0.00/0.00	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : appext
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : rpo6
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.20	% Computer   : n115.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 09:45:53 CST 2018
177.30/177.50	% done 29593 iterations in 177.292s
177.30/177.50	% SZS status Theorem for 'stdin'
177.30/177.50	% SZS output start Refutation
177.30/177.50	tff(zf_stmt_190, axiom, (linorder(real))).
177.30/177.50	tff('0', plain, linorder(real),
177.30/177.50	    inference('cnf', [status(esa)], [zf_stmt_190])).
177.30/177.50	tff(zf_stmt_145, axiom,
177.30/177.50	  (![A:$tType]:
177.30/177.50	     (linorder(A) =>
177.30/177.50	      (![X1:A,Y1:A]:
177.30/177.50	         ((~
177.30/177.50	            app_encode_app(A,$o,
177.30/177.50	                           app_encode_app(A,app_encode_fun(A,$o),
177.30/177.50	                                          ord_less_eq(A),Y1),
177.30/177.50	                           X1)) =>
177.30/177.50	          app_encode_app(A,$o,
177.30/177.50	                         app_encode_app(A,app_encode_fun(A,$o),ord_less(A),X1),
177.30/177.50	                         Y1)))))).
177.30/177.50	tff('1', plain,
177.30/177.50	    ![X293 : $tType, X294 : X293, X295 : X293]:
177.30/177.50	      (app_encode_app(X293, $o, 
177.30/177.50	         app_encode_app(X293, app_encode_fun(X293, $o), ord_less_eq(X293), 
177.30/177.50	           X294), X295)
177.30/177.50	       | app_encode_app(X293, $o, 
177.30/177.50	           app_encode_app(X293, app_encode_fun(X293, $o), ord_less(X293), 
177.30/177.50	             X295), X294)
177.30/177.50	       | ~ linorder(X293)),
177.30/177.50	    inference('cnf', [status(esa)], [zf_stmt_145])).
177.30/177.50	tff('2', plain,
177.30/177.50	    ![X0 : real, X1 : real]:
177.30/177.50	      (~ $true
177.30/177.50	       | app_encode_app(real, $o, 
177.30/177.50	           app_encode_app(real, app_encode_fun(real, $o), ord_less(real), X1), 
177.30/177.50	           X0)
177.30/177.50	       | app_encode_app(real, $o, 
177.30/177.50	           app_encode_app(real, app_encode_fun(real, $o), ord_less_eq(real), 
177.30/177.50	             X0), X1)),
177.30/177.50	    inference('sup-', [status(thm)], ['0', '1'])).
177.30/177.50	tff('3', plain,
177.30/177.50	    ![X0 : real, X1 : real]:
177.30/177.50	      (app_encode_app(real, $o, 
177.30/177.50	         app_encode_app(real, app_encode_fun(real, $o), ord_less_eq(real), 
177.30/177.50	           X0), X1)
177.30/177.50	       | app_encode_app(real, $o, 
177.30/177.50	           app_encode_app(real, app_encode_fun(real, $o), ord_less(real), X1), 
177.30/177.50	           X0)),
177.30/177.50	    inference('simplify', [status(thm)], ['2'])).
177.30/177.50	tff(zf_stmt_244, conjecture,
177.30/177.50	  (app_encode_app(real,$o,
177.30/177.50	                  app_encode_app(real,app_encode_fun(real,$o),
177.30/177.50	                                 ord_less_eq(real),
177.30/177.50	                                 app_encode_app(complex,real,
177.30/177.50	                                                norm_norm(complex),
177.30/177.50	                                                app_encode_app(complex,
177.30/177.50	                                                               complex,
177.30/177.50	                                                               app_encode_app(
177.30/177.50	                                                               fun(complex,
177.30/177.50	                                                                   complex),
177.30/177.50	                                                               app_encode_fun(
177.30/177.50	                                                               complex,
177.30/177.50	                                                               complex),
177.30/177.50	                                                               aa(complex,
177.30/177.50	                                                                  complex),
177.30/177.50	                                                               app_encode_app(
177.30/177.50	                                                               poly1(complex),
177.30/177.50	                                                               fun(complex,
177.30/177.50	                                                                   complex),
177.30/177.50	                                                               poly(complex),
177.30/177.50	                                                               app_encode_app(
177.30/177.50	                                                               poly1(complex),
177.30/177.50	                                                               poly1(complex),
177.30/177.50	                                                               app_encode_app(
177.30/177.50	                                                               complex,
177.30/177.50	                                                               app_encode_fun(
177.30/177.50	                                                               poly1(complex),
177.30/177.50	                                                               poly1(complex)),
177.30/177.50	                                                               pCons(complex),
177.30/177.50	                                                               c),cs))),z))),
177.30/177.50	                  app_encode_app(real,real,
177.30/177.50	                                 app_encode_app(real,
177.30/177.50	                                                app_encode_fun(real,real),
177.30/177.50	                                                plus_plus(real),
177.30/177.50	                                                app_encode_app(complex,real,
177.30/177.50	                                                               norm_norm(
177.30/177.50	                                                               complex),c)),
177.30/177.50	                                 app_encode_app(complex,real,
177.30/177.50	                                                norm_norm(complex),
177.30/177.50	                                                app_encode_app(complex,
177.30/177.50	                                                               complex,
177.30/177.50	                                                               app_encode_app(
177.30/177.50	                                                               complex,
177.30/177.50	                                                               app_encode_fun(
177.30/177.50	                                                               complex,
177.30/177.50	                                                               complex),
177.30/177.50	                                                               times_times(
177.30/177.50	                                                               complex),z),
177.30/177.50	                                                               app_encode_app(
177.30/177.50	                                                               complex,
177.30/177.50	                                                               complex,
177.30/177.50	                                                               app_encode_app(
177.30/177.50	                                                               fun(complex,
177.30/177.50	                                                                   complex),
177.30/177.50	                                                               app_encode_fun(
177.30/177.50	                                                               complex,
177.30/177.50	                                                               complex),
177.30/177.50	                                                               aa(complex,
177.30/177.50	                                                                  complex),
177.30/177.50	                                                               app_encode_app(
177.30/177.50	                                                               poly1(complex),
177.30/177.50	                                                               fun(complex,
177.30/177.50	                                                                   complex),
177.30/177.50	                                                               poly(complex),
177.30/177.50	                                                               cs)),z))))))).
