0.00/0.00	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : app
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : 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 $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.20	% Computer   : n170.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 07:50:08 CST 2018
0.74/0.92	% done 885 iterations in 0.722s
0.74/0.92	% SZS status Theorem for 'stdin'
0.74/0.92	% SZS output start Refutation
0.74/0.93	tff(zf_stmt_117, axiom,
0.74/0.93	  (![X1:int,Ma:int]:
0.74/0.93	     (app_encode_app(int,$o,
0.74/0.93	                     app_encode_app(int,app_encode_fun(int,$o),quadRes,Ma),X1) <=>
0.74/0.93	      (?[Y1:int]:
0.74/0.93	         app_encode_app(int,$o,
0.74/0.93	                        app_encode_app(int,app_encode_fun(int,$o),
0.74/0.93	                                       app_encode_app(int,
0.74/0.93	                                                      app_encode_fun(
0.74/0.93	                                                      int,
0.74/0.93	                                                      app_encode_fun(int,$o)),
0.74/0.93	                                                      zcong,
0.74/0.93	                                                      app_encode_app(
0.74/0.93	                                                      nat,int,
0.74/0.93	                                                      app_encode_app(
0.74/0.93	                                                      int,
0.74/0.93	                                                      app_encode_fun(nat,int),
0.74/0.93	                                                      power_power(int),Y1),
0.74/0.93	                                                      app_encode_app(
0.74/0.93	                                                      int,nat,
0.74/0.93	                                                      number_number_of(nat),
0.74/0.93	                                                      app_encode_app(
0.74/0.93	                                                      int,int,bit0,
0.74/0.93	                                                      app_encode_app(
0.74/0.93	                                                      int,int,bit1,pls))))),
0.74/0.93	                                       X1),
0.74/0.93	                        Ma))))).
0.74/0.93	tff('0', plain,
0.74/0.93	    ![X145 : int, X146 : int]:
0.74/0.93	      (app_encode_app(int, $o, 
0.74/0.93	         app_encode_app(int, app_encode_fun(int, $o), 
0.74/0.93	           app_encode_app(int, app_encode_fun(int, app_encode_fun(int, $o)), 
0.74/0.93	             zcong, 
0.74/0.93	             app_encode_app(nat, int, 
0.74/0.93	               app_encode_app(int, app_encode_fun(nat, int), 
0.74/0.93	                 power_power(int), sk_Y1(X145, X146)), 
0.74/0.93	               app_encode_app(int, nat, number_number_of(nat), 
0.74/0.93	                 app_encode_app(int, int, bit0, 
0.74/0.93	                   app_encode_app(int, int, bit1, pls))))), X146), X145)
0.74/0.93	       | ~ app_encode_app(int, $o, 
0.74/0.93	             app_encode_app(int, app_encode_fun(int, $o), quadRes, X145), 
0.74/0.93	             X146)),
0.74/0.93	    inference('cnf', [status(esa)], [zf_stmt_117])).
0.74/0.93	tff(zf_stmt_136, axiom, (number(int))).
0.74/0.93	tff('1', plain, number(int), inference('cnf', [status(esa)], [zf_stmt_136])).
0.74/0.93	tff(zf_stmt_36, axiom,
0.74/0.93	  (![B2:$tType]:
0.74/0.93	     ((monoid_mult(B2) & number(B2)) =>
0.74/0.93	      (![W:int]:
0.74/0.93	         (app_encode_app(nat,B2,
0.74/0.93	                         app_encode_app(B2,app_encode_fun(nat,B2),
0.74/0.93	                                        power_power(B2),
0.74/0.93	                                        app_encode_app(int,B2,
0.74/0.93	                                                       number_number_of(B2),W)),
0.74/0.93	                         app_encode_app(int,nat,number_number_of(nat),
0.74/0.93	                                        app_encode_app(int,int,bit0,
0.74/0.93	                                                       app_encode_app(
0.74/0.93	                                                       int,int,bit1,pls)))) =
0.74/0.93	          app_encode_app(B2,B2,
0.74/0.93	                         app_encode_app(B2,app_encode_fun(B2,B2),
0.74/0.93	                                        times_times(B2),
0.74/0.93	                                        app_encode_app(int,B2,
0.74/0.93	                                                       number_number_of(B2),W)),
0.74/0.93	                         app_encode_app(int,B2,number_number_of(B2),W))))))).
0.74/0.93	tff('2', plain,
0.74/0.93	    ![X0 : $tType, X1 : int]:
0.74/0.93	      (app_encode_app(nat, X0, 
0.74/0.93	         app_encode_app(X0, app_encode_fun(nat, X0), power_power(X0), 
0.74/0.93	           app_encode_app(int, X0, number_number_of(X0), X1)), 
0.74/0.93	         app_encode_app(int, nat, number_number_of(nat), 
0.74/0.93	           app_encode_app(int, int, bit0, 
0.74/0.93	             app_encode_app(int, int, bit1, pls))))
0.74/0.93	        = app_encode_app(X0, X0, 
0.74/0.93	            app_encode_app(X0, app_encode_fun(X0, X0), times_times(X0), 
0.74/0.93	              app_encode_app(int, X0, number_number_of(X0), X1)), 
0.74/0.93	            app_encode_app(int, X0, number_number_of(X0), X1))
0.74/0.93	       | ~ number(X0)
0.74/0.93	       | ~ monoid_mult(X0)),
0.74/0.93	    inference('cnf', [status(esa)], [zf_stmt_36])).
0.74/0.93	tff('3', plain,
0.74/0.93	    ![X0 : int]:
0.74/0.93	      (~ $true
0.74/0.93	       | ~ monoid_mult(int)
0.74/0.93	       | app_encode_app(nat, int, 
0.74/0.93	           app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
0.74/0.93	             app_encode_app(int, int, number_number_of(int), X0)), 
0.74/0.93	           app_encode_app(int, nat, number_number_of(nat), 
0.74/0.93	             app_encode_app(int, int, bit0, 
0.74/0.93	               app_encode_app(int, int, bit1, pls))))
0.74/0.93	          = app_encode_app(int, int, 
0.74/0.93	              app_encode_app(int, app_encode_fun(int, int), 
0.74/0.93	                times_times(int), 
0.74/0.93	                app_encode_app(int, int, number_number_of(int), X0)), 
0.74/0.93	              app_encode_app(int, int, number_number_of(int), X0))),
0.74/0.93	    inference('sup-', [status(thm)], ['1', '2'])).
