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    : 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   : n124.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 08:18:08 CST 2018
6.15/6.38	% done 1015 iterations in 6.175s
6.15/6.38	% SZS status Theorem for 'stdin'
6.15/6.38	% SZS output start Refutation
6.15/6.38	tff(zf_stmt_177, conjecture,
6.15/6.38	  (app_encode_app(int,int,
6.15/6.38	                  app_encode_app(int,app_encode_fun(int,int),plus_plus(int),
6.15/6.38	                                 app_encode_app(int,int,
6.15/6.38	                                                app_encode_app(int,
6.15/6.38	                                                               app_encode_fun(
6.15/6.38	                                                               int,int),
6.15/6.38	                                                               times_times(
6.15/6.38	                                                               int),
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,int,
6.15/6.38	                                                               number_number_of(
6.15/6.38	                                                               int),
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,int,bit0,
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,int,bit0,
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,int,bit1,
6.15/6.38	                                                               pls))))),
6.15/6.38	                                                app_encode_app(nat,int,
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,
6.15/6.38	                                                               app_encode_fun(
6.15/6.38	                                                               nat,int),
6.15/6.38	                                                               power_power(
6.15/6.38	                                                               int),v),
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,nat,
6.15/6.38	                                                               number_number_of(
6.15/6.38	                                                               nat),
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,int,bit0,
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,int,bit1,
6.15/6.38	                                                               pls)))))),
6.15/6.38	                  app_encode_app(int,int,
6.15/6.38	                                 app_encode_app(int,app_encode_fun(int,int),
6.15/6.38	                                                times_times(int),
6.15/6.38	                                                app_encode_app(int,int,
6.15/6.38	                                                               number_number_of(
6.15/6.38	                                                               int),
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,int,bit0,
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,int,bit0,
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,int,bit1,
6.15/6.38	                                                               pls))))),
6.15/6.38	                                 app_encode_app(nat,int,
6.15/6.38	                                                app_encode_app(int,
6.15/6.38	                                                               app_encode_fun(
6.15/6.38	                                                               nat,int),
6.15/6.38	                                                               power_power(
6.15/6.38	                                                               int),w),
6.15/6.38	                                                app_encode_app(int,nat,
6.15/6.38	                                                               number_number_of(
6.15/6.38	                                                               nat),
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,int,bit0,
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,int,bit1,
6.15/6.38	                                                               pls)))))) =
6.15/6.38	   app_encode_app(int,int,
6.15/6.38	                  app_encode_app(int,app_encode_fun(int,int),plus_plus(int),
6.15/6.38	                                 app_encode_app(nat,int,
6.15/6.38	                                                app_encode_app(int,
6.15/6.38	                                                               app_encode_fun(
6.15/6.38	                                                               nat,int),
6.15/6.38	                                                               power_power(
6.15/6.38	                                                               int),
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,int,
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,
6.15/6.38	                                                               app_encode_fun(
6.15/6.38	                                                               int,int),
6.15/6.38	                                                               times_times(
6.15/6.38	                                                               int),
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,int,
6.15/6.38	                                                               number_number_of(
6.15/6.38	                                                               int),
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,int,bit0,
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,int,bit1,
6.15/6.38	                                                               pls)))),
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,int,
6.15/6.38	                                                               abs_abs(int),v))),
6.15/6.38	                                                app_encode_app(int,nat,
6.15/6.38	                                                               number_number_of(
6.15/6.38	                                                               nat),
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,int,bit0,
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,int,bit1,
6.15/6.38	                                                               pls))))),
6.15/6.38	                  app_encode_app(nat,int,
6.15/6.38	                                 app_encode_app(int,app_encode_fun(nat,int),
6.15/6.38	                                                power_power(int),
6.15/6.38	                                                app_encode_app(int,int,
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,
6.15/6.38	                                                               app_encode_fun(
6.15/6.38	                                                               int,int),
6.15/6.38	                                                               times_times(
6.15/6.38	                                                               int),
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,int,
6.15/6.38	                                                               number_number_of(
6.15/6.38	                                                               int),
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,int,bit0,
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,int,bit1,
6.15/6.38	                                                               pls)))),
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,int,
6.15/6.38	                                                               abs_abs(int),w))),
6.15/6.38	                                 app_encode_app(int,nat,
6.15/6.38	                                                number_number_of(nat),
6.15/6.38	                                                app_encode_app(int,int,bit0,
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,int,bit1,
6.15/6.38	                                                               pls))))))).
6.15/6.38	tff(zf_stmt_0, negated_conjecture,
6.15/6.38	  (app_encode_app(int,int,
6.15/6.38	                  app_encode_app(int,app_encode_fun(int,int),plus_plus(int),
6.15/6.38	                                 app_encode_app(int,int,
6.15/6.38	                                                app_encode_app(int,
6.15/6.38	                                                               app_encode_fun(
6.15/6.38	                                                               int,int),
6.15/6.38	                                                               times_times(
6.15/6.38	                                                               int),
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,int,
6.15/6.38	                                                               number_number_of(
6.15/6.38	                                                               int),
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,int,bit0,
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,int,bit0,
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,int,bit1,
6.15/6.38	                                                               pls))))),
6.15/6.38	                                                app_encode_app(nat,int,
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,
6.15/6.38	                                                               app_encode_fun(
6.15/6.38	                                                               nat,int),
6.15/6.38	                                                               power_power(
6.15/6.38	                                                               int),v),
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,nat,
6.15/6.38	                                                               number_number_of(
6.15/6.38	                                                               nat),
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,int,bit0,
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,int,bit1,
6.15/6.38	                                                               pls)))))),
6.15/6.38	                  app_encode_app(int,int,
6.15/6.38	                                 app_encode_app(int,app_encode_fun(int,int),
6.15/6.38	                                                times_times(int),
6.15/6.38	                                                app_encode_app(int,int,
6.15/6.38	                                                               number_number_of(
6.15/6.38	                                                               int),
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,int,bit0,
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,int,bit0,
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,int,bit1,
6.15/6.38	                                                               pls))))),
6.15/6.38	                                 app_encode_app(nat,int,
6.15/6.38	                                                app_encode_app(int,
6.15/6.38	                                                               app_encode_fun(
6.15/6.38	                                                               nat,int),
6.15/6.38	                                                               power_power(
6.15/6.38	                                                               int),w),
6.15/6.38	                                                app_encode_app(int,nat,
6.15/6.38	                                                               number_number_of(
6.15/6.38	                                                               nat),
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,int,bit0,
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,int,bit1,
6.15/6.38	                                                               pls)))))) !=
6.15/6.38	   app_encode_app(int,int,
6.15/6.38	                  app_encode_app(int,app_encode_fun(int,int),plus_plus(int),
6.15/6.38	                                 app_encode_app(nat,int,
6.15/6.38	                                                app_encode_app(int,
6.15/6.38	                                                               app_encode_fun(
6.15/6.38	                                                               nat,int),
6.15/6.38	                                                               power_power(
6.15/6.38	                                                               int),
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,int,
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,
6.15/6.38	                                                               app_encode_fun(
6.15/6.38	                                                               int,int),
6.15/6.38	                                                               times_times(
6.15/6.38	                                                               int),
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,int,
6.15/6.38	                                                               number_number_of(
6.15/6.38	                                                               int),
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,int,bit0,
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,int,bit1,
6.15/6.38	                                                               pls)))),
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,int,
6.15/6.38	                                                               abs_abs(int),v))),
6.15/6.38	                                                app_encode_app(int,nat,
6.15/6.38	                                                               number_number_of(
6.15/6.38	                                                               nat),
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,int,bit0,
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,int,bit1,
6.15/6.38	                                                               pls))))),
6.15/6.38	                  app_encode_app(nat,int,
6.15/6.38	                                 app_encode_app(int,app_encode_fun(nat,int),
6.15/6.38	                                                power_power(int),
6.15/6.38	                                                app_encode_app(int,int,
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,
6.15/6.38	                                                               app_encode_fun(
6.15/6.38	                                                               int,int),
6.15/6.38	                                                               times_times(
6.15/6.38	                                                               int),
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,int,
6.15/6.38	                                                               number_number_of(
6.15/6.38	                                                               int),
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,int,bit0,
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,int,bit1,
6.15/6.38	                                                               pls)))),
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,int,
6.15/6.38	                                                               abs_abs(int),w))),
6.15/6.38	                                 app_encode_app(int,nat,
6.15/6.38	                                                number_number_of(nat),
6.15/6.38	                                                app_encode_app(int,int,bit0,
6.15/6.38	                                                               app_encode_app(
6.15/6.38	                                                               int,int,bit1,
6.15/6.38	                                                               pls))))))).
