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 $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.20	% Computer   : n070.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 08:17:38 CST 2018
0.79/1.02	% done 909 iterations in 0.814s
0.79/1.02	% SZS status Theorem for 'stdin'
0.79/1.02	% SZS output start Refutation
0.79/1.02	tff(zf_stmt_34, axiom,
0.79/1.02	  (app_encode_app(int,$o,twoSqu1567020053sum2sq,
0.79/1.02	                  app_encode_app(int,int,
0.79/1.02	                                 app_encode_app(int,app_encode_fun(int,int),
0.79/1.02	                                                times_times(int),
0.79/1.02	                                                app_encode_app(int,int,
0.79/1.02	                                                               app_encode_app(
0.79/1.02	                                                               int,
0.79/1.02	                                                               app_encode_fun(
0.79/1.02	                                                               int,int),
0.79/1.02	                                                               plus_plus(int),
0.79/1.02	                                                               app_encode_app(
0.79/1.02	                                                               int,int,
0.79/1.02	                                                               app_encode_app(
0.79/1.02	                                                               int,
0.79/1.02	                                                               app_encode_fun(
0.79/1.02	                                                               int,int),
0.79/1.02	                                                               times_times(
0.79/1.02	                                                               int),
0.79/1.02	                                                               app_encode_app(
0.79/1.02	                                                               int,int,
0.79/1.02	                                                               number_number_of(
0.79/1.02	                                                               int),
0.79/1.02	                                                               app_encode_app(
0.79/1.02	                                                               int,int,bit0,
0.79/1.02	                                                               app_encode_app(
0.79/1.02	                                                               int,int,bit0,
0.79/1.02	                                                               app_encode_app(
0.79/1.02	                                                               int,int,bit1,
0.79/1.02	                                                               pls))))),m)),
0.79/1.02	                                                               one_one(int))),
0.79/1.02	                                 t)))).
0.79/1.02	tff('0', plain,
0.79/1.02	    app_encode_app(int, $o, twoSqu1567020053sum2sq, 
0.79/1.02	      app_encode_app(int, int, 
0.79/1.02	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.79/1.02	          app_encode_app(int, int, 
0.79/1.02	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.79/1.02	              app_encode_app(int, int, 
0.79/1.02	                app_encode_app(int, app_encode_fun(int, int), 
0.79/1.02	                  times_times(int), 
0.79/1.02	                  app_encode_app(int, int, number_number_of(int), 
0.79/1.02	                    app_encode_app(int, int, bit0, 
0.79/1.02	                      app_encode_app(int, int, bit0, 
0.79/1.02	                        app_encode_app(int, int, bit1, pls))))), m)), 
0.79/1.02	            one_one(int))), t)),
0.79/1.02	    inference('cnf', [status(esa)], [zf_stmt_34])).
0.79/1.02	tff(zf_stmt_33, axiom, (t = one_one(int))).
0.79/1.02	tff('1', plain, t = one_one(int),
0.79/1.02	    inference('cnf', [status(esa)], [zf_stmt_33])).
0.79/1.02	tff('2', plain,
0.79/1.02	    app_encode_app(int, $o, twoSqu1567020053sum2sq, 
0.79/1.02	      app_encode_app(int, int, 
0.79/1.02	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.79/1.02	          app_encode_app(int, int, 
0.79/1.02	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.79/1.02	              app_encode_app(int, int, 
0.79/1.02	                app_encode_app(int, app_encode_fun(int, int), 
0.79/1.02	                  times_times(int), 
0.79/1.02	                  app_encode_app(int, int, number_number_of(int), 
0.79/1.02	                    app_encode_app(int, int, bit0, 
0.79/1.02	                      app_encode_app(int, int, bit0, 
0.79/1.02	                        app_encode_app(int, int, bit1, pls))))), m)), 
0.79/1.02	            one_one(int))), one_one(int))),
0.79/1.02	    inference('demod', [status(thm)], ['0', '1'])).
0.79/1.02	tff(zf_stmt_64, axiom,
0.79/1.02	  (![K3:int]: (app_encode_app(int,int,number_number_of(int),K3) = K3))).
0.79/1.02	tff('3', plain,
0.79/1.02	    ![X69 : int]: app_encode_app(int, int, number_number_of(int), X69) = X69,
0.79/1.02	    inference('cnf', [status(esa)], [zf_stmt_64])).
