82/3.08	             app_encode_app(int, int, bit1, zero_zero(int)))))
2.82/3.08	        = app_encode_app(X144, X144, 
2.82/3.08	            app_encode_app(X144, app_encode_fun(X144, X144), 
2.82/3.08	              times_times(X144), X145), X145)
2.82/3.08	       | ~ monoid_mult(X144)),
2.82/3.08	    inference('demod', [status(thm)], ['3', '1'])).
2.82/3.08	tff('5', plain,
2.82/3.08	    ![X0 : real]:
2.82/3.08	      (~ $true
2.82/3.08	       | app_encode_app(nat, real, 
2.82/3.08	           app_encode_app(real, app_encode_fun(nat, real), 
2.82/3.08	             power_power(real), X0), 
2.82/3.08	           app_encode_app(int, nat, number_number_of(nat), 
2.82/3.08	             app_encode_app(int, int, bit0, 
2.82/3.08	               app_encode_app(int, int, bit1, zero_zero(int)))))
2.82/3.08	          = app_encode_app(real, real, 
2.82/3.08	              app_encode_app(real, app_encode_fun(real, real), 
2.82/3.08	                times_times(real), X0), X0)),
2.82/3.08	    inference('sup-', [status(thm)], ['2', '4'])).
2.82/3.08	tff('6', plain,
2.82/3.08	    ![X0 : real]:
2.82/3.08	      app_encode_app(nat, real, 
2.82/3.08	        app_encode_app(real, app_encode_fun(nat, real), power_power(real), 
2.82/3.08	          X0), 
2.82/3.08	        app_encode_app(int, nat, number_number_of(nat), 
2.82/3.08	          app_encode_app(int, int, bit0, 
2.82/3.08	            app_encode_app(int, int, bit1, zero_zero(int)))))
2.82/3.08	       = app_encode_app(real, real, 
2.82/3.08	           app_encode_app(real, app_encode_fun(real, real), 
2.82/3.08	             times_times(real), X0), X0),
2.82/3.08	    inference('simplify', [status(thm)], ['5'])).
2.82/3.08	tff(zf_stmt_184, axiom, (number_ring(real))).
2.82/3.08	tff('7', plain, number_ring(real),
2.82/3.08	    inference('cnf', [status(esa)], [zf_stmt_184])).
2.82/3.08	tff(zf_stmt_77, axiom,
2.82/3.08	  (![A:$tType]:
2.82/3.08	     (number_ring(A) =>
2.82/3.08	      (![W:int,V:int]:
2.82/3.08	         (app_encode_app(A,A,
2.82/3.08	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
2.82/3.08	                                        app_encode_app(int,A,
2.82/3.08	                                                       number_number_of(A),V)),
2.82/3.08	                         app_encode_app(int,A,number_number_of(A),W)) =
2.82/3.08	          app_encode_app(int,A,number_number_of(A),
2.82/3.08	                         app_encode_app(int,int,
2.82/3.08	                                        app_encode_app(int,
2.82/3.08	                                                       app_encode_fun(
2.82/3.08	                                                       int,int),
2.82/3.08	                                                       times_times(int),V),
2.82/3.08	                                        W))))))).
2.82/3.08	tff('8', plain,
2.82/3.08	    ![X62 : $tType, X63 : int, X64 : int]:
2.82/3.08	      (app_encode_app(X62, X62, 
2.82/3.08	         app_encode_app(X62, app_encode_fun(X62, X62), times_times(X62), 
2.82/3.08	           app_encode_app(int, X62, number_number_of(X62), X63)), 
2.82/3.08	         app_encode_app(int, X62, number_number_of(X62), X64))
2.82/3.08	        = app_encode_app(int, X62, number_number_of(X62), 
2.82/3.08	            app_encode_app(int, int, 
2.82/3.08	              app_encode_app(int, app_encode_fun(int, int), 
2.82/3.08	                times_times(int), X63), X64))
2.82/3.08	       | ~ number_ring(X62)),
2.82/3.08	    inference('cnf', [status(esa)], [zf_stmt_77])).