6.15/6.38	tff('0', plain,
6.15/6.38	    app_encode_app(int, int, 
6.15/6.38	      app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
6.15/6.38	        app_encode_app(int, int, 
6.15/6.38	          app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.15/6.38	            app_encode_app(int, int, number_number_of(int), 
6.15/6.38	              app_encode_app(int, int, bit0, 
6.15/6.38	                app_encode_app(int, int, bit0, 
6.15/6.38	                  app_encode_app(int, int, bit1, pls))))), 
6.15/6.38	          app_encode_app(nat, int, 
6.15/6.38	            app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
6.15/6.38	              v), 
6.15/6.38	            app_encode_app(int, nat, number_number_of(nat), 
6.15/6.38	              app_encode_app(int, int, bit0, 
6.15/6.38	                app_encode_app(int, int, bit1, pls)))))), 
6.15/6.38	      app_encode_app(int, int, 
6.15/6.38	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.15/6.38	          app_encode_app(int, int, number_number_of(int), 
6.15/6.38	            app_encode_app(int, int, bit0, 
6.15/6.38	              app_encode_app(int, int, bit0, 
6.15/6.38	                app_encode_app(int, int, bit1, pls))))), 
6.15/6.38	        app_encode_app(nat, int, 
6.15/6.38	          app_encode_app(int, app_encode_fun(nat, int), power_power(int), w), 
6.15/6.38	          app_encode_app(int, nat, number_number_of(nat), 
6.15/6.38	            app_encode_app(int, int, bit0, 
6.15/6.38	              app_encode_app(int, int, bit1, pls))))))
6.15/6.38	     != app_encode_app(int, int, 
6.15/6.38	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
6.15/6.38	            app_encode_app(nat, int, 
6.15/6.38	              app_encode_app(int, app_encode_fun(nat, int), 
6.15/6.38	                power_power(int), 
6.15/6.38	                app_encode_app(int, int, 
6.15/6.38	                  app_encode_app(int, app_encode_fun(int, int), 
6.15/6.38	                    times_times(int), 
6.15/6.38	                    app_encode_app(int, int, number_number_of(int), 
6.15/6.38	                      app_encode_app(int, int, bit0, 
6.15/6.38	                        app_encode_app(int, int, bit1, pls)))), 
6.15/6.38	                  app_encode_app(int, int, abs_abs(int), v))), 
6.15/6.38	              app_encode_app(int, nat, number_number_of(nat), 
6.15/6.38	                app_encode_app(int, int, bit0, 
6.15/6.38	                  app_encode_app(int, int, bit1, pls))))), 
6.15/6.38	          app_encode_app(nat, int, 
6.15/6.38	            app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
6.15/6.38	              app_encode_app(int, int, 
6.15/6.38	                app_encode_app(int, app_encode_fun(int, int), 
6.15/6.38	                  times_times(int), 
6.15/6.38	                  app_encode_app(int, int, number_number_of(int), 
6.15/6.38	                    app_encode_app(int, int, bit0, 
6.15/6.38	                      app_encode_app(int, int, bit1, pls)))), 
6.15/6.38	                app_encode_app(int, int, abs_abs(int), w))), 
6.15/6.38	            app_encode_app(int, nat, number_number_of(nat), 
6.15/6.38	              app_encode_app(int, int, bit0, 
6.15/6.38	                app_encode_app(int, int, bit1, pls))))),
6.15/6.38	    inference('cnf', [status(esa)], [zf_stmt_0])).
6.15/6.38	tff(zf_stmt_68, axiom,
6.15/6.38	  (![K:int]: (app_encode_app(int,int,number_number_of(int),K) = K))).
6.15/6.38	tff('1', plain,
6.15/6.38	    ![X79 : int]: app_encode_app(int, int, number_number_of(int), X79) = X79,
6.15/6.38	    inference('cnf', [status(esa)], [zf_stmt_68])).
6.15/6.38	tff(zf_stmt_36, axiom,
6.15/6.38	  (![B2:$tType]:
6.15/6.38	     ((monoid_mult(B2) & number(B2)) =>
6.15/6.38	      (![W:int]:
6.15/6.38	         (app_encode_app(nat,B2,
6.15/6.38	                         app_encode_app(B2,app_encode_fun(nat,B2),
6.15/6.38	                                        power_power(B2),
6.15/6.38	                                        app_encode_app(int,B2,
6.15/6.38	                                                       number_number_of(B2),W)),
6.15/6.38	                         app_encode_app(int,nat,number_number_of(nat),
6.15/6.38	                                        app_encode_app(int,int,bit0,
6.15/6.38	                                                       app_encode_app(
6.15/6.38	                                                       int,int,bit1,pls)))) =
6.15/6.38	          app_encode_app(B2,B2,
6.15/6.38	                         app_encode_app(B2,app_encode_fun(B2,B2),
6.15/6.38	                                        times_times(B2),
6.15/6.38	                                        app_encode_app(int,B2,
6.15/6.38	                                                       number_number_of(B2),W)),
6.15/6.38	                         app_encode_app(int,B2,number_number_of(B2),W))))))).
6.15/6.38	tff('2', plain,
6.15/6.38	    ![X4 : $tType, X5 : int]:
6.15/6.38	      (app_encode_app(nat, X4, 
6.15/6.38	         app_encode_app(X4, app_encode_fun(nat, X4), power_power(X4), 
6.15/6.38	           app_encode_app(int, X4, number_number_of(X4), X5)), 
6.15/6.38	         app_encode_app(int, nat, number_number_of(nat), 
6.15/6.38	           app_encode_app(int, int, bit0, 
6.15/6.38	             app_encode_app(int, int, bit1, pls))))
6.15/6.38	        = app_encode_app(X4, X4, 
6.15/6.38	            app_encode_app(X4, app_encode_fun(X4, X4), times_times(X4), 
6.15/6.38	              app_encode_app(int, X4, number_number_of(X4), X5)), 
6.15/6.38	            app_encode_app(int, X4, number_number_of(X4), X5))
6.15/6.38	       | ~ number(X4)
6.15/6.38	       | ~ monoid_mult(X4)),
6.15/6.38	    inference('cnf', [status(esa)], [zf_stmt_36])).