177.30/177.50	tff(zf_stmt_0, negated_conjecture,
177.30/177.50	  (~
177.30/177.50	    app_encode_app(real,$o,
177.30/177.50	                   app_encode_app(real,app_encode_fun(real,$o),
177.30/177.50	                                  ord_less_eq(real),
177.30/177.50	                                  app_encode_app(complex,real,
177.30/177.50	                                                 norm_norm(complex),
177.30/177.50	                                                 app_encode_app(complex,
177.30/177.50	                                                                complex,
177.30/177.50	                                                                app_encode_app(
177.30/177.50	                                                                fun(complex,
177.30/177.50	                                                                    complex),
177.30/177.50	                                                                app_encode_fun(
177.30/177.50	                                                                complex,
177.30/177.50	                                                                complex),
177.30/177.50	                                                                aa(complex,
177.30/177.50	                                                                   complex),
177.30/177.50	                                                                app_encode_app(
177.30/177.50	                                                                poly1(
177.30/177.50	                                                                complex),
177.30/177.50	                                                                fun(complex,
177.30/177.50	                                                                    complex),
177.30/177.50	                                                                poly(complex),
177.30/177.50	                                                                app_encode_app(
177.30/177.50	                                                                poly1(
177.30/177.50	                                                                complex),
177.30/177.50	                                                                poly1(
177.30/177.50	                                                                complex),
177.30/177.50	                                                                app_encode_app(
177.30/177.50	                                                                complex,
177.30/177.50	                                                                app_encode_fun(
177.30/177.50	                                                                poly1(
177.30/177.50	                                                                complex),
177.30/177.50	                                                                poly1(
177.30/177.50	                                                                complex)),
177.30/177.50	                                                                pCons(
177.30/177.50	                                                                complex),c),
177.30/177.50	                                                                cs))),z))),
177.30/177.50	                   app_encode_app(real,real,
177.30/177.50	                                  app_encode_app(real,
177.30/177.50	                                                 app_encode_fun(real,real),
177.30/177.50	                                                 plus_plus(real),
177.30/177.50	                                                 app_encode_app(complex,real,
177.30/177.50	                                                                norm_norm(
177.30/177.50	                                                                complex),c)),
177.30/177.50	                                  app_encode_app(complex,real,
177.30/177.50	                                                 norm_norm(complex),
177.30/177.50	                                                 app_encode_app(complex,
177.30/177.50	                                                                complex,
177.30/177.50	                                                                app_encode_app(
177.30/177.50	                                                                complex,
177.30/177.50	                                                                app_encode_fun(
177.30/177.50	                                                                complex,
177.30/177.50	                                                                complex),
177.30/177.50	                                                                times_times(
177.30/177.50	                                                                complex),z),
177.30/177.50	                                                                app_encode_app(
177.30/177.50	                                                                complex,
177.30/177.50	                                                                complex,
177.30/177.50	                                                                app_encode_app(
177.30/177.50	                                                                fun(complex,
177.30/177.50	                                                                    complex),
177.30/177.50	                                                                app_encode_fun(
177.30/177.50	                                                                complex,
177.30/177.50	                                                                complex),
177.30/177.50	                                                                aa(complex,
177.30/177.50	                                                                   complex),
177.30/177.50	                                                                app_encode_app(
177.30/177.50	                                                                poly1(
177.30/177.50	                                                                complex),
177.30/177.50	                                                                fun(complex,
177.30/177.50	                                                                    complex),
177.30/177.50	                                                                poly(complex),
177.30/177.50	                                                                cs)),z))))))).
177.30/177.50	tff('4', plain,
177.30/177.50	    ~ app_encode_app(real, $o, 
177.30/177.50	        app_encode_app(real, app_encode_fun(real, $o), ord_less_eq(real), 
177.30/177.50	          app_encode_app(complex, real, norm_norm(complex), 
177.30/177.50	            app_encode_app(complex, complex, 
177.30/177.50	              app_encode_app(fun(complex, complex), 
177.30/177.50	                app_encode_fun(complex, complex), aa(complex, complex), 
177.30/177.50	                app_encode_app(poly1(complex), fun(complex, complex), 
177.30/177.50	                  poly(complex), 
177.30/177.50	                  app_encode_app(poly1(complex), poly1(complex), 
177.30/177.50	                    app_encode_app(complex, 
177.30/177.50	                      app_encode_fun(poly1(complex), poly1(complex)), 
177.30/177.50	                      pCons(complex), c), cs))), z))), 
177.30/177.50	        app_encode_app(real, real, 
177.30/177.50	          app_encode_app(real, app_encode_fun(real, real), plus_plus(real), 
177.30/177.50	            app_encode_app(complex, real, norm_norm(complex), c)), 
177.30/177.50	          app_encode_app(complex, real, norm_norm(complex), 
177.30/177.50	            app_encode_app(complex, complex, 
177.30/177.50	              app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	                times_times(complex), z), 
177.30/177.50	              app_encode_app(complex, complex, 
177.30/177.50	                app_encode_app(fun(complex, complex), 
177.30/177.50	                  app_encode_fun(complex, complex), aa(complex, complex), 
177.30/177.50	                  app_encode_app(poly1(complex), fun(complex, complex), 
177.30/177.50	                    poly(complex), cs)), z))))),
177.30/177.50	    inference('cnf', [status(esa)], [zf_stmt_0])).
177.30/177.50	tff(zf_stmt_198, axiom, (real_n1866405975lgebra(complex))).
177.30/177.50	tff('5', plain, real_n1866405975lgebra(complex),
177.30/177.50	    inference('cnf', [status(esa)], [zf_stmt_198])).
177.30/177.50	tff(zf_stmt_87, axiom,
177.30/177.50	  (![A:$tType]:
177.30/177.50	     (real_n1866405975lgebra(A) =>
177.30/177.50	      (![Y1:A,X1:A]:
177.30/177.50	         (app_encode_app(A,real,norm_norm(A),
177.30/177.50	                         app_encode_app(A,A,
177.30/177.50	                                        app_encode_app(A,app_encode_fun(A,A),
177.30/177.50	                                                       times_times(A),X1),
177.30/177.50	                                        Y1)) =
177.30/177.50	          app_encode_app(real,real,
177.30/177.50	                         app_encode_app(real,app_encode_fun(real,real),
177.30/177.50	                                        times_times(real),
177.30/177.50	                                        app_encode_app(A,real,norm_norm(A),X1)),
177.30/177.50	                         app_encode_app(A,real,norm_norm(A),Y1))))))).
177.30/177.50	tff('6', plain,
177.30/177.50	    ![X106 : $tType, X107 : X106, X108 : X106]:
177.30/177.50	      (app_encode_app(X106, real, norm_norm(X106), 
177.30/177.50	         app_encode_app(X106, X106, 
177.30/177.50	           app_encode_app(X106, app_encode_fun(X106, X106), 
177.30/177.50	             times_times(X106), X107), X108))
177.30/177.50	        = app_encode_app(real, real, 
177.30/177.50	            app_encode_app(real, app_encode_fun(real, real), 
177.30/177.50	              times_times(real), 
177.30/177.50	              app_encode_app(X106, real, norm_norm(X106), X107)), 
177.30/177.50	            app_encode_app(X106, real, norm_norm(X106), X108))
177.30/177.50	       | ~ real_n1866405975lgebra(X106)),
177.30/177.50	    inference('cnf', [status(esa)], [zf_stmt_87])).
177.30/177.50	tff('7', plain,
177.30/177.50	    ![X0 : complex, X1 : complex]:
177.30/177.50	      (~ $true
177.30/177.50	       | app_encode_app(complex, real, norm_norm(complex), 
177.30/177.50	           app_encode_app(complex, complex, 
177.30/177.50	             app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	               times_times(complex), X1), X0))
177.30/177.50	          = app_encode_app(real, real, 
177.30/177.50	              app_encode_app(real, app_encode_fun(real, real), 
177.30/177.50	                times_times(real), 
177.30/177.50	                app_encode_app(complex, real, norm_norm(complex), X1)), 
177.30/177.50	              app_encode_app(complex, real, norm_norm(complex), X0))),
177.30/177.50	    inference('sup-', [status(thm)], ['5', '6'])).