2.82/3.08	tff('9', plain,
2.82/3.08	    ![X0 : int, X1 : int]:
2.82/3.08	      (~ $true
2.82/3.08	       | app_encode_app(real, real, 
2.82/3.08	           app_encode_app(real, app_encode_fun(real, real), 
2.82/3.08	             times_times(real), 
2.82/3.08	             app_encode_app(int, real, number_number_of(real), X1)), 
2.82/3.08	           app_encode_app(int, real, number_number_of(real), X0))
2.82/3.08	          = app_encode_app(int, real, number_number_of(real), 
2.82/3.08	              app_encode_app(int, int, 
2.82/3.08	                app_encode_app(int, app_encode_fun(int, int), 
2.82/3.08	                  times_times(int), X1), X0))),
2.82/3.08	    inference('sup-', [status(thm)], ['7', '8'])).
2.82/3.08	tff('10', plain,
2.82/3.08	    ![X0 : int, X1 : int]:
2.82/3.08	      app_encode_app(real, real, 
2.82/3.08	        app_encode_app(real, app_encode_fun(real, real), times_times(real), 
2.82/3.08	          app_encode_app(int, real, number_number_of(real), X1)), 
2.82/3.08	        app_encode_app(int, real, number_number_of(real), X0))
2.82/3.08	       = app_encode_app(int, real, number_number_of(real), 
2.82/3.08	           app_encode_app(int, int, 
2.82/3.08	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.82/3.08	               X1), X0)),
2.82/3.08	    inference('simplify', [status(thm)], ['9'])).
2.82/3.08	tff(zf_stmt_176, axiom, (comm_semiring_1(real))).
2.82/3.08	tff('11', plain, comm_semiring_1(real),
2.82/3.08	    inference('cnf', [status(esa)], [zf_stmt_176])).
2.82/3.08	tff(zf_stmt_129, axiom,
2.82/3.08	  (![A:$tType]:
2.82/3.08	     (comm_semiring_1(A) =>
2.82/3.08	      (![B:A,A1:A]:
2.82/3.08	         (app_encode_app(A,A,
2.82/3.08	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
2.82/3.08	                                        A1),
2.82/3.08	                         B) =
2.82/3.08	          app_encode_app(A,A,
2.82/3.08	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
2.82/3.08	                                        B),
2.82/3.08	                         A1)))))).
2.82/3.08	tff('12', plain,
2.82/3.08	    ![X193 : $tType, X194 : X193, X195 : X193]:
2.82/3.08	      (app_encode_app(X193, X193, 
2.82/3.08	         app_encode_app(X193, app_encode_fun(X193, X193), times_times(X193), 
2.82/3.08	           X195), X194)
2.82/3.08	        = app_encode_app(X193, X193, 
2.82/3.08	            app_encode_app(X193, app_encode_fun(X193, X193), 
2.82/3.08	              times_times(X193), X194), X195)
2.82/3.08	       | ~ comm_semiring_1(X193)),
2.82/3.08	    inference('cnf', [status(esa)], [zf_stmt_129])).
2.82/3.08	tff('13', plain,
2.82/3.08	    ![X0 : real, X1 : real]:
2.82/3.08	      (~ $true
2.82/3.08	       | app_encode_app(real, real, 
2.82/3.08	           app_encode_app(real, app_encode_fun(real, real), 
2.82/3.08	             times_times(real), X1), X0)
2.82/3.08	          = app_encode_app(real, real, 
2.82/3.08	              app_encode_app(real, app_encode_fun(real, real), 
2.82/3.08	                times_times(real), X0), X1)),
2.82/3.08	    inference('sup-', [status(thm)], ['11', '12'])).
2.82/3.08	tff('14', plain,
2.82/3.08	    ![X0 : real, X1 : real]:
2.82/3.08	      app_encode_app(real, real, 
2.82/3.08	        app_encode_app(real, app_encode_fun(real, real), times_times(real), 
2.82/3.08	          X1), X0)
2.82/3.08	       = app_encode_app(real, real, 
2.82/3.08	           app_encode_app(real, app_encode_fun(real, real), 
2.82/3.08	             times_times(real), X0), X1),
2.82/3.08	    inference('simplify', [status(thm)], ['13'])).