6.15/6.38	tff('3', plain,
6.15/6.38	    ![X0 : int]:
6.15/6.38	      (app_encode_app(nat, int, 
6.15/6.38	         app_encode_app(int, app_encode_fun(nat, int), power_power(int), X0), 
6.15/6.38	         app_encode_app(int, nat, number_number_of(nat), 
6.15/6.38	           app_encode_app(int, int, bit0, 
6.15/6.38	             app_encode_app(int, int, bit1, pls))))
6.15/6.38	        = app_encode_app(int, int, 
6.15/6.38	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.15/6.38	              app_encode_app(int, int, number_number_of(int), X0)), 
6.15/6.38	            app_encode_app(int, int, number_number_of(int), X0))
6.15/6.38	       | ~ monoid_mult(int)
6.15/6.38	       | ~ number(int)),
6.15/6.38	    inference('sup+', [status(thm)], ['1', '2'])).
6.15/6.38	tff(zf_stmt_144, axiom, (monoid_mult(int))).
6.15/6.38	tff('4', plain, monoid_mult(int),
6.15/6.38	    inference('cnf', [status(esa)], [zf_stmt_144])).
6.15/6.38	tff(zf_stmt_148, axiom, (number(int))).
6.15/6.38	tff('5', plain, number(int), inference('cnf', [status(esa)], [zf_stmt_148])).
6.15/6.38	tff('6', plain,
6.15/6.38	    ![X0 : int]:
6.15/6.38	      (app_encode_app(nat, int, 
6.15/6.38	         app_encode_app(int, app_encode_fun(nat, int), power_power(int), X0), 
6.15/6.38	         app_encode_app(int, nat, number_number_of(nat), 
6.15/6.38	           app_encode_app(int, int, bit0, 
6.15/6.38	             app_encode_app(int, int, bit1, pls))))
6.15/6.38	        = app_encode_app(int, int, 
6.15/6.38	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.15/6.38	              X0), X0)
6.15/6.38	       | ~ $true
6.15/6.38	       | ~ $true),
6.15/6.38	    inference('demod', [status(thm)], ['3', '1', '1', '4', '5'])).
6.15/6.38	tff('7', plain,
6.15/6.38	    ![X0 : int]:
6.15/6.38	      app_encode_app(nat, int, 
6.15/6.38	        app_encode_app(int, app_encode_fun(nat, int), power_power(int), X0), 
6.15/6.38	        app_encode_app(int, nat, number_number_of(nat), 
6.15/6.38	          app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls))))
6.15/6.38	       = app_encode_app(int, int, 
6.15/6.38	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.15/6.38	             X0), X0),
6.15/6.38	    inference('simplify', [status(thm)], ['6'])).
6.15/6.38	tff(zf_stmt_72, axiom,
6.15/6.38	  (![K:int]:
6.15/6.38	     (app_encode_app(int,int,bit0,K) =
6.15/6.38	      app_encode_app(int,int,
6.15/6.38	                     app_encode_app(int,app_encode_fun(int,int),
6.15/6.38	                                    plus_plus(int),K),
6.15/6.38	                     K)))).
6.15/6.38	tff('8', plain,
6.15/6.38	    ![X85 : int]:
6.15/6.38	      app_encode_app(int, int, bit0, X85)
6.15/6.38	       = app_encode_app(int, int, 
6.15/6.38	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X85), 
6.15/6.38	           X85),
6.15/6.38	    inference('cnf', [status(esa)], [zf_stmt_72])).
6.15/6.38	tff(zf_stmt_62, axiom,
6.15/6.38	  (![B2:$tType]:
6.15/6.38	     ((number(B2) & semiring(B2)) =>
6.15/6.38	      (![C:B2,B:B2,V:int]:
6.15/6.38	         (app_encode_app(B2,B2,
6.15/6.38	                         app_encode_app(B2,app_encode_fun(B2,B2),
6.15/6.38	                                        times_times(B2),
6.15/6.38	                                        app_encode_app(int,B2,
6.15/6.38	                                                       number_number_of(B2),V)),
6.15/6.38	                         app_encode_app(B2,B2,
6.15/6.38	                                        app_encode_app(B2,
6.15/6.38	                                                       app_encode_fun(B2,B2),
6.15/6.38	                                                       plus_plus(B2),B),
6.15/6.38	                                        C)) =
6.15/6.38	          app_encode_app(B2,B2,
6.15/6.38	                         app_encode_app(B2,app_encode_fun(B2,B2),
6.15/6.38	                                        plus_plus(B2),
6.15/6.38	                                        app_encode_app(B2,B2,
6.15/6.38	                                                       app_encode_app(
6.15/6.38	                                                       B2,
6.15/6.38	                                                       app_encode_fun(B2,B2),
6.15/6.38	                                                       times_times(B2),
6.15/6.38	                                                       app_encode_app(
6.15/6.38	                                                       int,B2,
6.15/6.38	                                                       number_number_of(B2),V)),
6.15/6.38	                                                       B)),
6.15/6.38	                         app_encode_app(B2,B2,
6.15/6.38	                                        app_encode_app(B2,
6.15/6.38	                                                       app_encode_fun(B2,B2),
6.15/6.38	                                                       times_times(B2),
6.15/6.38	                                                       app_encode_app(
6.15/6.38	                                                       int,B2,
6.15/6.38	                                                       number_number_of(B2),V)),
6.15/6.38	                                        C))))))).
6.15/6.38	tff('9', plain,
6.15/6.38	    ![X62 : $tType, X63 : int, X64 : X62, X65 : X62]:
6.15/6.38	      (app_encode_app(X62, X62, 
6.15/6.38	         app_encode_app(X62, app_encode_fun(X62, X62), times_times(X62), 
6.15/6.38	           app_encode_app(int, X62, number_number_of(X62), X63)), 
6.15/6.38	         app_encode_app(X62, X62, 
6.15/6.38	           app_encode_app(X62, app_encode_fun(X62, X62), plus_plus(X62), X64), 
6.15/6.38	           X65))
6.15/6.38	        = app_encode_app(X62, X62, 
6.15/6.38	            app_encode_app(X62, app_encode_fun(X62, X62), plus_plus(X62), 
6.15/6.38	              app_encode_app(X62, X62, 
6.15/6.38	                app_encode_app(X62, app_encode_fun(X62, X62), 
6.15/6.38	                  times_times(X62), 
6.15/6.38	                  app_encode_app(int, X62, number_number_of(X62), X63)), X64)), 
6.15/6.38	            app_encode_app(X62, X62, 
6.15/6.38	              app_encode_app(X62, app_encode_fun(X62, X62), 
6.15/6.38	                times_times(X62), 
6.15/6.38	                app_encode_app(int, X62, number_number_of(X62), X63)), X65))
6.15/6.38	       | ~ semiring(X62)
6.15/6.38	       | ~ number(X62)),
6.15/6.38	    inference('cnf', [status(esa)], [zf_stmt_62])).
