0.00/0.00	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : appext
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : rpo6
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n046.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 07:50:08 CST 2018
0.75/0.92	% done 892 iterations in 0.724s
0.75/0.92	% SZS status Theorem for 'stdin'
0.75/0.92	% SZS output start Refutation
0.75/0.93	tff(zf_stmt_118, axiom,
0.75/0.93	  (![X1:int,Ma:int]:
0.75/0.93	     (app_encode_app(int,$o,
0.75/0.93	                     app_encode_app(int,app_encode_fun(int,$o),quadRes,Ma),X1) <=>
0.75/0.93	      (?[Y1:int]:
0.75/0.93	         app_encode_app(int,$o,
0.75/0.93	                        app_encode_app(int,app_encode_fun(int,$o),
0.75/0.93	                                       app_encode_app(int,
0.75/0.93	                                                      app_encode_fun(
0.75/0.93	                                                      int,
0.75/0.93	                                                      app_encode_fun(int,$o)),
0.75/0.93	                                                      zcong,
0.75/0.93	                                                      app_encode_app(
0.75/0.93	                                                      nat,int,
0.75/0.93	                                                      app_encode_app(
0.75/0.93	                                                      int,
0.75/0.93	                                                      app_encode_fun(nat,int),
0.75/0.93	                                                      power_power(int),Y1),
0.75/0.93	                                                      app_encode_app(
0.75/0.93	                                                      int,nat,
0.75/0.93	                                                      number_number_of(nat),
0.75/0.93	                                                      app_encode_app(
0.75/0.93	                                                      int,int,bit0,
0.75/0.93	                                                      app_encode_app(
0.75/0.93	                                                      int,int,bit1,pls))))),
0.75/0.93	                                       X1),
0.75/0.93	                        Ma))))).
0.75/0.93	tff('0', plain,
0.75/0.93	    ![X149 : int, X150 : int]:
0.75/0.93	      (app_encode_app(int, $o, 
0.75/0.93	         app_encode_app(int, app_encode_fun(int, $o), 
0.75/0.93	           app_encode_app(int, app_encode_fun(int, app_encode_fun(int, $o)), 
0.75/0.93	             zcong, 
0.75/0.93	             app_encode_app(nat, int, 
0.75/0.93	               app_encode_app(int, app_encode_fun(nat, int), 
0.75/0.93	                 power_power(int), sk_Y1(X149, X150)), 
0.75/0.93	               app_encode_app(int, nat, number_number_of(nat), 
0.75/0.93	                 app_encode_app(int, int, bit0, 
0.75/0.93	                   app_encode_app(int, int, bit1, pls))))), X150), X149)
0.75/0.93	       | ~ app_encode_app(int, $o, 
0.75/0.93	             app_encode_app(int, app_encode_fun(int, $o), quadRes, X149), 
0.75/0.93	             X150)),
0.75/0.93	    inference('cnf', [status(esa)], [zf_stmt_118])).
0.75/0.93	tff(zf_stmt_137, axiom, (number(int))).
0.75/0.93	tff('1', plain, number(int), inference('cnf', [status(esa)], [zf_stmt_137])).
0.75/0.93	tff(zf_stmt_37, axiom,
0.75/0.93	  (![B2:$tType]:
0.75/0.93	     ((monoid_mult(B2) & number(B2)) =>
0.75/0.93	      (![W:int]:
0.75/0.93	         (app_encode_app(nat,B2,
0.75/0.93	                         app_encode_app(B2,app_encode_fun(nat,B2),
0.75/0.93	                                        power_power(B2),
0.75/0.93	                                        app_encode_app(int,B2,
0.75/0.93	                                                       number_number_of(B2),W)),
0.75/0.93	                         app_encode_app(int,nat,number_number_of(nat),
0.75/0.93	                                        app_encode_app(int,int,bit0,
0.75/0.93	                                                       app_encode_app(
0.75/0.93	                                                       int,int,bit1,pls)))) =
0.75/0.93	          app_encode_app(B2,B2,
0.75/0.93	                         app_encode_app(B2,app_encode_fun(B2,B2),
0.75/0.93	                                        times_times(B2),
0.75/0.93	                                        app_encode_app(int,B2,
0.75/0.93	                                                       number_number_of(B2),W)),
0.75/0.93	                         app_encode_app(int,B2,number_number_of(B2),W))))))).
0.75/0.93	tff('2', plain,
0.75/0.93	    ![X4 : $tType, X5 : int]:
0.75/0.93	      (app_encode_app(nat, X4, 
0.75/0.93	         app_encode_app(X4, app_encode_fun(nat, X4), power_power(X4), 
0.75/0.93	           app_encode_app(int, X4, number_number_of(X4), X5)), 
0.75/0.93	         app_encode_app(int, nat, number_number_of(nat), 
0.75/0.93	           app_encode_app(int, int, bit0, 
0.75/0.93	             app_encode_app(int, int, bit1, pls))))
0.75/0.93	        = app_encode_app(X4, X4, 
0.75/0.93	            app_encode_app(X4, app_encode_fun(X4, X4), times_times(X4), 
0.75/0.93	              app_encode_app(int, X4, number_number_of(X4), X5)), 
0.75/0.93	            app_encode_app(int, X4, number_number_of(X4), X5))
0.75/0.93	       | ~ number(X4)
0.75/0.93	       | ~ monoid_mult(X4)),
0.75/0.93	    inference('cnf', [status(esa)], [zf_stmt_37])).
0.75/0.93	tff('3', plain,
0.75/0.93	    ![X0 : int]:
0.75/0.93	      (~ $true
0.75/0.93	       | ~ monoid_mult(int)
0.75/0.93	       | app_encode_app(nat, int, 
0.75/0.93	           app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
0.75/0.93	             app_encode_app(int, int, number_number_of(int), X0)), 
0.75/0.93	           app_encode_app(int, nat, number_number_of(nat), 
0.75/0.93	             app_encode_app(int, int, bit0, 
0.75/0.93	               app_encode_app(int, int, bit1, pls))))
0.75/0.93	          = app_encode_app(int, int, 
0.75/0.93	              app_encode_app(int, app_encode_fun(int, int), 
0.75/0.93	                times_times(int), 
0.75/0.93	                app_encode_app(int, int, number_number_of(int), X0)), 
0.75/0.93	              app_encode_app(int, int, number_number_of(int), X0))),
0.75/0.93	    inference('sup-', [status(thm)], ['1', '2'])).
