0.00/0.00	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : app
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : kbo
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.20	% Computer   : n082.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 08:18:09 CST 2018
6.11/6.28	% done 1008 iterations in 6.074s
6.11/6.28	% SZS status Theorem for 'stdin'
6.11/6.28	% SZS output start Refutation
6.11/6.28	tff(zf_stmt_176, conjecture,
6.11/6.28	  (app_encode_app(int,int,
6.11/6.28	                  app_encode_app(int,app_encode_fun(int,int),plus_plus(int),
6.11/6.28	                                 app_encode_app(int,int,
6.11/6.28	                                                app_encode_app(int,
6.11/6.28	                                                               app_encode_fun(
6.11/6.28	                                                               int,int),
6.11/6.28	                                                               times_times(
6.11/6.28	                                                               int),
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,int,
6.11/6.28	                                                               number_number_of(
6.11/6.28	                                                               int),
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,int,bit0,
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,int,bit0,
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,int,bit1,
6.11/6.28	                                                               pls))))),
6.11/6.28	                                                app_encode_app(nat,int,
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,
6.11/6.28	                                                               app_encode_fun(
6.11/6.28	                                                               nat,int),
6.11/6.28	                                                               power_power(
6.11/6.28	                                                               int),v),
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,nat,
6.11/6.28	                                                               number_number_of(
6.11/6.28	                                                               nat),
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,int,bit0,
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,int,bit1,
6.11/6.28	                                                               pls)))))),
6.11/6.28	                  app_encode_app(int,int,
6.11/6.28	                                 app_encode_app(int,app_encode_fun(int,int),
6.11/6.28	                                                times_times(int),
6.11/6.28	                                                app_encode_app(int,int,
6.11/6.28	                                                               number_number_of(
6.11/6.28	                                                               int),
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,int,bit0,
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,int,bit0,
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,int,bit1,
6.11/6.28	                                                               pls))))),
6.11/6.28	                                 app_encode_app(nat,int,
6.11/6.28	                                                app_encode_app(int,
6.11/6.28	                                                               app_encode_fun(
6.11/6.28	                                                               nat,int),
6.11/6.28	                                                               power_power(
6.11/6.28	                                                               int),w),
6.11/6.28	                                                app_encode_app(int,nat,
6.11/6.28	                                                               number_number_of(
6.11/6.28	                                                               nat),
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,int,bit0,
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,int,bit1,
6.11/6.28	                                                               pls)))))) =
6.11/6.28	   app_encode_app(int,int,
6.11/6.28	                  app_encode_app(int,app_encode_fun(int,int),plus_plus(int),
6.11/6.28	                                 app_encode_app(nat,int,
6.11/6.28	                                                app_encode_app(int,
6.11/6.28	                                                               app_encode_fun(
6.11/6.28	                                                               nat,int),
6.11/6.28	                                                               power_power(
6.11/6.28	                                                               int),
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,int,
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,
6.11/6.28	                                                               app_encode_fun(
6.11/6.28	                                                               int,int),
6.11/6.28	                                                               times_times(
6.11/6.28	                                                               int),
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,int,
6.11/6.28	                                                               number_number_of(
6.11/6.28	                                                               int),
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,int,bit0,
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,int,bit1,
6.11/6.28	                                                               pls)))),
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,int,
6.11/6.28	                                                               abs_abs(int),v))),
6.11/6.28	                                                app_encode_app(int,nat,
6.11/6.28	                                                               number_number_of(
6.11/6.28	                                                               nat),
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,int,bit0,
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,int,bit1,
6.11/6.28	                                                               pls))))),
6.11/6.28	                  app_encode_app(nat,int,
6.11/6.28	                                 app_encode_app(int,app_encode_fun(nat,int),
6.11/6.28	                                                power_power(int),
6.11/6.28	                                                app_encode_app(int,int,
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,
6.11/6.28	                                                               app_encode_fun(
6.11/6.28	                                                               int,int),
6.11/6.28	                                                               times_times(
6.11/6.28	                                                               int),
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,int,
6.11/6.28	                                                               number_number_of(
6.11/6.28	                                                               int),
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,int,bit0,
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,int,bit1,
6.11/6.28	                                                               pls)))),
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,int,
6.11/6.28	                                                               abs_abs(int),w))),
6.11/6.28	                                 app_encode_app(int,nat,
6.11/6.28	                                                number_number_of(nat),
6.11/6.28	                                                app_encode_app(int,int,bit0,
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,int,bit1,
6.11/6.28	                                                               pls))))))).
6.11/6.28	tff(zf_stmt_0, negated_conjecture,
6.11/6.28	  (app_encode_app(int,int,
6.11/6.28	                  app_encode_app(int,app_encode_fun(int,int),plus_plus(int),
6.11/6.28	                                 app_encode_app(int,int,
6.11/6.28	                                                app_encode_app(int,
6.11/6.28	                                                               app_encode_fun(
6.11/6.28	                                                               int,int),
6.11/6.28	                                                               times_times(
6.11/6.28	                                                               int),
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,int,
6.11/6.28	                                                               number_number_of(
6.11/6.28	                                                               int),
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,int,bit0,
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,int,bit0,
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,int,bit1,
6.11/6.28	                                                               pls))))),
6.11/6.28	                                                app_encode_app(nat,int,
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,
6.11/6.28	                                                               app_encode_fun(
6.11/6.28	                                                               nat,int),
6.11/6.28	                                                               power_power(
6.11/6.28	                                                               int),v),
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,nat,
6.11/6.28	                                                               number_number_of(
6.11/6.28	                                                               nat),
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,int,bit0,
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,int,bit1,
6.11/6.28	                                                               pls)))))),
6.11/6.28	                  app_encode_app(int,int,
6.11/6.28	                                 app_encode_app(int,app_encode_fun(int,int),
6.11/6.28	                                                times_times(int),
6.11/6.28	                                                app_encode_app(int,int,
6.11/6.28	                                                               number_number_of(
6.11/6.28	                                                               int),
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,int,bit0,
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,int,bit0,
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,int,bit1,
6.11/6.28	                                                               pls))))),
6.11/6.28	                                 app_encode_app(nat,int,
6.11/6.28	                                                app_encode_app(int,
6.11/6.28	                                                               app_encode_fun(
6.11/6.28	                                                               nat,int),
6.11/6.28	                                                               power_power(
6.11/6.28	                                                               int),w),
6.11/6.28	                                                app_encode_app(int,nat,
6.11/6.28	                                                               number_number_of(
6.11/6.28	                                                               nat),
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,int,bit0,
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,int,bit1,
6.11/6.28	                                                               pls)))))) !=
6.11/6.28	   app_encode_app(int,int,
6.11/6.28	                  app_encode_app(int,app_encode_fun(int,int),plus_plus(int),
6.11/6.28	                                 app_encode_app(nat,int,
6.11/6.28	                                                app_encode_app(int,
6.11/6.28	                                                               app_encode_fun(
6.11/6.28	                                                               nat,int),
6.11/6.28	                                                               power_power(
6.11/6.28	                                                               int),
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,int,
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,
6.11/6.28	                                                               app_encode_fun(
6.11/6.28	                                                               int,int),
6.11/6.28	                                                               times_times(
6.11/6.28	                                                               int),
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,int,
6.11/6.28	                                                               number_number_of(
6.11/6.28	                                                               int),
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,int,bit0,
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,int,bit1,
6.11/6.28	                                                               pls)))),
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,int,
6.11/6.28	                                                               abs_abs(int),v))),
6.11/6.28	                                                app_encode_app(int,nat,
6.11/6.28	                                                               number_number_of(
6.11/6.28	                                                               nat),
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,int,bit0,
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,int,bit1,
6.11/6.28	                                                               pls))))),
6.11/6.28	                  app_encode_app(nat,int,
6.11/6.28	                                 app_encode_app(int,app_encode_fun(nat,int),
6.11/6.28	                                                power_power(int),
6.11/6.28	                                                app_encode_app(int,int,
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,
6.11/6.28	                                                               app_encode_fun(
6.11/6.28	                                                               int,int),
6.11/6.28	                                                               times_times(
6.11/6.28	                                                               int),
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,int,
6.11/6.28	                                                               number_number_of(
6.11/6.28	                                                               int),
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,int,bit0,
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,int,bit1,
6.11/6.28	                                                               pls)))),
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,int,
6.11/6.28	                                                               abs_abs(int),w))),
6.11/6.28	                                 app_encode_app(int,nat,
6.11/6.28	                                                number_number_of(nat),
6.11/6.28	                                                app_encode_app(int,int,bit0,
6.11/6.28	                                                               app_encode_app(
6.11/6.28	                                                               int,int,bit1,
6.11/6.28	                                                               pls))))))).