6.15/6.38	tff('10', plain,
6.15/6.38	    ![X0 : int, X1 : int]:
6.15/6.38	      (app_encode_app(int, int, 
6.15/6.38	         app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.15/6.38	           app_encode_app(int, int, number_number_of(int), X1)), 
6.15/6.38	         app_encode_app(int, int, 
6.15/6.38	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X0), 
6.15/6.38	           X0))
6.15/6.38	        = app_encode_app(int, int, bit0, 
6.15/6.38	            app_encode_app(int, int, 
6.15/6.38	              app_encode_app(int, app_encode_fun(int, int), 
6.15/6.38	                times_times(int), 
6.15/6.38	                app_encode_app(int, int, number_number_of(int), X1)), X0))
6.15/6.38	       | ~ number(int)
6.15/6.38	       | ~ semiring(int)),
6.15/6.38	    inference('sup+', [status(thm)], ['8', '9'])).
6.15/6.38	tff(zf_stmt_147, axiom, (semiring(int))).
6.15/6.38	tff('11', plain, semiring(int),
6.15/6.38	    inference('cnf', [status(esa)], [zf_stmt_147])).
6.15/6.38	tff('12', plain,
6.15/6.38	    ![X0 : int, X1 : int]:
6.15/6.38	      (app_encode_app(int, int, 
6.15/6.38	         app_encode_app(int, app_encode_fun(int, int), times_times(int), X1), 
6.15/6.38	         app_encode_app(int, int, bit0, X0))
6.15/6.38	        = app_encode_app(int, int, bit0, 
6.15/6.38	            app_encode_app(int, int, 
6.15/6.38	              app_encode_app(int, app_encode_fun(int, int), 
6.15/6.38	                times_times(int), X1), X0))
6.15/6.38	       | ~ $true
6.15/6.38	       | ~ $true),
6.15/6.38	    inference('demod', [status(thm)], ['10', '1', '8', '1', '5', '11'])).
6.15/6.38	tff('13', plain,
6.15/6.38	    ![X0 : int, X1 : int]:
6.15/6.38	      app_encode_app(int, int, 
6.15/6.38	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X1), 
6.15/6.38	        app_encode_app(int, int, bit0, X0))
6.15/6.38	       = app_encode_app(int, int, bit0, 
6.15/6.38	           app_encode_app(int, int, 
6.15/6.38	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.15/6.38	               X1), X0)),
6.15/6.38	    inference('simplify', [status(thm)], ['12'])).
6.15/6.38	tff(zf_stmt_105, axiom,
6.15/6.38	  (![A:$tType]:
6.15/6.38	     (comm_semiring_1(A) =>
6.15/6.38	      (![B:A,A1:A]:
6.15/6.38	         (app_encode_app(A,A,
6.15/6.38	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
6.15/6.38	                                        A1),
6.15/6.38	                         B) =
6.15/6.38	          app_encode_app(A,A,
6.15/6.38	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
6.15/6.38	                                        B),
6.15/6.38	                         A1)))))).
6.15/6.38	tff('14', plain,
6.15/6.38	    ![X159 : $tType, X160 : X159, X161 : X159]:
6.15/6.38	      (app_encode_app(X159, X159, 
6.15/6.38	         app_encode_app(X159, app_encode_fun(X159, X159), times_times(X159), 
6.15/6.38	           X161), X160)
6.15/6.38	        = app_encode_app(X159, X159, 
6.15/6.38	            app_encode_app(X159, app_encode_fun(X159, X159), 
6.15/6.38	              times_times(X159), X160), X161)
6.15/6.38	       | ~ comm_semiring_1(X159)),
6.15/6.38	    inference('cnf', [status(esa)], [zf_stmt_105])).
6.15/6.38	tff('15', plain,
6.15/6.38	    ![X0 : int, X1 : int]:
6.15/6.38	      (app_encode_app(int, int, bit0, 
6.15/6.38	         app_encode_app(int, int, 
6.15/6.38	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.15/6.38	             X1), X0))
6.15/6.38	        = app_encode_app(int, int, 
6.15/6.38	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.15/6.38	              app_encode_app(int, int, bit0, X0)), X1)
6.15/6.38	       | ~ comm_semiring_1(int)),
6.15/6.38	    inference('sup+', [status(thm)], ['13', '14'])).
6.15/6.38	tff(zf_stmt_141, axiom, (comm_semiring_1(int))).
6.15/6.38	tff('16', plain, comm_semiring_1(int),
6.15/6.38	    inference('cnf', [status(esa)], [zf_stmt_141])).
6.15/6.38	tff('17', plain,
6.15/6.38	    ![X0 : int, X1 : int]:
6.15/6.38	      (app_encode_app(int, int, bit0, 
6.15/6.38	         app_encode_app(int, int, 
6.15/6.38	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.15/6.38	             X1), X0))
6.15/6.38	        = app_encode_app(int, int, 
6.15/6.38	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.15/6.38	              app_encode_app(int, int, bit0, X0)), X1)
6.15/6.38	       | ~ $true),
6.15/6.38	    inference('demod', [status(thm)], ['15', '16'])).
6.15/6.38	tff('18', plain,
6.15/6.38	    ![X0 : int, X1 : int]:
6.15/6.38	      app_encode_app(int, int, bit0, 
6.15/6.38	        app_encode_app(int, int, 
6.15/6.38	          app_encode_app(int, app_encode_fun(int, int), times_times(int), X1), 
6.15/6.38	          X0))
6.15/6.38	       = app_encode_app(int, int, 
6.15/6.38	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.15/6.38	             app_encode_app(int, int, bit0, X0)), X1),
6.15/6.38	    inference('simplify', [status(thm)], ['17'])).
6.15/6.38	tff(zf_stmt_63, axiom,
6.15/6.38	  (![A:$tType]:
6.15/6.38	     (number_ring(A) =>
6.15/6.38	      (![Z1:A,W:int,V:int]:
6.15/6.38	         (app_encode_app(A,A,
6.15/6.38	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
6.15/6.38	                                        app_encode_app(int,A,
6.15/6.38	                                                       number_number_of(A),V)),
6.15/6.38	                         app_encode_app(A,A,
6.15/6.38	                                        app_encode_app(A,app_encode_fun(A,A),
6.15/6.38	                                                       times_times(A),
6.15/6.38	                                                       app_encode_app(
6.15/6.38	                                                       int,A,
6.15/6.38	                                                       number_number_of(A),W)),
6.15/6.38	                                        Z1)) =
6.15/6.38	          app_encode_app(A,A,
6.15/6.38	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
6.15/6.38	                                        app_encode_app(int,A,
6.15/6.38	                                                       number_number_of(A),
6.15/6.38	                                                       app_encode_app(
6.15/6.38	                                                       int,int,
6.15/6.38	                                                       app_encode_app(
6.15/6.38	                                                       int,
6.15/6.38	                                                       app_encode_fun(
6.15/6.38	                                                       int,int),
6.15/6.38	                                                       times_times(int),V),W))),
6.15/6.38	                         Z1)))))).
