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    : rpo6
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n146.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 09:45:54 CST 2018
170.23/170.47	% done 29136 iterations in 170.279s
170.23/170.47	% SZS status Theorem for 'stdin'
170.23/170.47	% SZS output start Refutation
170.23/170.48	tff(zf_stmt_189, axiom, (linorder(real))).
170.23/170.48	tff('0', plain, linorder(real),
170.23/170.48	    inference('cnf', [status(esa)], [zf_stmt_189])).
170.23/170.48	tff(zf_stmt_144, axiom,
170.23/170.48	  (![A:$tType]:
170.23/170.48	     (linorder(A) =>
170.23/170.48	      (![X1:A,Y1:A]:
170.23/170.48	         ((~
170.23/170.48	            app_encode_app(A,$o,
170.23/170.48	                           app_encode_app(A,app_encode_fun(A,$o),
170.23/170.48	                                          ord_less_eq(A),Y1),
170.23/170.48	                           X1)) =>
170.23/170.48	          app_encode_app(A,$o,
170.23/170.48	                         app_encode_app(A,app_encode_fun(A,$o),ord_less(A),X1),
170.23/170.48	                         Y1)))))).
170.23/170.48	tff('1', plain,
170.23/170.48	    ![X289 : $tType, X290 : X289, X291 : X289]:
170.23/170.48	      (app_encode_app(X289, $o, 
170.23/170.48	         app_encode_app(X289, app_encode_fun(X289, $o), ord_less_eq(X289), 
170.23/170.48	           X290), X291)
170.23/170.48	       | app_encode_app(X289, $o, 
170.23/170.48	           app_encode_app(X289, app_encode_fun(X289, $o), ord_less(X289), 
170.23/170.48	             X291), X290)
170.23/170.48	       | ~ linorder(X289)),
170.23/170.48	    inference('cnf', [status(esa)], [zf_stmt_144])).
170.23/170.48	tff('2', plain,
170.23/170.48	    ![X0 : real, X1 : real]:
170.23/170.48	      (~ $true
170.23/170.48	       | app_encode_app(real, $o, 
170.23/170.48	           app_encode_app(real, app_encode_fun(real, $o), ord_less(real), X1), 
170.23/170.48	           X0)
170.23/170.48	       | app_encode_app(real, $o, 
170.23/170.48	           app_encode_app(real, app_encode_fun(real, $o), ord_less_eq(real), 
170.23/170.48	             X0), X1)),
170.23/170.48	    inference('sup-', [status(thm)], ['0', '1'])).
170.23/170.48	tff('3', plain,
170.23/170.48	    ![X0 : real, X1 : real]:
170.23/170.48	      (app_encode_app(real, $o, 
170.23/170.48	         app_encode_app(real, app_encode_fun(real, $o), ord_less_eq(real), 
170.23/170.48	           X0), X1)
170.23/170.48	       | app_encode_app(real, $o, 
170.23/170.48	           app_encode_app(real, app_encode_fun(real, $o), ord_less(real), X1), 
170.23/170.48	           X0)),
170.23/170.48	    inference('simplify', [status(thm)], ['2'])).
170.23/170.48	tff(zf_stmt_243, conjecture,
170.23/170.48	  (app_encode_app(real,$o,
170.23/170.48	                  app_encode_app(real,app_encode_fun(real,$o),
170.23/170.48	                                 ord_less_eq(real),
170.23/170.48	                                 app_encode_app(complex,real,
170.23/170.48	                                                norm_norm(complex),
170.23/170.48	                                                app_encode_app(complex,
170.23/170.48	                                                               complex,
170.23/170.48	                                                               app_encode_app(
170.23/170.48	                                                               fun(complex,
170.23/170.48	                                                                   complex),
170.23/170.48	                                                               app_encode_fun(
170.23/170.48	                                                               complex,
170.23/170.48	                                                               complex),
170.23/170.48	                                                               aa(complex,
170.23/170.48	                                                                  complex),
170.23/170.48	                                                               app_encode_app(
170.23/170.48	                                                               poly1(complex),
170.23/170.48	                                                               fun(complex,
170.23/170.48	                                                                   complex),
170.23/170.48	                                                               poly(complex),
170.23/170.48	                                                               app_encode_app(
170.23/170.48	                                                               poly1(complex),
170.23/170.48	                                                               poly1(complex),
170.23/170.48	                                                               app_encode_app(
170.23/170.48	                                                               complex,
170.23/170.48	                                                               app_encode_fun(
170.23/170.48	                                                               poly1(complex),
170.23/170.48	                                                               poly1(complex)),
170.23/170.48	                                                               pCons(complex),
170.23/170.48	                                                               c),cs))),z))),
170.23/170.48	                  app_encode_app(real,real,
170.23/170.48	                                 app_encode_app(real,
170.23/170.48	                                                app_encode_fun(real,real),
170.23/170.48	                                                plus_plus(real),
170.23/170.48	                                                app_encode_app(complex,real,
170.23/170.48	                                                               norm_norm(
170.23/170.48	                                                               complex),c)),
170.23/170.48	                                 app_encode_app(complex,real,
170.23/170.48	                                                norm_norm(complex),
170.23/170.48	                                                app_encode_app(complex,
170.23/170.48	                                                               complex,
170.23/170.48	                                                               app_encode_app(
170.23/170.48	                                                               complex,
170.23/170.48	                                                               app_encode_fun(
170.23/170.48	                                                               complex,
170.23/170.48	                                                               complex),
170.23/170.48	                                                               times_times(
170.23/170.48	                                                               complex),z),
170.23/170.48	                                                               app_encode_app(
170.23/170.48	                                                               complex,
170.23/170.48	                                                               complex,
170.23/170.48	                                                               app_encode_app(
170.23/170.48	                                                               fun(complex,
170.23/170.48	                                                                   complex),
170.23/170.48	                                                               app_encode_fun(
170.23/170.48	                                                               complex,
170.23/170.48	                                                               complex),
170.23/170.48	                                                               aa(complex,
170.23/170.48	                                                                  complex),
170.23/170.48	                                                               app_encode_app(
170.23/170.48	                                                               poly1(complex),
170.23/170.48	                                                               fun(complex,
170.23/170.48	                                                                   complex),
170.23/170.48	                                                               poly(complex),
170.23/170.48	                                                               cs)),z))))))).