177.30/177.50	tff('8', plain,
177.30/177.50	    ![X0 : complex, X1 : complex]:
177.30/177.50	      app_encode_app(complex, real, norm_norm(complex), 
177.30/177.50	        app_encode_app(complex, complex, 
177.30/177.50	          app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	            times_times(complex), X1), X0))
177.30/177.50	       = app_encode_app(real, real, 
177.30/177.50	           app_encode_app(real, app_encode_fun(real, real), 
177.30/177.50	             times_times(real), 
177.30/177.50	             app_encode_app(complex, real, norm_norm(complex), X1)), 
177.30/177.50	           app_encode_app(complex, real, norm_norm(complex), X0)),
177.30/177.50	    inference('simplify', [status(thm)], ['7'])).
177.30/177.50	tff('9', plain,
177.30/177.50	    ~ app_encode_app(real, $o, 
177.30/177.50	        app_encode_app(real, app_encode_fun(real, $o), ord_less_eq(real), 
177.30/177.50	          app_encode_app(complex, real, norm_norm(complex), 
177.30/177.50	            app_encode_app(complex, complex, 
177.30/177.50	              app_encode_app(fun(complex, complex), 
177.30/177.50	                app_encode_fun(complex, complex), aa(complex, complex), 
177.30/177.50	                app_encode_app(poly1(complex), fun(complex, complex), 
177.30/177.50	                  poly(complex), 
177.30/177.50	                  app_encode_app(poly1(complex), poly1(complex), 
177.30/177.50	                    app_encode_app(complex, 
177.30/177.50	                      app_encode_fun(poly1(complex), poly1(complex)), 
177.30/177.50	                      pCons(complex), c), cs))), z))), 
177.30/177.50	        app_encode_app(real, real, 
177.30/177.50	          app_encode_app(real, app_encode_fun(real, real), plus_plus(real), 
177.30/177.50	            app_encode_app(complex, real, norm_norm(complex), c)), 
177.30/177.50	          app_encode_app(real, real, 
177.30/177.50	            app_encode_app(real, app_encode_fun(real, real), 
177.30/177.50	              times_times(real), 
177.30/177.50	              app_encode_app(complex, real, norm_norm(complex), z)), 
177.30/177.50	            app_encode_app(complex, real, norm_norm(complex), 
177.30/177.50	              app_encode_app(complex, complex, 
177.30/177.50	                app_encode_app(fun(complex, complex), 
177.30/177.50	                  app_encode_fun(complex, complex), aa(complex, complex), 
177.30/177.50	                  app_encode_app(poly1(complex), fun(complex, complex), 
177.30/177.50	                    poly(complex), cs)), z))))),
177.30/177.50	    inference('demod', [status(thm)], ['4', '8'])).
177.30/177.50	tff('10', plain,
177.30/177.50	    (~ $true
177.30/177.50	     | app_encode_app(real, $o, 
177.30/177.50	         app_encode_app(real, app_encode_fun(real, $o), ord_less(real), 
177.30/177.50	           app_encode_app(real, real, 
177.30/177.50	             app_encode_app(real, app_encode_fun(real, real), 
177.30/177.50	               plus_plus(real), 
177.30/177.50	               app_encode_app(complex, real, norm_norm(complex), c)), 
177.30/177.50	             app_encode_app(real, real, 
177.30/177.50	               app_encode_app(real, app_encode_fun(real, real), 
177.30/177.50	                 times_times(real), 
177.30/177.50	                 app_encode_app(complex, real, norm_norm(complex), z)), 
177.30/177.50	               app_encode_app(complex, real, norm_norm(complex), 
177.30/177.50	                 app_encode_app(complex, complex, 
177.30/177.50	                   app_encode_app(fun(complex, complex), 
177.30/177.50	                     app_encode_fun(complex, complex), aa(complex, complex), 
177.30/177.50	                     app_encode_app(poly1(complex), fun(complex, complex), 
177.30/177.50	                       poly(complex), cs)), z))))), 
177.30/177.50	         app_encode_app(complex, real, norm_norm(complex), 
177.30/177.50	           app_encode_app(complex, complex, 
177.30/177.50	             app_encode_app(fun(complex, complex), 
177.30/177.50	               app_encode_fun(complex, complex), aa(complex, complex), 
177.30/177.50	               app_encode_app(poly1(complex), fun(complex, complex), 
177.30/177.50	                 poly(complex), 
177.30/177.50	                 app_encode_app(poly1(complex), poly1(complex), 
177.30/177.50	                   app_encode_app(complex, 
177.30/177.50	                     app_encode_fun(poly1(complex), poly1(complex)), 
177.30/177.50	                     pCons(complex), c), cs))), z)))),
177.30/177.50	    inference('sup-', [status(thm)], ['3', '9'])).
177.30/177.50	tff('11', plain,
177.30/177.50	    app_encode_app(real, $o, 
177.30/177.50	      app_encode_app(real, app_encode_fun(real, $o), ord_less(real), 
177.30/177.50	        app_encode_app(real, real, 
177.30/177.50	          app_encode_app(real, app_encode_fun(real, real), plus_plus(real), 
177.30/177.50	            app_encode_app(complex, real, norm_norm(complex), c)), 
177.30/177.50	          app_encode_app(real, real, 
177.30/177.50	            app_encode_app(real, app_encode_fun(real, real), 
177.30/177.50	              times_times(real), 
177.30/177.50	              app_encode_app(complex, real, norm_norm(complex), z)), 
177.30/177.50	            app_encode_app(complex, real, norm_norm(complex), 
177.30/177.50	              app_encode_app(complex, complex, 
177.30/177.50	                app_encode_app(fun(complex, complex), 
177.30/177.50	                  app_encode_fun(complex, complex), aa(complex, complex), 
177.30/177.50	                  app_encode_app(poly1(complex), fun(complex, complex), 
177.30/177.50	                    poly(complex), cs)), z))))), 
177.30/177.50	      app_encode_app(complex, real, norm_norm(complex), 
177.30/177.50	        app_encode_app(complex, complex, 
177.30/177.50	          app_encode_app(fun(complex, complex), 
177.30/177.50	            app_encode_fun(complex, complex), aa(complex, complex), 
177.30/177.50	            app_encode_app(poly1(complex), fun(complex, complex), 
177.30/177.50	              poly(complex), 
177.30/177.50	              app_encode_app(poly1(complex), poly1(complex), 
177.30/177.50	                app_encode_app(complex, 
177.30/177.50	                  app_encode_fun(poly1(complex), poly1(complex)), 
177.30/177.50	                  pCons(complex), c), cs))), z))),
177.30/177.50	    inference('simplify', [status(thm)], ['10'])).
177.30/177.50	tff(zf_stmt_209, axiom, (comm_semiring_0(complex))).
177.30/177.50	tff('12', plain, comm_semiring_0(complex),
177.30/177.50	    inference('cnf', [status(esa)], [zf_stmt_209])).
177.30/177.50	tff(zf_stmt_62, axiom,
177.30/177.50	  (![A:$tType]:
177.30/177.50	     (comm_semiring_0(A) =>
177.30/177.50	      (![X1:A,P:poly1(A),A1:A]:
177.30/177.50	         (app_encode_app(A,A,
177.30/177.50	                         app_encode_app(fun(A,A),app_encode_fun(A,A),
177.30/177.50	                                        aa(A,A),
177.30/177.50	                                        app_encode_app(poly1(A),fun(A,A),
177.30/177.50	                                                       poly(A),
177.30/177.50	                                                       app_encode_app(
177.30/177.50	                                                       poly1(A),poly1(A),
177.30/177.50	                                                       app_encode_app(
177.30/177.50	                                                       A,
177.30/177.50	                                                       app_encode_fun(
177.30/177.50	                                                       poly1(A),poly1(A)),
177.30/177.50	                                                       pCons(A),A1),P))),
177.30/177.50	                         X1) =
177.30/177.50	          app_encode_app(A,A,
177.30/177.50	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),A1),
177.30/177.50	                         app_encode_app(A,A,
177.30/177.50	                                        app_encode_app(A,app_encode_fun(A,A),
177.30/177.50	                                                       times_times(A),X1),
177.30/177.50	                                        app_encode_app(A,A,
177.30/177.50	                                                       app_encode_app(
177.30/177.50	                                                       fun(A,A),
177.30/177.50	                                                       app_encode_fun(A,A),
177.30/177.50	                                                       aa(A,A),
177.30/177.50	                                                       app_encode_app(
177.30/177.50	                                                       poly1(A),fun(A,A),
177.30/177.50	                                                       poly(A),P)),X1)))))))).