0.79/1.02	tff('4', plain,
0.79/1.02	    app_encode_app(int, $o, twoSqu1567020053sum2sq, 
0.79/1.02	      app_encode_app(int, int, 
0.79/1.02	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.79/1.02	          app_encode_app(int, int, 
0.79/1.02	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.79/1.02	              app_encode_app(int, int, 
0.79/1.02	                app_encode_app(int, app_encode_fun(int, int), 
0.79/1.02	                  times_times(int), 
0.79/1.02	                  app_encode_app(int, int, bit0, 
0.79/1.02	                    app_encode_app(int, int, bit0, 
0.79/1.02	                      app_encode_app(int, int, bit1, pls)))), m)), 
0.79/1.02	            one_one(int))), one_one(int))),
0.79/1.02	    inference('demod', [status(thm)], ['2', '3'])).
0.79/1.02	tff(zf_stmt_60, axiom,
0.79/1.02	  (![L1:int,K3:int]:
0.79/1.02	     (app_encode_app(int,int,
0.79/1.02	                     app_encode_app(int,app_encode_fun(int,int),
0.79/1.02	                                    times_times(int),
0.79/1.02	                                    app_encode_app(int,int,bit0,K3)),
0.79/1.02	                     L1) =
0.79/1.02	      app_encode_app(int,int,bit0,
0.79/1.02	                     app_encode_app(int,int,
0.79/1.02	                                    app_encode_app(int,
0.79/1.02	                                                   app_encode_fun(int,int),
0.79/1.02	                                                   times_times(int),K3),
0.79/1.02	                                    L1))))).
0.79/1.02	tff('5', plain,
0.79/1.02	    ![X57 : int, X58 : int]:
0.79/1.02	      app_encode_app(int, int, 
0.79/1.02	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.79/1.02	          app_encode_app(int, int, bit0, X57)), X58)
0.79/1.02	       = app_encode_app(int, int, bit0, 
0.79/1.02	           app_encode_app(int, int, 
0.79/1.02	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.79/1.02	               X57), X58)),
0.79/1.02	    inference('cnf', [status(esa)], [zf_stmt_60])).
0.79/1.02	tff(zf_stmt_59, axiom,
0.79/1.02	  (![W:int]:
0.79/1.02	     (app_encode_app(int,int,
0.79/1.02	                     app_encode_app(int,app_encode_fun(int,int),
0.79/1.02	                                    times_times(int),pls),
0.79/1.02	                     W) =
0.79/1.02	      pls))).
0.79/1.02	tff('6', plain,
0.79/1.02	    ![X56 : int]:
0.79/1.02	      app_encode_app(int, int, 
0.79/1.02	        app_encode_app(int, app_encode_fun(int, int), times_times(int), pls), 
0.79/1.02	        X56)
0.79/1.02	       = pls,
0.79/1.02	    inference('cnf', [status(esa)], [zf_stmt_59])).
0.79/1.02	tff(zf_stmt_40, axiom,
0.79/1.02	  (![L1:int,K3:int]:
0.79/1.02	     (app_encode_app(int,int,
0.79/1.02	                     app_encode_app(int,app_encode_fun(int,int),
0.79/1.02	                                    times_times(int),
0.79/1.02	                                    app_encode_app(int,int,bit1,K3)),
0.79/1.02	                     L1) =
0.79/1.02	      app_encode_app(int,int,
0.79/1.02	                     app_encode_app(int,app_encode_fun(int,int),
0.79/1.02	                                    plus_plus(int),
0.79/1.02	                                    app_encode_app(int,int,bit0,
0.79/1.02	                                                   app_encode_app(int,int,
0.79/1.02	                                                                  app_encode_app(
0.79/1.02	                                                                  int,
0.79/1.02	                                                                  app_encode_fun(
0.79/1.02	                                                                  int,int),
0.79/1.02	                                                                  times_times(
0.79/1.02	                                                                  int),K3),L1))),
0.79/1.02	                     L1)))).