0.74/0.93	tff(zf_stmt_131, axiom, (monoid_mult(int))).
0.74/0.93	tff('4', plain, monoid_mult(int),
0.74/0.93	    inference('cnf', [status(esa)], [zf_stmt_131])).
0.74/0.93	tff(zf_stmt_82, axiom,
0.74/0.93	  (![K1:int]: (app_encode_app(int,int,number_number_of(int),K1) = K1))).
0.74/0.93	tff('5', plain,
0.74/0.93	    ![X84 : int]: app_encode_app(int, int, number_number_of(int), X84) = X84,
0.74/0.93	    inference('cnf', [status(esa)], [zf_stmt_82])).
0.74/0.93	tff('6', plain,
0.74/0.93	    ![X0 : int]:
0.74/0.93	      (~ $true
0.74/0.93	       | ~ $true
0.74/0.93	       | app_encode_app(nat, int, 
0.74/0.93	           app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
0.74/0.93	             X0), 
0.74/0.93	           app_encode_app(int, nat, number_number_of(nat), 
0.74/0.93	             app_encode_app(int, int, bit0, 
0.74/0.93	               app_encode_app(int, int, bit1, pls))))
0.74/0.93	          = app_encode_app(int, int, 
0.74/0.93	              app_encode_app(int, app_encode_fun(int, int), 
0.74/0.93	                times_times(int), X0), X0)),
0.74/0.93	    inference('demod', [status(thm)], ['3', '4', '5', '5', '5'])).
0.74/0.93	tff('7', plain,
0.74/0.93	    ![X0 : int]:
0.74/0.93	      app_encode_app(nat, int, 
0.74/0.93	        app_encode_app(int, app_encode_fun(nat, int), power_power(int), X0), 
0.74/0.93	        app_encode_app(int, nat, number_number_of(nat), 
0.74/0.93	          app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls))))
0.74/0.93	       = app_encode_app(int, int, 
0.74/0.93	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.74/0.93	             X0), X0),
0.74/0.93	    inference('simplify', [status(thm)], ['6'])).
0.74/0.93	tff('8', plain,
0.74/0.93	    ![X145 : int, X146 : int]:
0.74/0.93	      (app_encode_app(int, $o, 
0.74/0.93	         app_encode_app(int, app_encode_fun(int, $o), 
0.74/0.93	           app_encode_app(int, app_encode_fun(int, app_encode_fun(int, $o)), 
0.74/0.93	             zcong, 
0.74/0.93	             app_encode_app(int, int, 
0.74/0.93	               app_encode_app(int, app_encode_fun(int, int), 
0.74/0.93	                 times_times(int), sk_Y1(X145, X146)), sk_Y1(X145, X146))), 
0.74/0.93	           X146), X145)
0.74/0.93	       | ~ app_encode_app(int, $o, 
0.74/0.93	             app_encode_app(int, app_encode_fun(int, $o), quadRes, X145), 
0.74/0.93	             X146)),
0.74/0.93	    inference('demod', [status(thm)], ['0', '7'])).
0.74/0.93	tff(zf_stmt_153, axiom,
0.74/0.93	  (![S1:int]:
0.74/0.93	     (app_encode_app(int,$o,
0.74/0.93	                     app_encode_app(int,app_encode_fun(int,$o),
0.74/0.93	                                    app_encode_app(int,
0.74/0.93	                                                   app_encode_fun(int,
0.74/0.93	                                                                  app_encode_fun(
0.74/0.93	                                                                  int,$o)),
0.74/0.93	                                                   zcong,
0.74/0.93	                                                   app_encode_app(nat,int,
0.74/0.93	                                                                  app_encode_app(
0.74/0.93	                                                                  int,
0.74/0.93	                                                                  app_encode_fun(
0.74/0.93	                                                                  nat,int),
0.74/0.93	                                                                  power_power(
0.74/0.93	                                                                  int),S1),
0.74/0.93	                                                                  app_encode_app(
0.74/0.93	                                                                  int,nat,
0.74/0.93	                                                                  number_number_of(
0.74/0.93	                                                                  nat),
0.74/0.93	                                                                  app_encode_app(
0.74/0.93	                                                                  int,int,
0.74/0.93	                                                                  bit0,
0.74/0.93	                                                                  app_encode_app(
0.74/0.93	                                                                  int,int,
0.74/0.93	                                                                  bit1,pls))))),
0.74/0.93	                                    app_encode_app(int,int,
0.74/0.93	                                                   number_number_of(int),min)),
0.74/0.93	                     app_encode_app(int,int,
0.74/0.93	                                    app_encode_app(int,
0.74/0.93	                                                   app_encode_fun(int,int),
0.74/0.93	                                                   plus_plus(int),
0.74/0.93	                                                   app_encode_app(int,int,
0.74/0.93	                                                                  app_encode_app(
0.74/0.93	                                                                  int,
0.74/0.93	                                                                  app_encode_fun(
0.74/0.93	                                                                  int,int),
0.74/0.93	                                                                  times_times(
0.74/0.93	                                                                  int),
0.74/0.93	                                                                  app_encode_app(
0.74/0.93	                                                                  int,int,
0.74/0.93	                                                                  number_number_of(
0.74/0.93	                                                                  int),
0.74/0.93	                                                                  app_encode_app(
0.74/0.93	                                                                  int,int,
0.74/0.93	                                                                  bit0,
0.74/0.93	                                                                  app_encode_app(
0.74/0.93	                                                                  int,int,
0.74/0.93	                                                                  bit0,
0.74/0.93	                                                                  app_encode_app(
0.74/0.93	                                                                  int,int,
0.74/0.93	                                                                  bit1,pls))))),
0.74/0.93	                                                                  m)),
0.74/0.93	                                    one_one(int))) =>
0.74/0.93	      thesis))).