170.23/170.48	tff(zf_stmt_0, negated_conjecture,
170.23/170.48	  (~
170.23/170.48	    app_encode_app(real,$o,
170.23/170.48	                   app_encode_app(real,app_encode_fun(real,$o),
170.23/170.48	                                  ord_less_eq(real),
170.23/170.48	                                  app_encode_app(complex,real,
170.23/170.48	                                                 norm_norm(complex),
170.23/170.48	                                                 app_encode_app(complex,
170.23/170.48	                                                                complex,
170.23/170.48	                                                                app_encode_app(
170.23/170.48	                                                                fun(complex,
170.23/170.48	                                                                    complex),
170.23/170.48	                                                                app_encode_fun(
170.23/170.48	                                                                complex,
170.23/170.48	                                                                complex),
170.23/170.48	                                                                aa(complex,
170.23/170.48	                                                                   complex),
170.23/170.48	                                                                app_encode_app(
170.23/170.48	                                                                poly1(
170.23/170.48	                                                                complex),
170.23/170.48	                                                                fun(complex,
170.23/170.48	                                                                    complex),
170.23/170.48	                                                                poly(complex),
170.23/170.48	                                                                app_encode_app(
170.23/170.48	                                                                poly1(
170.23/170.48	                                                                complex),
170.23/170.48	                                                                poly1(
170.23/170.48	                                                                complex),
170.23/170.48	                                                                app_encode_app(
170.23/170.48	                                                                complex,
170.23/170.48	                                                                app_encode_fun(
170.23/170.48	                                                                poly1(
170.23/170.48	                                                                complex),
170.23/170.48	                                                                poly1(
170.23/170.48	                                                                complex)),
170.23/170.48	                                                                pCons(
170.23/170.48	                                                                complex),c),
170.23/170.48	                                                                cs))),z))),
170.23/170.48	                   app_encode_app(real,real,
170.23/170.48	                                  app_encode_app(real,
170.23/170.48	                                                 app_encode_fun(real,real),
170.23/170.48	                                                 plus_plus(real),
170.23/170.48	                                                 app_encode_app(complex,real,
170.23/170.48	                                                                norm_norm(
170.23/170.48	                                                                complex),c)),
170.23/170.48	                                  app_encode_app(complex,real,
170.23/170.48	                                                 norm_norm(complex),
170.23/170.48	                                                 app_encode_app(complex,
170.23/170.48	                                                                complex,
170.23/170.48	                                                                app_encode_app(
170.23/170.48	                                                                complex,
170.23/170.48	                                                                app_encode_fun(
170.23/170.48	                                                                complex,
170.23/170.48	                                                                complex),
170.23/170.48	                                                                times_times(
170.23/170.48	                                                                complex),z),
170.23/170.48	                                                                app_encode_app(
170.23/170.48	                                                                complex,
170.23/170.48	                                                                complex,
170.23/170.48	                                                                app_encode_app(
170.23/170.48	                                                                fun(complex,
170.23/170.48	                                                                    complex),
170.23/170.48	                                                                app_encode_fun(
170.23/170.48	                                                                complex,
170.23/170.48	                                                                complex),
170.23/170.48	                                                                aa(complex,
170.23/170.48	                                                                   complex),
170.23/170.48	                                                                app_encode_app(
170.23/170.48	                                                                poly1(
170.23/170.48	                                                                complex),
170.23/170.48	                                                                fun(complex,
170.23/170.48	                                                                    complex),
170.23/170.48	                                                                poly(complex),
170.23/170.48	                                                                cs)),z))))))).
170.23/170.48	tff('4', plain,
170.23/170.48	    ~ app_encode_app(real, $o, 
170.23/170.48	        app_encode_app(real, app_encode_fun(real, $o), ord_less_eq(real), 
170.23/170.48	          app_encode_app(complex, real, norm_norm(complex), 
170.23/170.48	            app_encode_app(complex, complex, 
170.23/170.48	              app_encode_app(fun(complex, complex), 
170.23/170.48	                app_encode_fun(complex, complex), aa(complex, complex), 
170.23/170.48	                app_encode_app(poly1(complex), fun(complex, complex), 
170.23/170.48	                  poly(complex), 
170.23/170.48	                  app_encode_app(poly1(complex), poly1(complex), 
170.23/170.48	                    app_encode_app(complex, 
170.23/170.48	                      app_encode_fun(poly1(complex), poly1(complex)), 
170.23/170.48	                      pCons(complex), c), cs))), z))), 
170.23/170.48	        app_encode_app(real, real, 
170.23/170.48	          app_encode_app(real, app_encode_fun(real, real), plus_plus(real), 
170.23/170.48	            app_encode_app(complex, real, norm_norm(complex), c)), 
170.23/170.48	          app_encode_app(complex, real, norm_norm(complex), 
170.23/170.48	            app_encode_app(complex, complex, 
170.23/170.48	              app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	                times_times(complex), z), 
170.23/170.48	              app_encode_app(complex, complex, 
170.23/170.48	                app_encode_app(fun(complex, complex), 
170.23/170.48	                  app_encode_fun(complex, complex), aa(complex, complex), 
170.23/170.48	                  app_encode_app(poly1(complex), fun(complex, complex), 
170.23/170.48	                    poly(complex), cs)), z))))),
170.23/170.48	    inference('cnf', [status(esa)], [zf_stmt_0])).
170.23/170.48	tff(zf_stmt_197, axiom, (real_n1866405975lgebra(complex))).
170.23/170.48	tff('5', plain, real_n1866405975lgebra(complex),
170.23/170.48	    inference('cnf', [status(esa)], [zf_stmt_197])).
170.23/170.48	tff(zf_stmt_86, axiom,
170.23/170.48	  (![A:$tType]:
170.23/170.48	     (real_n1866405975lgebra(A) =>
170.23/170.48	      (![Y1:A,X1:A]:
170.23/170.48	         (app_encode_app(A,real,norm_norm(A),
170.23/170.48	                         app_encode_app(A,A,
170.23/170.48	                                        app_encode_app(A,app_encode_fun(A,A),
170.23/170.48	                                                       times_times(A),X1),
170.23/170.48	                                        Y1)) =
170.23/170.48	          app_encode_app(real,real,
170.23/170.48	                         app_encode_app(real,app_encode_fun(real,real),
170.23/170.48	                                        times_times(real),
170.23/170.48	                                        app_encode_app(A,real,norm_norm(A),X1)),
170.23/170.48	                         app_encode_app(A,real,norm_norm(A),Y1))))))).
170.23/170.48	tff('6', plain,
170.23/170.48	    ![X102 : $tType, X103 : X102, X104 : X102]:
170.23/170.48	      (app_encode_app(X102, real, norm_norm(X102), 
170.23/170.48	         app_encode_app(X102, X102, 
170.23/170.48	           app_encode_app(X102, app_encode_fun(X102, X102), 
170.23/170.48	             times_times(X102), X103), X104))
170.23/170.48	        = app_encode_app(real, real, 
170.23/170.48	            app_encode_app(real, app_encode_fun(real, real), 
170.23/170.48	              times_times(real), 
170.23/170.48	              app_encode_app(X102, real, norm_norm(X102), X103)), 
170.23/170.48	            app_encode_app(X102, real, norm_norm(X102), X104))
170.23/170.48	       | ~ real_n1866405975lgebra(X102)),
170.23/170.48	    inference('cnf', [status(esa)], [zf_stmt_86])).
170.23/170.48	tff('7', plain,
170.23/170.48	    ![X0 : complex, X1 : complex]:
170.23/170.48	      (~ $true
170.23/170.48	       | app_encode_app(complex, real, norm_norm(complex), 
170.23/170.48	           app_encode_app(complex, complex, 
170.23/170.48	             app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	               times_times(complex), X1), X0))
170.23/170.48	          = app_encode_app(real, real, 
170.23/170.48	              app_encode_app(real, app_encode_fun(real, real), 
170.23/170.48	                times_times(real), 
170.23/170.48	                app_encode_app(complex, real, norm_norm(complex), X1)), 
170.23/170.48	              app_encode_app(complex, real, norm_norm(complex), X0))),
170.23/170.48	    inference('sup-', [status(thm)], ['5', '6'])).
170.23/170.48	tff('8', plain,
170.23/170.48	    ![X0 : complex, X1 : complex]:
170.23/170.48	      app_encode_app(complex, real, norm_norm(complex), 
170.23/170.48	        app_encode_app(complex, complex, 
170.23/170.48	          app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	            times_times(complex), X1), X0))
170.23/170.48	       = app_encode_app(real, real, 
170.23/170.48	           app_encode_app(real, app_encode_fun(real, real), 
170.23/170.48	             times_times(real), 
170.23/170.48	             app_encode_app(complex, real, norm_norm(complex), X1)), 
170.23/170.48	           app_encode_app(complex, real, norm_norm(complex), X0)),
170.23/170.48	    inference('simplify', [status(thm)], ['7'])).