6.11/6.28	tff('0', plain,
6.11/6.28	    app_encode_app(int, int, 
6.11/6.28	      app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
6.11/6.28	        app_encode_app(int, int, 
6.11/6.28	          app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.11/6.28	            app_encode_app(int, int, number_number_of(int), 
6.11/6.28	              app_encode_app(int, int, bit0, 
6.11/6.28	                app_encode_app(int, int, bit0, 
6.11/6.28	                  app_encode_app(int, int, bit1, pls))))), 
6.11/6.28	          app_encode_app(nat, int, 
6.11/6.28	            app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
6.11/6.28	              v), 
6.11/6.28	            app_encode_app(int, nat, number_number_of(nat), 
6.11/6.28	              app_encode_app(int, int, bit0, 
6.11/6.28	                app_encode_app(int, int, bit1, pls)))))), 
6.11/6.28	      app_encode_app(int, int, 
6.11/6.28	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.11/6.28	          app_encode_app(int, int, number_number_of(int), 
6.11/6.28	            app_encode_app(int, int, bit0, 
6.11/6.28	              app_encode_app(int, int, bit0, 
6.11/6.28	                app_encode_app(int, int, bit1, pls))))), 
6.11/6.28	        app_encode_app(nat, int, 
6.11/6.28	          app_encode_app(int, app_encode_fun(nat, int), power_power(int), w), 
6.11/6.28	          app_encode_app(int, nat, number_number_of(nat), 
6.11/6.28	            app_encode_app(int, int, bit0, 
6.11/6.28	              app_encode_app(int, int, bit1, pls))))))
6.11/6.28	     != app_encode_app(int, int, 
6.11/6.28	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
6.11/6.28	            app_encode_app(nat, int, 
6.11/6.28	              app_encode_app(int, app_encode_fun(nat, int), 
6.11/6.28	                power_power(int), 
6.11/6.28	                app_encode_app(int, int, 
6.11/6.28	                  app_encode_app(int, app_encode_fun(int, int), 
6.11/6.28	                    times_times(int), 
6.11/6.28	                    app_encode_app(int, int, number_number_of(int), 
6.11/6.28	                      app_encode_app(int, int, bit0, 
6.11/6.28	                        app_encode_app(int, int, bit1, pls)))), 
6.11/6.28	                  app_encode_app(int, int, abs_abs(int), v))), 
6.11/6.28	              app_encode_app(int, nat, number_number_of(nat), 
6.11/6.28	                app_encode_app(int, int, bit0, 
6.11/6.28	                  app_encode_app(int, int, bit1, pls))))), 
6.11/6.28	          app_encode_app(nat, int, 
6.11/6.28	            app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
6.11/6.28	              app_encode_app(int, int, 
6.11/6.28	                app_encode_app(int, app_encode_fun(int, int), 
6.11/6.28	                  times_times(int), 
6.11/6.28	                  app_encode_app(int, int, number_number_of(int), 
6.11/6.28	                    app_encode_app(int, int, bit0, 
6.11/6.28	                      app_encode_app(int, int, bit1, pls)))), 
6.11/6.28	                app_encode_app(int, int, abs_abs(int), w))), 
6.11/6.28	            app_encode_app(int, nat, number_number_of(nat), 
6.11/6.28	              app_encode_app(int, int, bit0, 
6.11/6.28	                app_encode_app(int, int, bit1, pls))))),
6.11/6.28	    inference('cnf', [status(esa)], [zf_stmt_0])).
6.11/6.28	tff(zf_stmt_67, axiom,
6.11/6.28	  (![K:int]: (app_encode_app(int,int,number_number_of(int),K) = K))).
6.11/6.28	tff('1', plain,
6.11/6.28	    ![X75 : int]: app_encode_app(int, int, number_number_of(int), X75) = X75,
6.11/6.28	    inference('cnf', [status(esa)], [zf_stmt_67])).
6.11/6.28	tff(zf_stmt_35, axiom,
6.11/6.28	  (![B2:$tType]:
6.11/6.28	     ((monoid_mult(B2) & number(B2)) =>
6.11/6.28	      (![W:int]:
6.11/6.28	         (app_encode_app(nat,B2,
6.11/6.28	                         app_encode_app(B2,app_encode_fun(nat,B2),
6.11/6.28	                                        power_power(B2),
6.11/6.28	                                        app_encode_app(int,B2,
6.11/6.28	                                                       number_number_of(B2),W)),
6.11/6.28	                         app_encode_app(int,nat,number_number_of(nat),
6.11/6.28	                                        app_encode_app(int,int,bit0,
6.11/6.28	                                                       app_encode_app(
6.11/6.28	                                                       int,int,bit1,pls)))) =
6.11/6.28	          app_encode_app(B2,B2,
6.11/6.28	                         app_encode_app(B2,app_encode_fun(B2,B2),
6.11/6.28	                                        times_times(B2),
6.11/6.28	                                        app_encode_app(int,B2,
6.11/6.28	                                                       number_number_of(B2),W)),
6.11/6.28	                         app_encode_app(int,B2,number_number_of(B2),W))))))).