0.74/0.93	tff('9', plain,
0.74/0.93	    ![X182 : int]:
0.74/0.93	      (thesis
0.74/0.93	       | ~ app_encode_app(int, $o, 
0.74/0.93	             app_encode_app(int, app_encode_fun(int, $o), 
0.74/0.93	               app_encode_app(int, 
0.74/0.93	                 app_encode_fun(int, app_encode_fun(int, $o)), zcong, 
0.74/0.93	                 app_encode_app(nat, int, 
0.74/0.93	                   app_encode_app(int, app_encode_fun(nat, int), 
0.74/0.93	                     power_power(int), X182), 
0.74/0.93	                   app_encode_app(int, nat, number_number_of(nat), 
0.74/0.93	                     app_encode_app(int, int, bit0, 
0.74/0.93	                       app_encode_app(int, int, bit1, pls))))), 
0.74/0.93	               app_encode_app(int, int, number_number_of(int), min)), 
0.74/0.93	             app_encode_app(int, int, 
0.74/0.93	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.74/0.93	                 app_encode_app(int, int, 
0.74/0.93	                   app_encode_app(int, app_encode_fun(int, int), 
0.74/0.93	                     times_times(int), 
0.74/0.93	                     app_encode_app(int, int, number_number_of(int), 
0.74/0.93	                       app_encode_app(int, int, bit0, 
0.74/0.93	                         app_encode_app(int, int, bit0, 
0.74/0.93	                           app_encode_app(int, int, bit1, pls))))), m)), 
0.74/0.93	               one_one(int)))),
0.74/0.93	    inference('cnf', [status(esa)], [zf_stmt_153])).
0.74/0.93	tff(zf_stmt_59, axiom,
0.74/0.93	  (![L:int,K1:int]:
0.74/0.93	     (app_encode_app(int,int,
0.74/0.93	                     app_encode_app(int,app_encode_fun(int,int),
0.74/0.93	                                    times_times(int),
0.74/0.93	                                    app_encode_app(int,int,bit0,K1)),
0.74/0.93	                     L) =
0.74/0.93	      app_encode_app(int,int,bit0,
0.74/0.93	                     app_encode_app(int,int,
0.74/0.93	                                    app_encode_app(int,
0.74/0.93	                                                   app_encode_fun(int,int),
0.74/0.93	                                                   times_times(int),K1),
0.74/0.93	                                    L))))).
0.74/0.93	tff('10', plain,
0.74/0.93	    ![X43 : int, X44 : int]:
0.74/0.93	      app_encode_app(int, int, 
0.74/0.93	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.74/0.93	          app_encode_app(int, int, bit0, X43)), X44)
0.74/0.93	       = app_encode_app(int, int, bit0, 
0.74/0.93	           app_encode_app(int, int, 
0.74/0.93	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.74/0.93	               X43), X44)),
0.74/0.93	    inference('cnf', [status(esa)], [zf_stmt_59])).
0.74/0.93	tff(zf_stmt_58, axiom,
0.74/0.93	  (![W:int]:
0.74/0.93	     (app_encode_app(int,int,
0.74/0.93	                     app_encode_app(int,app_encode_fun(int,int),
0.74/0.93	                                    times_times(int),pls),
0.74/0.93	                     W) =
0.74/0.93	      pls))).
0.74/0.93	tff('11', plain,
0.74/0.93	    ![X42 : int]:
0.74/0.93	      app_encode_app(int, int, 
0.74/0.93	        app_encode_app(int, app_encode_fun(int, int), times_times(int), pls), 
0.74/0.93	        X42)
0.74/0.93	       = pls,
0.74/0.93	    inference('cnf', [status(esa)], [zf_stmt_58])).
0.74/0.93	tff(zf_stmt_41, axiom,
0.74/0.93	  (![L:int,K1:int]:
0.74/0.93	     (app_encode_app(int,int,
0.74/0.93	                     app_encode_app(int,app_encode_fun(int,int),
0.74/0.93	                                    times_times(int),
0.74/0.93	                                    app_encode_app(int,int,bit1,K1)),
0.74/0.93	                     L) =
0.74/0.93	      app_encode_app(int,int,
0.74/0.93	                     app_encode_app(int,app_encode_fun(int,int),
0.74/0.93	                                    plus_plus(int),
0.74/0.93	                                    app_encode_app(int,int,bit0,
0.74/0.93	                                                   app_encode_app(int,int,
0.74/0.93	                                                                  app_encode_app(
0.74/0.93	                                                                  int,
0.74/0.93	                                                                  app_encode_fun(
0.74/0.93	                                                                  int,int),
0.74/0.93	                                                                  times_times(
0.74/0.93	                                                                  int),K1),L))),
0.74/0.93	                     L)))).
0.74/0.93	tff('12', plain,
0.74/0.93	    ![X8 : int, X9 : int]:
0.74/0.93	      app_encode_app(int, int, 
0.74/0.93	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.74/0.93	          app_encode_app(int, int, bit1, X8)), X9)
0.74/0.93	       = app_encode_app(int, int, 
0.74/0.93	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.74/0.93	             app_encode_app(int, int, bit0, 
0.74/0.93	               app_encode_app(int, int, 
0.74/0.93	                 app_encode_app(int, app_encode_fun(int, int), 
0.74/0.93	                   times_times(int), X8), X9))), X9),
0.74/0.93	    inference('cnf', [status(esa)], [zf_stmt_41])).
0.74/0.93	tff('13', plain,
0.74/0.93	    ![X0 : int]:
0.74/0.93	      app_encode_app(int, int, 
0.74/0.93	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.74/0.93	          app_encode_app(int, int, bit1, pls)), X0)
0.74/0.93	       = app_encode_app(int, int, 
0.74/0.93	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.74/0.93	             app_encode_app(int, int, bit0, pls)), X0),
0.74/0.93	    inference('sup+', [status(thm)], ['11', '12'])).