170.23/170.48	tff('9', plain,
170.23/170.48	    ~ app_encode_app(real, $o, 
170.23/170.48	        app_encode_app(real, app_encode_fun(real, $o), ord_less_eq(real), 
170.23/170.48	          app_encode_app(complex, real, norm_norm(complex), 
170.23/170.48	            app_encode_app(complex, complex, 
170.23/170.48	              app_encode_app(fun(complex, complex), 
170.23/170.48	                app_encode_fun(complex, complex), aa(complex, complex), 
170.23/170.48	                app_encode_app(poly1(complex), fun(complex, complex), 
170.23/170.48	                  poly(complex), 
170.23/170.48	                  app_encode_app(poly1(complex), poly1(complex), 
170.23/170.48	                    app_encode_app(complex, 
170.23/170.48	                      app_encode_fun(poly1(complex), poly1(complex)), 
170.23/170.48	                      pCons(complex), c), cs))), z))), 
170.23/170.48	        app_encode_app(real, real, 
170.23/170.48	          app_encode_app(real, app_encode_fun(real, real), plus_plus(real), 
170.23/170.48	            app_encode_app(complex, real, norm_norm(complex), c)), 
170.23/170.48	          app_encode_app(real, real, 
170.23/170.48	            app_encode_app(real, app_encode_fun(real, real), 
170.23/170.48	              times_times(real), 
170.23/170.48	              app_encode_app(complex, real, norm_norm(complex), z)), 
170.23/170.48	            app_encode_app(complex, real, norm_norm(complex), 
170.23/170.48	              app_encode_app(complex, complex, 
170.23/170.48	                app_encode_app(fun(complex, complex), 
170.23/170.48	                  app_encode_fun(complex, complex), aa(complex, complex), 
170.23/170.48	                  app_encode_app(poly1(complex), fun(complex, complex), 
170.23/170.48	                    poly(complex), cs)), z))))),
170.23/170.48	    inference('demod', [status(thm)], ['4', '8'])).
170.23/170.48	tff('10', plain,
170.23/170.48	    (~ $true
170.23/170.48	     | app_encode_app(real, $o, 
170.23/170.48	         app_encode_app(real, app_encode_fun(real, $o), ord_less(real), 
170.23/170.48	           app_encode_app(real, real, 
170.23/170.48	             app_encode_app(real, app_encode_fun(real, real), 
170.23/170.48	               plus_plus(real), 
170.23/170.48	               app_encode_app(complex, real, norm_norm(complex), c)), 
170.23/170.48	             app_encode_app(real, real, 
170.23/170.48	               app_encode_app(real, app_encode_fun(real, real), 
170.23/170.48	                 times_times(real), 
170.23/170.48	                 app_encode_app(complex, real, norm_norm(complex), z)), 
170.23/170.48	               app_encode_app(complex, real, norm_norm(complex), 
170.23/170.48	                 app_encode_app(complex, complex, 
170.23/170.48	                   app_encode_app(fun(complex, complex), 
170.23/170.48	                     app_encode_fun(complex, complex), aa(complex, complex), 
170.23/170.48	                     app_encode_app(poly1(complex), fun(complex, complex), 
170.23/170.48	                       poly(complex), cs)), z))))), 
170.23/170.48	         app_encode_app(complex, real, norm_norm(complex), 
170.23/170.48	           app_encode_app(complex, complex, 
170.23/170.48	             app_encode_app(fun(complex, complex), 
170.23/170.48	               app_encode_fun(complex, complex), aa(complex, complex), 
170.23/170.48	               app_encode_app(poly1(complex), fun(complex, complex), 
170.23/170.48	                 poly(complex), 
170.23/170.48	                 app_encode_app(poly1(complex), poly1(complex), 
170.23/170.48	                   app_encode_app(complex, 
170.23/170.48	                     app_encode_fun(poly1(complex), poly1(complex)), 
170.23/170.48	                     pCons(complex), c), cs))), z)))),
170.23/170.48	    inference('sup-', [status(thm)], ['3', '9'])).
170.23/170.48	tff('11', plain,
170.23/170.48	    app_encode_app(real, $o, 
170.23/170.48	      app_encode_app(real, app_encode_fun(real, $o), ord_less(real), 
170.23/170.48	        app_encode_app(real, real, 
170.23/170.48	          app_encode_app(real, app_encode_fun(real, real), plus_plus(real), 
170.23/170.48	            app_encode_app(complex, real, norm_norm(complex), c)), 
170.23/170.48	          app_encode_app(real, real, 
170.23/170.48	            app_encode_app(real, app_encode_fun(real, real), 
170.23/170.48	              times_times(real), 
170.23/170.48	              app_encode_app(complex, real, norm_norm(complex), z)), 
170.23/170.48	            app_encode_app(complex, real, norm_norm(complex), 
170.23/170.48	              app_encode_app(complex, complex, 
170.23/170.48	                app_encode_app(fun(complex, complex), 
170.23/170.48	                  app_encode_fun(complex, complex), aa(complex, complex), 
170.23/170.48	                  app_encode_app(poly1(complex), fun(complex, complex), 
170.23/170.48	                    poly(complex), cs)), z))))), 
170.23/170.48	      app_encode_app(complex, real, norm_norm(complex), 
170.23/170.48	        app_encode_app(complex, complex, 
170.23/170.48	          app_encode_app(fun(complex, complex), 
170.23/170.48	            app_encode_fun(complex, complex), aa(complex, complex), 
170.23/170.48	            app_encode_app(poly1(complex), fun(complex, complex), 
170.23/170.48	              poly(complex), 
170.23/170.48	              app_encode_app(poly1(complex), poly1(complex), 
170.23/170.48	                app_encode_app(complex, 
170.23/170.48	                  app_encode_fun(poly1(complex), poly1(complex)), 
170.23/170.48	                  pCons(complex), c), cs))), z))),
170.23/170.48	    inference('simplify', [status(thm)], ['10'])).
170.23/170.48	tff(zf_stmt_208, axiom, (comm_semiring_0(complex))).
170.23/170.48	tff('12', plain, comm_semiring_0(complex),
170.23/170.48	    inference('cnf', [status(esa)], [zf_stmt_208])).
170.23/170.48	tff(zf_stmt_61, axiom,
170.23/170.48	  (![A:$tType]:
170.23/170.48	     (comm_semiring_0(A) =>
170.23/170.48	      (![X1:A,P:poly1(A),A1:A]:
170.23/170.48	         (app_encode_app(A,A,
170.23/170.48	                         app_encode_app(fun(A,A),app_encode_fun(A,A),
170.23/170.48	                                        aa(A,A),
170.23/170.48	                                        app_encode_app(poly1(A),fun(A,A),
170.23/170.48	                                                       poly(A),
170.23/170.48	                                                       app_encode_app(
170.23/170.48	                                                       poly1(A),poly1(A),
170.23/170.48	                                                       app_encode_app(
170.23/170.48	                                                       A,
170.23/170.48	                                                       app_encode_fun(
170.23/170.48	                                                       poly1(A),poly1(A)),
170.23/170.48	                                                       pCons(A),A1),P))),
170.23/170.48	                         X1) =
170.23/170.48	          app_encode_app(A,A,
170.23/170.48	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),A1),
170.23/170.48	                         app_encode_app(A,A,
170.23/170.48	                                        app_encode_app(A,app_encode_fun(A,A),
170.23/170.48	                                                       times_times(A),X1),
170.23/170.48	                                        app_encode_app(A,A,
170.23/170.48	                                                       app_encode_app(
170.23/170.48	                                                       fun(A,A),
170.23/170.48	                                                       app_encode_fun(A,A),
170.23/170.48	                                                       aa(A,A),
170.23/170.48	                                                       app_encode_app(
170.23/170.48	                                                       poly1(A),fun(A,A),
170.23/170.48	                                                       poly(A),P)),X1)))))))).