6.11/6.28	tff('2', plain,
6.11/6.28	    ![X0 : $tType, X1 : int]:
6.11/6.28	      (app_encode_app(nat, X0, 
6.11/6.28	         app_encode_app(X0, app_encode_fun(nat, X0), power_power(X0), 
6.11/6.28	           app_encode_app(int, X0, number_number_of(X0), X1)), 
6.11/6.28	         app_encode_app(int, nat, number_number_of(nat), 
6.11/6.28	           app_encode_app(int, int, bit0, 
6.11/6.28	             app_encode_app(int, int, bit1, pls))))
6.11/6.28	        = app_encode_app(X0, X0, 
6.11/6.28	            app_encode_app(X0, app_encode_fun(X0, X0), times_times(X0), 
6.11/6.28	              app_encode_app(int, X0, number_number_of(X0), X1)), 
6.11/6.28	            app_encode_app(int, X0, number_number_of(X0), X1))
6.11/6.28	       | ~ number(X0)
6.11/6.28	       | ~ monoid_mult(X0)),
6.11/6.28	    inference('cnf', [status(esa)], [zf_stmt_35])).
6.11/6.28	tff('3', plain,
6.11/6.28	    ![X0 : int]:
6.11/6.28	      (app_encode_app(nat, int, 
6.11/6.28	         app_encode_app(int, app_encode_fun(nat, int), power_power(int), X0), 
6.11/6.28	         app_encode_app(int, nat, number_number_of(nat), 
6.11/6.28	           app_encode_app(int, int, bit0, 
6.11/6.28	             app_encode_app(int, int, bit1, pls))))
6.11/6.28	        = app_encode_app(int, int, 
6.11/6.28	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.11/6.28	              app_encode_app(int, int, number_number_of(int), X0)), 
6.11/6.28	            app_encode_app(int, int, number_number_of(int), X0))
6.11/6.28	       | ~ monoid_mult(int)
6.11/6.28	       | ~ number(int)),
6.11/6.28	    inference('sup+', [status(thm)], ['1', '2'])).
6.11/6.28	tff(zf_stmt_143, axiom, (monoid_mult(int))).
6.11/6.28	tff('4', plain, monoid_mult(int),
6.11/6.28	    inference('cnf', [status(esa)], [zf_stmt_143])).
6.11/6.28	tff(zf_stmt_147, axiom, (number(int))).
6.11/6.28	tff('5', plain, number(int), inference('cnf', [status(esa)], [zf_stmt_147])).
6.11/6.28	tff('6', plain,
6.11/6.28	    ![X0 : int]:
6.11/6.28	      (app_encode_app(nat, int, 
6.11/6.28	         app_encode_app(int, app_encode_fun(nat, int), power_power(int), X0), 
6.11/6.28	         app_encode_app(int, nat, number_number_of(nat), 
6.11/6.28	           app_encode_app(int, int, bit0, 
6.11/6.28	             app_encode_app(int, int, bit1, pls))))
6.11/6.28	        = app_encode_app(int, int, 
6.11/6.28	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.11/6.28	              X0), X0)
6.11/6.28	       | ~ $true
6.11/6.28	       | ~ $true),
6.11/6.28	    inference('demod', [status(thm)], ['3', '1', '1', '4', '5'])).
6.11/6.28	tff('7', plain,
6.11/6.28	    ![X0 : int]:
6.11/6.28	      app_encode_app(nat, int, 
6.11/6.28	        app_encode_app(int, app_encode_fun(nat, int), power_power(int), X0), 
6.11/6.28	        app_encode_app(int, nat, number_number_of(nat), 
6.11/6.28	          app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls))))
6.11/6.28	       = app_encode_app(int, int, 
6.11/6.28	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.11/6.28	             X0), X0),
6.11/6.28	    inference('simplify', [status(thm)], ['6'])).
6.11/6.28	tff(zf_stmt_71, axiom,
6.11/6.28	  (![K:int]:
6.11/6.28	     (app_encode_app(int,int,bit0,K) =
6.11/6.28	      app_encode_app(int,int,
6.11/6.28	                     app_encode_app(int,app_encode_fun(int,int),
6.11/6.28	                                    plus_plus(int),K),
6.11/6.28	                     K)))).
6.11/6.28	tff('8', plain,
6.11/6.28	    ![X81 : int]:
6.11/6.28	      app_encode_app(int, int, bit0, X81)
6.11/6.28	       = app_encode_app(int, int, 
6.11/6.28	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X81), 
6.11/6.28	           X81),
6.11/6.28	    inference('cnf', [status(esa)], [zf_stmt_71])).
6.11/6.28	tff(zf_stmt_61, axiom,
6.11/6.28	  (![B2:$tType]:
6.11/6.28	     ((number(B2) & semiring(B2)) =>
6.11/6.28	      (![C:B2,B:B2,V:int]:
6.11/6.28	         (app_encode_app(B2,B2,
6.11/6.28	                         app_encode_app(B2,app_encode_fun(B2,B2),
6.11/6.28	                                        times_times(B2),
6.11/6.28	                                        app_encode_app(int,B2,
6.11/6.28	                                                       number_number_of(B2),V)),
6.11/6.28	                         app_encode_app(B2,B2,
6.11/6.28	                                        app_encode_app(B2,
6.11/6.28	                                                       app_encode_fun(B2,B2),
6.11/6.28	                                                       plus_plus(B2),B),
6.11/6.28	                                        C)) =
6.11/6.28	          app_encode_app(B2,B2,
6.11/6.28	                         app_encode_app(B2,app_encode_fun(B2,B2),
6.11/6.28	                                        plus_plus(B2),
6.11/6.28	                                        app_encode_app(B2,B2,
6.11/6.28	                                                       app_encode_app(
6.11/6.28	                                                       B2,
6.11/6.28	                                                       app_encode_fun(B2,B2),
6.11/6.28	                                                       times_times(B2),
6.11/6.28	                                                       app_encode_app(
6.11/6.28	                                                       int,B2,
6.11/6.28	                                                       number_number_of(B2),V)),
6.11/6.28	                                                       B)),
6.11/6.28	                         app_encode_app(B2,B2,
6.11/6.28	                                        app_encode_app(B2,
6.11/6.28	                                                       app_encode_fun(B2,B2),
6.11/6.28	                                                       times_times(B2),
6.11/6.28	                                                       app_encode_app(
6.11/6.28	                                                       int,B2,
6.11/6.28	                                                       number_number_of(B2),V)),
6.11/6.28	                                        C))))))).