0.75/0.93	tff(zf_stmt_132, axiom, (monoid_mult(int))).
0.75/0.93	tff('4', plain, monoid_mult(int),
0.75/0.93	    inference('cnf', [status(esa)], [zf_stmt_132])).
0.75/0.93	tff(zf_stmt_83, axiom,
0.75/0.93	  (![K1:int]: (app_encode_app(int,int,number_number_of(int),K1) = K1))).
0.75/0.93	tff('5', plain,
0.75/0.93	    ![X88 : int]: app_encode_app(int, int, number_number_of(int), X88) = X88,
0.75/0.93	    inference('cnf', [status(esa)], [zf_stmt_83])).
0.75/0.93	tff('6', plain,
0.75/0.93	    ![X0 : int]:
0.75/0.93	      (~ $true
0.75/0.93	       | ~ $true
0.75/0.93	       | app_encode_app(nat, int, 
0.75/0.93	           app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
0.75/0.93	             X0), 
0.75/0.93	           app_encode_app(int, nat, number_number_of(nat), 
0.75/0.93	             app_encode_app(int, int, bit0, 
0.75/0.93	               app_encode_app(int, int, bit1, pls))))
0.75/0.93	          = app_encode_app(int, int, 
0.75/0.93	              app_encode_app(int, app_encode_fun(int, int), 
0.75/0.93	                times_times(int), X0), X0)),
0.75/0.93	    inference('demod', [status(thm)], ['3', '4', '5', '5', '5'])).
0.75/0.93	tff('7', plain,
0.75/0.93	    ![X0 : int]:
0.75/0.93	      app_encode_app(nat, int, 
0.75/0.93	        app_encode_app(int, app_encode_fun(nat, int), power_power(int), X0), 
0.75/0.93	        app_encode_app(int, nat, number_number_of(nat), 
0.75/0.93	          app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls))))
0.75/0.93	       = app_encode_app(int, int, 
0.75/0.93	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.75/0.93	             X0), X0),
0.75/0.93	    inference('simplify', [status(thm)], ['6'])).
0.75/0.93	tff('8', plain,
0.75/0.93	    ![X149 : int, X150 : int]:
0.75/0.93	      (app_encode_app(int, $o, 
0.75/0.93	         app_encode_app(int, app_encode_fun(int, $o), 
0.75/0.93	           app_encode_app(int, app_encode_fun(int, app_encode_fun(int, $o)), 
0.75/0.93	             zcong, 
0.75/0.93	             app_encode_app(int, int, 
0.75/0.93	               app_encode_app(int, app_encode_fun(int, int), 
0.75/0.93	                 times_times(int), sk_Y1(X149, X150)), sk_Y1(X149, X150))), 
0.75/0.93	           X150), X149)
0.75/0.93	       | ~ app_encode_app(int, $o, 
0.75/0.93	             app_encode_app(int, app_encode_fun(int, $o), quadRes, X149), 
0.75/0.93	             X150)),
0.75/0.93	    inference('demod', [status(thm)], ['0', '7'])).
0.75/0.93	tff(zf_stmt_154, axiom,
0.75/0.93	  (![S1:int]:
0.75/0.93	     (app_encode_app(int,$o,
0.75/0.93	                     app_encode_app(int,app_encode_fun(int,$o),
0.75/0.93	                                    app_encode_app(int,
0.75/0.93	                                                   app_encode_fun(int,
0.75/0.93	                                                                  app_encode_fun(
0.75/0.93	                                                                  int,$o)),
0.75/0.93	                                                   zcong,
0.75/0.93	                                                   app_encode_app(nat,int,
0.75/0.93	                                                                  app_encode_app(
0.75/0.93	                                                                  int,
0.75/0.93	                                                                  app_encode_fun(
0.75/0.93	                                                                  nat,int),
0.75/0.93	                                                                  power_power(
0.75/0.93	                                                                  int),S1),
0.75/0.93	                                                                  app_encode_app(
0.75/0.93	                                                                  int,nat,
0.75/0.93	                                                                  number_number_of(
0.75/0.93	                                                                  nat),
0.75/0.93	                                                                  app_encode_app(
0.75/0.93	                                                                  int,int,
0.75/0.93	                                                                  bit0,
0.75/0.93	                                                                  app_encode_app(
0.75/0.93	                                                                  int,int,
0.75/0.93	                                                                  bit1,pls))))),
0.75/0.93	                                    app_encode_app(int,int,
0.75/0.93	                                                   number_number_of(int),min)),
0.75/0.93	                     app_encode_app(int,int,
0.75/0.93	                                    app_encode_app(int,
0.75/0.93	                                                   app_encode_fun(int,int),
0.75/0.93	                                                   plus_plus(int),
0.75/0.93	                                                   app_encode_app(int,int,
0.75/0.93	                                                                  app_encode_app(
0.75/0.93	                                                                  int,
0.75/0.93	                                                                  app_encode_fun(
0.75/0.93	                                                                  int,int),
0.75/0.93	                                                                  times_times(
0.75/0.93	                                                                  int),
0.75/0.93	                                                                  app_encode_app(
0.75/0.93	                                                                  int,int,
0.75/0.93	                                                                  number_number_of(
0.75/0.93	                                                                  int),
0.75/0.93	                                                                  app_encode_app(
0.75/0.93	                                                                  int,int,
0.75/0.93	                                                                  bit0,
0.75/0.93	                                                                  app_encode_app(
0.75/0.93	                                                                  int,int,
0.75/0.93	                                                                  bit0,
0.75/0.93	                                                                  app_encode_app(
0.75/0.93	                                                                  int,int,
0.75/0.93	                                                                  bit1,pls))))),
0.75/0.93	                                                                  m)),
0.75/0.93	                                    one_one(int))) =>
0.75/0.93	      thesis))).