170.23/170.48	tff('13', plain,
170.23/170.48	    ![X1 : $tType, X2 : X1, X3 : X1, X4 : poly1(X1)]:
170.23/170.48	      (app_encode_app(X1, X1, 
170.23/170.48	         app_encode_app(fun(X1, X1), app_encode_fun(X1, X1), aa(X1, X1), 
170.23/170.48	           app_encode_app(poly1(X1), fun(X1, X1), poly(X1), 
170.23/170.48	             app_encode_app(poly1(X1), poly1(X1), 
170.23/170.48	               app_encode_app(X1, app_encode_fun(poly1(X1), poly1(X1)), 
170.23/170.48	                 pCons(X1), X2), X4))), X3)
170.23/170.48	        = app_encode_app(X1, X1, 
170.23/170.48	            app_encode_app(X1, app_encode_fun(X1, X1), plus_plus(X1), X2), 
170.23/170.48	            app_encode_app(X1, X1, 
170.23/170.48	              app_encode_app(X1, app_encode_fun(X1, X1), times_times(X1), X3), 
170.23/170.48	              app_encode_app(X1, X1, 
170.23/170.48	                app_encode_app(fun(X1, X1), app_encode_fun(X1, X1), 
170.23/170.48	                  aa(X1, X1), 
170.23/170.48	                  app_encode_app(poly1(X1), fun(X1, X1), poly(X1), X4)), X3)))
170.23/170.48	       | ~ comm_semiring_0(X1)),
170.23/170.48	    inference('cnf', [status(esa)], [zf_stmt_61])).
170.23/170.48	tff('14', plain,
170.23/170.48	    ![X0 : complex, X1 : poly1(complex), X2 : complex]:
170.23/170.48	      (~ $true
170.23/170.48	       | app_encode_app(complex, complex, 
170.23/170.48	           app_encode_app(fun(complex, complex), 
170.23/170.48	             app_encode_fun(complex, complex), aa(complex, complex), 
170.23/170.48	             app_encode_app(poly1(complex), fun(complex, complex), 
170.23/170.48	               poly(complex), 
170.23/170.48	               app_encode_app(poly1(complex), poly1(complex), 
170.23/170.48	                 app_encode_app(complex, 
170.23/170.48	                   app_encode_fun(poly1(complex), poly1(complex)), 
170.23/170.48	                   pCons(complex), X2), X1))), X0)
170.23/170.48	          = app_encode_app(complex, complex, 
170.23/170.48	              app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	                plus_plus(complex), X2), 
170.23/170.48	              app_encode_app(complex, complex, 
170.23/170.48	                app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	                  times_times(complex), X0), 
170.23/170.48	                app_encode_app(complex, complex, 
170.23/170.48	                  app_encode_app(fun(complex, complex), 
170.23/170.48	                    app_encode_fun(complex, complex), aa(complex, complex), 
170.23/170.48	                    app_encode_app(poly1(complex), fun(complex, complex), 
170.23/170.48	                      poly(complex), X1)), X0)))),
170.23/170.48	    inference('sup-', [status(thm)], ['12', '13'])).
170.23/170.48	tff('15', plain,
170.23/170.48	    ![X0 : complex, X1 : poly1(complex), X2 : complex]:
170.23/170.48	      app_encode_app(complex, complex, 
170.23/170.48	        app_encode_app(fun(complex, complex), 
170.23/170.48	          app_encode_fun(complex, complex), aa(complex, complex), 
170.23/170.48	          app_encode_app(poly1(complex), fun(complex, complex), 
170.23/170.48	            poly(complex), 
170.23/170.48	            app_encode_app(poly1(complex), poly1(complex), 
170.23/170.48	              app_encode_app(complex, 
170.23/170.48	                app_encode_fun(poly1(complex), poly1(complex)), 
170.23/170.48	                pCons(complex), X2), X1))), X0)
170.23/170.48	       = app_encode_app(complex, complex, 
170.23/170.48	           app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	             plus_plus(complex), X2), 
170.23/170.48	           app_encode_app(complex, complex, 
170.23/170.48	             app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	               times_times(complex), X0), 
170.23/170.48	             app_encode_app(complex, complex, 
170.23/170.48	               app_encode_app(fun(complex, complex), 
170.23/170.48	                 app_encode_fun(complex, complex), aa(complex, complex), 
170.23/170.48	                 app_encode_app(poly1(complex), fun(complex, complex), 
170.23/170.48	                   poly(complex), X1)), X0))),
170.23/170.48	    inference('simplify', [status(thm)], ['14'])).
170.23/170.48	tff('16', plain,
170.23/170.48	    app_encode_app(real, $o, 
170.23/170.48	      app_encode_app(real, app_encode_fun(real, $o), ord_less(real), 
170.23/170.48	        app_encode_app(real, real, 
170.23/170.48	          app_encode_app(real, app_encode_fun(real, real), plus_plus(real), 
170.23/170.48	            app_encode_app(complex, real, norm_norm(complex), c)), 
170.23/170.48	          app_encode_app(real, real, 
170.23/170.48	            app_encode_app(real, app_encode_fun(real, real), 
170.23/170.48	              times_times(real), 
170.23/170.48	              app_encode_app(complex, real, norm_norm(complex), z)), 
170.23/170.48	            app_encode_app(complex, real, norm_norm(complex), 
170.23/170.48	              app_encode_app(complex, complex, 
170.23/170.48	                app_encode_app(fun(complex, complex), 
170.23/170.48	                  app_encode_fun(complex, complex), aa(complex, complex), 
170.23/170.48	                  app_encode_app(poly1(complex), fun(complex, complex), 
170.23/170.48	                    poly(complex), cs)), z))))), 
170.23/170.48	      app_encode_app(complex, real, norm_norm(complex), 
170.23/170.48	        app_encode_app(complex, complex, 
170.23/170.48	          app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	            plus_plus(complex), c), 
170.23/170.48	          app_encode_app(complex, complex, 
170.23/170.48	            app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	              times_times(complex), z), 
170.23/170.48	            app_encode_app(complex, complex, 
170.23/170.48	              app_encode_app(fun(complex, complex), 
170.23/170.48	                app_encode_fun(complex, complex), aa(complex, complex), 
170.23/170.48	                app_encode_app(poly1(complex), fun(complex, complex), 
170.23/170.48	                  poly(complex), cs)), z))))),
170.23/170.48	    inference('demod', [status(thm)], ['11', '15'])).
170.23/170.48	tff(zf_stmt_209, axiom, (mult_zero(complex))).
170.23/170.48	tff('17', plain, mult_zero(complex),
170.23/170.48	    inference('cnf', [status(esa)], [zf_stmt_209])).
170.23/170.48	tff(zf_stmt_95, axiom,
170.23/170.48	  (![A:$tType]:
170.23/170.48	     (mult_zero(A) =>
170.23/170.48	      (![A1:A]:
170.23/170.48	         (app_encode_app(A,A,
170.23/170.48	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
170.23/170.48	                                        zero_zero(A)),
170.23/170.48	                         A1) =
170.23/170.48	          zero_zero(A)))))).
170.23/170.48	tff('18', plain,
170.23/170.48	    ![X130 : $tType, X131 : X130]:
170.23/170.48	      (app_encode_app(X130, X130, 
170.23/170.48	         app_encode_app(X130, app_encode_fun(X130, X130), times_times(X130), 
170.23/170.48	           zero_zero(X130)), X131)
170.23/170.48	        = zero_zero(X130)
170.23/170.48	       | ~ mult_zero(X130)),
170.23/170.48	    inference('cnf', [status(esa)], [zf_stmt_95])).