6.11/6.28	tff('9', plain,
6.11/6.28	    ![X58 : $tType, X59 : int, X60 : X58, X61 : X58]:
6.11/6.28	      (app_encode_app(X58, X58, 
6.11/6.28	         app_encode_app(X58, app_encode_fun(X58, X58), times_times(X58), 
6.11/6.28	           app_encode_app(int, X58, number_number_of(X58), X59)), 
6.11/6.28	         app_encode_app(X58, X58, 
6.11/6.28	           app_encode_app(X58, app_encode_fun(X58, X58), plus_plus(X58), X60), 
6.11/6.28	           X61))
6.11/6.28	        = app_encode_app(X58, X58, 
6.11/6.28	            app_encode_app(X58, app_encode_fun(X58, X58), plus_plus(X58), 
6.11/6.28	              app_encode_app(X58, X58, 
6.11/6.28	                app_encode_app(X58, app_encode_fun(X58, X58), 
6.11/6.28	                  times_times(X58), 
6.11/6.28	                  app_encode_app(int, X58, number_number_of(X58), X59)), X60)), 
6.11/6.28	            app_encode_app(X58, X58, 
6.11/6.28	              app_encode_app(X58, app_encode_fun(X58, X58), 
6.11/6.28	                times_times(X58), 
6.11/6.28	                app_encode_app(int, X58, number_number_of(X58), X59)), X61))
6.11/6.28	       | ~ semiring(X58)
6.11/6.28	       | ~ number(X58)),
6.11/6.28	    inference('cnf', [status(esa)], [zf_stmt_61])).
6.11/6.28	tff('10', plain,
6.11/6.28	    ![X0 : int, X1 : int]:
6.11/6.28	      (app_encode_app(int, int, 
6.11/6.28	         app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.11/6.28	           app_encode_app(int, int, number_number_of(int), X1)), 
6.11/6.28	         app_encode_app(int, int, 
6.11/6.28	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
6.11/6.28	           X0))
6.11/6.28	        = app_encode_app(int, int, bit0, 
6.11/6.28	            app_encode_app(int, int, 
6.11/6.28	              app_encode_app(int, app_encode_fun(int, int), 
6.11/6.28	                times_times(int), 
6.11/6.28	                app_encode_app(int, int, number_number_of(int), X1)), X0))
6.11/6.28	       | ~ number(int)
6.11/6.28	       | ~ semiring(int)),
6.11/6.28	    inference('sup+', [status(thm)], ['8', '9'])).
6.11/6.28	tff(zf_stmt_146, axiom, (semiring(int))).
6.11/6.28	tff('11', plain, semiring(int),
6.11/6.28	    inference('cnf', [status(esa)], [zf_stmt_146])).
6.11/6.28	tff('12', plain,
6.11/6.28	    ![X0 : int, X1 : int]:
6.11/6.28	      (app_encode_app(int, int, 
6.11/6.28	         app_encode_app(int, app_encode_fun(int, int), times_times(int), X1), 
6.11/6.28	         app_encode_app(int, int, bit0, X0))
6.11/6.28	        = app_encode_app(int, int, bit0, 
6.11/6.28	            app_encode_app(int, int, 
6.11/6.28	              app_encode_app(int, app_encode_fun(int, int), 
6.11/6.28	                times_times(int), X1), X0))
6.11/6.28	       | ~ $true
6.11/6.28	       | ~ $true),
6.11/6.28	    inference('demod', [status(thm)], ['10', '1', '8', '1', '5', '11'])).
6.11/6.28	tff('13', plain,
6.11/6.28	    ![X0 : int, X1 : int]:
6.11/6.28	      app_encode_app(int, int, 
6.11/6.28	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X1), 
6.11/6.28	        app_encode_app(int, int, bit0, X0))
6.11/6.28	       = app_encode_app(int, int, bit0, 
6.11/6.28	           app_encode_app(int, int, 
6.11/6.28	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.11/6.28	               X1), X0)),
6.11/6.28	    inference('simplify', [status(thm)], ['12'])).
6.11/6.28	tff(zf_stmt_104, axiom,
6.11/6.28	  (![A:$tType]:
6.11/6.28	     (comm_semiring_1(A) =>
6.11/6.28	      (![B:A,A1:A]:
6.11/6.28	         (app_encode_app(A,A,
6.11/6.28	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
6.11/6.28	                                        A1),
6.11/6.28	                         B) =
6.11/6.28	          app_encode_app(A,A,
6.11/6.28	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
6.11/6.28	                                        B),
6.11/6.28	                         A1)))))).
6.11/6.28	tff('14', plain,
6.11/6.28	    ![X155 : $tType, X156 : X155, X157 : X155]:
6.11/6.28	      (app_encode_app(X155, X155, 
6.11/6.28	         app_encode_app(X155, app_encode_fun(X155, X155), times_times(X155), 
6.11/6.28	           X157), X156)
6.11/6.28	        = app_encode_app(X155, X155, 
6.11/6.28	            app_encode_app(X155, app_encode_fun(X155, X155), 
6.11/6.28	              times_times(X155), X156), X157)
6.11/6.28	       | ~ comm_semiring_1(X155)),
6.11/6.28	    inference('cnf', [status(esa)], [zf_stmt_104])).
6.11/6.28	tff('15', plain,
6.11/6.28	    ![X0 : int, X1 : int]:
6.11/6.28	      (app_encode_app(int, int, bit0, 
6.11/6.28	         app_encode_app(int, int, 
6.11/6.28	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.11/6.28	             X1), X0))
6.11/6.28	        = app_encode_app(int, int, 
6.11/6.28	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.11/6.28	              app_encode_app(int, int, bit0, X0)), X1)
6.11/6.28	       | ~ comm_semiring_1(int)),
6.11/6.28	    inference('sup+', [status(thm)], ['13', '14'])).
6.11/6.28	tff(zf_stmt_140, axiom, (comm_semiring_1(int))).
6.11/6.28	tff('16', plain, comm_semiring_1(int),
6.11/6.28	    inference('cnf', [status(esa)], [zf_stmt_140])).
6.11/6.28	tff('17', plain,
6.11/6.28	    ![X0 : int, X1 : int]:
6.11/6.28	      (app_encode_app(int, int, bit0, 
6.11/6.28	         app_encode_app(int, int, 
6.11/6.28	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.11/6.28	             X1), X0))
6.11/6.28	        = app_encode_app(int, int, 
6.11/6.28	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.11/6.28	              app_encode_app(int, int, bit0, X0)), X1)
6.11/6.28	       | ~ $true),
6.11/6.28	    inference('demod', [status(thm)], ['15', '16'])).
6.11/6.28	tff('18', plain,
6.11/6.28	    ![X0 : int, X1 : int]:
6.11/6.28	      app_encode_app(int, int, bit0, 
6.11/6.28	        app_encode_app(int, int, 
6.11/6.28	          app_encode_app(int, app_encode_fun(int, int), times_times(int), X1), 
6.11/6.28	          X0))
6.11/6.28	       = app_encode_app(int, int, 
6.11/6.28	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.11/6.28	             app_encode_app(int, int, bit0, X0)), X1),
6.11/6.28	    inference('simplify', [status(thm)], ['17'])).