0.79/1.02	tff('7', plain,
0.79/1.02	    ![X11 : int, X12 : int]:
0.79/1.02	      app_encode_app(int, int, 
0.79/1.02	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.79/1.02	          app_encode_app(int, int, bit1, X11)), X12)
0.79/1.02	       = app_encode_app(int, int, 
0.79/1.02	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.79/1.02	             app_encode_app(int, int, bit0, 
0.79/1.02	               app_encode_app(int, int, 
0.79/1.02	                 app_encode_app(int, app_encode_fun(int, int), 
0.79/1.02	                   times_times(int), X11), X12))), X12),
0.79/1.02	    inference('cnf', [status(esa)], [zf_stmt_40])).
0.79/1.02	tff('8', plain,
0.79/1.02	    ![X0 : int]:
0.79/1.02	      app_encode_app(int, int, 
0.79/1.02	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.79/1.02	          app_encode_app(int, int, bit1, pls)), X0)
0.79/1.02	       = app_encode_app(int, int, 
0.79/1.02	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.79/1.02	             app_encode_app(int, int, bit0, pls)), X0),
0.79/1.02	    inference('sup+', [status(thm)], ['6', '7'])).
0.79/1.02	tff(zf_stmt_58, axiom, (app_encode_app(int,int,bit0,pls) = pls)).
0.79/1.02	tff('9', plain, app_encode_app(int, int, bit0, pls) = pls,
0.79/1.02	    inference('cnf', [status(esa)], [zf_stmt_58])).
0.79/1.02	tff(zf_stmt_66, axiom,
0.79/1.02	  (![K3:int]:
0.79/1.02	     (app_encode_app(int,int,
0.79/1.02	                     app_encode_app(int,app_encode_fun(int,int),
0.79/1.02	                                    plus_plus(int),pls),
0.79/1.02	                     K3) =
0.79/1.02	      K3))).
0.79/1.02	tff('10', plain,
0.79/1.02	    ![X71 : int]:
0.79/1.02	      app_encode_app(int, int, 
0.79/1.02	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
0.79/1.02	        X71)
0.79/1.02	       = X71,
0.79/1.02	    inference('cnf', [status(esa)], [zf_stmt_66])).
0.79/1.02	tff('11', plain,
0.79/1.02	    ![X0 : int]:
0.79/1.02	      app_encode_app(int, int, 
0.79/1.02	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.79/1.02	          app_encode_app(int, int, bit1, pls)), X0)
0.79/1.02	       = X0,
0.79/1.02	    inference('demod', [status(thm)], ['8', '9', '10'])).
0.79/1.02	tff(zf_stmt_2, axiom,
0.79/1.02	  (![X:app_encode_fun(Alpha,Beta),Y:app_encode_fun(Alpha,Beta)]:
0.79/1.02	     ((![Z:Alpha]:
0.79/1.02	         (app_encode_app(Alpha,Beta,X,Z) = app_encode_app(Alpha,Beta,Y,Z))) =>
0.79/1.02	      (X = Y)))).
0.79/1.02	tff('12', plain,
0.79/1.02	    ![X0 : $tType, X1 : $tType, X2 : app_encode_fun(X0, X1), 
0.79/1.02	      X3 : app_encode_fun(X0, X1)]:
0.79/1.02	      (X3 = X2
0.79/1.02	       | app_encode_app(X0, X1, X3, sk_Z(X1, X0, X2, X3))
0.79/1.02	          != app_encode_app(X0, X1, X2, sk_Z(X1, X0, X2, X3))),
0.79/1.02	    inference('cnf', [status(esa)], [zf_stmt_2])).
0.79/1.02	tff('13', plain,
0.79/1.02	    ![X0 : app_encode_fun(int, int)]:
0.79/1.02	      (app_encode_app(int, int, X0, 
0.79/1.02	         sk_Z(int, int, number_number_of(int), X0))
0.79/1.02	        != sk_Z(int, int, number_number_of(int), X0)
0.79/1.02	       | X0 = number_number_of(int)),
0.79/1.02	    inference('sup-', [status(thm)], ['3', '12'])).
0.79/1.02	tff('14', plain,
0.79/1.02	    (sk_Z(int, int, number_number_of(int), 
0.79/1.02	       app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.79/1.02	         app_encode_app(int, int, bit1, pls)))
0.79/1.02	      != sk_Z(int, int, number_number_of(int), 
0.79/1.02	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.79/1.02	             app_encode_app(int, int, bit1, pls)))
0.79/1.02	     | app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.79/1.02	         app_encode_app(int, int, bit1, pls))
0.79/1.02	        = number_number_of(int)),
0.79/1.02	    inference('sup-', [status(thm)], ['11', '13'])).