6.15/6.38	tff('19', plain,
6.15/6.38	    ![X66 : $tType, X67 : int, X68 : int, X69 : X66]:
6.15/6.38	      (app_encode_app(X66, X66, 
6.15/6.38	         app_encode_app(X66, app_encode_fun(X66, X66), times_times(X66), 
6.15/6.38	           app_encode_app(int, X66, number_number_of(X66), X67)), 
6.15/6.38	         app_encode_app(X66, X66, 
6.15/6.38	           app_encode_app(X66, app_encode_fun(X66, X66), times_times(X66), 
6.15/6.38	             app_encode_app(int, X66, number_number_of(X66), X68)), X69))
6.15/6.38	        = app_encode_app(X66, X66, 
6.15/6.38	            app_encode_app(X66, app_encode_fun(X66, X66), times_times(X66), 
6.15/6.38	              app_encode_app(int, X66, number_number_of(X66), 
6.15/6.38	                app_encode_app(int, int, 
6.15/6.38	                  app_encode_app(int, app_encode_fun(int, int), 
6.15/6.38	                    times_times(int), X67), X68))), X69)
6.15/6.38	       | ~ number_ring(X66)),
6.15/6.38	    inference('cnf', [status(esa)], [zf_stmt_63])).
6.15/6.38	tff('20', plain,
6.15/6.38	    ![X0 : int, X1 : int, X2 : int]:
6.15/6.38	      (app_encode_app(int, int, 
6.15/6.38	         app_encode_app(int, app_encode_fun(int, int), times_times(int), X0), 
6.15/6.38	         app_encode_app(int, int, 
6.15/6.38	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.15/6.38	             app_encode_app(int, int, number_number_of(int), X2)), X1))
6.15/6.38	        = app_encode_app(int, int, 
6.15/6.38	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.15/6.38	              app_encode_app(int, int, number_number_of(int), 
6.15/6.38	                app_encode_app(int, int, 
6.15/6.38	                  app_encode_app(int, app_encode_fun(int, int), 
6.15/6.38	                    times_times(int), X0), X2))), X1)
6.15/6.38	       | ~ number_ring(int)),
6.15/6.38	    inference('sup+', [status(thm)], ['1', '19'])).
6.15/6.38	tff(zf_stmt_146, axiom, (number_ring(int))).
6.15/6.38	tff('21', plain, number_ring(int),
6.15/6.38	    inference('cnf', [status(esa)], [zf_stmt_146])).
6.15/6.38	tff('22', plain,
6.15/6.38	    ![X0 : int, X1 : int, X2 : int]:
6.15/6.38	      (app_encode_app(int, int, 
6.15/6.38	         app_encode_app(int, app_encode_fun(int, int), times_times(int), X0), 
6.15/6.38	         app_encode_app(int, int, 
6.15/6.38	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.15/6.38	             X2), X1))
6.15/6.38	        = app_encode_app(int, int, 
6.15/6.38	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.15/6.38	              app_encode_app(int, int, 
6.15/6.38	                app_encode_app(int, app_encode_fun(int, int), 
6.15/6.38	                  times_times(int), X0), X2)), X1)
6.15/6.38	       | ~ $true),
6.15/6.38	    inference('demod', [status(thm)], ['20', '1', '1', '21'])).
6.15/6.38	tff('23', plain,
6.15/6.38	    ![X0 : int, X1 : int, X2 : int]:
6.15/6.38	      app_encode_app(int, int, 
6.15/6.38	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X0), 
6.15/6.38	        app_encode_app(int, int, 
6.15/6.38	          app_encode_app(int, app_encode_fun(int, int), times_times(int), X2), 
6.15/6.38	          X1))
6.15/6.38	       = app_encode_app(int, int, 
6.15/6.38	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.15/6.38	             app_encode_app(int, int, 
6.15/6.38	               app_encode_app(int, app_encode_fun(int, int), 
6.15/6.38	                 times_times(int), X0), X2)), X1),
6.15/6.38	    inference('simplify', [status(thm)], ['22'])).
6.15/6.38	tff(zf_stmt_59, axiom,
6.15/6.38	  (![L:int,K:int]:
6.15/6.38	     (app_encode_app(int,int,
6.15/6.38	                     app_encode_app(int,app_encode_fun(int,int),
6.15/6.38	                                    times_times(int),
6.15/6.38	                                    app_encode_app(int,int,bit0,K)),
6.15/6.38	                     L) =
6.15/6.38	      app_encode_app(int,int,bit0,
6.15/6.38	                     app_encode_app(int,int,
6.15/6.38	                                    app_encode_app(int,
6.15/6.38	                                                   app_encode_fun(int,int),
6.15/6.38	                                                   times_times(int),K),
6.15/6.38	                                    L))))).
6.15/6.38	tff('24', plain,
6.15/6.38	    ![X54 : int, X55 : int]:
6.15/6.38	      app_encode_app(int, int, 
6.15/6.38	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.15/6.38	          app_encode_app(int, int, bit0, X54)), X55)
6.15/6.38	       = app_encode_app(int, int, bit0, 
6.15/6.38	           app_encode_app(int, int, 
6.15/6.38	             app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.15/6.38	               X54), X55)),
6.15/6.38	    inference('cnf', [status(esa)], [zf_stmt_59])).
6.15/6.38	tff('25', plain,
6.15/6.38	    ![X0 : int, X1 : int]:
6.15/6.38	      (app_encode_app(int, int, bit0, 
6.15/6.38	         app_encode_app(int, int, 
6.15/6.38	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.15/6.38	             X1), X0))
6.15/6.38	        = app_encode_app(int, int, 
6.15/6.38	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.15/6.38	              X0), app_encode_app(int, int, bit0, X1))
6.15/6.38	       | ~ comm_semiring_1(int)),
6.15/6.38	    inference('sup+', [status(thm)], ['24', '14'])).
6.15/6.38	tff('26', plain,
6.15/6.38	    ![X0 : int, X1 : int]:
6.15/6.38	      (app_encode_app(int, int, bit0, 
6.15/6.38	         app_encode_app(int, int, 
6.15/6.38	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.15/6.38	             X1), X0))
6.15/6.38	        = app_encode_app(int, int, 
6.15/6.38	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.15/6.38	              X0), app_encode_app(int, int, bit0, X1))
6.15/6.38	       | ~ $true),
6.15/6.38	    inference('demod', [status(thm)], ['25', '16'])).
6.15/6.38	tff('27', plain,
6.15/6.38	    ![X0 : int, X1 : int]:
6.15/6.38	      app_encode_app(int, int, bit0, 
6.15/6.38	        app_encode_app(int, int, 
6.15/6.38	          app_encode_app(int, app_encode_fun(int, int), times_times(int), X1), 
6.15/6.38	          X0))
6.15/6.38	       = app_encode_app(int, int, 
6.15/6.38	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.15/6.38	             X0), app_encode_app(int, int, bit0, X1)),
6.15/6.39	    inference('simplify', [status(thm)], ['26'])).