177.30/177.50	tff('13', plain,
177.30/177.50	    ![X5 : $tType, X6 : X5, X7 : X5, X8 : poly1(X5)]:
177.30/177.50	      (app_encode_app(X5, X5, 
177.30/177.50	         app_encode_app(fun(X5, X5), app_encode_fun(X5, X5), aa(X5, X5), 
177.30/177.50	           app_encode_app(poly1(X5), fun(X5, X5), poly(X5), 
177.30/177.50	             app_encode_app(poly1(X5), poly1(X5), 
177.30/177.50	               app_encode_app(X5, app_encode_fun(poly1(X5), poly1(X5)), 
177.30/177.50	                 pCons(X5), X6), X8))), X7)
177.30/177.50	        = app_encode_app(X5, X5, 
177.30/177.50	            app_encode_app(X5, app_encode_fun(X5, X5), plus_plus(X5), X6), 
177.30/177.50	            app_encode_app(X5, X5, 
177.30/177.50	              app_encode_app(X5, app_encode_fun(X5, X5), times_times(X5), X7), 
177.30/177.50	              app_encode_app(X5, X5, 
177.30/177.50	                app_encode_app(fun(X5, X5), app_encode_fun(X5, X5), 
177.30/177.50	                  aa(X5, X5), 
177.30/177.50	                  app_encode_app(poly1(X5), fun(X5, X5), poly(X5), X8)), X7)))
177.30/177.50	       | ~ comm_semiring_0(X5)),
177.30/177.50	    inference('cnf', [status(esa)], [zf_stmt_62])).
177.30/177.50	tff('14', plain,
177.30/177.50	    ![X0 : complex, X1 : poly1(complex), X2 : complex]:
177.30/177.50	      (~ $true
177.30/177.50	       | app_encode_app(complex, complex, 
177.30/177.50	           app_encode_app(fun(complex, complex), 
177.30/177.50	             app_encode_fun(complex, complex), aa(complex, complex), 
177.30/177.50	             app_encode_app(poly1(complex), fun(complex, complex), 
177.30/177.50	               poly(complex), 
177.30/177.50	               app_encode_app(poly1(complex), poly1(complex), 
177.30/177.50	                 app_encode_app(complex, 
177.30/177.50	                   app_encode_fun(poly1(complex), poly1(complex)), 
177.30/177.50	                   pCons(complex), X2), X1))), X0)
177.30/177.50	          = app_encode_app(complex, complex, 
177.30/177.50	              app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	                plus_plus(complex), X2), 
177.30/177.50	              app_encode_app(complex, complex, 
177.30/177.50	                app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	                  times_times(complex), X0), 
177.30/177.50	                app_encode_app(complex, complex, 
177.30/177.50	                  app_encode_app(fun(complex, complex), 
177.30/177.50	                    app_encode_fun(complex, complex), aa(complex, complex), 
177.30/177.50	                    app_encode_app(poly1(complex), fun(complex, complex), 
177.30/177.50	                      poly(complex), X1)), X0)))),
177.30/177.50	    inference('sup-', [status(thm)], ['12', '13'])).
177.30/177.50	tff('15', plain,
177.30/177.50	    ![X0 : complex, X1 : poly1(complex), X2 : complex]:
177.30/177.50	      app_encode_app(complex, complex, 
177.30/177.50	        app_encode_app(fun(complex, complex), 
177.30/177.50	          app_encode_fun(complex, complex), aa(complex, complex), 
177.30/177.50	          app_encode_app(poly1(complex), fun(complex, complex), 
177.30/177.50	            poly(complex), 
177.30/177.50	            app_encode_app(poly1(complex), poly1(complex), 
177.30/177.50	              app_encode_app(complex, 
177.30/177.50	                app_encode_fun(poly1(complex), poly1(complex)), 
177.30/177.50	                pCons(complex), X2), X1))), X0)
177.30/177.50	       = app_encode_app(complex, complex, 
177.30/177.50	           app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	             plus_plus(complex), X2), 
177.30/177.50	           app_encode_app(complex, complex, 
177.30/177.50	             app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	               times_times(complex), X0), 
177.30/177.50	             app_encode_app(complex, complex, 
177.30/177.50	               app_encode_app(fun(complex, complex), 
177.30/177.50	                 app_encode_fun(complex, complex), aa(complex, complex), 
177.30/177.50	                 app_encode_app(poly1(complex), fun(complex, complex), 
177.30/177.50	                   poly(complex), X1)), X0))),
177.30/177.50	    inference('simplify', [status(thm)], ['14'])).
177.30/177.50	tff('16', plain,
177.30/177.50	    app_encode_app(real, $o, 
177.30/177.50	      app_encode_app(real, app_encode_fun(real, $o), ord_less(real), 
177.30/177.50	        app_encode_app(real, real, 
177.30/177.50	          app_encode_app(real, app_encode_fun(real, real), plus_plus(real), 
177.30/177.50	            app_encode_app(complex, real, norm_norm(complex), c)), 
177.30/177.50	          app_encode_app(real, real, 
177.30/177.50	            app_encode_app(real, app_encode_fun(real, real), 
177.30/177.50	              times_times(real), 
177.30/177.50	              app_encode_app(complex, real, norm_norm(complex), z)), 
177.30/177.50	            app_encode_app(complex, real, norm_norm(complex), 
177.30/177.50	              app_encode_app(complex, complex, 
177.30/177.50	                app_encode_app(fun(complex, complex), 
177.30/177.50	                  app_encode_fun(complex, complex), aa(complex, complex), 
177.30/177.50	                  app_encode_app(poly1(complex), fun(complex, complex), 
177.30/177.50	                    poly(complex), cs)), z))))), 
177.30/177.50	      app_encode_app(complex, real, norm_norm(complex), 
177.30/177.50	        app_encode_app(complex, complex, 
177.30/177.50	          app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	            plus_plus(complex), c), 
177.30/177.50	          app_encode_app(complex, complex, 
177.30/177.50	            app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	              times_times(complex), z), 
177.30/177.50	            app_encode_app(complex, complex, 
177.30/177.50	              app_encode_app(fun(complex, complex), 
177.30/177.50	                app_encode_fun(complex, complex), aa(complex, complex), 
177.30/177.50	                app_encode_app(poly1(complex), fun(complex, complex), 
177.30/177.50	                  poly(complex), cs)), z))))),
177.30/177.50	    inference('demod', [status(thm)], ['11', '15'])).
177.30/177.50	tff(zf_stmt_210, axiom, (mult_zero(complex))).
177.30/177.50	tff('17', plain, mult_zero(complex),
177.30/177.50	    inference('cnf', [status(esa)], [zf_stmt_210])).