0.79/1.02	tff('15', plain,
0.79/1.02	    app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.79/1.02	      app_encode_app(int, int, bit1, pls))
0.79/1.02	     = number_number_of(int),
0.79/1.02	    inference('simplify', [status(thm)], ['14'])).
0.79/1.02	tff(zf_stmt_81, axiom,
0.79/1.02	  (one_one(int) =
0.79/1.02	   app_encode_app(int,int,number_number_of(int),
0.79/1.02	                  app_encode_app(int,int,bit1,pls)))).
0.79/1.02	tff('16', plain,
0.79/1.02	    one_one(int)
0.79/1.02	     = app_encode_app(int, int, number_number_of(int), 
0.79/1.02	         app_encode_app(int, int, bit1, pls)),
0.79/1.02	    inference('cnf', [status(esa)], [zf_stmt_81])).
0.79/1.02	tff('17', plain, one_one(int) = app_encode_app(int, int, bit1, pls),
0.79/1.02	    inference('demod', [status(thm)], ['16', '3'])).
0.79/1.02	tff(zf_stmt_67, axiom,
0.79/1.02	  (![K3:int]:
0.79/1.02	     (app_encode_app(int,int,bit0,K3) =
0.79/1.02	      app_encode_app(int,int,
0.79/1.02	                     app_encode_app(int,app_encode_fun(int,int),
0.79/1.02	                                    plus_plus(int),K3),
0.79/1.02	                     K3)))).
0.79/1.02	tff('18', plain,
0.79/1.02	    ![X72 : int]:
0.79/1.02	      app_encode_app(int, int, bit0, X72)
0.79/1.02	       = app_encode_app(int, int, 
0.79/1.02	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X72), 
0.79/1.02	           X72),
0.79/1.02	    inference('cnf', [status(esa)], [zf_stmt_67])).
0.79/1.02	tff(zf_stmt_135, axiom, (number_ring(int))).
0.79/1.02	tff('19', plain, number_ring(int),
0.79/1.02	    inference('cnf', [status(esa)], [zf_stmt_135])).
0.79/1.02	tff(zf_stmt_45, axiom,
0.79/1.02	  (![A:$tType]:
0.79/1.02	     (number_ring(A) =>
0.79/1.02	      (![Z:A,W:int,V:int]:
0.79/1.02	         (app_encode_app(A,A,
0.79/1.02	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
0.79/1.02	                                        app_encode_app(int,A,
0.79/1.02	                                                       number_number_of(A),V)),
0.79/1.02	                         app_encode_app(A,A,
0.79/1.02	                                        app_encode_app(A,app_encode_fun(A,A),
0.79/1.02	                                                       plus_plus(A),
0.79/1.02	                                                       app_encode_app(
0.79/1.02	                                                       int,A,
0.79/1.02	                                                       number_number_of(A),W)),
0.79/1.02	                                        Z)) =
0.79/1.02	          app_encode_app(A,A,
0.79/1.02	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
0.79/1.02	                                        app_encode_app(int,A,
0.79/1.02	                                                       number_number_of(A),
0.79/1.02	                                                       app_encode_app(
0.79/1.02	                                                       int,int,
0.79/1.02	                                                       app_encode_app(
0.79/1.02	                                                       int,
0.79/1.02	                                                       app_encode_fun(
0.79/1.02	                                                       int,int),
0.79/1.02	                                                       plus_plus(int),V),W))),
0.79/1.02	                         Z)))))).
0.79/1.02	tff('20', plain,
0.79/1.02	    ![X21 : $tType, X22 : int, X23 : int, X24 : X21]:
0.79/1.02	      (app_encode_app(X21, X21, 
0.79/1.02	         app_encode_app(X21, app_encode_fun(X21, X21), plus_plus(X21), 
0.79/1.02	           app_encode_app(int, X21, number_number_of(X21), X22)), 
0.79/1.02	         app_encode_app(X21, X21, 
0.79/1.02	           app_encode_app(X21, app_encode_fun(X21, X21), plus_plus(X21), 
0.79/1.02	             app_encode_app(int, X21, number_number_of(X21), X23)), X24))
0.79/1.02	        = app_encode_app(X21, X21, 
0.79/1.02	            app_encode_app(X21, app_encode_fun(X21, X21), plus_plus(X21), 
0.79/1.02	              app_encode_app(int, X21, number_number_of(X21), 
0.79/1.02	                app_encode_app(int, int, 
0.79/1.02	                  app_encode_app(int, app_encode_fun(int, int), 
0.79/1.02	                    plus_plus(int), X22), X23))), X24)
0.79/1.02	       | ~ number_ring(X21)),
0.79/1.02	    inference('cnf', [status(esa)], [zf_stmt_45])).