6.15/6.39	tff(zf_stmt_58, axiom,
6.15/6.39	  (![W:int]:
6.15/6.39	     (app_encode_app(int,int,
6.15/6.39	                     app_encode_app(int,app_encode_fun(int,int),
6.15/6.39	                                    times_times(int),pls),
6.15/6.39	                     W) =
6.15/6.39	      pls))).
6.15/6.39	tff('28', plain,
6.15/6.39	    ![X53 : int]:
6.15/6.39	      app_encode_app(int, int, 
6.15/6.39	        app_encode_app(int, app_encode_fun(int, int), times_times(int), pls), 
6.15/6.39	        X53)
6.15/6.39	       = pls,
6.15/6.39	    inference('cnf', [status(esa)], [zf_stmt_58])).
6.15/6.39	tff(zf_stmt_39, axiom,
6.15/6.39	  (![L:int,K:int]:
6.15/6.39	     (app_encode_app(int,int,
6.15/6.39	                     app_encode_app(int,app_encode_fun(int,int),
6.15/6.39	                                    times_times(int),
6.15/6.39	                                    app_encode_app(int,int,bit1,K)),
6.15/6.39	                     L) =
6.15/6.39	      app_encode_app(int,int,
6.15/6.39	                     app_encode_app(int,app_encode_fun(int,int),
6.15/6.39	                                    plus_plus(int),
6.15/6.39	                                    app_encode_app(int,int,bit0,
6.15/6.39	                                                   app_encode_app(int,int,
6.15/6.39	                                                                  app_encode_app(
6.15/6.39	                                                                  int,
6.15/6.39	                                                                  app_encode_fun(
6.15/6.39	                                                                  int,int),
6.15/6.39	                                                                  times_times(
6.15/6.39	                                                                  int),K),L))),
6.15/6.39	                     L)))).
6.15/6.39	tff('29', plain,
6.15/6.39	    ![X10 : int, X11 : int]:
6.15/6.39	      app_encode_app(int, int, 
6.15/6.39	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.15/6.39	          app_encode_app(int, int, bit1, X10)), X11)
6.15/6.39	       = app_encode_app(int, int, 
6.15/6.39	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
6.15/6.39	             app_encode_app(int, int, bit0, 
6.15/6.39	               app_encode_app(int, int, 
6.15/6.39	                 app_encode_app(int, app_encode_fun(int, int), 
6.15/6.39	                   times_times(int), X10), X11))), X11),
6.15/6.39	    inference('cnf', [status(esa)], [zf_stmt_39])).
6.15/6.39	tff('30', plain,
6.15/6.39	    ![X0 : int]:
6.15/6.39	      app_encode_app(int, int, 
6.15/6.39	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.15/6.39	          app_encode_app(int, int, bit1, pls)), X0)
6.15/6.39	       = app_encode_app(int, int, 
6.15/6.39	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
6.15/6.39	             app_encode_app(int, int, bit0, pls)), X0),
6.15/6.39	    inference('sup+', [status(thm)], ['28', '29'])).
6.15/6.39	tff(zf_stmt_57, axiom, (app_encode_app(int,int,bit0,pls) = pls)).
6.15/6.39	tff('31', plain, app_encode_app(int, int, bit0, pls) = pls,
6.15/6.39	    inference('cnf', [status(esa)], [zf_stmt_57])).
6.15/6.39	tff('32', plain,
6.15/6.39	    ![X0 : int]:
6.15/6.39	      app_encode_app(int, int, 
6.15/6.39	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.15/6.39	          app_encode_app(int, int, bit1, pls)), X0)
6.15/6.39	       = app_encode_app(int, int, 
6.15/6.39	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
6.15/6.39	           X0),
6.15/6.39	    inference('demod', [status(thm)], ['30', '31'])).
6.15/6.39	tff(zf_stmt_71, axiom,
6.15/6.39	  (![K:int]:
6.15/6.39	     (app_encode_app(int,int,
6.15/6.39	                     app_encode_app(int,app_encode_fun(int,int),
6.15/6.39	                                    plus_plus(int),pls),
6.15/6.39	                     K) =
6.15/6.39	      K))).
6.15/6.39	tff('33', plain,
6.15/6.39	    ![X84 : int]:
6.15/6.39	      app_encode_app(int, int, 
6.15/6.39	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
6.15/6.39	        X84)
6.15/6.39	       = X84,
6.15/6.39	    inference('cnf', [status(esa)], [zf_stmt_71])).
6.15/6.39	tff('34', plain,
6.15/6.39	    ![X0 : int]:
6.15/6.39	      app_encode_app(int, int, 
6.15/6.39	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.15/6.39	          app_encode_app(int, int, bit1, pls)), X0)
6.15/6.39	       = X0,
6.15/6.39	    inference('demod', [status(thm)], ['32', '33'])).
6.15/6.39	tff(zf_stmt_2, axiom,
6.15/6.39	  (![X:app_encode_fun(Alpha,Beta),Y:app_encode_fun(Alpha,Beta)]:
6.15/6.39	     ((![Z:Alpha]:
6.15/6.39	         (app_encode_app(Alpha,Beta,X,Z) = app_encode_app(Alpha,Beta,Y,Z))) =>
6.15/6.39	      (X = Y)))).
6.15/6.39	tff('35', plain,
6.15/6.39	    ![X0 : $tType, X1 : $tType, X2 : app_encode_fun(X0, X1), 
6.15/6.39	      X3 : app_encode_fun(X0, X1)]:
6.15/6.39	      (X3 = X2
6.15/6.39	       | app_encode_app(X0, X1, X3, sk_Z(X1, X0, X2, X3))
6.15/6.39	          != app_encode_app(X0, X1, X2, sk_Z(X1, X0, X2, X3))),
6.15/6.39	    inference('cnf', [status(esa)], [zf_stmt_2])).
6.15/6.39	tff('36', plain,
6.15/6.39	    ![X0 : app_encode_fun(int, int)]:
6.15/6.39	      (app_encode_app(int, int, X0, 
6.15/6.39	         sk_Z(int, int, number_number_of(int), X0))
6.15/6.39	        != sk_Z(int, int, number_number_of(int), X0)
6.15/6.39	       | X0 = number_number_of(int)),
6.15/6.39	    inference('sup-', [status(thm)], ['1', '35'])).
6.15/6.39	tff('37', plain,
6.15/6.39	    (sk_Z(int, int, number_number_of(int), 
6.15/6.39	       app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.15/6.39	         app_encode_app(int, int, bit1, pls)))
6.15/6.39	      != sk_Z(int, int, number_number_of(int), 
6.15/6.39	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.15/6.39	             app_encode_app(int, int, bit1, pls)))
6.15/6.39	     | app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.15/6.39	         app_encode_app(int, int, bit1, pls))
6.15/6.39	        = number_number_of(int)),
6.15/6.39	    inference('sup-', [status(thm)], ['34', '36'])).
6.15/6.39	tff('38', plain,
6.15/6.39	    app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.15/6.39	      app_encode_app(int, int, bit1, pls))
6.15/6.39	     = number_number_of(int),
6.15/6.39	    inference('simplify', [status(thm)], ['37'])).