0.75/0.93	tff('9', plain,
0.75/0.93	    ![X186 : int]:
0.75/0.93	      (thesis
0.75/0.93	       | ~ app_encode_app(int, $o, 
0.75/0.93	             app_encode_app(int, app_encode_fun(int, $o), 
0.75/0.93	               app_encode_app(int, 
0.75/0.93	                 app_encode_fun(int, app_encode_fun(int, $o)), zcong, 
0.75/0.93	                 app_encode_app(nat, int, 
0.75/0.93	                   app_encode_app(int, app_encode_fun(nat, int), 
0.75/0.93	                     power_power(int), X186), 
0.75/0.93	                   app_encode_app(int, nat, number_number_of(nat), 
0.75/0.93	                     app_encode_app(int, int, bit0, 
0.75/0.93	                       app_encode_app(int, int, bit1, pls))))), 
0.75/0.93	               app_encode_app(int, int, number_number_of(int), min)), 
0.75/0.93	             app_encode_app(int, int, 
0.75/0.93	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.75/0.93	                 app_encode_app(int, int, 
0.75/0.93	                   app_encode_app(int, app_encode_fun(int, int), 
0.75/0.93	                     times_times(int), 
0.75/0.93	                     app_encode_app(int, int, number_number_of(int), 
0.75/0.93	                       app_encode_app(int, int, bit0, 
0.75/0.93	                         app_encode_app(int, int, bit0, 
0.75/0.93	                           app_encode_app(int, int, bit1, pls))))), m)), 
0.75/0.93	               one_one(int)))),
0.75/0.93	    inference('cnf', [status(esa)], [zf_stmt_154])).
0.75/0.93	tff(zf_stmt_60, axiom,
0.75/0.93	  (![L:int,K1:int]:
0.75/0.93	     (app_encode_app(int,int,
0.75/0.93	                     app_encode_app(int,app_encode_fun(int,int),
0.75/0.93	                                    times_times(int),
0.75/0.93	                                    app_encode_app(int,int,bit0,K1)),
0.75/0.93	                     L) =
0.75/0.93	      app_encode_app(int,int,bit0,
0.75/0.93	                     app_encode_app(int,int,
0.75/0.93	                                    app_encode_app(int,
0.75/0.93	                                                   app_encode_fun(int,int),
0.75/0.93	                                                   times_times(int),K1),
0.75/0.93	                                    L))))).
0.75/0.93	tff('10', plain,
0.75/0.93	    ![X47 : int, X48 : int]:
0.75/0.93	      app_encode_app(int, int, 
0.75/0.93	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.75/0.93	          app_encode_app(int, int, bit0, X47)), X48)
0.75/0.93	       = app_encode_app(int, int, bit0, 
0.75/0.93	           app_encode_app(int, int, 
0.75/0.93	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.75/0.93	               X47), X48)),
0.75/0.93	    inference('cnf', [status(esa)], [zf_stmt_60])).
0.75/0.93	tff(zf_stmt_59, axiom,
0.75/0.93	  (![W:int]:
0.75/0.93	     (app_encode_app(int,int,
0.75/0.93	                     app_encode_app(int,app_encode_fun(int,int),
0.75/0.93	                                    times_times(int),pls),
0.75/0.93	                     W) =
0.75/0.93	      pls))).
0.75/0.93	tff('11', plain,
0.75/0.93	    ![X46 : int]:
0.75/0.93	      app_encode_app(int, int, 
0.75/0.93	        app_encode_app(int, app_encode_fun(int, int), times_times(int), pls), 
0.75/0.93	        X46)
0.75/0.93	       = pls,
0.75/0.93	    inference('cnf', [status(esa)], [zf_stmt_59])).
0.75/0.93	tff(zf_stmt_42, axiom,
0.75/0.93	  (![L:int,K1:int]:
0.75/0.93	     (app_encode_app(int,int,
0.75/0.93	                     app_encode_app(int,app_encode_fun(int,int),
0.75/0.93	                                    times_times(int),
0.75/0.93	                                    app_encode_app(int,int,bit1,K1)),
0.75/0.93	                     L) =
0.75/0.93	      app_encode_app(int,int,
0.75/0.93	                     app_encode_app(int,app_encode_fun(int,int),
0.75/0.93	                                    plus_plus(int),
0.75/0.93	                                    app_encode_app(int,int,bit0,
0.75/0.93	                                                   app_encode_app(int,int,
0.75/0.93	                                                                  app_encode_app(
0.75/0.93	                                                                  int,
0.75/0.93	                                                                  app_encode_fun(
0.75/0.93	                                                                  int,int),
0.75/0.93	                                                                  times_times(
0.75/0.93	                                                                  int),K1),L))),
0.75/0.93	                     L)))).
0.75/0.93	tff('12', plain,
0.75/0.93	    ![X12 : int, X13 : int]:
0.75/0.93	      app_encode_app(int, int, 
0.75/0.93	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.75/0.93	          app_encode_app(int, int, bit1, X12)), X13)
0.75/0.93	       = app_encode_app(int, int, 
0.75/0.93	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.75/0.93	             app_encode_app(int, int, bit0, 
0.75/0.93	               app_encode_app(int, int, 
0.75/0.93	                 app_encode_app(int, app_encode_fun(int, int), 
0.75/0.93	                   times_times(int), X12), X13))), X13),
0.75/0.93	    inference('cnf', [status(esa)], [zf_stmt_42])).
0.75/0.93	tff('13', plain,
0.75/0.93	    ![X0 : int]:
0.75/0.93	      app_encode_app(int, int, 
0.75/0.93	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.75/0.93	          app_encode_app(int, int, bit1, pls)), X0)
0.75/0.93	       = app_encode_app(int, int, 
0.75/0.93	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.75/0.93	             app_encode_app(int, int, bit0, pls)), X0),
0.75/0.93	    inference('sup+', [status(thm)], ['11', '12'])).
0.75/0.93	tff(zf_stmt_58, axiom, (app_encode_app(int,int,bit0,pls) = pls)).
0.75/0.93	tff('14', plain, app_encode_app(int, int, bit0, pls) = pls,
0.75/0.93	    inference('cnf', [status(esa)], [zf_stmt_58])).
0.75/0.93	tff('15', plain,
0.75/0.93	    ![X0 : int]:
0.75/0.93	      app_encode_app(int, int, 
0.75/0.93	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.75/0.93	          app_encode_app(int, int, bit1, pls)), X0)
0.75/0.93	       = app_encode_app(int, int, 
0.75/0.93	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
0.75/0.93	           X0),
0.75/0.93	    inference('demod', [status(thm)], ['13', '14'])).