6.11/6.28	tff(zf_stmt_62, axiom,
6.11/6.28	  (![A:$tType]:
6.11/6.28	     (number_ring(A) =>
6.11/6.28	      (![Z1:A,W:int,V:int]:
6.11/6.28	         (app_encode_app(A,A,
6.11/6.28	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
6.11/6.28	                                        app_encode_app(int,A,
6.11/6.28	                                                       number_number_of(A),V)),
6.11/6.28	                         app_encode_app(A,A,
6.11/6.28	                                        app_encode_app(A,app_encode_fun(A,A),
6.11/6.28	                                                       times_times(A),
6.11/6.28	                                                       app_encode_app(
6.11/6.28	                                                       int,A,
6.11/6.28	                                                       number_number_of(A),W)),
6.11/6.28	                                        Z1)) =
6.11/6.28	          app_encode_app(A,A,
6.11/6.28	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
6.11/6.28	                                        app_encode_app(int,A,
6.11/6.28	                                                       number_number_of(A),
6.11/6.28	                                                       app_encode_app(
6.11/6.28	                                                       int,int,
6.11/6.28	                                                       app_encode_app(
6.11/6.28	                                                       int,
6.11/6.28	                                                       app_encode_fun(
6.11/6.28	                                                       int,int),
6.11/6.28	                                                       times_times(int),V),W))),
6.11/6.28	                         Z1)))))).
6.11/6.28	tff('19', plain,
6.11/6.28	    ![X62 : $tType, X63 : int, X64 : int, X65 : X62]:
6.11/6.28	      (app_encode_app(X62, X62, 
6.11/6.28	         app_encode_app(X62, app_encode_fun(X62, X62), times_times(X62), 
6.11/6.28	           app_encode_app(int, X62, number_number_of(X62), X63)), 
6.11/6.28	         app_encode_app(X62, X62, 
6.11/6.28	           app_encode_app(X62, app_encode_fun(X62, X62), times_times(X62), 
6.11/6.28	             app_encode_app(int, X62, number_number_of(X62), X64)), X65))
6.11/6.28	        = app_encode_app(X62, X62, 
6.11/6.28	            app_encode_app(X62, app_encode_fun(X62, X62), times_times(X62), 
6.11/6.28	              app_encode_app(int, X62, number_number_of(X62), 
6.11/6.28	                app_encode_app(int, int, 
6.11/6.28	                  app_encode_app(int, app_encode_fun(int, int), 
6.11/6.28	                    times_times(int), X63), X64))), X65)
6.11/6.28	       | ~ number_ring(X62)),
6.11/6.28	    inference('cnf', [status(esa)], [zf_stmt_62])).
6.11/6.28	tff('20', plain,
6.11/6.28	    ![X0 : int, X1 : int, X2 : int]:
6.11/6.28	      (app_encode_app(int, int, 
6.11/6.28	         app_encode_app(int, app_encode_fun(int, int), times_times(int), X0), 
6.11/6.28	         app_encode_app(int, int, 
6.11/6.28	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.11/6.28	             app_encode_app(int, int, number_number_of(int), X2)), X1))
6.11/6.28	        = app_encode_app(int, int, 
6.11/6.28	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.11/6.28	              app_encode_app(int, int, number_number_of(int), 
6.11/6.28	                app_encode_app(int, int, 
6.11/6.28	                  app_encode_app(int, app_encode_fun(int, int), 
6.11/6.28	                    times_times(int), X0), X2))), X1)
6.11/6.28	       | ~ number_ring(int)),
6.11/6.28	    inference('sup+', [status(thm)], ['1', '19'])).
6.11/6.28	tff(zf_stmt_145, axiom, (number_ring(int))).
6.11/6.28	tff('21', plain, number_ring(int),
6.11/6.28	    inference('cnf', [status(esa)], [zf_stmt_145])).
6.11/6.28	tff('22', plain,
6.11/6.28	    ![X0 : int, X1 : int, X2 : int]:
6.11/6.28	      (app_encode_app(int, int, 
6.11/6.28	         app_encode_app(int, app_encode_fun(int, int), times_times(int), X0), 
6.11/6.28	         app_encode_app(int, int, 
6.11/6.28	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.11/6.28	             X2), X1))
6.11/6.28	        = app_encode_app(int, int, 
6.11/6.28	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.11/6.28	              app_encode_app(int, int, 
6.11/6.28	                app_encode_app(int, app_encode_fun(int, int), 
6.11/6.28	                  times_times(int), X0), X2)), X1)
6.11/6.28	       | ~ $true),
6.11/6.28	    inference('demod', [status(thm)], ['20', '1', '1', '21'])).
6.11/6.28	tff('23', plain,
6.11/6.28	    ![X0 : int, X1 : int, X2 : int]:
6.11/6.28	      app_encode_app(int, int, 
6.11/6.28	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X0), 
6.11/6.28	        app_encode_app(int, int, 
6.11/6.28	          app_encode_app(int, app_encode_fun(int, int), times_times(int), X2), 
6.11/6.28	          X1))
6.11/6.28	       = app_encode_app(int, int, 
6.11/6.28	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.11/6.28	             app_encode_app(int, int, 
6.11/6.28	               app_encode_app(int, app_encode_fun(int, int), 
6.11/6.28	                 times_times(int), X0), X2)), X1),
6.11/6.28	    inference('simplify', [status(thm)], ['22'])).
6.11/6.28	tff(zf_stmt_58, axiom,
6.11/6.28	  (![L:int,K:int]:
6.11/6.28	     (app_encode_app(int,int,
6.11/6.28	                     app_encode_app(int,app_encode_fun(int,int),
6.11/6.28	                                    times_times(int),
6.11/6.28	                                    app_encode_app(int,int,bit0,K)),
6.11/6.28	                     L) =
6.11/6.28	      app_encode_app(int,int,bit0,
6.11/6.28	                     app_encode_app(int,int,
6.11/6.28	                                    app_encode_app(int,
6.11/6.28	                                                   app_encode_fun(int,int),
6.11/6.28	                                                   times_times(int),K),
6.11/6.28	                                    L))))).
6.11/6.28	tff('24', plain,
6.11/6.28	    ![X50 : int, X51 : int]:
6.11/6.28	      app_encode_app(int, int, 
6.11/6.28	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.11/6.28	          app_encode_app(int, int, bit0, X50)), X51)
6.11/6.28	       = app_encode_app(int, int, bit0, 
6.11/6.28	           app_encode_app(int, int, 
6.11/6.28	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.11/6.28	               X50), X51)),
6.11/6.28	    inference('cnf', [status(esa)], [zf_stmt_58])).