0.74/0.93	tff(zf_stmt_57, axiom, (app_encode_app(int,int,bit0,pls) = pls)).
0.74/0.93	tff('14', plain, app_encode_app(int, int, bit0, pls) = pls,
0.74/0.93	    inference('cnf', [status(esa)], [zf_stmt_57])).
0.74/0.93	tff('15', plain,
0.74/0.93	    ![X0 : int]:
0.74/0.93	      app_encode_app(int, int, 
0.74/0.93	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.74/0.93	          app_encode_app(int, int, bit1, pls)), X0)
0.74/0.93	       = app_encode_app(int, int, 
0.74/0.93	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
0.74/0.93	           X0),
0.74/0.93	    inference('demod', [status(thm)], ['13', '14'])).
0.74/0.93	tff(zf_stmt_87, axiom,
0.74/0.93	  (![K1:int]:
0.74/0.93	     (app_encode_app(int,int,
0.74/0.93	                     app_encode_app(int,app_encode_fun(int,int),
0.74/0.93	                                    plus_plus(int),pls),
0.74/0.93	                     K1) =
0.74/0.93	      K1))).
0.74/0.93	tff('16', plain,
0.74/0.93	    ![X92 : int]:
0.74/0.93	      app_encode_app(int, int, 
0.74/0.93	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
0.74/0.93	        X92)
0.74/0.93	       = X92,
0.74/0.93	    inference('cnf', [status(esa)], [zf_stmt_87])).
0.74/0.93	tff('17', plain,
0.74/0.93	    ![X0 : int]:
0.74/0.93	      app_encode_app(int, int, 
0.74/0.93	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.74/0.93	          app_encode_app(int, int, bit1, pls)), X0)
0.74/0.93	       = X0,
0.74/0.93	    inference('sup+', [status(thm)], ['15', '16'])).
0.74/0.93	tff(zf_stmt_104, axiom,
0.74/0.93	  (one_one(int) =
0.74/0.93	   app_encode_app(int,int,number_number_of(int),
0.74/0.93	                  app_encode_app(int,int,bit1,pls)))).
0.74/0.93	tff('18', plain,
0.74/0.93	    one_one(int)
0.74/0.93	     = app_encode_app(int, int, number_number_of(int), 
0.74/0.93	         app_encode_app(int, int, bit1, pls)),
0.74/0.93	    inference('cnf', [status(esa)], [zf_stmt_104])).
0.74/0.93	tff('19', plain, one_one(int) = app_encode_app(int, int, bit1, pls),
0.74/0.93	    inference('demod', [status(thm)], ['18', '5'])).
0.74/0.93	tff(zf_stmt_88, axiom,
0.74/0.93	  (![K1:int]:
0.74/0.93	     (app_encode_app(int,int,bit0,K1) =
0.74/0.93	      app_encode_app(int,int,
0.74/0.93	                     app_encode_app(int,app_encode_fun(int,int),
0.74/0.93	                                    plus_plus(int),K1),
0.74/0.93	                     K1)))).
0.74/0.93	tff('20', plain,
0.74/0.93	    ![X93 : int]:
0.74/0.93	      app_encode_app(int, int, bit0, X93)
0.74/0.93	       = app_encode_app(int, int, 
0.74/0.93	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X93), 
0.74/0.93	           X93),
0.74/0.93	    inference('cnf', [status(esa)], [zf_stmt_88])).
0.74/0.93	tff(zf_stmt_134, axiom, (number_ring(int))).
0.74/0.93	tff('21', plain, number_ring(int),
0.74/0.93	    inference('cnf', [status(esa)], [zf_stmt_134])).
0.74/0.93	tff(zf_stmt_72, axiom,
0.74/0.93	  (![A:$tType]:
0.74/0.93	     (number_ring(A) =>
0.74/0.93	      (![Z:A,W:int,V:int]:
0.74/0.93	         (app_encode_app(A,A,
0.74/0.93	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
0.74/0.93	                                        app_encode_app(int,A,
0.74/0.93	                                                       number_number_of(A),V)),
0.74/0.93	                         app_encode_app(A,A,
0.74/0.93	                                        app_encode_app(A,app_encode_fun(A,A),
0.74/0.93	                                                       plus_plus(A),
0.74/0.93	                                                       app_encode_app(
0.74/0.93	                                                       int,A,
0.74/0.93	                                                       number_number_of(A),W)),
0.74/0.93	                                        Z)) =
0.74/0.93	          app_encode_app(A,A,
0.74/0.93	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
0.74/0.93	                                        app_encode_app(int,A,
0.74/0.93	                                                       number_number_of(A),
0.74/0.93	                                                       app_encode_app(
0.74/0.93	                                                       int,int,
0.74/0.93	                                                       app_encode_app(
0.74/0.93	                                                       int,
0.74/0.93	                                                       app_encode_fun(
0.74/0.93	                                                       int,int),
0.74/0.93	                                                       plus_plus(int),V),W))),
0.74/0.93	                         Z)))))).
0.74/0.93	tff('22', plain,
0.74/0.93	    ![X68 : $tType, X69 : int, X70 : int, X71 : X68]:
0.74/0.93	      (app_encode_app(X68, X68, 
0.74/0.93	         app_encode_app(X68, app_encode_fun(X68, X68), plus_plus(X68), 
0.74/0.93	           app_encode_app(int, X68, number_number_of(X68), X69)), 
0.74/0.93	         app_encode_app(X68, X68, 
0.74/0.93	           app_encode_app(X68, app_encode_fun(X68, X68), plus_plus(X68), 
0.74/0.93	             app_encode_app(int, X68, number_number_of(X68), X70)), X71))
0.74/0.93	        = app_encode_app(X68, X68, 
0.74/0.93	            app_encode_app(X68, app_encode_fun(X68, X68), plus_plus(X68), 
0.74/0.93	              app_encode_app(int, X68, number_number_of(X68), 
0.74/0.93	                app_encode_app(int, int, 
0.74/0.93	                  app_encode_app(int, app_encode_fun(int, int), 
0.74/0.93	                    plus_plus(int), X69), X70))), X71)
0.74/0.93	       | ~ number_ring(X68)),
0.74/0.93	    inference('cnf', [status(esa)], [zf_stmt_72])).