2.82/3.08	tff('15', plain,
2.82/3.08	    ![X0 : int, X1 : int]:
2.82/3.08	      app_encode_app(real, real, 
2.82/3.08	        app_encode_app(real, app_encode_fun(real, real), times_times(real), 
2.82/3.08	          app_encode_app(int, real, number_number_of(real), X0)), 
2.82/3.08	        app_encode_app(int, real, number_number_of(real), X1))
2.82/3.08	       = app_encode_app(int, real, number_number_of(real), 
2.82/3.08	           app_encode_app(int, int, 
2.82/3.08	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.82/3.08	               X1), X0)),
2.82/3.08	    inference('sup+', [status(thm)], ['10', '14'])).
2.82/3.08	tff(zf_stmt_148, axiom, (comm_semiring_1(int))).
2.82/3.08	tff('16', plain, comm_semiring_1(int),
2.82/3.08	    inference('cnf', [status(esa)], [zf_stmt_148])).
2.82/3.08	tff('17', plain,
2.82/3.08	    ![X0 : int, X1 : int]:
2.82/3.08	      (~ $true
2.82/3.08	       | app_encode_app(int, int, 
2.82/3.08	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.82/3.08	             X1), X0)
2.82/3.08	          = app_encode_app(int, int, 
2.82/3.08	              app_encode_app(int, app_encode_fun(int, int), 
2.82/3.08	                times_times(int), X0), X1)),
2.82/3.08	    inference('sup-', [status(thm)], ['16', '12'])).
2.82/3.08	tff('18', plain,
2.82/3.08	    ![X0 : int, X1 : int]:
2.82/3.08	      app_encode_app(int, int, 
2.82/3.08	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X1), 
2.82/3.08	        X0)
2.82/3.08	       = app_encode_app(int, int, 
2.82/3.08	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.82/3.08	             X0), X1),
2.82/3.08	    inference('simplify', [status(thm)], ['17'])).
2.82/3.08	tff(zf_stmt_73, axiom,
2.82/3.08	  (![L:int,K:int]:
2.82/3.08	     (app_encode_app(int,int,
2.82/3.08	                     app_encode_app(int,app_encode_fun(int,int),
2.82/3.08	                                    times_times(int),
2.82/3.08	                                    app_encode_app(int,int,bit0,K)),
2.82/3.08	                     L) =
2.82/3.08	      app_encode_app(int,int,bit0,
2.82/3.08	                     app_encode_app(int,int,
2.82/3.08	                                    app_encode_app(int,
2.82/3.08	                                                   app_encode_fun(int,int),
2.82/3.08	                                                   times_times(int),K),
2.82/3.08	                                    L))))).
2.82/3.08	tff('19', plain,
2.82/3.08	    ![X57 : int, X58 : int]:
2.82/3.08	      app_encode_app(int, int, 
2.82/3.08	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.82/3.08	          app_encode_app(int, int, bit0, X57)), X58)
2.82/3.08	       = app_encode_app(int, int, bit0, 
2.82/3.08	           app_encode_app(int, int, 
2.82/3.08	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.82/3.08	               X57), X58)),
2.82/3.08	    inference('cnf', [status(esa)], [zf_stmt_73])).
2.82/3.08	tff('20', plain,
2.82/3.08	    ![X0 : int, X1 : int]:
2.82/3.08	      app_encode_app(int, int, 
2.82/3.08	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X1), 
2.82/3.08	        app_encode_app(int, int, bit0, X0))
2.82/3.08	       = app_encode_app(int, int, bit0, 
2.82/3.08	           app_encode_app(int, int, 
2.82/3.08	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.82/3.08	               X0), X1)),
2.82/3.08	    inference('sup+', [status(thm)], ['18', '19'])).
2.82/3.08	tff('21', plain,
2.82/3.08	    ![X0 : int, X1 : int]:
2.82/3.08	      app_encode_app(int, int, 
2.82/3.08	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X1), 
2.82/3.08	        app_encode_app(int, int, bit0, X0))
2.82/3.08	       = app_encode_app(int, int, bit0, 
2.82/3.08	           app_encode_app(int, int, 
2.82/3.08	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.82/3.08	               X1), X0)),
2.82/3.08	    inference('sup+', [status(thm)], ['18', '20'])).
2.82/3.08	tff('22', plain,
2.82/3.08	    ![X0 : int, X1 : int]:
2.82/3.08	      app_encode_app(int, int, 
2.82/3.08	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X0), 
2.82/3.08	        app_encode_app(int, int, bit0, X1))
2.82/3.08	       = app_encode_app(int, int, 
2.82/3.08	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.82/3.08	             X1), app_encode_app(int, int, bit0, X0)),
2.82/3.08	    inference('sup+', [status(thm)], ['21', '20'])).