6.11/6.28	tff('25', plain,
6.11/6.28	    ![X0 : int, X1 : int]:
6.11/6.28	      (app_encode_app(int, int, bit0, 
6.11/6.28	         app_encode_app(int, int, 
6.11/6.28	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.11/6.28	             X1), X0))
6.11/6.28	        = app_encode_app(int, int, 
6.11/6.28	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.11/6.28	              X0), app_encode_app(int, int, bit0, X1))
6.11/6.28	       | ~ comm_semiring_1(int)),
6.11/6.28	    inference('sup+', [status(thm)], ['24', '14'])).
6.11/6.28	tff('26', plain,
6.11/6.28	    ![X0 : int, X1 : int]:
6.11/6.28	      (app_encode_app(int, int, bit0, 
6.11/6.28	         app_encode_app(int, int, 
6.11/6.28	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.11/6.28	             X1), X0))
6.11/6.28	        = app_encode_app(int, int, 
6.11/6.28	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.11/6.28	              X0), app_encode_app(int, int, bit0, X1))
6.11/6.28	       | ~ $true),
6.11/6.28	    inference('demod', [status(thm)], ['25', '16'])).
6.11/6.28	tff('27', plain,
6.11/6.28	    ![X0 : int, X1 : int]:
6.11/6.28	      app_encode_app(int, int, bit0, 
6.11/6.28	        app_encode_app(int, int, 
6.11/6.28	          app_encode_app(int, app_encode_fun(int, int), times_times(int), X1), 
6.11/6.28	          X0))
6.11/6.28	       = app_encode_app(int, int, 
6.11/6.28	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.11/6.28	             X0), app_encode_app(int, int, bit0, X1)),
6.11/6.28	    inference('simplify', [status(thm)], ['26'])).
6.11/6.28	tff(zf_stmt_57, axiom,
6.11/6.28	  (![W:int]:
6.11/6.28	     (app_encode_app(int,int,
6.11/6.28	                     app_encode_app(int,app_encode_fun(int,int),
6.11/6.28	                                    times_times(int),pls),
6.11/6.28	                     W) =
6.11/6.28	      pls))).
6.11/6.28	tff('28', plain,
6.11/6.28	    ![X49 : int]:
6.11/6.28	      app_encode_app(int, int, 
6.11/6.28	        app_encode_app(int, app_encode_fun(int, int), times_times(int), pls), 
6.11/6.28	        X49)
6.11/6.28	       = pls,
6.11/6.28	    inference('cnf', [status(esa)], [zf_stmt_57])).
6.11/6.28	tff(zf_stmt_38, axiom,
6.11/6.28	  (![L:int,K:int]:
6.11/6.28	     (app_encode_app(int,int,
6.11/6.28	                     app_encode_app(int,app_encode_fun(int,int),
6.11/6.28	                                    times_times(int),
6.11/6.28	                                    app_encode_app(int,int,bit1,K)),
6.11/6.28	                     L) =
6.11/6.28	      app_encode_app(int,int,
6.11/6.28	                     app_encode_app(int,app_encode_fun(int,int),
6.11/6.28	                                    plus_plus(int),
6.11/6.28	                                    app_encode_app(int,int,bit0,
6.11/6.28	                                                   app_encode_app(int,int,
6.11/6.28	                                                                  app_encode_app(
6.11/6.28	                                                                  int,
6.11/6.28	                                                                  app_encode_fun(
6.11/6.28	                                                                  int,int),
6.11/6.28	                                                                  times_times(
6.11/6.28	                                                                  int),K),L))),
6.11/6.28	                     L)))).
6.11/6.28	tff('29', plain,
6.11/6.28	    ![X6 : int, X7 : int]:
6.11/6.28	      app_encode_app(int, int, 
6.11/6.28	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.11/6.28	          app_encode_app(int, int, bit1, X6)), X7)
6.11/6.28	       = app_encode_app(int, int, 
6.11/6.28	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
6.11/6.28	             app_encode_app(int, int, bit0, 
6.11/6.28	               app_encode_app(int, int, 
6.11/6.28	                 app_encode_app(int, app_encode_fun(int, int), 
6.11/6.28	                   times_times(int), X6), X7))), X7),
6.11/6.28	    inference('cnf', [status(esa)], [zf_stmt_38])).
6.11/6.28	tff('30', plain,
6.11/6.28	    ![X0 : int]:
6.11/6.28	      app_encode_app(int, int, 
6.11/6.28	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.11/6.28	          app_encode_app(int, int, bit1, pls)), X0)
6.11/6.28	       = app_encode_app(int, int, 
6.11/6.28	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
6.11/6.28	             app_encode_app(int, int, bit0, pls)), X0),
6.11/6.28	    inference('sup+', [status(thm)], ['28', '29'])).
6.11/6.28	tff(zf_stmt_56, axiom, (app_encode_app(int,int,bit0,pls) = pls)).
6.11/6.28	tff('31', plain, app_encode_app(int, int, bit0, pls) = pls,
6.11/6.28	    inference('cnf', [status(esa)], [zf_stmt_56])).
6.11/6.28	tff('32', plain,
6.11/6.28	    ![X0 : int]:
6.11/6.28	      app_encode_app(int, int, 
6.11/6.28	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.11/6.28	          app_encode_app(int, int, bit1, pls)), X0)
6.11/6.28	       = app_encode_app(int, int, 
6.11/6.28	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
6.11/6.28	           X0),
6.11/6.28	    inference('demod', [status(thm)], ['30', '31'])).
6.11/6.29	tff(zf_stmt_70, axiom,
6.11/6.29	  (![K:int]:
6.11/6.29	     (app_encode_app(int,int,
6.11/6.29	                     app_encode_app(int,app_encode_fun(int,int),
6.11/6.29	                                    plus_plus(int),pls),
6.11/6.29	                     K) =
6.11/6.29	      K))).
6.11/6.29	tff('33', plain,
6.11/6.29	    ![X80 : int]:
6.11/6.29	      app_encode_app(int, int, 
6.11/6.29	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
6.11/6.29	        X80)
6.11/6.29	       = X80,
6.11/6.29	    inference('cnf', [status(esa)], [zf_stmt_70])).
6.11/6.29	tff('34', plain,
6.11/6.29	    ![X0 : int]:
6.11/6.29	      app_encode_app(int, int, 
6.11/6.29	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.11/6.29	          app_encode_app(int, int, bit1, pls)), X0)
6.11/6.29	       = X0,
6.11/6.29	    inference('demod', [status(thm)], ['32', '33'])).
6.11/6.29	tff(zf_stmt_59, axiom,
6.11/6.29	  (![L:int,K:int]:
6.11/6.29	     (app_encode_app(int,int,
6.11/6.29	                     app_encode_app(int,app_encode_fun(int,int),
6.11/6.29	                                    plus_plus(int),
6.11/6.29	                                    app_encode_app(int,int,bit0,K)),
6.11/6.29	                     app_encode_app(int,int,bit0,L)) =
6.11/6.29	      app_encode_app(int,int,bit0,
6.11/6.29	                     app_encode_app(int,int,
6.11/6.29	                                    app_encode_app(int,
6.11/6.29	                                                   app_encode_fun(int,int),
6.11/6.29	                                                   plus_plus(int),K),
6.11/6.29	                                    L))))).