0.74/0.93	tff('23', plain,
0.74/0.93	    ![X0 : int, X1 : int, X2 : int]:
0.74/0.93	      (~ $true
0.74/0.93	       | app_encode_app(int, int, 
0.74/0.93	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.74/0.93	             app_encode_app(int, int, number_number_of(int), X2)), 
0.74/0.93	           app_encode_app(int, int, 
0.74/0.93	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.74/0.93	               app_encode_app(int, int, number_number_of(int), X1)), X0))
0.74/0.93	          = app_encode_app(int, int, 
0.74/0.93	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.74/0.93	                app_encode_app(int, int, number_number_of(int), 
0.74/0.93	                  app_encode_app(int, int, 
0.74/0.93	                    app_encode_app(int, app_encode_fun(int, int), 
0.74/0.93	                      plus_plus(int), X2), X1))), X0)),
0.74/0.93	    inference('sup-', [status(thm)], ['21', '22'])).
0.74/0.93	tff('24', plain,
0.74/0.93	    ![X0 : int, X1 : int, X2 : int]:
0.74/0.93	      (~ $true
0.74/0.93	       | app_encode_app(int, int, 
0.74/0.93	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X2), 
0.74/0.93	           app_encode_app(int, int, 
0.74/0.93	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.74/0.93	               X1), X0))
0.74/0.93	          = app_encode_app(int, int, 
0.74/0.93	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.74/0.93	                app_encode_app(int, int, 
0.74/0.93	                  app_encode_app(int, app_encode_fun(int, int), 
0.74/0.93	                    plus_plus(int), X2), X1)), X0)),
0.74/0.93	    inference('demod', [status(thm)], ['23', '5', '5', '5'])).
0.74/0.93	tff('25', plain,
0.74/0.93	    ![X0 : int, X1 : int, X2 : int]:
0.74/0.93	      app_encode_app(int, int, 
0.74/0.93	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X2), 
0.74/0.93	        app_encode_app(int, int, 
0.74/0.93	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X1), 
0.74/0.93	          X0))
0.74/0.93	       = app_encode_app(int, int, 
0.74/0.93	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.74/0.93	             app_encode_app(int, int, 
0.74/0.93	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.74/0.93	                 X2), X1)), X0),
0.74/0.93	    inference('simplify', [status(thm)], ['24'])).
0.74/0.93	tff('26', plain,
0.74/0.93	    ![X0 : int, X1 : int]:
0.74/0.93	      app_encode_app(int, int, 
0.74/0.93	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
0.74/0.93	        app_encode_app(int, int, 
0.74/0.93	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
0.74/0.93	          X1))
0.74/0.93	       = app_encode_app(int, int, 
0.74/0.93	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.74/0.93	             app_encode_app(int, int, bit0, X0)), X1),
0.74/0.93	    inference('sup+', [status(thm)], ['20', '25'])).
0.74/0.93	tff(zf_stmt_46, axiom,
0.74/0.93	  (![L:int,K1:int]:
0.74/0.93	     (app_encode_app(int,int,
0.74/0.93	                     app_encode_app(int,app_encode_fun(int,int),
0.74/0.93	                                    plus_plus(int),
0.74/0.93	                                    app_encode_app(int,int,bit0,K1)),
0.74/0.93	                     app_encode_app(int,int,bit1,L)) =
0.74/0.93	      app_encode_app(int,int,bit1,
0.74/0.93	                     app_encode_app(int,int,
0.74/0.93	                                    app_encode_app(int,
0.74/0.93	                                                   app_encode_fun(int,int),
0.74/0.93	                                                   plus_plus(int),K1),
0.74/0.93	                                    L))))).
0.74/0.93	tff('27', plain,
0.74/0.93	    ![X18 : int, X19 : int]:
0.74/0.93	      app_encode_app(int, int, 
0.74/0.93	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.74/0.93	          app_encode_app(int, int, bit0, X18)), 
0.74/0.93	        app_encode_app(int, int, bit1, X19))
0.74/0.93	       = app_encode_app(int, int, bit1, 
0.74/0.93	           app_encode_app(int, int, 
0.74/0.93	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.74/0.93	               X18), X19)),
0.74/0.93	    inference('cnf', [status(esa)], [zf_stmt_46])).
0.74/0.93	tff('28', plain,
0.74/0.93	    ![X18 : int, X19 : int]:
0.74/0.93	      app_encode_app(int, int, 
0.74/0.93	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X18), 
0.74/0.93	        app_encode_app(int, int, 
0.74/0.93	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X18), 
0.74/0.93	          app_encode_app(int, int, bit1, X19)))
0.74/0.93	       = app_encode_app(int, int, bit1, 
0.74/0.93	           app_encode_app(int, int, 
0.74/0.93	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.74/0.93	               X18), X19)),
0.74/0.93	    inference('demod', [status(thm)], ['27', '26'])).
0.74/0.93	tff(zf_stmt_86, axiom,
0.74/0.93	  (![K1:int]:
0.74/0.93	     (app_encode_app(int,int,
0.74/0.93	                     app_encode_app(int,app_encode_fun(int,int),
0.74/0.93	                                    plus_plus(int),K1),
0.74/0.93	                     pls) =
0.74/0.93	      K1))).
0.74/0.93	tff('29', plain,
0.74/0.93	    ![X91 : int]:
0.74/0.93	      app_encode_app(int, int, 
0.74/0.93	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X91), 
0.74/0.93	        pls)
0.74/0.93	       = X91,
0.74/0.93	    inference('cnf', [status(esa)], [zf_stmt_86])).
0.74/0.93	tff(zf_stmt_130, axiom, (number_semiring(int))).
0.74/0.93	tff('30', plain, number_semiring(int),
0.74/0.93	    inference('cnf', [status(esa)], [zf_stmt_130])).