6.15/6.39	tff(zf_stmt_60, axiom,
6.15/6.39	  (![L:int,K:int]:
6.15/6.39	     (app_encode_app(int,int,
6.15/6.39	                     app_encode_app(int,app_encode_fun(int,int),
6.15/6.39	                                    plus_plus(int),
6.15/6.39	                                    app_encode_app(int,int,bit0,K)),
6.15/6.39	                     app_encode_app(int,int,bit0,L)) =
6.15/6.39	      app_encode_app(int,int,bit0,
6.15/6.39	                     app_encode_app(int,int,
6.15/6.39	                                    app_encode_app(int,
6.15/6.39	                                                   app_encode_fun(int,int),
6.15/6.39	                                                   plus_plus(int),K),
6.15/6.39	                                    L))))).
6.15/6.39	tff('39', plain,
6.15/6.39	    ![X56 : int, X57 : int]:
6.15/6.39	      app_encode_app(int, int, 
6.15/6.39	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
6.15/6.39	          app_encode_app(int, int, bit0, X56)), 
6.15/6.39	        app_encode_app(int, int, bit0, X57))
6.15/6.39	       = app_encode_app(int, int, bit0, 
6.15/6.39	           app_encode_app(int, int, 
6.15/6.39	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
6.15/6.39	               X56), X57)),
6.15/6.39	    inference('cnf', [status(esa)], [zf_stmt_60])).
6.15/6.39	tff(zf_stmt_114, axiom,
6.15/6.39	  (![A:$tType]:
6.15/6.39	     (comm_semiring_1(A) =>
6.15/6.39	      (![C:A,A1:A]:
6.15/6.39	         (app_encode_app(A,A,
6.15/6.39	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),A1),
6.15/6.39	                         C) =
6.15/6.39	          app_encode_app(A,A,
6.15/6.39	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),C),
6.15/6.39	                         A1)))))).
6.15/6.39	tff('40', plain,
6.15/6.39	    ![X197 : $tType, X198 : X197, X199 : X197]:
6.15/6.39	      (app_encode_app(X197, X197, 
6.15/6.39	         app_encode_app(X197, app_encode_fun(X197, X197), plus_plus(X197), 
6.15/6.39	           X199), X198)
6.15/6.39	        = app_encode_app(X197, X197, 
6.15/6.39	            app_encode_app(X197, app_encode_fun(X197, X197), 
6.15/6.39	              plus_plus(X197), X198), X199)
6.15/6.39	       | ~ comm_semiring_1(X197)),
6.15/6.39	    inference('cnf', [status(esa)], [zf_stmt_114])).
6.15/6.39	tff('41', plain,
6.15/6.39	    ![X0 : int, X1 : int]:
6.15/6.39	      (app_encode_app(int, int, bit0, 
6.15/6.39	         app_encode_app(int, int, 
6.15/6.39	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X1), 
6.15/6.39	           X0))
6.15/6.39	        = app_encode_app(int, int, 
6.15/6.39	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
6.15/6.39	              app_encode_app(int, int, bit0, X0)), 
6.15/6.39	            app_encode_app(int, int, bit0, X1))
6.15/6.39	       | ~ comm_semiring_1(int)),
6.15/6.39	    inference('sup+', [status(thm)], ['39', '40'])).
6.15/6.39	tff('42', plain,
6.15/6.39	    ![X0 : int, X1 : int]:
6.15/6.39	      (app_encode_app(int, int, bit0, 
6.15/6.39	         app_encode_app(int, int, 
6.15/6.39	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X1), 
6.15/6.39	           X0))
6.15/6.39	        = app_encode_app(int, int, 
6.15/6.39	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
6.15/6.39	              app_encode_app(int, int, bit0, X0)), 
6.15/6.39	            app_encode_app(int, int, bit0, X1))
6.15/6.39	       | ~ $true),
6.15/6.39	    inference('demod', [status(thm)], ['41', '16'])).
6.15/6.39	tff('43', plain,
6.15/6.39	    ![X0 : int, X1 : int]:
6.15/6.39	      app_encode_app(int, int, bit0, 
6.15/6.39	        app_encode_app(int, int, 
6.15/6.39	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X1), 
6.15/6.39	          X0))
6.15/6.39	       = app_encode_app(int, int, 
6.15/6.39	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
6.15/6.39	             app_encode_app(int, int, bit0, X0)), 
6.15/6.39	           app_encode_app(int, int, bit0, X1)),
6.15/6.39	    inference('simplify', [status(thm)], ['42'])).
6.15/6.39	tff(zf_stmt_82, axiom,
6.15/6.39	  (![A:$tType]:
6.15/6.39	     (number_ring(A) =>
6.15/6.39	      (![A1:A]:
6.15/6.39	         (app_encode_app(A,A,
6.15/6.39	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
6.15/6.39	                                        A1),
6.15/6.39	                         app_encode_app(int,A,number_number_of(A),
6.15/6.39	                                        app_encode_app(int,int,bit1,pls))) =
6.15/6.39	          A1))))).
6.15/6.39	tff('44', plain,
6.15/6.39	    ![X108 : $tType, X109 : X108]:
6.15/6.39	      (app_encode_app(X108, X108, 
6.15/6.39	         app_encode_app(X108, app_encode_fun(X108, X108), times_times(X108), 
6.15/6.39	           X109), 
6.15/6.39	         app_encode_app(int, X108, number_number_of(X108), 
6.15/6.39	           app_encode_app(int, int, bit1, pls)))
6.15/6.39	        = X109
6.15/6.39	       | ~ number_ring(X108)),
6.15/6.39	    inference('cnf', [status(esa)], [zf_stmt_82])).
6.15/6.39	tff('45', plain,
6.15/6.39	    ![X0 : int]:
6.15/6.39	      (app_encode_app(int, int, 
6.15/6.39	         app_encode_app(int, app_encode_fun(int, int), times_times(int), X0), 
6.15/6.39	         app_encode_app(int, int, bit1, pls))
6.15/6.39	        = X0
6.15/6.39	       | ~ number_ring(int)),
6.15/6.39	    inference('sup+', [status(thm)], ['1', '44'])).
6.15/6.39	tff('46', plain,
6.15/6.39	    ![X0 : int]:
6.15/6.39	      (app_encode_app(int, int, 
6.15/6.39	         app_encode_app(int, app_encode_fun(int, int), times_times(int), X0), 
6.15/6.39	         app_encode_app(int, int, bit1, pls))
6.15/6.39	        = X0
6.15/6.39	       | ~ $true),
6.15/6.39	    inference('demod', [status(thm)], ['45', '21'])).
6.15/6.39	tff('47', plain,
6.15/6.39	    ![X0 : int]:
6.15/6.39	      app_encode_app(int, int, 
6.15/6.39	        app_encode_app(int, app_encode_fun(int, int), times_times(int), X0), 
6.15/6.39	        app_encode_app(int, int, bit1, pls))
6.15/6.39	       = X0,
6.15/6.39	    inference('simplify', [status(thm)], ['46'])).