0.75/0.93	tff(zf_stmt_88, axiom,
0.75/0.93	  (![K1:int]:
0.75/0.93	     (app_encode_app(int,int,
0.75/0.93	                     app_encode_app(int,app_encode_fun(int,int),
0.75/0.93	                                    plus_plus(int),pls),
0.75/0.93	                     K1) =
0.75/0.93	      K1))).
0.75/0.93	tff('16', plain,
0.75/0.93	    ![X96 : int]:
0.75/0.93	      app_encode_app(int, int, 
0.75/0.93	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
0.75/0.93	        X96)
0.75/0.93	       = X96,
0.75/0.93	    inference('cnf', [status(esa)], [zf_stmt_88])).
0.75/0.93	tff('17', plain,
0.75/0.93	    ![X0 : int]:
0.75/0.93	      app_encode_app(int, int, 
0.75/0.93	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.75/0.93	          app_encode_app(int, int, bit1, pls)), X0)
0.75/0.93	       = X0,
0.75/0.93	    inference('sup+', [status(thm)], ['15', '16'])).
0.75/0.93	tff(zf_stmt_2, axiom,
0.75/0.93	  (![X:app_encode_fun(Alpha,Beta),Y:app_encode_fun(Alpha,Beta)]:
0.75/0.93	     ((![Z:Alpha]:
0.75/0.93	         (app_encode_app(Alpha,Beta,X,Z) = app_encode_app(Alpha,Beta,Y,Z))) =>
0.75/0.93	      (X = Y)))).
0.75/0.93	tff('18', plain,
0.75/0.93	    ![X0 : $tType, X1 : $tType, X2 : app_encode_fun(X0, X1), 
0.75/0.93	      X3 : app_encode_fun(X0, X1)]:
0.75/0.93	      (X3 = X2
0.75/0.93	       | app_encode_app(X0, X1, X3, sk_Z(X1, X0, X2, X3))
0.75/0.93	          != app_encode_app(X0, X1, X2, sk_Z(X1, X0, X2, X3))),
0.75/0.93	    inference('cnf', [status(esa)], [zf_stmt_2])).
0.75/0.93	tff('19', plain,
0.75/0.93	    ![X0 : app_encode_fun(int, int)]:
0.75/0.93	      (app_encode_app(int, int, X0, 
0.75/0.93	         sk_Z(int, int, number_number_of(int), X0))
0.75/0.93	        != sk_Z(int, int, number_number_of(int), X0)
0.75/0.93	       | X0 = number_number_of(int)),
0.75/0.93	    inference('sup-', [status(thm)], ['5', '18'])).
0.75/0.93	tff('20', plain,
0.75/0.93	    (sk_Z(int, int, number_number_of(int), 
0.75/0.93	       app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.75/0.93	         app_encode_app(int, int, bit1, pls)))
0.75/0.93	      != sk_Z(int, int, number_number_of(int), 
0.75/0.93	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.75/0.93	             app_encode_app(int, int, bit1, pls)))
0.75/0.93	     | app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.75/0.93	         app_encode_app(int, int, bit1, pls))
0.75/0.93	        = number_number_of(int)),
0.75/0.93	    inference('sup-', [status(thm)], ['17', '19'])).
0.75/0.93	tff('21', plain,
0.75/0.93	    app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.75/0.93	      app_encode_app(int, int, bit1, pls))
0.75/0.93	     = number_number_of(int),
0.75/0.93	    inference('simplify', [status(thm)], ['20'])).
0.75/0.93	tff(zf_stmt_105, axiom,
0.75/0.93	  (one_one(int) =
0.75/0.93	   app_encode_app(int,int,number_number_of(int),
0.75/0.93	                  app_encode_app(int,int,bit1,pls)))).
0.75/0.93	tff('22', plain,
0.75/0.93	    one_one(int)
0.75/0.93	     = app_encode_app(int, int, number_number_of(int), 
0.75/0.93	         app_encode_app(int, int, bit1, pls)),
0.75/0.93	    inference('cnf', [status(esa)], [zf_stmt_105])).
0.75/0.93	tff('23', plain, one_one(int) = app_encode_app(int, int, bit1, pls),
0.75/0.93	    inference('demod', [status(thm)], ['22', '5'])).
0.75/0.93	tff(zf_stmt_89, axiom,
0.75/0.93	  (![K1:int]:
0.75/0.93	     (app_encode_app(int,int,bit0,K1) =
0.75/0.93	      app_encode_app(int,int,
0.75/0.93	                     app_encode_app(int,app_encode_fun(int,int),
0.75/0.93	                                    plus_plus(int),K1),
0.75/0.93	                     K1)))).
0.75/0.93	tff('24', plain,
0.75/0.93	    ![X97 : int]:
0.75/0.93	      app_encode_app(int, int, bit0, X97)
0.75/0.93	       = app_encode_app(int, int, 
0.75/0.93	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X97), 
0.75/0.93	           X97),
0.75/0.93	    inference('cnf', [status(esa)], [zf_stmt_89])).
0.75/0.93	tff(zf_stmt_135, axiom, (number_ring(int))).
0.75/0.93	tff('25', plain, number_ring(int),
0.75/0.93	    inference('cnf', [status(esa)], [zf_stmt_135])).
0.75/0.93	tff(zf_stmt_73, axiom,
0.75/0.93	  (![A:$tType]:
0.75/0.93	     (number_ring(A) =>
0.75/0.93	      (![Z:A,W:int,V:int]:
0.75/0.93	         (app_encode_app(A,A,
0.75/0.93	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
0.75/0.93	                                        app_encode_app(int,A,
0.75/0.93	                                                       number_number_of(A),V)),
0.75/0.93	                         app_encode_app(A,A,
0.75/0.93	                                        app_encode_app(A,app_encode_fun(A,A),
0.75/0.93	                                                       plus_plus(A),
0.75/0.93	                                                       app_encode_app(
0.75/0.93	                                                       int,A,
0.75/0.93	                                                       number_number_of(A),W)),
0.75/0.93	                                        Z)) =
0.75/0.93	          app_encode_app(A,A,
0.75/0.93	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
0.75/0.93	                                        app_encode_app(int,A,
0.75/0.93	                                                       number_number_of(A),
0.75/0.93	                                                       app_encode_app(
0.75/0.93	                                                       int,int,
0.75/0.93	                                                       app_encode_app(
0.75/0.93	                                                       int,
0.75/0.93	                                                       app_encode_fun(
0.75/0.93	                                                       int,int),
0.75/0.93	                                                       plus_plus(int),V),W))),
0.75/0.93	                         Z)))))).