0.74/0.93	tff(zf_stmt_112, axiom,
0.74/0.93	  (![A:$tType]:
0.74/0.93	     (number_semiring(A) =>
0.74/0.93	      (![Z:A]:
0.74/0.93	         (app_encode_app(A,A,
0.74/0.93	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
0.74/0.93	                                        Z),
0.74/0.93	                         app_encode_app(int,A,number_number_of(A),
0.74/0.93	                                        app_encode_app(int,int,bit0,
0.74/0.93	                                                       app_encode_app(
0.74/0.93	                                                       int,int,bit1,pls)))) =
0.74/0.93	          app_encode_app(A,A,
0.74/0.93	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),Z),
0.74/0.93	                         Z)))))).
0.74/0.93	tff('31', plain,
0.74/0.93	    ![X137 : $tType, X138 : X137]:
0.74/0.93	      (app_encode_app(X137, X137, 
0.74/0.93	         app_encode_app(X137, app_encode_fun(X137, X137), times_times(X137), 
0.74/0.93	           X138), 
0.74/0.93	         app_encode_app(int, X137, number_number_of(X137), 
0.74/0.93	           app_encode_app(int, int, bit0, 
0.74/0.93	             app_encode_app(int, int, bit1, pls))))
0.74/0.93	        = app_encode_app(X137, X137, 
0.74/0.93	            app_encode_app(X137, app_encode_fun(X137, X137), 
0.74/0.93	              plus_plus(X137), X138), X138)
0.74/0.93	       | ~ number_semiring(X137)),
0.74/0.93	    inference('cnf', [status(esa)], [zf_stmt_112])).
0.74/0.93	tff('32', plain,
0.74/0.93	    ![X0 : int]:
0.74/0.93	      (~ $true
0.74/0.93	       | app_encode_app(int, int, 
0.74/0.93	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.74/0.93	             X0), 
0.74/0.93	           app_encode_app(int, int, number_number_of(int), 
0.74/0.93	             app_encode_app(int, int, bit0, 
0.74/0.93	               app_encode_app(int, int, bit1, pls))))
0.74/0.93	          = app_encode_app(int, int, 
0.74/0.93	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.74/0.93	                X0), X0)),
0.74/0.93	    inference('sup-', [status(thm)], ['30', '31'])).
0.74/0.93	tff('33', plain,
0.74/0.93	    ![X0 : int]:
0.74/0.93	      (~ $true
0.74/0.93	       | app_encode_app(int, int, 
0.74/0.93	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.74/0.93	             X0), 
0.74/0.93	           app_encode_app(int, int, bit0, 
0.74/0.93	             app_encode_app(int, int, bit1, pls)))
0.74/0.93	          = app_encode_app(int, int, 
0.74/0.93	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.74/0.93	                X0), X0)),
0.74/0.93	    inference('demod', [status(thm)], ['32', '5'])).
0.74/0.93	tff('34', plain,
0.74/0.93	    ![X0 : int]:
0.74/0.93	      app_encode_app(int, int, 
0.74/0.93	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X0), 
0.74/0.93	        app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls)))
0.74/0.93	       = app_encode_app(int, int, 
0.74/0.93	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
0.74/0.93	           X0),
0.74/0.93	    inference('simplify', [status(thm)], ['33'])).
0.74/0.93	tff(zf_stmt_101, axiom,
0.74/0.93	  (![A:$tType]:
0.74/0.93	     (number_ring(A) =>
0.74/0.93	      (![A1:A]:
0.74/0.93	         (app_encode_app(A,A,
0.74/0.93	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
0.74/0.93	                                        A1),
0.74/0.93	                         app_encode_app(int,A,number_number_of(A),
0.74/0.93	                                        app_encode_app(int,int,bit1,pls))) =
0.74/0.93	          A1))))).
0.74/0.93	tff('35', plain,
0.74/0.93	    ![X119 : $tType, X120 : X119]:
0.74/0.93	      (app_encode_app(X119, X119, 
0.74/0.93	         app_encode_app(X119, app_encode_fun(X119, X119), times_times(X119), 
0.74/0.93	           X120), 
0.74/0.93	         app_encode_app(int, X119, number_number_of(X119), 
0.74/0.93	           app_encode_app(int, int, bit1, pls)))
0.74/0.93	        = X120
0.74/0.93	       | ~ number_ring(X119)),
0.74/0.93	    inference('cnf', [status(esa)], [zf_stmt_101])).
0.74/0.93	tff('36', plain,
0.74/0.93	    ![X0 : int]:
0.74/0.93	      (~ $true
0.74/0.93	       | app_encode_app(int, int, 
0.74/0.93	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.74/0.93	             X0), 
0.74/0.93	           app_encode_app(int, int, number_number_of(int), 
0.74/0.93	             app_encode_app(int, int, bit1, pls)))
0.74/0.93	          = X0),
0.74/0.93	    inference('sup-', [status(thm)], ['21', '35'])).
0.74/0.93	tff('37', plain,
0.74/0.93	    ![X0 : int]:
0.74/0.93	      (~ $true
0.74/0.93	       | app_encode_app(int, int, 
0.74/0.93	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.74/0.93	             X0), app_encode_app(int, int, bit1, pls))
0.74/0.93	          = X0),
0.74/0.93	    inference('demod', [status(thm)], ['36', '5'])).
0.74/0.93	tff('38', plain,
0.74/0.93	    ![X0 : int]:
0.74/0.93	      app_encode_app(int, int, 
0.74/0.93	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X0), 
0.74/0.93	        app_encode_app(int, int, bit1, pls))
0.74/0.93	       = X0,
0.74/0.93	    inference('simplify', [status(thm)], ['37'])).