2.82/3.08	tff('23', plain,
2.82/3.08	    ![X0 : int, X1 : int]:
2.82/3.08	      app_encode_app(int, int, 
2.82/3.08	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X1), 
2.82/3.08	        app_encode_app(int, int, bit0, X0))
2.82/3.08	       = app_encode_app(int, int, 
2.82/3.08	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.82/3.08	             app_encode_app(int, int, bit0, X1)), X0),
2.82/3.08	    inference('sup+', [status(thm)], ['22', '18'])).
2.82/3.08	tff(zf_stmt_155, axiom, (number_ring(int))).
2.82/3.08	tff('24', plain, number_ring(int),
2.82/3.08	    inference('cnf', [status(esa)], [zf_stmt_155])).
2.82/3.08	tff(zf_stmt_107, axiom,
2.82/3.08	  (![A:$tType]:
2.82/3.08	     (number_ring(A) =>
2.82/3.08	      (![A1:A]:
2.82/3.08	         (app_encode_app(A,A,
2.82/3.08	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
2.82/3.08	                                        app_encode_app(int,A,
2.82/3.08	                                                       number_number_of(A),
2.82/3.08	                                                       app_encode_app(
2.82/3.08	                                                       int,int,bit1,pls))),
2.82/3.08	                         A1) =
2.82/3.08	          A1))))).
2.82/3.08	tff('25', plain,
2.82/3.08	    ![X137 : $tType, X138 : X137]:
2.82/3.08	      (app_encode_app(X137, X137, 
2.82/3.08	         app_encode_app(X137, app_encode_fun(X137, X137), times_times(X137), 
2.82/3.08	           app_encode_app(int, X137, number_number_of(X137), 
2.82/3.08	             app_encode_app(int, int, bit1, pls))), X138)
2.82/3.08	        = X138
2.82/3.08	       | ~ number_ring(X137)),
2.82/3.08	    inference('cnf', [status(esa)], [zf_stmt_107])).
2.82/3.08	tff('26', plain,
2.82/3.08	    ![X137 : $tType, X138 : X137]:
2.82/3.08	      (app_encode_app(X137, X137, 
2.82/3.08	         app_encode_app(X137, app_encode_fun(X137, X137), times_times(X137), 
2.82/3.08	           app_encode_app(int, X137, number_number_of(X137), 
2.82/3.08	             app_encode_app(int, int, bit1, zero_zero(int)))), X138)
2.82/3.08	        = X138
2.82/3.08	       | ~ number_ring(X137)),
2.82/3.08	    inference('demod', [status(thm)], ['25', '1'])).
2.82/3.08	tff('27', plain,
2.82/3.08	    ![X0 : int]:
2.82/3.08	      (~ $true
2.82/3.08	       | app_encode_app(int, int, 
2.82/3.08	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.82/3.08	             app_encode_app(int, int, number_number_of(int), 
2.82/3.08	               app_encode_app(int, int, bit1, zero_zero(int)))), X0)
2.82/3.08	          = X0),
2.82/3.08	    inference('sup-', [status(thm)], ['24', '26'])).
2.82/3.08	tff(zf_stmt_126, axiom,
2.82/3.08	  (![K:int]: (app_encode_app(int,int,number_number_of(int),K) = K))).
2.82/3.08	tff('28', plain,
2.82/3.08	    ![X187 : int]:
2.82/3.08	      app_encode_app(int, int, number_number_of(int), X187) = X187,
2.82/3.08	    inference('cnf', [status(esa)], [zf_stmt_126])).
2.82/3.08	tff('29', plain,
2.82/3.08	    ![X0 : int]:
2.82/3.08	      (~ $true
2.82/3.08	       | app_encode_app(int, int, 
2.82/3.08	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.82/3.08	             app_encode_app(int, int, bit1, zero_zero(int))), X0)
2.82/3.08	          = X0),
2.82/3.08	    inference('demod', [status(thm)], ['27', '28'])).