177.30/177.50	tff(zf_stmt_96, axiom,
177.30/177.50	  (![A:$tType]:
177.30/177.50	     (mult_zero(A) =>
177.30/177.50	      (![A1:A]:
177.30/177.50	         (app_encode_app(A,A,
177.30/177.50	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
177.30/177.50	                                        zero_zero(A)),
177.30/177.50	                         A1) =
177.30/177.50	          zero_zero(A)))))).
177.30/177.50	tff('18', plain,
177.30/177.50	    ![X134 : $tType, X135 : X134]:
177.30/177.50	      (app_encode_app(X134, X134, 
177.30/177.50	         app_encode_app(X134, app_encode_fun(X134, X134), times_times(X134), 
177.30/177.50	           zero_zero(X134)), X135)
177.30/177.50	        = zero_zero(X134)
177.30/177.50	       | ~ mult_zero(X134)),
177.30/177.50	    inference('cnf', [status(esa)], [zf_stmt_96])).
177.30/177.50	tff('19', plain,
177.30/177.50	    ![X0 : complex]:
177.30/177.50	      (~ $true
177.30/177.50	       | app_encode_app(complex, complex, 
177.30/177.50	           app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	             times_times(complex), zero_zero(complex)), X0)
177.30/177.50	          = zero_zero(complex)),
177.30/177.50	    inference('sup-', [status(thm)], ['17', '18'])).
177.30/177.50	tff('20', plain,
177.30/177.50	    ![X0 : complex]:
177.30/177.50	      app_encode_app(complex, complex, 
177.30/177.50	        app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	          times_times(complex), zero_zero(complex)), X0)
177.30/177.50	       = zero_zero(complex),
177.30/177.50	    inference('simplify', [status(thm)], ['19'])).
177.30/177.50	tff(zf_stmt_208, axiom, (comm_semiring_1(complex))).
177.30/177.50	tff('21', plain, comm_semiring_1(complex),
177.30/177.50	    inference('cnf', [status(esa)], [zf_stmt_208])).
177.30/177.50	tff(zf_stmt_94, axiom,
177.30/177.50	  (![A:$tType]:
177.30/177.50	     (comm_semiring_1(A) =>
177.30/177.50	      (![B:A,M:A,A1:A]:
177.30/177.50	         (app_encode_app(A,A,
177.30/177.50	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
177.30/177.50	                                        app_encode_app(A,A,
177.30/177.50	                                                       app_encode_app(
177.30/177.50	                                                       A,app_encode_fun(A,A),
177.30/177.50	                                                       times_times(A),A1),M)),
177.30/177.50	                         app_encode_app(A,A,
177.30/177.50	                                        app_encode_app(A,app_encode_fun(A,A),
177.30/177.50	                                                       times_times(A),B),
177.30/177.50	                                        M)) =
177.30/177.50	          app_encode_app(A,A,
177.30/177.50	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
177.30/177.50	                                        app_encode_app(A,A,
177.30/177.50	                                                       app_encode_app(
177.30/177.50	                                                       A,app_encode_fun(A,A),
177.30/177.50	                                                       plus_plus(A),A1),B)),
177.30/177.50	                         M)))))).
177.30/177.50	tff('22', plain,
177.30/177.50	    ![X126 : $tType, X127 : X126, X128 : X126, X129 : X126]:
177.30/177.50	      (app_encode_app(X126, X126, 
177.30/177.50	         app_encode_app(X126, app_encode_fun(X126, X126), plus_plus(X126), 
177.30/177.50	           app_encode_app(X126, X126, 
177.30/177.50	             app_encode_app(X126, app_encode_fun(X126, X126), 
177.30/177.50	               times_times(X126), X127), X129)), 
177.30/177.50	         app_encode_app(X126, X126, 
177.30/177.50	           app_encode_app(X126, app_encode_fun(X126, X126), 
177.30/177.50	             times_times(X126), X128), X129))
177.30/177.50	        = app_encode_app(X126, X126, 
177.30/177.50	            app_encode_app(X126, app_encode_fun(X126, X126), 
177.30/177.50	              times_times(X126), 
177.30/177.50	              app_encode_app(X126, X126, 
177.30/177.50	                app_encode_app(X126, app_encode_fun(X126, X126), 
177.30/177.50	                  plus_plus(X126), X127), X128)), X129)
177.30/177.50	       | ~ comm_semiring_1(X126)),
177.30/177.50	    inference('cnf', [status(esa)], [zf_stmt_94])).
177.30/177.50	tff('23', plain,
177.30/177.50	    ![X0 : complex, X1 : complex, X2 : complex]:
177.30/177.50	      (~ $true
177.30/177.50	       | app_encode_app(complex, complex, 
177.30/177.50	           app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	             plus_plus(complex), 
177.30/177.50	             app_encode_app(complex, complex, 
177.30/177.50	               app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	                 times_times(complex), X2), X0)), 
177.30/177.50	           app_encode_app(complex, complex, 
177.30/177.50	             app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	               times_times(complex), X1), X0))
177.30/177.50	          = app_encode_app(complex, complex, 
177.30/177.50	              app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	                times_times(complex), 
177.30/177.50	                app_encode_app(complex, complex, 
177.30/177.50	                  app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	                    plus_plus(complex), X2), X1)), X0)),
177.30/177.50	    inference('sup-', [status(thm)], ['21', '22'])).
177.30/177.50	tff('24', plain,
177.30/177.50	    ![X0 : complex, X1 : complex, X2 : complex]:
177.30/177.50	      app_encode_app(complex, complex, 
177.30/177.50	        app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	          plus_plus(complex), 
177.30/177.50	          app_encode_app(complex, complex, 
177.30/177.50	            app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	              times_times(complex), X2), X0)), 
177.30/177.50	        app_encode_app(complex, complex, 
177.30/177.50	          app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	            times_times(complex), X1), X0))
177.30/177.50	       = app_encode_app(complex, complex, 
177.30/177.50	           app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	             times_times(complex), 
177.30/177.50	             app_encode_app(complex, complex, 
177.30/177.50	               app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	                 plus_plus(complex), X2), X1)), X0),
177.30/177.50	    inference('simplify', [status(thm)], ['23'])).
177.30/177.50	tff('25', plain,
177.30/177.50	    ![X0 : complex, X1 : complex]:
177.30/177.50	      app_encode_app(complex, complex, 
177.30/177.50	        app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	          plus_plus(complex), zero_zero(complex)), 
177.30/177.50	        app_encode_app(complex, complex, 
177.30/177.50	          app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	            times_times(complex), X1), X0))
177.30/177.50	       = app_encode_app(complex, complex, 
177.30/177.50	           app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	             times_times(complex), 
177.30/177.50	             app_encode_app(complex, complex, 
177.30/177.50	               app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	                 plus_plus(complex), zero_zero(complex)), X1)), X0),
177.30/177.50	    inference('sup+', [status(thm)], ['20', '24'])).
177.30/177.50	tff('26', plain,
177.30/177.50	    ![X0 : complex, X1 : complex]:
177.30/177.50	      app_encode_app(complex, real, norm_norm(complex), 
177.30/177.50	        app_encode_app(complex, complex, 
177.30/177.50	          app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	            plus_plus(complex), zero_zero(complex)), 
177.30/177.50	          app_encode_app(complex, complex, 
177.30/177.50	            app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	              times_times(complex), X1), X0)))
177.30/177.50	       = app_encode_app(real, real, 
177.30/177.50	           app_encode_app(real, app_encode_fun(real, real), 
177.30/177.50	             times_times(real), 
177.30/177.50	             app_encode_app(complex, real, norm_norm(complex), 
177.30/177.50	               app_encode_app(complex, complex, 
177.30/177.50	                 app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	                   plus_plus(complex), zero_zero(complex)), X1))), 
177.30/177.50	           app_encode_app(complex, real, norm_norm(complex), X0)),
177.30/177.50	    inference('sup+', [status(thm)], ['25', '8'])).