0.75/0.93	tff('26', plain,
0.75/0.93	    ![X72 : $tType, X73 : int, X74 : int, X75 : X72]:
0.75/0.93	      (app_encode_app(X72, X72, 
0.75/0.93	         app_encode_app(X72, app_encode_fun(X72, X72), plus_plus(X72), 
0.75/0.93	           app_encode_app(int, X72, number_number_of(X72), X73)), 
0.75/0.93	         app_encode_app(X72, X72, 
0.75/0.93	           app_encode_app(X72, app_encode_fun(X72, X72), plus_plus(X72), 
0.75/0.93	             app_encode_app(int, X72, number_number_of(X72), X74)), X75))
0.75/0.93	        = app_encode_app(X72, X72, 
0.75/0.93	            app_encode_app(X72, app_encode_fun(X72, X72), plus_plus(X72), 
0.75/0.93	              app_encode_app(int, X72, number_number_of(X72), 
0.75/0.93	                app_encode_app(int, int, 
0.75/0.93	                  app_encode_app(int, app_encode_fun(int, int), 
0.75/0.93	                    plus_plus(int), X73), X74))), X75)
0.75/0.93	       | ~ number_ring(X72)),
0.75/0.93	    inference('cnf', [status(esa)], [zf_stmt_73])).
0.75/0.93	tff('27', plain,
0.75/0.93	    ![X0 : int, X1 : int, X2 : int]:
0.75/0.93	      (~ $true
0.75/0.93	       | app_encode_app(int, int, 
0.75/0.93	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.75/0.93	             app_encode_app(int, int, number_number_of(int), X2)), 
0.75/0.93	           app_encode_app(int, int, 
0.75/0.93	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.75/0.93	               app_encode_app(int, int, number_number_of(int), X1)), X0))
0.75/0.93	          = app_encode_app(int, int, 
0.75/0.93	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.75/0.93	                app_encode_app(int, int, number_number_of(int), 
0.75/0.93	                  app_encode_app(int, int, 
0.75/0.93	                    app_encode_app(int, app_encode_fun(int, int), 
0.75/0.93	                      plus_plus(int), X2), X1))), X0)),
0.75/0.93	    inference('sup-', [status(thm)], ['25', '26'])).
0.75/0.93	tff('28', plain,
0.75/0.93	    ![X0 : int, X1 : int, X2 : int]:
0.75/0.93	      (~ $true
0.75/0.93	       | app_encode_app(int, int, 
0.75/0.93	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X2), 
0.75/0.93	           app_encode_app(int, int, 
0.75/0.93	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.75/0.93	               X1), X0))
0.75/0.93	          = app_encode_app(int, int, 
0.75/0.93	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.75/0.93	                app_encode_app(int, int, 
0.75/0.93	                  app_encode_app(int, app_encode_fun(int, int), 
0.75/0.93	                    plus_plus(int), X2), X1)), X0)),
0.75/0.93	    inference('demod', [status(thm)], ['27', '5', '5', '5'])).
0.75/0.93	tff('29', plain,
0.75/0.93	    ![X0 : int, X1 : int, X2 : int]:
0.75/0.93	      app_encode_app(int, int, 
0.75/0.93	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X2), 
0.75/0.93	        app_encode_app(int, int, 
0.75/0.93	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X1), 
0.75/0.93	          X0))
0.75/0.93	       = app_encode_app(int, int, 
0.75/0.93	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.75/0.93	             app_encode_app(int, int, 
0.75/0.93	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.75/0.93	                 X2), X1)), X0),
0.75/0.93	    inference('simplify', [status(thm)], ['28'])).
0.75/0.93	tff('30', plain,
0.75/0.93	    ![X0 : int, X1 : int]:
0.75/0.93	      app_encode_app(int, int, 
0.75/0.93	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
0.75/0.93	        app_encode_app(int, int, 
0.75/0.93	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
0.75/0.93	          X1))
0.75/0.93	       = app_encode_app(int, int, 
0.75/0.93	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.75/0.93	             app_encode_app(int, int, bit0, X0)), X1),
0.75/0.93	    inference('sup+', [status(thm)], ['24', '29'])).
0.75/0.93	tff(zf_stmt_47, axiom,
0.75/0.93	  (![L:int,K1:int]:
0.75/0.93	     (app_encode_app(int,int,
0.75/0.93	                     app_encode_app(int,app_encode_fun(int,int),
0.75/0.93	                                    plus_plus(int),
0.75/0.93	                                    app_encode_app(int,int,bit0,K1)),
0.75/0.93	                     app_encode_app(int,int,bit1,L)) =
0.75/0.93	      app_encode_app(int,int,bit1,
0.75/0.93	                     app_encode_app(int,int,
0.75/0.93	                                    app_encode_app(int,
0.75/0.93	                                                   app_encode_fun(int,int),
0.75/0.93	                                                   plus_plus(int),K1),
0.75/0.93	                                    L))))).
0.75/0.93	tff('31', plain,
0.75/0.93	    ![X22 : int, X23 : int]:
0.75/0.93	      app_encode_app(int, int, 
0.75/0.93	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.75/0.93	          app_encode_app(int, int, bit0, X22)), 
0.75/0.93	        app_encode_app(int, int, bit1, X23))
0.75/0.93	       = app_encode_app(int, int, bit1, 
0.75/0.93	           app_encode_app(int, int, 
0.75/0.93	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.75/0.93	               X22), X23)),
0.75/0.93	    inference('cnf', [status(esa)], [zf_stmt_47])).
0.75/0.93	tff('32', plain,
0.75/0.93	    ![X22 : int, X23 : int]:
0.75/0.93	      app_encode_app(int, int, 
0.75/0.93	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X22), 
0.75/0.93	        app_encode_app(int, int, 
0.75/0.93	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X22), 
0.75/0.93	          app_encode_app(int, int, bit1, X23)))
0.75/0.93	       = app_encode_app(int, int, bit1, 
0.75/0.93	           app_encode_app(int, int, 
0.75/0.93	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.75/0.93	               X22), X23)),
0.75/0.93	    inference('demod', [status(thm)], ['31', '30'])).