0.79/1.02	tff('21', plain,
0.79/1.02	    ![X0 : int, X1 : int, X2 : int]:
0.79/1.02	      (~ $true
0.79/1.02	       | app_encode_app(int, int, 
0.79/1.02	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.79/1.02	             app_encode_app(int, int, number_number_of(int), X2)), 
0.79/1.02	           app_encode_app(int, int, 
0.79/1.02	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.79/1.02	               app_encode_app(int, int, number_number_of(int), X1)), X0))
0.79/1.02	          = app_encode_app(int, int, 
0.79/1.02	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.79/1.02	                app_encode_app(int, int, number_number_of(int), 
0.79/1.02	                  app_encode_app(int, int, 
0.79/1.02	                    app_encode_app(int, app_encode_fun(int, int), 
0.79/1.02	                      plus_plus(int), X2), X1))), X0)),
0.79/1.02	    inference('sup-', [status(thm)], ['19', '20'])).
0.79/1.02	tff('22', plain,
0.79/1.02	    ![X0 : int, X1 : int, X2 : int]:
0.79/1.02	      (~ $true
0.79/1.02	       | app_encode_app(int, int, 
0.79/1.02	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X2), 
0.79/1.02	           app_encode_app(int, int, 
0.79/1.02	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.79/1.02	               X1), X0))
0.79/1.02	          = app_encode_app(int, int, 
0.79/1.02	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.79/1.02	                app_encode_app(int, int, 
0.79/1.02	                  app_encode_app(int, app_encode_fun(int, int), 
0.79/1.02	                    plus_plus(int), X2), X1)), X0)),
0.79/1.02	    inference('demod', [status(thm)], ['21', '3', '3', '3'])).
0.79/1.02	tff('23', plain,
0.79/1.02	    ![X0 : int, X1 : int, X2 : int]:
0.79/1.02	      app_encode_app(int, int, 
0.79/1.02	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X2), 
0.79/1.02	        app_encode_app(int, int, 
0.79/1.02	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X1), 
0.79/1.02	          X0))
0.79/1.02	       = app_encode_app(int, int, 
0.79/1.02	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.79/1.02	             app_encode_app(int, int, 
0.79/1.02	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.79/1.02	                 X2), X1)), X0),
0.79/1.02	    inference('simplify', [status(thm)], ['22'])).
0.79/1.02	tff('24', plain,
0.79/1.02	    ![X0 : int, X1 : int]:
0.79/1.02	      app_encode_app(int, int, 
0.79/1.02	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
0.79/1.02	        app_encode_app(int, int, 
0.79/1.02	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
0.79/1.02	          X1))
0.79/1.02	       = app_encode_app(int, int, 
0.79/1.02	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.79/1.02	             app_encode_app(int, int, bit0, X0)), X1),
0.79/1.02	    inference('sup+', [status(thm)], ['18', '23'])).
0.79/1.02	tff(zf_stmt_42, axiom,
0.79/1.02	  (![L1:int,K3:int]:
0.79/1.02	     (app_encode_app(int,int,
0.79/1.02	                     app_encode_app(int,app_encode_fun(int,int),
0.79/1.02	                                    plus_plus(int),
0.79/1.02	                                    app_encode_app(int,int,bit0,K3)),
0.79/1.02	                     app_encode_app(int,int,bit1,L1)) =
0.79/1.02	      app_encode_app(int,int,bit1,
0.79/1.02	                     app_encode_app(int,int,
0.79/1.02	                                    app_encode_app(int,
0.79/1.02	                                                   app_encode_fun(int,int),
0.79/1.02	                                                   plus_plus(int),K3),
0.79/1.02	                                    L1))))).