6.11/6.29	tff('35', plain,
6.11/6.29	    ![X52 : int, X53 : int]:
6.11/6.29	      app_encode_app(int, int, 
6.11/6.29	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
6.11/6.29	          app_encode_app(int, int, bit0, X52)), 
6.11/6.29	        app_encode_app(int, int, bit0, X53))
6.11/6.29	       = app_encode_app(int, int, bit0, 
6.11/6.29	           app_encode_app(int, int, 
6.11/6.29	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
6.11/6.29	               X52), X53)),
6.11/6.29	    inference('cnf', [status(esa)], [zf_stmt_59])).
6.11/6.29	tff(zf_stmt_113, axiom,
6.11/6.29	  (![A:$tType]:
6.11/6.29	     (comm_semiring_1(A) =>
6.11/6.29	      (![C:A,A1:A]:
6.11/6.29	         (app_encode_app(A,A,
6.11/6.29	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),A1),
6.11/6.29	                         C) =
6.11/6.29	          app_encode_app(A,A,
6.11/6.29	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),C),
6.11/6.29	                         A1)))))).
6.11/6.29	tff('36', plain,
6.11/6.29	    ![X193 : $tType, X194 : X193, X195 : X193]:
6.11/6.29	      (app_encode_app(X193, X193, 
6.11/6.29	         app_encode_app(X193, app_encode_fun(X193, X193), plus_plus(X193), 
6.11/6.29	           X195), X194)
6.11/6.29	        = app_encode_app(X193, X193, 
6.11/6.29	            app_encode_app(X193, app_encode_fun(X193, X193), 
6.11/6.29	              plus_plus(X193), X194), X195)
6.11/6.29	       | ~ comm_semiring_1(X193)),
6.11/6.29	    inference('cnf', [status(esa)], [zf_stmt_113])).
6.11/6.29	tff('37', plain,
6.11/6.29	    ![X0 : int, X1 : int]:
6.11/6.29	      (app_encode_app(int, int, bit0, 
6.11/6.29	         app_encode_app(int, int, 
6.11/6.29	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X1), 
6.11/6.29	           X0))
6.11/6.29	        = app_encode_app(int, int, 
6.11/6.29	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
6.11/6.29	              app_encode_app(int, int, bit0, X0)), 
6.11/6.29	            app_encode_app(int, int, bit0, X1))
6.11/6.29	       | ~ comm_semiring_1(int)),
6.11/6.29	    inference('sup+', [status(thm)], ['35', '36'])).
6.11/6.29	tff('38', plain,
6.11/6.29	    ![X0 : int, X1 : int]:
6.11/6.29	      (app_encode_app(int, int, bit0, 
6.11/6.29	         app_encode_app(int, int, 
6.11/6.29	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X1), 
6.11/6.29	           X0))
6.11/6.29	        = app_encode_app(int, int, 
6.11/6.29	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
6.11/6.29	              app_encode_app(int, int, bit0, X0)), 
6.11/6.29	            app_encode_app(int, int, bit0, X1))
6.11/6.29	       | ~ $true),
6.11/6.29	    inference('demod', [status(thm)], ['37', '16'])).
6.11/6.29	tff('39', plain,
6.11/6.29	    ![X0 : int, X1 : int]:
6.11/6.29	      app_encode_app(int, int, bit0, 
6.11/6.29	        app_encode_app(int, int, 
6.11/6.29	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X1), 
6.11/6.29	          X0))
6.11/6.29	       = app_encode_app(int, int, 
6.11/6.29	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
6.11/6.29	             app_encode_app(int, int, bit0, X0)), 
6.11/6.29	           app_encode_app(int, int, bit0, X1)),
6.11/6.29	    inference('simplify', [status(thm)], ['38'])).
6.11/6.29	tff(zf_stmt_81, axiom,
6.11/6.29	  (![A:$tType]:
6.11/6.29	     (number_ring(A) =>
6.11/6.29	      (![A1:A]:
6.11/6.29	         (app_encode_app(A,A,
6.11/6.29	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
6.11/6.29	                                        A1),
6.11/6.29	                         app_encode_app(int,A,number_number_of(A),
6.11/6.29	                                        app_encode_app(int,int,bit1,pls))) =
6.11/6.29	          A1))))).
6.11/6.29	tff('40', plain,
6.11/6.29	    ![X104 : $tType, X105 : X104]:
6.11/6.29	      (app_encode_app(X104, X104, 
6.11/6.29	         app_encode_app(X104, app_encode_fun(X104, X104), times_times(X104), 
6.11/6.29	           X105), 
6.11/6.29	         app_encode_app(int, X104, number_number_of(X104), 
6.11/6.29	           app_encode_app(int, int, bit1, pls)))
6.11/6.29	        = X105
6.11/6.29	       | ~ number_ring(X104)),
6.11/6.29	    inference('cnf', [status(esa)], [zf_stmt_81])).
6.11/6.29	tff('41', plain,
6.11/6.29	    ![X0 : int]:
6.11/6.29	      (app_encode_app(int, int, 
6.11/6.29	         app_encode_app(int, app_encode_fun(int, int), times_times(int), X0), 
6.11/6.29	         app_encode_app(int, int, bit1, pls))
6.11/6.29	        = X0
6.11/6.29	       | ~ number_ring(int)),
6.11/6.29	    inference('sup+', [status(thm)], ['1', '40'])).
6.11/6.29	tff('42', plain,
6.11/6.29	    ![X0 : int]:
6.11/6.29	      (app_encode_app(int, int, 
6.11/6.29	         app_encode_app(int, app_encode_fun(int, int), times_times(int), X0), 
6.11/6.29	         app_encode_app(int, int, bit1, pls))
6.11/6.29	        = X0
6.11/6.29	       | ~ $true),
6.11/6.29	    inference('demod', [status(thm)], ['41', '21'])).
6.11/6.29	tff('43', plain,
6.11/6.29	    ![X0 : int]:
6.11/6.29	      app_encode_app(int, int, 
6.11/6.29	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X0), 
6.11/6.29	        app_encode_app(int, int, bit1, pls))
6.11/6.29	       = X0,
6.11/6.29	    inference('simplify', [status(thm)], ['42'])).