0.75/0.93	tff(zf_stmt_87, axiom,
0.75/0.93	  (![K1:int]:
0.75/0.93	     (app_encode_app(int,int,
0.75/0.93	                     app_encode_app(int,app_encode_fun(int,int),
0.75/0.93	                                    plus_plus(int),K1),
0.75/0.93	                     pls) =
0.75/0.93	      K1))).
0.75/0.93	tff('33', plain,
0.75/0.93	    ![X95 : int]:
0.75/0.93	      app_encode_app(int, int, 
0.75/0.93	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X95), 
0.75/0.93	        pls)
0.75/0.93	       = X95,
0.75/0.93	    inference('cnf', [status(esa)], [zf_stmt_87])).
0.75/0.93	tff(zf_stmt_131, axiom, (number_semiring(int))).
0.75/0.93	tff('34', plain, number_semiring(int),
0.75/0.93	    inference('cnf', [status(esa)], [zf_stmt_131])).
0.75/0.93	tff(zf_stmt_113, axiom,
0.75/0.93	  (![A:$tType]:
0.75/0.93	     (number_semiring(A) =>
0.75/0.93	      (![Z:A]:
0.75/0.93	         (app_encode_app(A,A,
0.75/0.93	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
0.75/0.93	                                        Z),
0.75/0.93	                         app_encode_app(int,A,number_number_of(A),
0.75/0.93	                                        app_encode_app(int,int,bit0,
0.75/0.93	                                                       app_encode_app(
0.75/0.93	                                                       int,int,bit1,pls)))) =
0.75/0.93	          app_encode_app(A,A,
0.75/0.93	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),Z),
0.75/0.93	                         Z)))))).
0.75/0.93	tff('35', plain,
0.75/0.93	    ![X141 : $tType, X142 : X141]:
0.75/0.93	      (app_encode_app(X141, X141, 
0.75/0.93	         app_encode_app(X141, app_encode_fun(X141, X141), times_times(X141), 
0.75/0.93	           X142), 
0.75/0.93	         app_encode_app(int, X141, number_number_of(X141), 
0.75/0.93	           app_encode_app(int, int, bit0, 
0.75/0.93	             app_encode_app(int, int, bit1, pls))))
0.75/0.93	        = app_encode_app(X141, X141, 
0.75/0.93	            app_encode_app(X141, app_encode_fun(X141, X141), 
0.75/0.93	              plus_plus(X141), X142), X142)
0.75/0.93	       | ~ number_semiring(X141)),
0.75/0.93	    inference('cnf', [status(esa)], [zf_stmt_113])).
0.75/0.93	tff('36', plain,
0.75/0.93	    ![X0 : int]:
0.75/0.93	      (~ $true
0.75/0.93	       | app_encode_app(int, int, 
0.75/0.93	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.75/0.93	             X0), 
0.75/0.93	           app_encode_app(int, int, number_number_of(int), 
0.75/0.93	             app_encode_app(int, int, bit0, 
0.75/0.93	               app_encode_app(int, int, bit1, pls))))
0.75/0.93	          = app_encode_app(int, int, 
0.75/0.93	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.75/0.93	                X0), X0)),
0.75/0.93	    inference('sup-', [status(thm)], ['34', '35'])).
0.75/0.93	tff('37', plain,
0.75/0.93	    ![X0 : int]:
0.75/0.93	      (~ $true
0.75/0.93	       | app_encode_app(int, int, 
0.75/0.93	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.75/0.93	             X0), 
0.75/0.93	           app_encode_app(int, int, bit0, 
0.75/0.93	             app_encode_app(int, int, bit1, pls)))
0.75/0.93	          = app_encode_app(int, int, 
0.75/0.93	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.75/0.93	                X0), X0)),
0.75/0.93	    inference('demod', [status(thm)], ['36', '5'])).
0.75/0.93	tff('38', plain,
0.75/0.93	    ![X0 : int]:
0.75/0.93	      app_encode_app(int, int, 
0.75/0.93	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X0), 
0.75/0.93	        app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls)))
0.75/0.93	       = app_encode_app(int, int, 
0.75/0.93	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
0.75/0.93	           X0),
0.75/0.93	    inference('simplify', [status(thm)], ['37'])).
0.75/0.93	tff(zf_stmt_102, axiom,
0.75/0.93	  (![A:$tType]:
0.75/0.93	     (number_ring(A) =>
0.75/0.93	      (![A1:A]:
0.75/0.93	         (app_encode_app(A,A,
0.75/0.93	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
0.75/0.93	                                        A1),
0.75/0.93	                         app_encode_app(int,A,number_number_of(A),
0.75/0.93	                                        app_encode_app(int,int,bit1,pls))) =
0.75/0.93	          A1))))).
0.75/0.93	tff('39', plain,
0.75/0.93	    ![X123 : $tType, X124 : X123]:
0.75/0.93	      (app_encode_app(X123, X123, 
0.75/0.93	         app_encode_app(X123, app_encode_fun(X123, X123), times_times(X123), 
0.75/0.93	           X124), 
0.75/0.93	         app_encode_app(int, X123, number_number_of(X123), 
0.75/0.93	           app_encode_app(int, int, bit1, pls)))
0.75/0.93	        = X124
0.75/0.93	       | ~ number_ring(X123)),
0.75/0.93	    inference('cnf', [status(esa)], [zf_stmt_102])).
0.75/0.93	tff('40', plain,
0.75/0.93	    ![X0 : int]:
0.75/0.93	      (~ $true
0.75/0.93	       | app_encode_app(int, int, 
0.75/0.93	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.75/0.93	             X0), 
0.75/0.93	           app_encode_app(int, int, number_number_of(int), 
0.75/0.93	             app_encode_app(int, int, bit1, pls)))
0.75/0.93	          = X0),
0.75/0.93	    inference('sup-', [status(thm)], ['25', '39'])).
0.75/0.93	tff('41', plain,
0.75/0.93	    ![X0 : int]:
0.75/0.93	      (~ $true
0.75/0.93	       | app_encode_app(int, int, 
0.75/0.93	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.75/0.93	             X0), app_encode_app(int, int, bit1, pls))
0.75/0.93	          = X0),
0.75/0.93	    inference('demod', [status(thm)], ['40', '5'])).
0.75/0.93	tff('42', plain,
0.75/0.93	    ![X0 : int]:
0.75/0.93	      app_encode_app(int, int, 
0.75/0.93	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X0), 
0.75/0.93	        app_encode_app(int, int, bit1, pls))
0.75/0.93	       = X0,
0.75/0.93	    inference('simplify', [status(thm)], ['41'])).