0.79/1.02	tff('25', plain,
0.79/1.02	    ![X14 : int, X15 : int]:
0.79/1.02	      app_encode_app(int, int, 
0.79/1.02	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.79/1.02	          app_encode_app(int, int, bit0, X14)), 
0.79/1.02	        app_encode_app(int, int, bit1, X15))
0.79/1.02	       = app_encode_app(int, int, bit1, 
0.79/1.02	           app_encode_app(int, int, 
0.79/1.02	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.79/1.02	               X14), X15)),
0.79/1.02	    inference('cnf', [status(esa)], [zf_stmt_42])).
0.79/1.02	tff('26', plain,
0.79/1.02	    ![X14 : int, X15 : int]:
0.79/1.02	      app_encode_app(int, int, 
0.79/1.02	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X14), 
0.79/1.02	        app_encode_app(int, int, 
0.79/1.02	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X14), 
0.79/1.02	          app_encode_app(int, int, bit1, X15)))
0.79/1.02	       = app_encode_app(int, int, bit1, 
0.79/1.02	           app_encode_app(int, int, 
0.79/1.02	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.79/1.02	               X14), X15)),
0.79/1.02	    inference('demod', [status(thm)], ['25', '24'])).
0.79/1.02	tff(zf_stmt_65, axiom,
0.79/1.02	  (![K3:int]:
0.79/1.02	     (app_encode_app(int,int,
0.79/1.02	                     app_encode_app(int,app_encode_fun(int,int),
0.79/1.02	                                    plus_plus(int),K3),
0.79/1.02	                     pls) =
0.79/1.02	      K3))).
0.79/1.02	tff('27', plain,
0.79/1.02	    ![X70 : int]:
0.79/1.02	      app_encode_app(int, int, 
0.79/1.02	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X70), 
0.79/1.02	        pls)
0.79/1.02	       = X70,
0.79/1.02	    inference('cnf', [status(esa)], [zf_stmt_65])).
0.79/1.02	tff(zf_stmt_79, axiom,
0.79/1.02	  (![A:$tType]:
0.79/1.02	     (number_ring(A) =>
0.79/1.02	      (![A1:A]:
0.79/1.02	         (app_encode_app(A,A,
0.79/1.02	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
0.79/1.02	                                        A1),
0.79/1.02	                         app_encode_app(int,A,number_number_of(A),
0.79/1.02	                                        app_encode_app(int,int,bit1,pls))) =
0.79/1.02	          A1))))).
0.79/1.02	tff('28', plain,
0.79/1.02	    ![X98 : $tType, X99 : X98]:
0.79/1.02	      (app_encode_app(X98, X98, 
0.79/1.02	         app_encode_app(X98, app_encode_fun(X98, X98), times_times(X98), X99), 
0.79/1.02	         app_encode_app(int, X98, number_number_of(X98), 
0.79/1.02	           app_encode_app(int, int, bit1, pls)))
0.79/1.02	        = X99
0.79/1.02	       | ~ number_ring(X98)),
0.79/1.02	    inference('cnf', [status(esa)], [zf_stmt_79])).
0.79/1.02	tff('29', plain,
0.79/1.02	    ![X0 : int]:
0.79/1.02	      (~ $true
0.79/1.02	       | app_encode_app(int, int, 
0.79/1.02	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.79/1.02	             X0), 
0.79/1.02	           app_encode_app(int, int, number_number_of(int), 
0.79/1.02	             app_encode_app(int, int, bit1, pls)))
0.79/1.02	          = X0),
0.79/1.02	    inference('sup-', [status(thm)], ['19', '28'])).
0.79/1.02	tff('30', plain,
0.79/1.02	    ![X0 : int]:
0.79/1.02	      (~ $true
0.79/1.02	       | app_encode_app(int, int, 
0.79/1.02	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.79/1.02	             X0), app_encode_app(int, int, bit1, pls))
0.79/1.02	          = X0),
0.79/1.02	    inference('demod', [status(thm)], ['29', '3'])).
0.79/1.02	tff('31', plain,
0.79/1.02	    ![X0 : int]:
0.79/1.02	      app_encode_app(int, int, 
0.79/1.02	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X0), 
0.79/1.02	        app_encode_app(int, int, bit1, pls))
0.79/1.02	       = X0,
0.79/1.02	    inference('simplify', [status(thm)], ['30'])).