170.23/170.48	tff('19', plain,
170.23/170.48	    ![X0 : complex]:
170.23/170.48	      (~ $true
170.23/170.48	       | app_encode_app(complex, complex, 
170.23/170.48	           app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	             times_times(complex), zero_zero(complex)), X0)
170.23/170.48	          = zero_zero(complex)),
170.23/170.48	    inference('sup-', [status(thm)], ['17', '18'])).
170.23/170.48	tff('20', plain,
170.23/170.48	    ![X0 : complex]:
170.23/170.48	      app_encode_app(complex, complex, 
170.23/170.48	        app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	          times_times(complex), zero_zero(complex)), X0)
170.23/170.48	       = zero_zero(complex),
170.23/170.48	    inference('simplify', [status(thm)], ['19'])).
170.23/170.48	tff(zf_stmt_207, axiom, (comm_semiring_1(complex))).
170.23/170.48	tff('21', plain, comm_semiring_1(complex),
170.23/170.48	    inference('cnf', [status(esa)], [zf_stmt_207])).
170.23/170.48	tff(zf_stmt_93, axiom,
170.23/170.48	  (![A:$tType]:
170.23/170.48	     (comm_semiring_1(A) =>
170.23/170.48	      (![B:A,M:A,A1:A]:
170.23/170.48	         (app_encode_app(A,A,
170.23/170.48	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
170.23/170.48	                                        app_encode_app(A,A,
170.23/170.48	                                                       app_encode_app(
170.23/170.48	                                                       A,app_encode_fun(A,A),
170.23/170.48	                                                       times_times(A),A1),M)),
170.23/170.48	                         app_encode_app(A,A,
170.23/170.48	                                        app_encode_app(A,app_encode_fun(A,A),
170.23/170.48	                                                       times_times(A),B),
170.23/170.48	                                        M)) =
170.23/170.48	          app_encode_app(A,A,
170.23/170.48	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
170.23/170.48	                                        app_encode_app(A,A,
170.23/170.48	                                                       app_encode_app(
170.23/170.48	                                                       A,app_encode_fun(A,A),
170.23/170.48	                                                       plus_plus(A),A1),B)),
170.23/170.48	                         M)))))).
170.23/170.48	tff('22', plain,
170.23/170.48	    ![X122 : $tType, X123 : X122, X124 : X122, X125 : X122]:
170.23/170.48	      (app_encode_app(X122, X122, 
170.23/170.48	         app_encode_app(X122, app_encode_fun(X122, X122), plus_plus(X122), 
170.23/170.48	           app_encode_app(X122, X122, 
170.23/170.48	             app_encode_app(X122, app_encode_fun(X122, X122), 
170.23/170.48	               times_times(X122), X123), X125)), 
170.23/170.48	         app_encode_app(X122, X122, 
170.23/170.48	           app_encode_app(X122, app_encode_fun(X122, X122), 
170.23/170.48	             times_times(X122), X124), X125))
170.23/170.48	        = app_encode_app(X122, X122, 
170.23/170.48	            app_encode_app(X122, app_encode_fun(X122, X122), 
170.23/170.48	              times_times(X122), 
170.23/170.48	              app_encode_app(X122, X122, 
170.23/170.48	                app_encode_app(X122, app_encode_fun(X122, X122), 
170.23/170.48	                  plus_plus(X122), X123), X124)), X125)
170.23/170.48	       | ~ comm_semiring_1(X122)),
170.23/170.48	    inference('cnf', [status(esa)], [zf_stmt_93])).
170.23/170.48	tff('23', plain,
170.23/170.48	    ![X0 : complex, X1 : complex, X2 : complex]:
170.23/170.48	      (~ $true
170.23/170.48	       | app_encode_app(complex, complex, 
170.23/170.48	           app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	             plus_plus(complex), 
170.23/170.48	             app_encode_app(complex, complex, 
170.23/170.48	               app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	                 times_times(complex), X2), X0)), 
170.23/170.48	           app_encode_app(complex, complex, 
170.23/170.48	             app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	               times_times(complex), X1), X0))
170.23/170.48	          = app_encode_app(complex, complex, 
170.23/170.48	              app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	                times_times(complex), 
170.23/170.48	                app_encode_app(complex, complex, 
170.23/170.48	                  app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	                    plus_plus(complex), X2), X1)), X0)),
170.23/170.48	    inference('sup-', [status(thm)], ['21', '22'])).
170.23/170.48	tff('24', plain,
170.23/170.48	    ![X0 : complex, X1 : complex, X2 : complex]:
170.23/170.48	      app_encode_app(complex, complex, 
170.23/170.48	        app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	          plus_plus(complex), 
170.23/170.48	          app_encode_app(complex, complex, 
170.23/170.48	            app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	              times_times(complex), X2), X0)), 
170.23/170.48	        app_encode_app(complex, complex, 
170.23/170.48	          app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	            times_times(complex), X1), X0))
170.23/170.48	       = app_encode_app(complex, complex, 
170.23/170.48	           app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	             times_times(complex), 
170.23/170.48	             app_encode_app(complex, complex, 
170.23/170.48	               app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	                 plus_plus(complex), X2), X1)), X0),
170.23/170.48	    inference('simplify', [status(thm)], ['23'])).
170.23/170.48	tff('25', plain,
170.23/170.48	    ![X0 : complex, X1 : complex]:
170.23/170.48	      app_encode_app(complex, complex, 
170.23/170.48	        app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	          plus_plus(complex), zero_zero(complex)), 
170.23/170.48	        app_encode_app(complex, complex, 
170.23/170.48	          app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	            times_times(complex), X1), X0))
170.23/170.48	       = app_encode_app(complex, complex, 
170.23/170.48	           app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	             times_times(complex), 
170.23/170.48	             app_encode_app(complex, complex, 
170.23/170.48	               app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	                 plus_plus(complex), zero_zero(complex)), X1)), X0),
170.23/170.48	    inference('sup+', [status(thm)], ['20', '24'])).
170.23/170.48	tff('26', plain,
170.23/170.48	    ![X0 : complex, X1 : complex]:
170.23/170.48	      app_encode_app(complex, real, norm_norm(complex), 
170.23/170.48	        app_encode_app(complex, complex, 
170.23/170.48	          app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	            plus_plus(complex), zero_zero(complex)), 
170.23/170.48	          app_encode_app(complex, complex, 
170.23/170.48	            app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	              times_times(complex), X1), X0)))
170.23/170.48	       = app_encode_app(real, real, 
170.23/170.48	           app_encode_app(real, app_encode_fun(real, real), 
170.23/170.48	             times_times(real), 
170.23/170.48	             app_encode_app(complex, real, norm_norm(complex), 
170.23/170.48	               app_encode_app(complex, complex, 
170.23/170.48	                 app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	                   plus_plus(complex), zero_zero(complex)), X1))), 
170.23/170.48	           app_encode_app(complex, real, norm_norm(complex), X0)),
170.23/170.48	    inference('sup+', [status(thm)], ['25', '8'])).
170.23/170.48	tff(zf_stmt_200, axiom, (real_normed_vector(complex))).
170.23/170.48	tff('27', plain, real_normed_vector(complex),
170.23/170.48	    inference('cnf', [status(esa)], [zf_stmt_200])).