0.75/0.93	tff(zf_stmt_91, axiom,
0.75/0.93	  (![W:int,Z2:int,Z1:int]:
0.75/0.93	     (app_encode_app(int,int,
0.75/0.93	                     app_encode_app(int,app_encode_fun(int,int),
0.75/0.93	                                    times_times(int),
0.75/0.93	                                    app_encode_app(int,int,
0.75/0.93	                                                   app_encode_app(int,
0.75/0.93	                                                                  app_encode_fun(
0.75/0.93	                                                                  int,int),
0.75/0.93	                                                                  plus_plus(
0.75/0.93	                                                                  int),Z1),
0.75/0.93	                                                   Z2)),
0.75/0.93	                     W) =
0.75/0.93	      app_encode_app(int,int,
0.75/0.93	                     app_encode_app(int,app_encode_fun(int,int),
0.75/0.93	                                    plus_plus(int),
0.75/0.93	                                    app_encode_app(int,int,
0.75/0.93	                                                   app_encode_app(int,
0.75/0.93	                                                                  app_encode_fun(
0.75/0.93	                                                                  int,int),
0.75/0.93	                                                                  times_times(
0.75/0.93	                                                                  int),Z1),
0.75/0.93	                                                   W)),
0.75/0.93	                     app_encode_app(int,int,
0.75/0.93	                                    app_encode_app(int,
0.75/0.93	                                                   app_encode_fun(int,int),
0.75/0.93	                                                   times_times(int),Z2),
0.75/0.93	                                    W))))).
0.75/0.93	tff('43', plain,
0.75/0.93	    ![X100 : int, X101 : int, X102 : int]:
0.75/0.93	      app_encode_app(int, int, 
0.75/0.93	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.75/0.93	          app_encode_app(int, int, 
0.75/0.93	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.75/0.93	              X100), X102)), X101)
0.75/0.93	       = app_encode_app(int, int, 
0.75/0.93	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.75/0.93	             app_encode_app(int, int, 
0.75/0.93	               app_encode_app(int, app_encode_fun(int, int), 
0.75/0.93	                 times_times(int), X100), X101)), 
0.75/0.93	           app_encode_app(int, int, 
0.75/0.93	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.75/0.93	               X102), X101)),
0.75/0.93	    inference('cnf', [status(esa)], [zf_stmt_91])).
0.75/0.93	tff(zf_stmt_92, axiom,
0.75/0.93	  (![Z2:int,Z1:int,W:int]:
0.75/0.93	     (app_encode_app(int,int,
0.75/0.93	                     app_encode_app(int,app_encode_fun(int,int),
0.75/0.93	                                    times_times(int),W),
0.75/0.93	                     app_encode_app(int,int,
0.75/0.93	                                    app_encode_app(int,
0.75/0.93	                                                   app_encode_fun(int,int),
0.75/0.93	                                                   plus_plus(int),Z1),
0.75/0.93	                                    Z2)) =
0.75/0.93	      app_encode_app(int,int,
0.75/0.93	                     app_encode_app(int,app_encode_fun(int,int),
0.75/0.93	                                    plus_plus(int),
0.75/0.93	                                    app_encode_app(int,int,
0.75/0.93	                                                   app_encode_app(int,
0.75/0.93	                                                                  app_encode_fun(
0.75/0.93	                                                                  int,int),
0.75/0.93	                                                                  times_times(
0.75/0.93	                                                                  int),W),
0.75/0.93	                                                   Z1)),
0.75/0.93	                     app_encode_app(int,int,
0.75/0.93	                                    app_encode_app(int,
0.75/0.93	                                                   app_encode_fun(int,int),
0.75/0.93	                                                   times_times(int),W),
0.75/0.93	                                    Z2))))).
0.75/0.93	tff('44', plain,
0.75/0.93	    ![X103 : int, X104 : int, X105 : int]:
0.75/0.93	      app_encode_app(int, int, 
0.75/0.93	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X103), 
0.75/0.93	        app_encode_app(int, int, 
0.75/0.93	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X104), 
0.75/0.93	          X105))
0.75/0.93	       = app_encode_app(int, int, 
0.75/0.93	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.75/0.93	             app_encode_app(int, int, 
0.75/0.93	               app_encode_app(int, app_encode_fun(int, int), 
0.75/0.93	                 times_times(int), X103), X104)), 
0.75/0.93	           app_encode_app(int, int, 
0.75/0.93	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.75/0.93	               X103), X105)),
0.75/0.93	    inference('cnf', [status(esa)], [zf_stmt_92])).
0.75/0.93	tff('45', plain,
0.75/0.93	    ![X0 : int, X1 : int]:
0.75/0.93	      app_encode_app(int, int, 
0.75/0.93	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X1), 
0.75/0.93	        app_encode_app(int, int, 
0.75/0.93	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
0.75/0.93	          X0))
0.75/0.93	       = app_encode_app(int, int, 
0.75/0.93	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.75/0.93	             app_encode_app(int, int, 
0.75/0.93	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.75/0.93	                 X1), X1)), X0),
0.75/0.93	    inference('sup+', [status(thm)], ['43', '44'])).
0.75/0.93	tff('46', plain,
0.75/0.93	    ![X0 : int, X1 : int]:
0.75/0.93	      app_encode_app(int, int, 
0.75/0.93	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X1), 
0.75/0.93	        app_encode_app(int, int, bit0, X0))
0.75/0.93	       = app_encode_app(int, int, bit0, 
0.75/0.93	           app_encode_app(int, int, 
0.75/0.93	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
0.75/0.93	               X1), X0)),
0.75/0.93	    inference('demod', [status(thm)], ['45', '24', '24', '10'])).
0.75/0.93	tff('47', plain,
0.75/0.93	    ![X0 : int]:
0.75/0.93	      app_encode_app(int, int, 
0.75/0.93	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X0), 
0.75/0.93	        app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls)))
0.75/0.93	       = app_encode_app(int, int, bit0, X0),
0.75/0.93	    inference('sup+', [status(thm)], ['42', '46'])).