6.15/6.39	tff(zf_stmt_38, axiom,
6.15/6.39	  (![A:$tType]:
6.15/6.39	     (linordered_idom(A) =>
6.15/6.39	      (![A1:A]:
6.15/6.39	         (app_encode_app(nat,A,
6.15/6.39	                         app_encode_app(A,app_encode_fun(nat,A),
6.15/6.39	                                        power_power(A),
6.15/6.39	                                        app_encode_app(A,A,abs_abs(A),A1)),
6.15/6.39	                         app_encode_app(int,nat,number_number_of(nat),
6.15/6.39	                                        app_encode_app(int,int,bit0,
6.15/6.39	                                                       app_encode_app(
6.15/6.39	                                                       int,int,bit1,pls)))) =
6.15/6.39	          app_encode_app(nat,A,
6.15/6.39	                         app_encode_app(A,app_encode_fun(nat,A),
6.15/6.39	                                        power_power(A),A1),
6.15/6.39	                         app_encode_app(int,nat,number_number_of(nat),
6.15/6.39	                                        app_encode_app(int,int,bit0,
6.15/6.39	                                                       app_encode_app(
6.15/6.39	                                                       int,int,bit1,pls))))))))).
6.15/6.39	tff('48', plain,
6.15/6.39	    ![X8 : $tType, X9 : X8]:
6.15/6.39	      (app_encode_app(nat, X8, 
6.15/6.39	         app_encode_app(X8, app_encode_fun(nat, X8), power_power(X8), 
6.15/6.39	           app_encode_app(X8, X8, abs_abs(X8), X9)), 
6.15/6.39	         app_encode_app(int, nat, number_number_of(nat), 
6.15/6.39	           app_encode_app(int, int, bit0, 
6.15/6.39	             app_encode_app(int, int, bit1, pls))))
6.15/6.39	        = app_encode_app(nat, X8, 
6.15/6.39	            app_encode_app(X8, app_encode_fun(nat, X8), power_power(X8), X9), 
6.15/6.39	            app_encode_app(int, nat, number_number_of(nat), 
6.15/6.39	              app_encode_app(int, int, bit0, 
6.15/6.39	                app_encode_app(int, int, bit1, pls))))
6.15/6.39	       | ~ linordered_idom(X8)),
6.15/6.39	    inference('cnf', [status(esa)], [zf_stmt_38])).
6.15/6.39	tff('49', plain,
6.15/6.39	    ![X0 : int]:
6.15/6.39	      (app_encode_app(nat, int, 
6.15/6.39	         app_encode_app(int, app_encode_fun(nat, int), power_power(int), X0), 
6.15/6.39	         app_encode_app(int, nat, number_number_of(nat), 
6.15/6.39	           app_encode_app(int, int, bit0, 
6.15/6.39	             app_encode_app(int, int, bit1, pls))))
6.15/6.39	        = app_encode_app(int, int, 
6.15/6.39	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.15/6.39	              app_encode_app(int, int, abs_abs(int), X0)), 
6.15/6.39	            app_encode_app(int, int, abs_abs(int), X0))
6.15/6.39	       | ~ linordered_idom(int)),
6.15/6.39	    inference('sup+', [status(thm)], ['48', '7'])).
6.15/6.39	tff(zf_stmt_140, axiom, (linordered_idom(int))).
6.15/6.39	tff('50', plain, linordered_idom(int),
6.15/6.39	    inference('cnf', [status(esa)], [zf_stmt_140])).
6.15/6.39	tff('51', plain,
6.15/6.39	    ![X0 : int]:
6.15/6.39	      (app_encode_app(nat, int, 
6.15/6.39	         app_encode_app(int, app_encode_fun(nat, int), power_power(int), X0), 
6.15/6.39	         app_encode_app(int, nat, number_number_of(nat), 
6.15/6.39	           app_encode_app(int, int, bit0, 
6.15/6.39	             app_encode_app(int, int, bit1, pls))))
6.15/6.39	        = app_encode_app(int, int, 
6.15/6.39	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.15/6.39	              app_encode_app(int, int, abs_abs(int), X0)), 
6.15/6.39	            app_encode_app(int, int, abs_abs(int), X0))
6.15/6.39	       | ~ $true),
6.15/6.39	    inference('demod', [status(thm)], ['49', '50'])).
6.15/6.39	tff('52', plain,
6.15/6.39	    ![X0 : int]:
6.15/6.39	      app_encode_app(nat, int, 
6.15/6.39	        app_encode_app(int, app_encode_fun(nat, int), power_power(int), X0), 
6.15/6.39	        app_encode_app(int, nat, number_number_of(nat), 
6.15/6.39	          app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls))))
6.15/6.39	       = app_encode_app(int, int, 
6.15/6.39	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.15/6.39	             app_encode_app(int, int, abs_abs(int), X0)), 
6.15/6.39	           app_encode_app(int, int, abs_abs(int), X0)),
6.15/6.39	    inference('simplify', [status(thm)], ['51'])).
6.15/6.39	tff('53', plain,
6.15/6.39	    ![X0 : int]:
6.15/6.39	      app_encode_app(int, int, 
6.15/6.39	        app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.15/6.39	          app_encode_app(int, int, abs_abs(int), X0)), 
6.15/6.39	        app_encode_app(int, int, abs_abs(int), X0))
6.15/6.39	       = app_encode_app(int, int, 
6.15/6.39	           app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.15/6.39	             X0), X0),
6.15/6.39	    inference('sup+', [status(thm)], ['52', '7'])).
6.15/6.39	tff('54', plain,
6.15/6.39	    app_encode_app(int, int, bit0, 
6.15/6.39	      app_encode_app(int, int, bit0, 
6.15/6.39	        app_encode_app(int, int, 
6.15/6.39	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
6.15/6.39	            app_encode_app(int, int, 
6.15/6.39	              app_encode_app(int, app_encode_fun(int, int), 
6.15/6.39	                times_times(int), v), v)), 
6.15/6.39	          app_encode_app(int, int, 
6.15/6.39	            app_encode_app(int, app_encode_fun(int, int), times_times(int), 
6.15/6.39	              w), w))))
6.15/6.39	     != app_encode_app(int, int, bit0, 
6.15/6.39	          app_encode_app(int, int, bit0, 
6.15/6.39	            app_encode_app(int, int, 
6.15/6.39	              app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
6.15/6.39	                app_encode_app(int, int, 
6.15/6.39	                  app_encode_app(int, app_encode_fun(int, int), 
6.15/6.39	                    times_times(int), v), v)), 
6.15/6.39	              app_encode_app(int, int, 
6.15/6.39	                app_encode_app(int, app_encode_fun(int, int), 
6.15/6.39	                  times_times(int), w), w)))),
6.15/6.39	    inference('demod', [status(thm)],
6.15/6.39	              ['0', '1', '7', '18', '23', '27', '38', '1', '27', '1', '7', 
6.15/6.39	               '18', '23', '27', '38', '1', '27', '43', '43', '1', '18', 
6.15/6.39	               '47', '7', '18', '18', '53', '1', '18', '47', '7', '18', 
6.15/6.39	               '18', '53', '43', '43'])).
6.15/6.39	tff('55', plain, $false, inference('simplify', [status(thm)], ['54'])).
6.15/6.39	
6.15/6.39	% SZS output end Refutation
6.15/6.39	EOF