170.23/170.48	tff(zf_stmt_67, axiom,
170.23/170.48	  (![A:$tType]:
170.23/170.48	     (real_normed_vector(A) =>
170.23/170.48	      (![Y1:A,X1:A]:
170.23/170.48	         app_encode_app(real,$o,
170.23/170.48	                        app_encode_app(real,app_encode_fun(real,$o),
170.23/170.48	                                       ord_less_eq(real),
170.23/170.48	                                       app_encode_app(A,real,norm_norm(A),
170.23/170.48	                                                      app_encode_app(
170.23/170.48	                                                      A,A,
170.23/170.48	                                                      app_encode_app(
170.23/170.48	                                                      A,app_encode_fun(A,A),
170.23/170.48	                                                      plus_plus(A),X1),Y1))),
170.23/170.48	                        app_encode_app(real,real,
170.23/170.48	                                       app_encode_app(real,
170.23/170.48	                                                      app_encode_fun(
170.23/170.48	                                                      real,real),
170.23/170.48	                                                      plus_plus(real),
170.23/170.48	                                                      app_encode_app(
170.23/170.48	                                                      A,real,norm_norm(A),X1)),
170.23/170.48	                                       app_encode_app(A,real,norm_norm(A),Y1))))))).
170.23/170.48	tff('28', plain,
170.23/170.48	    ![X28 : $tType, X29 : X28, X30 : X28]:
170.23/170.48	      (app_encode_app(real, $o, 
170.23/170.48	         app_encode_app(real, app_encode_fun(real, $o), ord_less_eq(real), 
170.23/170.48	           app_encode_app(X28, real, norm_norm(X28), 
170.23/170.48	             app_encode_app(X28, X28, 
170.23/170.48	               app_encode_app(X28, app_encode_fun(X28, X28), plus_plus(X28), 
170.23/170.48	                 X29), X30))), 
170.23/170.48	         app_encode_app(real, real, 
170.23/170.48	           app_encode_app(real, app_encode_fun(real, real), plus_plus(real), 
170.23/170.48	             app_encode_app(X28, real, norm_norm(X28), X29)), 
170.23/170.48	           app_encode_app(X28, real, norm_norm(X28), X30)))
170.23/170.48	       | ~ real_normed_vector(X28)),
170.23/170.48	    inference('cnf', [status(esa)], [zf_stmt_67])).
170.23/170.48	tff('29', plain,
170.23/170.48	    ![X0 : complex, X1 : complex]:
170.23/170.48	      (~ $true
170.23/170.48	       | app_encode_app(real, $o, 
170.23/170.48	           app_encode_app(real, app_encode_fun(real, $o), ord_less_eq(real), 
170.23/170.48	             app_encode_app(complex, real, norm_norm(complex), 
170.23/170.48	               app_encode_app(complex, complex, 
170.23/170.48	                 app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	                   plus_plus(complex), X1), X0))), 
170.23/170.48	           app_encode_app(real, real, 
170.23/170.48	             app_encode_app(real, app_encode_fun(real, real), 
170.23/170.48	               plus_plus(real), 
170.23/170.48	               app_encode_app(complex, real, norm_norm(complex), X1)), 
170.23/170.48	             app_encode_app(complex, real, norm_norm(complex), X0)))),
170.23/170.48	    inference('sup-', [status(thm)], ['27', '28'])).
170.23/170.48	tff('30', plain,
170.23/170.48	    ![X0 : complex, X1 : complex]:
170.23/170.48	      app_encode_app(real, $o, 
170.23/170.48	        app_encode_app(real, app_encode_fun(real, $o), ord_less_eq(real), 
170.23/170.48	          app_encode_app(complex, real, norm_norm(complex), 
170.23/170.48	            app_encode_app(complex, complex, 
170.23/170.48	              app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	                plus_plus(complex), X1), X0))), 
170.23/170.48	        app_encode_app(real, real, 
170.23/170.48	          app_encode_app(real, app_encode_fun(real, real), plus_plus(real), 
170.23/170.48	            app_encode_app(complex, real, norm_norm(complex), X1)), 
170.23/170.48	          app_encode_app(complex, real, norm_norm(complex), X0))),
170.23/170.48	    inference('simplify', [status(thm)], ['29'])).
170.23/170.48	tff(zf_stmt_141, axiom,
170.23/170.48	  (![A:$tType]:
170.23/170.48	     (linorder(A) =>
170.23/170.48	      (![X1:A,Y1:A]:
170.23/170.48	         (app_encode_app(A,$o,
170.23/170.48	                         app_encode_app(A,app_encode_fun(A,$o),
170.23/170.48	                                        ord_less_eq(A),Y1),
170.23/170.48	                         X1) =>
170.23/170.48	          (~
170.23/170.48	            app_encode_app(A,$o,
170.23/170.48	                           app_encode_app(A,app_encode_fun(A,$o),ord_less(A),
170.23/170.48	                                          X1),
170.23/170.48	                           Y1))))))).
170.23/170.48	tff('31', plain,
170.23/170.48	    ![X280 : $tType, X281 : X280, X282 : X280]:
170.23/170.48	      (~ app_encode_app(X280, $o, 
170.23/170.48	           app_encode_app(X280, app_encode_fun(X280, $o), ord_less_eq(X280), 
170.23/170.48	             X281), X282)
170.23/170.48	       | ~ app_encode_app(X280, $o, 
170.23/170.48	             app_encode_app(X280, app_encode_fun(X280, $o), ord_less(X280), 
170.23/170.48	               X282), X281)
170.23/170.48	       | ~ linorder(X280)),
170.23/170.48	    inference('cnf', [status(esa)], [zf_stmt_141])).
170.23/170.48	tff('32', plain,
170.23/170.48	    ![X0 : complex, X1 : complex]:
170.23/170.48	      (~ $true
170.23/170.48	       | ~ linorder(real)
170.23/170.48	       | ~ app_encode_app(real, $o, 
170.23/170.48	             app_encode_app(real, app_encode_fun(real, $o), ord_less(real), 
170.23/170.48	               app_encode_app(real, real, 
170.23/170.48	                 app_encode_app(real, app_encode_fun(real, real), 
170.23/170.48	                   plus_plus(real), 
170.23/170.48	                   app_encode_app(complex, real, norm_norm(complex), X1)), 
170.23/170.48	                 app_encode_app(complex, real, norm_norm(complex), X0))), 
170.23/170.48	             app_encode_app(complex, real, norm_norm(complex), 
170.23/170.48	               app_encode_app(complex, complex, 
170.23/170.48	                 app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	                   plus_plus(complex), X1), X0)))),
170.23/170.48	    inference('sup-', [status(thm)], ['30', '31'])).
170.23/170.48	tff('33', plain,
170.23/170.48	    ![X0 : complex, X1 : complex]:
170.23/170.48	      (~ $true
170.23/170.48	       | ~ $true
170.23/170.48	       | ~ app_encode_app(real, $o, 
170.23/170.48	             app_encode_app(real, app_encode_fun(real, $o), ord_less(real), 
170.23/170.48	               app_encode_app(real, real, 
170.23/170.48	                 app_encode_app(real, app_encode_fun(real, real), 
170.23/170.48	                   plus_plus(real), 
170.23/170.48	                   app_encode_app(complex, real, norm_norm(complex), X1)), 
170.23/170.48	                 app_encode_app(complex, real, norm_norm(complex), X0))), 
170.23/170.48	             app_encode_app(complex, real, norm_norm(complex), 
170.23/170.48	               app_encode_app(complex, complex, 
170.23/170.48	                 app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	                   plus_plus(complex), X1), X0)))),
170.23/170.48	    inference('demod', [status(thm)], ['32', '0'])).