6.11/6.29	tff(zf_stmt_37, axiom,
6.11/6.29	  (![A:$tType]:
6.11/6.29	     (linordered_idom(A) =>
6.11/6.29	      (![A1:A]:
6.11/6.29	         (app_encode_app(nat,A,
6.11/6.29	                         app_encode_app(A,app_encode_fun(nat,A),
6.11/6.29	                                        power_power(A),
6.11/6.29	                                        app_encode_app(A,A,abs_abs(A),A1)),
6.11/6.29	                         app_encode_app(int,nat,number_number_of(nat),
6.11/6.29	                                        app_encode_app(int,int,bit0,
6.11/6.29	                                                       app_encode_app(
6.11/6.29	                                                       int,int,bit1,pls)))) =
6.11/6.29	          app_encode_app(nat,A,
6.11/6.29	                         app_encode_app(A,app_encode_fun(nat,A),
6.11/6.29	                                        power_power(A),A1),
6.11/6.29	                         app_encode_app(int,nat,number_number_of(nat),
6.11/6.29	                                        app_encode_app(int,int,bit0,
6.11/6.29	                                                       app_encode_app(
6.11/6.29	                                                       int,int,bit1,pls))))))))).
6.11/6.29	tff('44', plain,
6.11/6.29	    ![X4 : $tType, X5 : X4]:
6.11/6.29	      (app_encode_app(nat, X4, 
6.11/6.29	         app_encode_app(X4, app_encode_fun(nat, X4), power_power(X4), 
6.11/6.29	           app_encode_app(X4, X4, abs_abs(X4), X5)), 
6.11/6.29	         app_encode_app(int, nat, number_number_of(nat), 
6.11/6.29	           app_encode_app(int, int, bit0, 
6.11/6.29	             app_encode_app(int, int, bit1, pls))))
6.11/6.29	        = app_encode_app(nat, X4, 
6.11/6.29	            app_encode_app(X4, app_encode_fun(nat, X4), power_power(X4), X5), 
6.11/6.29	            app_encode_app(int, nat, number_number_of(nat), 
6.11/6.29	              app_encode_app(int, int, bit0, 
6.11/6.29	                app_encode_app(int, int, bit1, pls))))
6.11/6.29	       | ~ linordered_idom(X4)),
6.11/6.29	    inference('cnf', [status(esa)], [zf_stmt_37])).
6.11/6.29	tff('45', plain,
6.11/6.29	    ![X0 : int]:
6.11/6.29	      (app_encode_app(nat, int, 
6.11/6.29	         app_encode_app(int, app_encode_fun(nat, int), power_power(int), X0), 
6.11/6.29	         app_encode_app(int, nat, number_number_of(nat), 
6.11/6.29	           app_encode_app(int, int, bit0, 
6.11/6.29	             app_encode_app(int, int, bit1, pls))))
6.11/6.29	        = app_encode_app(int, int, 
6.11/6.29	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.11/6.29	              app_encode_app(int, int, abs_abs(int), X0)), 
6.11/6.29	            app_encode_app(int, int, abs_abs(int), X0))
6.11/6.29	       | ~ linordered_idom(int)),
6.11/6.29	    inference('sup+', [status(thm)], ['44', '7'])).
6.11/6.29	tff(zf_stmt_139, axiom, (linordered_idom(int))).
6.11/6.29	tff('46', plain, linordered_idom(int),
6.11/6.29	    inference('cnf', [status(esa)], [zf_stmt_139])).
6.11/6.29	tff('47', plain,
6.11/6.29	    ![X0 : int]:
6.11/6.29	      (app_encode_app(nat, int, 
6.11/6.29	         app_encode_app(int, app_encode_fun(nat, int), power_power(int), X0), 
6.11/6.29	         app_encode_app(int, nat, number_number_of(nat), 
6.11/6.29	           app_encode_app(int, int, bit0, 
6.11/6.29	             app_encode_app(int, int, bit1, pls))))
6.11/6.29	        = app_encode_app(int, int, 
6.11/6.29	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.11/6.29	              app_encode_app(int, int, abs_abs(int), X0)), 
6.11/6.29	            app_encode_app(int, int, abs_abs(int), X0))
6.11/6.29	       | ~ $true),
6.11/6.29	    inference('demod', [status(thm)], ['45', '46'])).
6.11/6.29	tff('48', plain,
6.11/6.29	    ![X0 : int]:
6.11/6.29	      app_encode_app(nat, int, 
6.11/6.29	        app_encode_app(int, app_encode_fun(nat, int), power_power(int), X0), 
6.11/6.29	        app_encode_app(int, nat, number_number_of(nat), 
6.11/6.29	          app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls))))
6.11/6.29	       = app_encode_app(int, int, 
6.11/6.29	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.11/6.29	             app_encode_app(int, int, abs_abs(int), X0)), 
6.11/6.29	           app_encode_app(int, int, abs_abs(int), X0)),
6.11/6.29	    inference('simplify', [status(thm)], ['47'])).
6.11/6.29	tff('49', plain,
6.11/6.29	    ![X0 : int]:
6.11/6.29	      app_encode_app(int, int, 
6.11/6.29	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.11/6.29	          app_encode_app(int, int, abs_abs(int), X0)), 
6.11/6.29	        app_encode_app(int, int, abs_abs(int), X0))
6.11/6.29	       = app_encode_app(int, int, 
6.11/6.29	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.11/6.29	             X0), X0),
6.11/6.29	    inference('sup+', [status(thm)], ['48', '7'])).
6.11/6.29	tff('50', plain,
6.11/6.29	    app_encode_app(int, int, bit0, 
6.11/6.29	      app_encode_app(int, int, bit0, 
6.11/6.29	        app_encode_app(int, int, 
6.11/6.29	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
6.11/6.29	            app_encode_app(int, int, 
6.11/6.29	              app_encode_app(int, app_encode_fun(int, int), 
6.11/6.29	                times_times(int), v), v)), 
6.11/6.29	          app_encode_app(int, int, 
6.11/6.29	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.11/6.29	              w), w))))
6.11/6.29	     != app_encode_app(int, int, bit0, 
6.11/6.29	          app_encode_app(int, int, bit0, 
6.11/6.29	            app_encode_app(int, int, 
6.11/6.29	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
6.11/6.29	                app_encode_app(int, int, 
6.11/6.29	                  app_encode_app(int, app_encode_fun(int, int), 
6.11/6.29	                    times_times(int), v), v)), 
6.11/6.29	              app_encode_app(int, int, 
6.11/6.29	                app_encode_app(int, app_encode_fun(int, int), 
6.11/6.29	                  times_times(int), w), w)))),
6.11/6.29	    inference('demod', [status(thm)],
6.11/6.29	              ['0', '1', '7', '18', '23', '27', '34', '27', '1', '7', '18', 
6.11/6.29	               '23', '27', '34', '27', '39', '39', '1', '18', '43', '7', 
6.11/6.29	               '18', '18', '49', '1', '18', '43', '7', '18', '18', '49', 
6.11/6.29	               '39', '39'])).
6.11/6.29	tff('51', plain, $false, inference('simplify', [status(thm)], ['50'])).
6.11/6.29	
6.11/6.29	% SZS output end Refutation
6.11/6.29	EOF