0.74/0.93	tff(zf_stmt_90, axiom,
0.74/0.93	  (![W:int,Z2:int,Z1:int]:
0.74/0.93	     (app_encode_app(int,int,
0.74/0.93	                     app_encode_app(int,app_encode_fun(int,int),
0.74/0.93	                                    times_times(int),
0.74/0.93	                                    app_encode_app(int,int,
0.74/0.93	                                                   app_encode_app(int,
0.74/0.93	                                                                  app_encode_fun(
0.74/0.93	                                                                  int,int),
0.74/0.93	                                                                  plus_plus(
0.74/0.93	                                                                  int),Z1),
0.74/0.93	                                                   Z2)),
0.74/0.93	                     W) =
0.74/0.93	      app_encode_app(int,int,
0.74/0.93	                     app_encode_app(int,app_encode_fun(int,int),
0.74/0.93	                                    plus_plus(int),
0.74/0.93	                                    app_encode_app(int,int,
0.74/0.93	                                                   app_encode_app(int,
0.74/0.93	                                                                  app_encode_fun(
0.74/0.93	                                                                  int,int),
0.74/0.93	                                                                  times_times(
0.74/0.93	                                                                  int),Z1),
0.74/0.93	                                                   W)),
0.74/0.93	                     app_encode_app(int,int,
0.74/0.93	                                    app_encode_app(int,
0.74/0.93	                                                   app_encode_fun(int,int),
0.74/0.93	                                                   times_times(int),Z2),
0.74/0.93	                                    W))))).
0.74/0.93	tff('39', plain,
0.74/0.93	    ![X96 : int, X97 : int, X98 : int]:
0.74/0.93	      app_encode_app(int, int, 
0.74/0.93	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.74/0.93	          app_encode_app(int, int, 
0.74/0.93	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.74/0.93	              X96), X98)), X97)
0.74/0.93	       = app_encode_app(int, int, 
0.74/0.93	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.74/0.93	             app_encode_app(int, int, 
0.74/0.93	               app_encode_app(int, app_encode_fun(int, int), 
0.74/0.93	                 times_times(int), X96), X97)), 
0.74/0.93	           app_encode_app(int, int, 
0.74/0.93	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.74/0.93	               X98), X97)),
0.74/0.93	    inference('cnf', [status(esa)], [zf_stmt_90])).
0.74/0.93	tff(zf_stmt_91, axiom,
0.74/0.93	  (![Z2:int,Z1:int,W:int]:
0.74/0.93	     (app_encode_app(int,int,
0.74/0.93	                     app_encode_app(int,app_encode_fun(int,int),
0.74/0.93	                                    times_times(int),W),
0.74/0.93	                     app_encode_app(int,int,
0.74/0.93	                                    app_encode_app(int,
0.74/0.93	                                                   app_encode_fun(int,int),
0.74/0.93	                                                   plus_plus(int),Z1),
0.74/0.93	                                    Z2)) =
0.74/0.93	      app_encode_app(int,int,
0.74/0.93	                     app_encode_app(int,app_encode_fun(int,int),
0.74/0.93	                                    plus_plus(int),
0.74/0.93	                                    app_encode_app(int,int,
0.74/0.93	                                                   app_encode_app(int,
0.74/0.93	                                                                  app_encode_fun(
0.74/0.93	                                                                  int,int),
0.74/0.93	                                                                  times_times(
0.74/0.93	                                                                  int),W),
0.74/0.93	                                                   Z1)),
0.74/0.93	                     app_encode_app(int,int,
0.74/0.93	                                    app_encode_app(int,
0.74/0.93	                                                   app_encode_fun(int,int),
0.74/0.93	                                                   times_times(int),W),
0.74/0.93	                                    Z2))))).
0.74/0.93	tff('40', plain,
0.74/0.93	    ![X99 : int, X100 : int, X101 : int]:
0.74/0.93	      app_encode_app(int, int, 
0.74/0.93	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X99), 
0.74/0.93	        app_encode_app(int, int, 
0.74/0.93	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X100), 
0.74/0.93	          X101))
0.74/0.93	       = app_encode_app(int, int, 
0.74/0.93	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.74/0.93	             app_encode_app(int, int, 
0.74/0.93	               app_encode_app(int, app_encode_fun(int, int), 
0.74/0.93	                 times_times(int), X99), X100)), 
0.74/0.93	           app_encode_app(int, int, 
0.74/0.93	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.74/0.93	               X99), X101)),
0.74/0.93	    inference('cnf', [status(esa)], [zf_stmt_91])).
0.74/0.93	tff('41', plain,
0.74/0.93	    ![X0 : int, X1 : int]:
0.74/0.93	      app_encode_app(int, int, 
0.74/0.93	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X1), 
0.74/0.93	        app_encode_app(int, int, 
0.74/0.93	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
0.74/0.93	          X0))
0.74/0.93	       = app_encode_app(int, int, 
0.74/0.93	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.74/0.93	             app_encode_app(int, int, 
0.74/0.93	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.74/0.93	                 X1), X1)), X0),
0.74/0.93	    inference('sup+', [status(thm)], ['39', '40'])).
0.74/0.93	tff('42', plain,
0.74/0.93	    ![X0 : int, X1 : int]:
0.74/0.93	      app_encode_app(int, int, 
0.74/0.93	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X1), 
0.74/0.93	        app_encode_app(int, int, bit0, X0))
0.74/0.93	       = app_encode_app(int, int, bit0, 
0.74/0.93	           app_encode_app(int, int, 
0.74/0.93	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.74/0.93	               X1), X0)),
0.74/0.93	    inference('demod', [status(thm)], ['41', '20', '20', '10'])).
0.74/0.93	tff('43', plain,
0.74/0.93	    ![X0 : int]:
0.74/0.93	      app_encode_app(int, int, 
0.74/0.93	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X0), 
0.74/0.93	        app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls)))
0.74/0.93	       = app_encode_app(int, int, bit0, X0),
0.74/0.93	    inference('sup+', [status(thm)], ['38', '42'])).