170.23/170.48	tff('34', plain,
170.23/170.48	    ![X0 : complex, X1 : complex]:
170.23/170.48	      ~ app_encode_app(real, $o, 
170.23/170.48	          app_encode_app(real, app_encode_fun(real, $o), ord_less(real), 
170.23/170.48	            app_encode_app(real, real, 
170.23/170.48	              app_encode_app(real, app_encode_fun(real, real), 
170.23/170.48	                plus_plus(real), 
170.23/170.48	                app_encode_app(complex, real, norm_norm(complex), X1)), 
170.23/170.48	              app_encode_app(complex, real, norm_norm(complex), X0))), 
170.23/170.48	          app_encode_app(complex, real, norm_norm(complex), 
170.23/170.48	            app_encode_app(complex, complex, 
170.23/170.48	              app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	                plus_plus(complex), X1), X0))),
170.23/170.48	    inference('simplify', [status(thm)], ['33'])).
170.23/170.48	tff('35', plain,
170.23/170.48	    ![X0 : complex, X1 : complex, X2 : complex]:
170.23/170.48	      ~ app_encode_app(real, $o, 
170.23/170.48	          app_encode_app(real, app_encode_fun(real, $o), ord_less(real), 
170.23/170.48	            app_encode_app(real, real, 
170.23/170.48	              app_encode_app(real, app_encode_fun(real, real), 
170.23/170.48	                plus_plus(real), 
170.23/170.48	                app_encode_app(complex, real, norm_norm(complex), X2)), 
170.23/170.48	              app_encode_app(real, real, 
170.23/170.48	                app_encode_app(real, app_encode_fun(real, real), 
170.23/170.48	                  times_times(real), 
170.23/170.48	                  app_encode_app(complex, real, norm_norm(complex), 
170.23/170.48	                    app_encode_app(complex, complex, 
170.23/170.48	                      app_encode_app(complex, 
170.23/170.48	                        app_encode_fun(complex, complex), 
170.23/170.48	                        plus_plus(complex), zero_zero(complex)), X1))), 
170.23/170.48	                app_encode_app(complex, real, norm_norm(complex), X0)))), 
170.23/170.48	          app_encode_app(complex, real, norm_norm(complex), 
170.23/170.48	            app_encode_app(complex, complex, 
170.23/170.48	              app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	                plus_plus(complex), X2), 
170.23/170.48	              app_encode_app(complex, complex, 
170.23/170.48	                app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	                  plus_plus(complex), zero_zero(complex)), 
170.23/170.48	                app_encode_app(complex, complex, 
170.23/170.48	                  app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	                    times_times(complex), X1), X0))))),
170.23/170.48	    inference('sup-', [status(thm)], ['26', '34'])).
170.23/170.48	tff(zf_stmt_96, axiom,
170.23/170.48	  (![A:$tType]:
170.23/170.48	     (mult_zero(A) =>
170.23/170.48	      (![A1:A]:
170.23/170.48	         (app_encode_app(A,A,
170.23/170.48	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
170.23/170.48	                                        A1),
170.23/170.48	                         zero_zero(A)) =
170.23/170.48	          zero_zero(A)))))).
170.23/170.48	tff('36', plain,
170.23/170.48	    ![X132 : $tType, X133 : X132]:
170.23/170.48	      (app_encode_app(X132, X132, 
170.23/170.48	         app_encode_app(X132, app_encode_fun(X132, X132), times_times(X132), 
170.23/170.48	           X133), zero_zero(X132))
170.23/170.48	        = zero_zero(X132)
170.23/170.48	       | ~ mult_zero(X132)),
170.23/170.48	    inference('cnf', [status(esa)], [zf_stmt_96])).
170.23/170.48	tff('37', plain,
170.23/170.48	    ![X0 : complex]:
170.23/170.48	      (~ $true
170.23/170.48	       | app_encode_app(complex, complex, 
170.23/170.48	           app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	             times_times(complex), X0), zero_zero(complex))
170.23/170.48	          = zero_zero(complex)),
170.23/170.48	    inference('sup-', [status(thm)], ['17', '36'])).
170.23/170.48	tff('38', plain,
170.23/170.48	    ![X0 : complex]:
170.23/170.48	      app_encode_app(complex, complex, 
170.23/170.48	        app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	          times_times(complex), X0), zero_zero(complex))
170.23/170.48	       = zero_zero(complex),
170.23/170.48	    inference('simplify', [status(thm)], ['37'])).
170.23/170.48	tff('39', plain,
170.23/170.48	    ![X0 : complex, X1 : complex]:
170.23/170.48	      app_encode_app(complex, complex, 
170.23/170.48	        app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	          plus_plus(complex), zero_zero(complex)), 
170.23/170.48	        app_encode_app(complex, complex, 
170.23/170.48	          app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	            times_times(complex), X0), zero_zero(complex)))
170.23/170.48	       = app_encode_app(complex, complex, 
170.23/170.48	           app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	             times_times(complex), 
170.23/170.48	             app_encode_app(complex, complex, 
170.23/170.48	               app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	                 plus_plus(complex), X1), X0)), zero_zero(complex)),
170.23/170.48	    inference('sup+', [status(thm)], ['38', '24'])).
170.23/170.48	tff('40', plain,
170.23/170.48	    app_encode_app(complex, complex, 
170.23/170.48	      app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	        plus_plus(complex), zero_zero(complex)), zero_zero(complex))
170.23/170.48	     = zero_zero(complex),
170.23/170.48	    inference('demod', [status(thm)], ['39', '38', '38'])).
170.23/170.48	tff(zf_stmt_204, axiom, (ab_semigroup_add(complex))).
170.23/170.48	tff('41', plain, ab_semigroup_add(complex),
170.23/170.48	    inference('cnf', [status(esa)], [zf_stmt_204])).
170.23/170.48	tff(zf_stmt_79, axiom,
170.23/170.48	  (![A:$tType]:
170.23/170.48	     (ab_semigroup_add(A) =>
170.23/170.48	      (![C:A,B:A,A1:A]:
170.23/170.48	         (app_encode_app(A,A,
170.23/170.48	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
170.23/170.48	                                        app_encode_app(A,A,
170.23/170.48	                                                       app_encode_app(
170.23/170.48	                                                       A,app_encode_fun(A,A),
170.23/170.48	                                                       plus_plus(A),A1),B)),
170.23/170.48	                         C) =
170.23/170.48	          app_encode_app(A,A,
170.23/170.48	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),A1),
170.23/170.48	                         app_encode_app(A,A,
170.23/170.48	                                        app_encode_app(A,app_encode_fun(A,A),
170.23/170.48	                                                       plus_plus(A),B),
170.23/170.48	                                        C))))))).
170.23/170.48	tff('42', plain,
170.23/170.48	    ![X73 : $tType, X74 : X73, X75 : X73, X76 : X73]:
170.23/170.48	      (app_encode_app(X73, X73, 
170.23/170.48	         app_encode_app(X73, app_encode_fun(X73, X73), plus_plus(X73), 
170.23/170.48	           app_encode_app(X73, X73, 
170.23/170.48	             app_encode_app(X73, app_encode_fun(X73, X73), plus_plus(X73), 
170.23/170.48	               X74), X75)), X76)
170.23/170.48	        = app_encode_app(X73, X73, 
170.23/170.48	            app_encode_app(X73, app_encode_fun(X73, X73), plus_plus(X73), 
170.23/170.48	              X74), 
170.23/170.48	            app_encode_app(X73, X73, 
170.23/170.48	              app_encode_app(X73, app_encode_fun(X73, X73), plus_plus(X73), 
170.23/170.48	                X75), X76))
170.23/170.48	       | ~ ab_semigroup_add(X73)),
170.23/170.48	    inference('cnf', [status(esa)], [zf_stmt_79])).