177.30/177.50	tff(zf_stmt_201, axiom, (real_normed_vector(complex))).
177.30/177.50	tff('27', plain, real_normed_vector(complex),
177.30/177.50	    inference('cnf', [status(esa)], [zf_stmt_201])).
177.30/177.50	tff(zf_stmt_68, axiom,
177.30/177.50	  (![A:$tType]:
177.30/177.50	     (real_normed_vector(A) =>
177.30/177.50	      (![Y1:A,X1:A]:
177.30/177.50	         app_encode_app(real,$o,
177.30/177.50	                        app_encode_app(real,app_encode_fun(real,$o),
177.30/177.50	                                       ord_less_eq(real),
177.30/177.50	                                       app_encode_app(A,real,norm_norm(A),
177.30/177.50	                                                      app_encode_app(
177.30/177.50	                                                      A,A,
177.30/177.50	                                                      app_encode_app(
177.30/177.50	                                                      A,app_encode_fun(A,A),
177.30/177.50	                                                      plus_plus(A),X1),Y1))),
177.30/177.50	                        app_encode_app(real,real,
177.30/177.50	                                       app_encode_app(real,
177.30/177.50	                                                      app_encode_fun(
177.30/177.50	                                                      real,real),
177.30/177.50	                                                      plus_plus(real),
177.30/177.50	                                                      app_encode_app(
177.30/177.50	                                                      A,real,norm_norm(A),X1)),
177.30/177.50	                                       app_encode_app(A,real,norm_norm(A),Y1))))))).
177.30/177.50	tff('28', plain,
177.30/177.50	    ![X32 : $tType, X33 : X32, X34 : X32]:
177.30/177.50	      (app_encode_app(real, $o, 
177.30/177.50	         app_encode_app(real, app_encode_fun(real, $o), ord_less_eq(real), 
177.30/177.50	           app_encode_app(X32, real, norm_norm(X32), 
177.30/177.50	             app_encode_app(X32, X32, 
177.30/177.50	               app_encode_app(X32, app_encode_fun(X32, X32), plus_plus(X32), 
177.30/177.50	                 X33), X34))), 
177.30/177.50	         app_encode_app(real, real, 
177.30/177.50	           app_encode_app(real, app_encode_fun(real, real), plus_plus(real), 
177.30/177.50	             app_encode_app(X32, real, norm_norm(X32), X33)), 
177.30/177.50	           app_encode_app(X32, real, norm_norm(X32), X34)))
177.30/177.50	       | ~ real_normed_vector(X32)),
177.30/177.50	    inference('cnf', [status(esa)], [zf_stmt_68])).
177.30/177.50	tff('29', plain,
177.30/177.50	    ![X0 : complex, X1 : complex]:
177.30/177.50	      (~ $true
177.30/177.50	       | app_encode_app(real, $o, 
177.30/177.50	           app_encode_app(real, app_encode_fun(real, $o), ord_less_eq(real), 
177.30/177.50	             app_encode_app(complex, real, norm_norm(complex), 
177.30/177.50	               app_encode_app(complex, complex, 
177.30/177.50	                 app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	                   plus_plus(complex), X1), X0))), 
177.30/177.50	           app_encode_app(real, real, 
177.30/177.50	             app_encode_app(real, app_encode_fun(real, real), 
177.30/177.50	               plus_plus(real), 
177.30/177.50	               app_encode_app(complex, real, norm_norm(complex), X1)), 
177.30/177.50	             app_encode_app(complex, real, norm_norm(complex), X0)))),
177.30/177.50	    inference('sup-', [status(thm)], ['27', '28'])).
177.30/177.50	tff('30', plain,
177.30/177.50	    ![X0 : complex, X1 : complex]:
177.30/177.50	      app_encode_app(real, $o, 
177.30/177.50	        app_encode_app(real, app_encode_fun(real, $o), ord_less_eq(real), 
177.30/177.50	          app_encode_app(complex, real, norm_norm(complex), 
177.30/177.50	            app_encode_app(complex, complex, 
177.30/177.50	              app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	                plus_plus(complex), X1), X0))), 
177.30/177.50	        app_encode_app(real, real, 
177.30/177.50	          app_encode_app(real, app_encode_fun(real, real), plus_plus(real), 
177.30/177.50	            app_encode_app(complex, real, norm_norm(complex), X1)), 
177.30/177.50	          app_encode_app(complex, real, norm_norm(complex), X0))),
177.30/177.50	    inference('simplify', [status(thm)], ['29'])).
177.30/177.50	tff(zf_stmt_142, axiom,
177.30/177.50	  (![A:$tType]:
177.30/177.50	     (linorder(A) =>
177.30/177.50	      (![X1:A,Y1:A]:
177.30/177.50	         (app_encode_app(A,$o,
177.30/177.50	                         app_encode_app(A,app_encode_fun(A,$o),
177.30/177.50	                                        ord_less_eq(A),Y1),
177.30/177.50	                         X1) =>
177.30/177.50	          (~
177.30/177.50	            app_encode_app(A,$o,
177.30/177.50	                           app_encode_app(A,app_encode_fun(A,$o),ord_less(A),
177.30/177.50	                                          X1),
177.30/177.50	                           Y1))))))).
177.30/177.50	tff('31', plain,
177.30/177.50	    ![X284 : $tType, X285 : X284, X286 : X284]:
177.30/177.50	      (~ app_encode_app(X284, $o, 
177.30/177.50	           app_encode_app(X284, app_encode_fun(X284, $o), ord_less_eq(X284), 
177.30/177.50	             X285), X286)
177.30/177.50	       | ~ app_encode_app(X284, $o, 
177.30/177.50	             app_encode_app(X284, app_encode_fun(X284, $o), ord_less(X284), 
177.30/177.50	               X286), X285)
177.30/177.50	       | ~ linorder(X284)),
177.30/177.50	    inference('cnf', [status(esa)], [zf_stmt_142])).
177.30/177.50	tff('32', plain,
177.30/177.50	    ![X0 : complex, X1 : complex]:
177.30/177.50	      (~ $true
177.30/177.50	       | ~ linorder(real)
177.30/177.50	       | ~ app_encode_app(real, $o, 
177.30/177.50	             app_encode_app(real, app_encode_fun(real, $o), ord_less(real), 
177.30/177.50	               app_encode_app(real, real, 
177.30/177.50	                 app_encode_app(real, app_encode_fun(real, real), 
177.30/177.50	                   plus_plus(real), 
177.30/177.50	                   app_encode_app(complex, real, norm_norm(complex), X1)), 
177.30/177.50	                 app_encode_app(complex, real, norm_norm(complex), X0))), 
177.30/177.50	             app_encode_app(complex, real, norm_norm(complex), 
177.30/177.50	               app_encode_app(complex, complex, 
177.30/177.50	                 app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	                   plus_plus(complex), X1), X0)))),
177.30/177.50	    inference('sup-', [status(thm)], ['30', '31'])).