0.74/0.93	tff('44', plain,
0.74/0.93	    ![X182 : int]:
0.74/0.93	      (thesis
0.74/0.93	       | ~ app_encode_app(int, $o, 
0.74/0.93	             app_encode_app(int, app_encode_fun(int, $o), 
0.74/0.93	               app_encode_app(int, 
0.74/0.93	                 app_encode_fun(int, app_encode_fun(int, $o)), zcong, 
0.74/0.93	                 app_encode_app(int, int, 
0.74/0.93	                   app_encode_app(int, app_encode_fun(int, int), 
0.74/0.93	                     times_times(int), X182), X182)), min), 
0.74/0.93	             app_encode_app(int, int, bit1, 
0.74/0.93	               app_encode_app(int, int, bit0, m)))),
0.74/0.93	    inference('demod', [status(thm)],
0.74/0.93	              ['9', '7', '5', '5', '10', '10', '17', '19', '26', '26', '28', 
0.74/0.93	               '29', '26', '28', '34', '43'])).
0.74/0.93	tff(zf_stmt_154, conjecture, (thesis)).
0.74/0.93	tff(zf_stmt_0, negated_conjecture, (~thesis)).
0.74/0.93	tff('45', plain, ~ thesis, inference('cnf', [status(esa)], [zf_stmt_0])).
0.74/0.93	tff('46', plain,
0.74/0.93	    ![X182 : int]:
0.74/0.93	      ~ app_encode_app(int, $o, 
0.74/0.93	          app_encode_app(int, app_encode_fun(int, $o), 
0.74/0.93	            app_encode_app(int, 
0.74/0.93	              app_encode_fun(int, app_encode_fun(int, $o)), zcong, 
0.74/0.93	              app_encode_app(int, int, 
0.74/0.93	                app_encode_app(int, app_encode_fun(int, int), 
0.74/0.93	                  times_times(int), X182), X182)), min), 
0.74/0.93	          app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m))),
0.74/0.93	    inference('clc', [status(thm)], ['44', '45'])).
0.74/0.93	tff('47', plain,
0.74/0.93	    (~ $true
0.74/0.93	     | ~ app_encode_app(int, $o, 
0.74/0.93	           app_encode_app(int, app_encode_fun(int, $o), quadRes, 
0.74/0.93	             app_encode_app(int, int, bit1, 
0.74/0.93	               app_encode_app(int, int, bit0, m))), min)),
0.74/0.93	    inference('sup-', [status(thm)], ['8', '46'])).
0.74/0.93	tff(zf_stmt_32, axiom,
0.74/0.93	  (app_encode_app(int,$o,
0.74/0.93	                  app_encode_app(int,app_encode_fun(int,$o),quadRes,
0.74/0.93	                                 app_encode_app(int,int,
0.74/0.93	                                                app_encode_app(int,
0.74/0.93	                                                               app_encode_fun(
0.74/0.93	                                                               int,int),
0.74/0.93	                                                               plus_plus(int),
0.74/0.93	                                                               app_encode_app(
0.74/0.93	                                                               int,int,
0.74/0.93	                                                               app_encode_app(
0.74/0.93	                                                               int,
0.74/0.93	                                                               app_encode_fun(
0.74/0.93	                                                               int,int),
0.74/0.93	                                                               times_times(
0.74/0.93	                                                               int),
0.74/0.93	                                                               app_encode_app(
0.74/0.93	                                                               int,int,
0.74/0.93	                                                               number_number_of(
0.74/0.93	                                                               int),
0.74/0.93	                                                               app_encode_app(
0.74/0.93	                                                               int,int,bit0,
0.74/0.93	                                                               app_encode_app(
0.74/0.93	                                                               int,int,bit0,
0.74/0.93	                                                               app_encode_app(
0.74/0.93	                                                               int,int,bit1,
0.74/0.93	                                                               pls))))),m)),
0.74/0.93	                                                one_one(int))),
0.74/0.93	                  app_encode_app(int,int,number_number_of(int),min)))).
0.74/0.93	tff('48', plain,
0.74/0.93	    app_encode_app(int, $o, 
0.74/0.93	      app_encode_app(int, app_encode_fun(int, $o), quadRes, 
0.74/0.93	        app_encode_app(int, int, 
0.74/0.93	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.74/0.93	            app_encode_app(int, int, 
0.74/0.93	              app_encode_app(int, app_encode_fun(int, int), 
0.74/0.93	                times_times(int), 
0.74/0.93	                app_encode_app(int, int, number_number_of(int), 
0.74/0.93	                  app_encode_app(int, int, bit0, 
0.74/0.93	                    app_encode_app(int, int, bit0, 
0.74/0.93	                      app_encode_app(int, int, bit1, pls))))), m)), 
0.74/0.93	          one_one(int))), 
0.74/0.93	      app_encode_app(int, int, number_number_of(int), min)),
0.74/0.93	    inference('cnf', [status(esa)], [zf_stmt_32])).
0.74/0.93	tff('49', plain,
0.74/0.93	    app_encode_app(int, $o, 
0.74/0.93	      app_encode_app(int, app_encode_fun(int, $o), quadRes, 
0.74/0.93	        app_encode_app(int, int, 
0.74/0.93	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.74/0.93	            app_encode_app(int, int, 
0.74/0.93	              app_encode_app(int, app_encode_fun(int, int), 
0.74/0.93	                times_times(int), 
0.74/0.93	                app_encode_app(int, int, bit0, 
0.74/0.93	                  app_encode_app(int, int, bit0, 
0.74/0.93	                    app_encode_app(int, int, bit1, pls)))), m)), 
0.74/0.93	          one_one(int))), min),
0.74/0.93	    inference('demod', [status(thm)], ['48', '5', '5'])).
0.74/0.93	tff('50', plain,
0.74/0.93	    app_encode_app(int, $o, 
0.74/0.93	      app_encode_app(int, app_encode_fun(int, $o), quadRes, 
0.74/0.93	        app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m))), 
0.74/0.93	      min),
0.74/0.93	    inference('demod', [status(thm)],
0.74/0.93	              ['49', '10', '10', '17', '19', '27', '29'])).
0.74/0.93	tff('51', plain, (~ $true | ~ $true),
0.74/0.93	    inference('demod', [status(thm)], ['47', '50'])).
0.74/0.93	tff('52', plain, $false, inference('simplify', [status(thm)], ['51'])).
0.74/0.93	
0.74/0.93	% SZS output end Refutation
0.74/0.93	EOF