170.23/170.48	tff('43', plain,
170.23/170.48	    ![X0 : complex, X1 : complex, X2 : complex]:
170.23/170.48	      (~ $true
170.23/170.48	       | app_encode_app(complex, complex, 
170.23/170.48	           app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	             plus_plus(complex), 
170.23/170.48	             app_encode_app(complex, complex, 
170.23/170.48	               app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	                 plus_plus(complex), X2), X1)), X0)
170.23/170.48	          = app_encode_app(complex, complex, 
170.23/170.48	              app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	                plus_plus(complex), X2), 
170.23/170.48	              app_encode_app(complex, complex, 
170.23/170.48	                app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	                  plus_plus(complex), X1), X0))),
170.23/170.48	    inference('sup-', [status(thm)], ['41', '42'])).
170.23/170.48	tff('44', plain,
170.23/170.48	    ![X0 : complex, X1 : complex, X2 : complex]:
170.23/170.48	      app_encode_app(complex, complex, 
170.23/170.48	        app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	          plus_plus(complex), 
170.23/170.48	          app_encode_app(complex, complex, 
170.23/170.48	            app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	              plus_plus(complex), X2), X1)), X0)
170.23/170.48	       = app_encode_app(complex, complex, 
170.23/170.48	           app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	             plus_plus(complex), X2), 
170.23/170.48	           app_encode_app(complex, complex, 
170.23/170.48	             app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	               plus_plus(complex), X1), X0)),
170.23/170.48	    inference('simplify', [status(thm)], ['43'])).
170.23/170.48	tff('45', plain,
170.23/170.48	    ![X0 : complex]:
170.23/170.48	      app_encode_app(complex, complex, 
170.23/170.48	        app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	          plus_plus(complex), zero_zero(complex)), X0)
170.23/170.48	       = app_encode_app(complex, complex, 
170.23/170.48	           app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	             plus_plus(complex), zero_zero(complex)), 
170.23/170.48	           app_encode_app(complex, complex, 
170.23/170.48	             app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	               plus_plus(complex), zero_zero(complex)), X0)),
170.23/170.48	    inference('sup+', [status(thm)], ['40', '44'])).
170.23/170.48	tff(zf_stmt_72, axiom,
170.23/170.48	  (![A:$tType]:
170.23/170.48	     (cancel_semigroup_add(A) =>
170.23/170.48	      (![Ca:A,B2:A,A2:A]:
170.23/170.48	         ((app_encode_app(A,A,
170.23/170.48	                          app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
170.23/170.48	                                         A2),
170.23/170.48	                          B2) =
170.23/170.48	           app_encode_app(A,A,
170.23/170.48	                          app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
170.23/170.48	                                         A2),
170.23/170.48	                          Ca)) <=>
170.23/170.48	          (B2 = Ca)))))).
170.23/170.48	tff('46', plain,
170.23/170.48	    ![X43 : $tType, X44 : X43, X45 : X43, X47 : X43]:
170.23/170.48	      (app_encode_app(X43, X43, 
170.23/170.48	         app_encode_app(X43, app_encode_fun(X43, X43), plus_plus(X43), X47), 
170.23/170.48	         X45)
170.23/170.48	        != app_encode_app(X43, X43, 
170.23/170.48	             app_encode_app(X43, app_encode_fun(X43, X43), plus_plus(X43), 
170.23/170.48	               X47), X44)
170.23/170.48	       | X45 = X44
170.23/170.48	       | ~ cancel_semigroup_add(X43)),
170.23/170.48	    inference('cnf', [status(esa)], [zf_stmt_72])).
170.23/170.48	tff('47', plain,
170.23/170.48	    ![X0 : complex, X1 : complex]:
170.23/170.48	      (app_encode_app(complex, complex, 
170.23/170.48	         app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	           plus_plus(complex), zero_zero(complex)), X1)
170.23/170.48	        != app_encode_app(complex, complex, 
170.23/170.48	             app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	               plus_plus(complex), zero_zero(complex)), X0)
170.23/170.48	       | ~ cancel_semigroup_add(complex)
170.23/170.48	       | X1
170.23/170.48	          = app_encode_app(complex, complex, 
170.23/170.48	              app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	                plus_plus(complex), zero_zero(complex)), X0)),
170.23/170.48	    inference('sup-', [status(thm)], ['45', '46'])).
170.23/170.48	tff(zf_stmt_202, axiom, (cancel_semigroup_add(complex))).
170.23/170.48	tff('48', plain, cancel_semigroup_add(complex),
170.23/170.48	    inference('cnf', [status(esa)], [zf_stmt_202])).
170.23/170.48	tff('49', plain,
170.23/170.48	    ![X0 : complex, X1 : complex]:
170.23/170.48	      (app_encode_app(complex, complex, 
170.23/170.48	         app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	           plus_plus(complex), zero_zero(complex)), X1)
170.23/170.48	        != app_encode_app(complex, complex, 
170.23/170.48	             app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	               plus_plus(complex), zero_zero(complex)), X0)
170.23/170.48	       | ~ $true
170.23/170.48	       | X1
170.23/170.48	          = app_encode_app(complex, complex, 
170.23/170.48	              app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	                plus_plus(complex), zero_zero(complex)), X0)),
170.23/170.48	    inference('demod', [status(thm)], ['47', '48'])).
170.23/170.48	tff('50', plain,
170.23/170.48	    ![X0 : complex, X1 : complex]:
170.23/170.48	      (X1
170.23/170.48	        = app_encode_app(complex, complex, 
170.23/170.48	            app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	              plus_plus(complex), zero_zero(complex)), X0)
170.23/170.48	       | app_encode_app(complex, complex, 
170.23/170.48	           app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	             plus_plus(complex), zero_zero(complex)), X1)
170.23/170.48	          != app_encode_app(complex, complex, 
170.23/170.48	               app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	                 plus_plus(complex), zero_zero(complex)), X0)),
170.23/170.48	    inference('simplify', [status(thm)], ['49'])).
170.23/170.48	tff('51', plain,
170.23/170.48	    ![X0 : complex]:
170.23/170.48	      X0
170.23/170.48	       = app_encode_app(complex, complex, 
170.23/170.48	           app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	             plus_plus(complex), zero_zero(complex)), X0),
170.23/170.48	    inference('eq_res', [status(thm)], ['50'])).
170.23/170.48	tff('52', plain,
170.23/170.48	    ![X0 : complex, X1 : complex, X2 : complex]:
170.23/170.48	      ~ app_encode_app(real, $o, 
170.23/170.48	          app_encode_app(real, app_encode_fun(real, $o), ord_less(real), 
170.23/170.48	            app_encode_app(real, real, 
170.23/170.48	              app_encode_app(real, app_encode_fun(real, real), 
170.23/170.48	                plus_plus(real), 
170.23/170.48	                app_encode_app(complex, real, norm_norm(complex), X2)), 
170.23/170.48	              app_encode_app(real, real, 
170.23/170.48	                app_encode_app(real, app_encode_fun(real, real), 
170.23/170.48	                  times_times(real), 
170.23/170.48	                  app_encode_app(complex, real, norm_norm(complex), X1)), 
170.23/170.48	                app_encode_app(complex, real, norm_norm(complex), X0)))), 
170.23/170.48	          app_encode_app(complex, real, norm_norm(complex), 
170.23/170.48	            app_encode_app(complex, complex, 
170.23/170.48	              app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	                plus_plus(complex), X2), 
170.23/170.48	              app_encode_app(complex, complex, 
170.23/170.48	                app_encode_app(complex, app_encode_fun(complex, complex), 
170.23/170.48	                  times_times(complex), X1), X0)))),
170.23/170.48	    inference('demod', [status(thm)], ['35', '51', '51'])).
170.23/170.48	tff('53', plain, ~ $true, inference('sup-', [status(thm)], ['16', '52'])).
170.23/170.48	tff('54', plain, $false, inference('simplify', [status(thm)], ['53'])).
170.23/170.48	
170.23/170.48	% SZS output end Refutation
170.23/170.48	EOF