2.82/3.08	tff('30', plain,
2.82/3.08	    ![X0 : int]:
2.82/3.08	      app_encode_app(int, int, 
2.82/3.08	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.82/3.08	          app_encode_app(int, int, bit1, zero_zero(int))), X0)
2.82/3.08	       = X0,
2.82/3.08	    inference('simplify', [status(thm)], ['29'])).
2.82/3.08	tff(zf_stmt_2, axiom,
2.82/3.08	  (![X:app_encode_fun(Alpha,Beta),Y:app_encode_fun(Alpha,Beta)]:
2.82/3.08	     ((![Z:Alpha]:
2.82/3.08	         (app_encode_app(Alpha,Beta,X,Z) = app_encode_app(Alpha,Beta,Y,Z))) =>
2.82/3.08	      (X = Y)))).
2.82/3.08	tff('31', plain,
2.82/3.08	    ![X0 : $tType, X1 : $tType, X2 : app_encode_fun(X0, X1), 
2.82/3.08	      X3 : app_encode_fun(X0, X1)]:
2.82/3.08	      (X3 = X2
2.82/3.08	       | app_encode_app(X0, X1, X3, sk_Z(X1, X0, X2, X3))
2.82/3.08	          != app_encode_app(X0, X1, X2, sk_Z(X1, X0, X2, X3))),
2.82/3.08	    inference('cnf', [status(esa)], [zf_stmt_2])).
2.82/3.08	tff('32', plain,
2.82/3.08	    ![X0 : app_encode_fun(int, int)]:
2.82/3.08	      (sk_Z(int, int, X0, number_number_of(int))
2.82/3.08	        != app_encode_app(int, int, X0, 
2.82/3.08	             sk_Z(int, int, X0, number_number_of(int)))
2.82/3.08	       | number_number_of(int) = X0),
2.82/3.08	    inference('sup-', [status(thm)], ['28', '31'])).
2.82/3.08	tff('33', plain,
2.82/3.08	    (sk_Z(int, int, 
2.82/3.08	       app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.82/3.08	         app_encode_app(int, int, bit1, zero_zero(int))), 
2.82/3.08	       number_number_of(int))
2.82/3.08	      != sk_Z(int, int, 
2.82/3.08	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.82/3.08	             app_encode_app(int, int, bit1, zero_zero(int))), 
2.82/3.08	           number_number_of(int))
2.82/3.08	     | number_number_of(int)
2.82/3.08	        = app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.82/3.08	            app_encode_app(int, int, bit1, zero_zero(int)))),
2.82/3.08	    inference('sup-', [status(thm)], ['30', '32'])).
2.82/3.08	tff('34', plain,
2.82/3.08	    number_number_of(int)
2.82/3.08	     = app_encode_app(int, app_encode_fun(int, int), times_times(int), 
2.82/3.08	         app_encode_app(int, int, bit1, zero_zero(int))),
2.82/3.08	    inference('simplify', [status(thm)], ['33'])).
2.82/3.08	tff('35', plain,
2.82/3.08	    app_encode_app(real, real, 
2.82/3.08	      app_encode_app(fun(real, real), app_encode_fun(real, real), 
2.82/3.08	        aa(real, real), sqrt), 
2.82/3.08	      app_encode_app(int, real, number_number_of(real), 
2.82/3.08	        app_encode_app(int, int, bit0, 
2.82/3.08	          app_encode_app(int, int, bit0, 
2.82/3.08	            app_encode_app(int, int, bit1, zero_zero(int))))))
2.82/3.08	     != app_encode_app(real, real, 
2.82/3.08	          app_encode_app(fun(real, real), app_encode_fun(real, real), 
2.82/3.08	            aa(real, real), sqrt), 
2.82/3.08	          app_encode_app(int, real, number_number_of(real), 
2.82/3.08	            app_encode_app(int, int, bit0, 
2.82/3.08	              app_encode_app(int, int, bit0, 
2.82/3.08	                app_encode_app(int, int, bit1, zero_zero(int)))))),
2.82/3.08	    inference('demod', [status(thm)],
2.82/3.08	              ['0', '1', '1', '1', '6', '15', '23', '34', '28'])).
2.82/3.08	tff('36', plain, $false, inference('simplify', [status(thm)], ['35'])).
2.82/3.08	
2.82/3.08	% SZS output end Refutation
2.82/3.08	EOF