0.75/0.93	tff('48', plain,
0.75/0.93	    ![X186 : int]:
0.75/0.93	      (thesis
0.75/0.93	       | ~ app_encode_app(int, $o, 
0.75/0.93	             app_encode_app(int, app_encode_fun(int, $o), 
0.75/0.93	               app_encode_app(int, 
0.75/0.93	                 app_encode_fun(int, app_encode_fun(int, $o)), zcong, 
0.75/0.93	                 app_encode_app(int, int, 
0.75/0.93	                   app_encode_app(int, app_encode_fun(int, int), 
0.75/0.93	                     times_times(int), X186), X186)), min), 
0.75/0.93	             app_encode_app(int, int, bit1, 
0.75/0.93	               app_encode_app(int, int, bit0, m)))),
0.75/0.93	    inference('demod', [status(thm)],
0.75/0.93	              ['9', '7', '5', '5', '10', '10', '21', '5', '23', '30', '30', 
0.75/0.93	               '32', '33', '30', '32', '38', '47'])).
0.75/0.93	tff(zf_stmt_155, conjecture, (thesis)).
0.75/0.93	tff(zf_stmt_0, negated_conjecture, (~thesis)).
0.75/0.93	tff('49', plain, ~ thesis, inference('cnf', [status(esa)], [zf_stmt_0])).
0.75/0.93	tff('50', plain,
0.75/0.93	    ![X186 : int]:
0.75/0.93	      ~ app_encode_app(int, $o, 
0.75/0.93	          app_encode_app(int, app_encode_fun(int, $o), 
0.75/0.93	            app_encode_app(int, 
0.75/0.93	              app_encode_fun(int, app_encode_fun(int, $o)), zcong, 
0.75/0.93	              app_encode_app(int, int, 
0.75/0.93	                app_encode_app(int, app_encode_fun(int, int), 
0.75/0.93	                  times_times(int), X186), X186)), min), 
0.75/0.93	          app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m))),
0.75/0.93	    inference('clc', [status(thm)], ['48', '49'])).
0.75/0.93	tff('51', plain,
0.75/0.93	    (~ $true
0.75/0.93	     | ~ app_encode_app(int, $o, 
0.75/0.93	           app_encode_app(int, app_encode_fun(int, $o), quadRes, 
0.75/0.93	             app_encode_app(int, int, bit1, 
0.75/0.93	               app_encode_app(int, int, bit0, m))), min)),
0.75/0.93	    inference('sup-', [status(thm)], ['8', '50'])).
0.75/0.93	tff(zf_stmt_33, axiom,
0.75/0.93	  (app_encode_app(int,$o,
0.75/0.93	                  app_encode_app(int,app_encode_fun(int,$o),quadRes,
0.75/0.93	                                 app_encode_app(int,int,
0.75/0.93	                                                app_encode_app(int,
0.75/0.93	                                                               app_encode_fun(
0.75/0.93	                                                               int,int),
0.75/0.93	                                                               plus_plus(int),
0.75/0.93	                                                               app_encode_app(
0.75/0.93	                                                               int,int,
0.75/0.93	                                                               app_encode_app(
0.75/0.93	                                                               int,
0.75/0.93	                                                               app_encode_fun(
0.75/0.93	                                                               int,int),
0.75/0.93	                                                               times_times(
0.75/0.93	                                                               int),
0.75/0.93	                                                               app_encode_app(
0.75/0.93	                                                               int,int,
0.75/0.93	                                                               number_number_of(
0.75/0.93	                                                               int),
0.75/0.93	                                                               app_encode_app(
0.75/0.93	                                                               int,int,bit0,
0.75/0.93	                                                               app_encode_app(
0.75/0.93	                                                               int,int,bit0,
0.75/0.93	                                                               app_encode_app(
0.75/0.93	                                                               int,int,bit1,
0.75/0.93	                                                               pls))))),m)),
0.75/0.93	                                                one_one(int))),
0.75/0.93	                  app_encode_app(int,int,number_number_of(int),min)))).
0.75/0.93	tff('52', plain,
0.75/0.93	    app_encode_app(int, $o, 
0.75/0.93	      app_encode_app(int, app_encode_fun(int, $o), quadRes, 
0.75/0.93	        app_encode_app(int, int, 
0.75/0.93	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.75/0.93	            app_encode_app(int, int, 
0.75/0.93	              app_encode_app(int, app_encode_fun(int, int), 
0.75/0.93	                times_times(int), 
0.75/0.93	                app_encode_app(int, int, number_number_of(int), 
0.75/0.93	                  app_encode_app(int, int, bit0, 
0.75/0.93	                    app_encode_app(int, int, bit0, 
0.75/0.93	                      app_encode_app(int, int, bit1, pls))))), m)), 
0.75/0.93	          one_one(int))), 
0.75/0.93	      app_encode_app(int, int, number_number_of(int), min)),
0.75/0.93	    inference('cnf', [status(esa)], [zf_stmt_33])).
0.75/0.93	tff('53', plain,
0.75/0.93	    app_encode_app(int, $o, 
0.75/0.93	      app_encode_app(int, app_encode_fun(int, $o), quadRes, 
0.75/0.93	        app_encode_app(int, int, 
0.75/0.93	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
0.75/0.93	            app_encode_app(int, int, 
0.75/0.93	              app_encode_app(int, app_encode_fun(int, int), 
0.75/0.93	                times_times(int), 
0.75/0.93	                app_encode_app(int, int, bit0, 
0.75/0.93	                  app_encode_app(int, int, bit0, 
0.75/0.93	                    app_encode_app(int, int, bit1, pls)))), m)), 
0.75/0.93	          one_one(int))), min),
0.75/0.93	    inference('demod', [status(thm)], ['52', '5', '5'])).
0.75/0.93	tff('54', plain,
0.75/0.93	    app_encode_app(int, $o, 
0.75/0.93	      app_encode_app(int, app_encode_fun(int, $o), quadRes, 
0.75/0.93	        app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, m))), 
0.75/0.93	      min),
0.75/0.93	    inference('demod', [status(thm)],
0.75/0.93	              ['53', '10', '10', '21', '5', '23', '31', '33'])).
0.75/0.93	tff('55', plain, (~ $true | ~ $true),
0.75/0.93	    inference('demod', [status(thm)], ['51', '54'])).
0.75/0.93	tff('56', plain, $false, inference('simplify', [status(thm)], ['55'])).
0.75/0.93	
0.75/0.93	% SZS output end Refutation
0.75/0.93	EOF