177.30/177.50	tff('33', plain,
177.30/177.50	    ![X0 : complex, X1 : complex]:
177.30/177.50	      (~ $true
177.30/177.50	       | ~ $true
177.30/177.50	       | ~ app_encode_app(real, $o, 
177.30/177.50	             app_encode_app(real, app_encode_fun(real, $o), ord_less(real), 
177.30/177.50	               app_encode_app(real, real, 
177.30/177.50	                 app_encode_app(real, app_encode_fun(real, real), 
177.30/177.50	                   plus_plus(real), 
177.30/177.50	                   app_encode_app(complex, real, norm_norm(complex), X1)), 
177.30/177.50	                 app_encode_app(complex, real, norm_norm(complex), X0))), 
177.30/177.50	             app_encode_app(complex, real, norm_norm(complex), 
177.30/177.50	               app_encode_app(complex, complex, 
177.30/177.50	                 app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	                   plus_plus(complex), X1), X0)))),
177.30/177.50	    inference('demod', [status(thm)], ['32', '0'])).
177.30/177.50	tff('34', plain,
177.30/177.50	    ![X0 : complex, X1 : complex]:
177.30/177.50	      ~ app_encode_app(real, $o, 
177.30/177.50	          app_encode_app(real, app_encode_fun(real, $o), ord_less(real), 
177.30/177.50	            app_encode_app(real, real, 
177.30/177.50	              app_encode_app(real, app_encode_fun(real, real), 
177.30/177.50	                plus_plus(real), 
177.30/177.50	                app_encode_app(complex, real, norm_norm(complex), X1)), 
177.30/177.50	              app_encode_app(complex, real, norm_norm(complex), X0))), 
177.30/177.50	          app_encode_app(complex, real, norm_norm(complex), 
177.30/177.50	            app_encode_app(complex, complex, 
177.30/177.50	              app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	                plus_plus(complex), X1), X0))),
177.30/177.50	    inference('simplify', [status(thm)], ['33'])).
177.30/177.50	tff('35', plain,
177.30/177.50	    ![X0 : complex, X1 : complex, X2 : complex]:
177.30/177.50	      ~ app_encode_app(real, $o, 
177.30/177.50	          app_encode_app(real, app_encode_fun(real, $o), ord_less(real), 
177.30/177.50	            app_encode_app(real, real, 
177.30/177.50	              app_encode_app(real, app_encode_fun(real, real), 
177.30/177.50	                plus_plus(real), 
177.30/177.50	                app_encode_app(complex, real, norm_norm(complex), X2)), 
177.30/177.50	              app_encode_app(real, real, 
177.30/177.50	                app_encode_app(real, app_encode_fun(real, real), 
177.30/177.50	                  times_times(real), 
177.30/177.50	                  app_encode_app(complex, real, norm_norm(complex), 
177.30/177.50	                    app_encode_app(complex, complex, 
177.30/177.50	                      app_encode_app(complex, 
177.30/177.50	                        app_encode_fun(complex, complex), 
177.30/177.50	                        plus_plus(complex), zero_zero(complex)), X1))), 
177.30/177.50	                app_encode_app(complex, real, norm_norm(complex), X0)))), 
177.30/177.50	          app_encode_app(complex, real, norm_norm(complex), 
177.30/177.50	            app_encode_app(complex, complex, 
177.30/177.50	              app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	                plus_plus(complex), X2), 
177.30/177.50	              app_encode_app(complex, complex, 
177.30/177.50	                app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	                  plus_plus(complex), zero_zero(complex)), 
177.30/177.50	                app_encode_app(complex, complex, 
177.30/177.50	                  app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	                    times_times(complex), X1), X0))))),
177.30/177.50	    inference('sup-', [status(thm)], ['26', '34'])).
177.30/177.50	tff(zf_stmt_97, axiom,
177.30/177.50	  (![A:$tType]:
177.30/177.50	     (mult_zero(A) =>
177.30/177.50	      (![A1:A]:
177.30/177.50	         (app_encode_app(A,A,
177.30/177.50	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
177.30/177.50	                                        A1),
177.30/177.50	                         zero_zero(A)) =
177.30/177.50	          zero_zero(A)))))).
177.30/177.50	tff('36', plain,
177.30/177.50	    ![X136 : $tType, X137 : X136]:
177.30/177.50	      (app_encode_app(X136, X136, 
177.30/177.50	         app_encode_app(X136, app_encode_fun(X136, X136), times_times(X136), 
177.30/177.50	           X137), zero_zero(X136))
177.30/177.50	        = zero_zero(X136)
177.30/177.50	       | ~ mult_zero(X136)),
177.30/177.50	    inference('cnf', [status(esa)], [zf_stmt_97])).
177.30/177.50	tff('37', plain,
177.30/177.50	    ![X0 : complex]:
177.30/177.50	      (~ $true
177.30/177.50	       | app_encode_app(complex, complex, 
177.30/177.50	           app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	             times_times(complex), X0), zero_zero(complex))
177.30/177.50	          = zero_zero(complex)),
177.30/177.50	    inference('sup-', [status(thm)], ['17', '36'])).
177.30/177.50	tff('38', plain,
177.30/177.50	    ![X0 : complex]:
177.30/177.50	      app_encode_app(complex, complex, 
177.30/177.50	        app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	          times_times(complex), X0), zero_zero(complex))
177.30/177.50	       = zero_zero(complex),
177.30/177.50	    inference('simplify', [status(thm)], ['37'])).
177.30/177.50	tff('39', plain,
177.30/177.50	    ![X0 : complex, X1 : complex]:
177.30/177.50	      app_encode_app(complex, complex, 
177.30/177.50	        app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	          plus_plus(complex), zero_zero(complex)), 
177.30/177.50	        app_encode_app(complex, complex, 
177.30/177.50	          app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	            times_times(complex), X0), zero_zero(complex)))
177.30/177.50	       = app_encode_app(complex, complex, 
177.30/177.50	           app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	             times_times(complex), 
177.30/177.50	             app_encode_app(complex, complex, 
177.30/177.50	               app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	                 plus_plus(complex), X1), X0)), zero_zero(complex)),
177.30/177.50	    inference('sup+', [status(thm)], ['38', '24'])).
177.30/177.50	tff('40', plain,
177.30/177.50	    app_encode_app(complex, complex, 
177.30/177.50	      app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	        plus_plus(complex), zero_zero(complex)), zero_zero(complex))
177.30/177.50	     = zero_zero(complex),
177.30/177.50	    inference('demod', [status(thm)], ['39', '38', '38'])).
177.30/177.50	tff(zf_stmt_205, axiom, (ab_semigroup_add(complex))).
177.30/177.50	tff('41', plain, ab_semigroup_add(complex),
177.30/177.50	    inference('cnf', [status(esa)], [zf_stmt_205])).
177.30/177.50	tff(zf_stmt_80, axiom,
177.30/177.50	  (![A:$tType]:
177.30/177.50	     (ab_semigroup_add(A) =>
177.30/177.50	      (![C:A,B:A,A1:A]:
177.30/177.50	         (app_encode_app(A,A,
177.30/177.50	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
177.30/177.50	                                        app_encode_app(A,A,
177.30/177.50	                                                       app_encode_app(
177.30/177.50	                                                       A,app_encode_fun(A,A),
177.30/177.50	                                                       plus_plus(A),A1),B)),
177.30/177.50	                         C) =
177.30/177.50	          app_encode_app(A,A,
177.30/177.50	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),A1),
177.30/177.50	                         app_encode_app(A,A,
177.30/177.50	                                        app_encode_app(A,app_encode_fun(A,A),
177.30/177.50	                                                       plus_plus(A),B),
177.30/177.50	                                        C))))))).