0.79/1.02	tff('32', plain,
0.79/1.02	    app_encode_app(int, $o, twoSqu1567020053sum2sq, 
0.79/1.02	      app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m))),
0.79/1.02	    inference('demod', [status(thm)],
0.79/1.02	              ['4', '5', '5', '15', '3', '17', '24', '24', '26', '27', '24', 
0.79/1.02	               '26', '18', '17', '31'])).
0.79/1.02	tff(zf_stmt_145, conjecture,
0.79/1.02	  (app_encode_app(int,$o,twoSqu1567020053sum2sq,
0.79/1.02	                  app_encode_app(int,int,
0.79/1.02	                                 app_encode_app(int,app_encode_fun(int,int),
0.79/1.02	                                                plus_plus(int),
0.79/1.02	                                                app_encode_app(int,int,
0.79/1.02	                                                               app_encode_app(
0.79/1.02	                                                               int,
0.79/1.02	                                                               app_encode_fun(
0.79/1.02	                                                               int,int),
0.79/1.02	                                                               times_times(
0.79/1.02	                                                               int),
0.79/1.02	                                                               app_encode_app(
0.79/1.02	                                                               int,int,
0.79/1.02	                                                               number_number_of(
0.79/1.02	                                                               int),
0.79/1.02	                                                               app_encode_app(
0.79/1.02	                                                               int,int,bit0,
0.79/1.02	                                                               app_encode_app(
0.79/1.02	                                                               int,int,bit0,
0.79/1.02	                                                               app_encode_app(
0.79/1.02	                                                               int,int,bit1,
0.79/1.02	                                                               pls))))),m)),
0.79/1.02	                                 one_one(int))))).
0.79/1.02	tff(zf_stmt_0, negated_conjecture,
0.79/1.02	  (~
0.79/1.02	    app_encode_app(int,$o,twoSqu1567020053sum2sq,
0.79/1.02	                   app_encode_app(int,int,
0.79/1.02	                                  app_encode_app(int,app_encode_fun(int,int),
0.79/1.02	                                                 plus_plus(int),
0.79/1.02	                                                 app_encode_app(int,int,
0.79/1.02	                                                                app_encode_app(
0.79/1.02	                                                                int,
0.79/1.02	                                                                app_encode_fun(
0.79/1.02	                                                                int,int),
0.79/1.02	                                                                times_times(
0.79/1.02	                                                                int),
0.79/1.02	                                                                app_encode_app(
0.79/1.02	                                                                int,int,
0.79/1.02	                                                                number_number_of(
0.79/1.02	                                                                int),
0.79/1.02	                                                                app_encode_app(
0.79/1.02	                                                                int,int,bit0,
0.79/1.02	                                                                app_encode_app(
0.79/1.02	                                                                int,int,bit0,
0.79/1.02	                                                                app_encode_app(
0.79/1.02	                                                                int,int,bit1,
0.79/1.02	                                                                pls))))),m)),
0.79/1.02	                                  one_one(int))))).
0.79/1.02	tff('33', plain,
0.79/1.02	    ~ app_encode_app(int, $o, twoSqu1567020053sum2sq, 
0.79/1.02	        app_encode_app(int, int, 
0.79/1.02	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.79/1.02	            app_encode_app(int, int, 
0.79/1.02	              app_encode_app(int, app_encode_fun(int, int), 
0.79/1.02	                times_times(int), 
0.79/1.02	                app_encode_app(int, int, number_number_of(int), 
0.79/1.02	                  app_encode_app(int, int, bit0, 
0.79/1.02	                    app_encode_app(int, int, bit0, 
0.79/1.02	                      app_encode_app(int, int, bit1, pls))))), m)), 
0.79/1.02	          one_one(int))),
0.79/1.02	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.79/1.02	tff('34', plain,
0.79/1.02	    ~ app_encode_app(int, $o, twoSqu1567020053sum2sq, 
0.79/1.02	        app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m))),
0.79/1.02	    inference('demod', [status(thm)],
0.79/1.02	              ['33', '3', '5', '5', '11', '17', '25', '27'])).
0.79/1.02	tff('35', plain, ~ $true, inference('sup-', [status(thm)], ['32', '34'])).
0.79/1.02	tff('36', plain, $false, inference('simplify', [status(thm)], ['35'])).
0.79/1.02	
0.79/1.02	% SZS output end Refutation
0.79/1.02	EOF