177.30/177.50	tff('42', plain,
177.30/177.50	    ![X77 : $tType, X78 : X77, X79 : X77, X80 : X77]:
177.30/177.50	      (app_encode_app(X77, X77, 
177.30/177.50	         app_encode_app(X77, app_encode_fun(X77, X77), plus_plus(X77), 
177.30/177.50	           app_encode_app(X77, X77, 
177.30/177.50	             app_encode_app(X77, app_encode_fun(X77, X77), plus_plus(X77), 
177.30/177.50	               X78), X79)), X80)
177.30/177.50	        = app_encode_app(X77, X77, 
177.30/177.50	            app_encode_app(X77, app_encode_fun(X77, X77), plus_plus(X77), 
177.30/177.50	              X78), 
177.30/177.50	            app_encode_app(X77, X77, 
177.30/177.50	              app_encode_app(X77, app_encode_fun(X77, X77), plus_plus(X77), 
177.30/177.50	                X79), X80))
177.30/177.50	       | ~ ab_semigroup_add(X77)),
177.30/177.50	    inference('cnf', [status(esa)], [zf_stmt_80])).
177.30/177.50	tff('43', plain,
177.30/177.50	    ![X0 : complex, X1 : complex, X2 : complex]:
177.30/177.50	      (~ $true
177.30/177.50	       | app_encode_app(complex, complex, 
177.30/177.50	           app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	             plus_plus(complex), 
177.30/177.50	             app_encode_app(complex, complex, 
177.30/177.50	               app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	                 plus_plus(complex), X2), X1)), X0)
177.30/177.50	          = app_encode_app(complex, complex, 
177.30/177.50	              app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	                plus_plus(complex), X2), 
177.30/177.50	              app_encode_app(complex, complex, 
177.30/177.50	                app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	                  plus_plus(complex), X1), X0))),
177.30/177.50	    inference('sup-', [status(thm)], ['41', '42'])).
177.30/177.50	tff('44', plain,
177.30/177.50	    ![X0 : complex, X1 : complex, X2 : complex]:
177.30/177.50	      app_encode_app(complex, complex, 
177.30/177.50	        app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	          plus_plus(complex), 
177.30/177.50	          app_encode_app(complex, complex, 
177.30/177.50	            app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	              plus_plus(complex), X2), X1)), X0)
177.30/177.50	       = app_encode_app(complex, complex, 
177.30/177.50	           app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	             plus_plus(complex), X2), 
177.30/177.50	           app_encode_app(complex, complex, 
177.30/177.50	             app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	               plus_plus(complex), X1), X0)),
177.30/177.50	    inference('simplify', [status(thm)], ['43'])).
177.30/177.50	tff('45', plain,
177.30/177.50	    ![X0 : complex]:
177.30/177.50	      app_encode_app(complex, complex, 
177.30/177.50	        app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	          plus_plus(complex), zero_zero(complex)), X0)
177.30/177.50	       = app_encode_app(complex, complex, 
177.30/177.50	           app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	             plus_plus(complex), zero_zero(complex)), 
177.30/177.50	           app_encode_app(complex, complex, 
177.30/177.50	             app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	               plus_plus(complex), zero_zero(complex)), X0)),
177.30/177.50	    inference('sup+', [status(thm)], ['40', '44'])).
177.30/177.50	tff(zf_stmt_73, axiom,
177.30/177.50	  (![A:$tType]:
177.30/177.50	     (cancel_semigroup_add(A) =>
177.30/177.50	      (![Ca:A,B2:A,A2:A]:
177.30/177.50	         ((app_encode_app(A,A,
177.30/177.50	                          app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
177.30/177.50	                                         A2),
177.30/177.50	                          B2) =
177.30/177.50	           app_encode_app(A,A,
177.30/177.50	                          app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
177.30/177.50	                                         A2),
177.30/177.50	                          Ca)) <=>
177.30/177.50	          (B2 = Ca)))))).
177.30/177.50	tff('46', plain,
177.30/177.50	    ![X47 : $tType, X48 : X47, X49 : X47, X51 : X47]:
177.30/177.50	      (app_encode_app(X47, X47, 
177.30/177.50	         app_encode_app(X47, app_encode_fun(X47, X47), plus_plus(X47), X51), 
177.30/177.50	         X49)
177.30/177.50	        != app_encode_app(X47, X47, 
177.30/177.50	             app_encode_app(X47, app_encode_fun(X47, X47), plus_plus(X47), 
177.30/177.50	               X51), X48)
177.30/177.50	       | X49 = X48
177.30/177.50	       | ~ cancel_semigroup_add(X47)),
177.30/177.50	    inference('cnf', [status(esa)], [zf_stmt_73])).
177.30/177.50	tff('47', plain,
177.30/177.50	    ![X0 : complex, X1 : complex]:
177.30/177.50	      (app_encode_app(complex, complex, 
177.30/177.50	         app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	           plus_plus(complex), zero_zero(complex)), X1)
177.30/177.50	        != app_encode_app(complex, complex, 
177.30/177.50	             app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	               plus_plus(complex), zero_zero(complex)), X0)
177.30/177.50	       | ~ cancel_semigroup_add(complex)
177.30/177.50	       | X1
177.30/177.50	          = app_encode_app(complex, complex, 
177.30/177.50	              app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	                plus_plus(complex), zero_zero(complex)), X0)),
177.30/177.50	    inference('sup-', [status(thm)], ['45', '46'])).
177.30/177.50	tff(zf_stmt_203, axiom, (cancel_semigroup_add(complex))).
177.30/177.50	tff('48', plain, cancel_semigroup_add(complex),
177.30/177.50	    inference('cnf', [status(esa)], [zf_stmt_203])).
177.30/177.50	tff('49', plain,
177.30/177.50	    ![X0 : complex, X1 : complex]:
177.30/177.50	      (app_encode_app(complex, complex, 
177.30/177.50	         app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	           plus_plus(complex), zero_zero(complex)), X1)
177.30/177.50	        != app_encode_app(complex, complex, 
177.30/177.50	             app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	               plus_plus(complex), zero_zero(complex)), X0)
177.30/177.50	       | ~ $true
177.30/177.50	       | X1
177.30/177.50	          = app_encode_app(complex, complex, 
177.30/177.50	              app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	                plus_plus(complex), zero_zero(complex)), X0)),
177.30/177.50	    inference('demod', [status(thm)], ['47', '48'])).
177.30/177.50	tff('50', plain,
177.30/177.50	    ![X0 : complex, X1 : complex]:
177.30/177.50	      (X1
177.30/177.50	        = app_encode_app(complex, complex, 
177.30/177.50	            app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	              plus_plus(complex), zero_zero(complex)), X0)
177.30/177.50	       | app_encode_app(complex, complex, 
177.30/177.50	           app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	             plus_plus(complex), zero_zero(complex)), X1)
177.30/177.50	          != app_encode_app(complex, complex, 
177.30/177.50	               app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	                 plus_plus(complex), zero_zero(complex)), X0)),
177.30/177.50	    inference('simplify', [status(thm)], ['49'])).
177.30/177.50	tff('51', plain,
177.30/177.50	    ![X0 : complex]:
177.30/177.50	      X0
177.30/177.50	       = app_encode_app(complex, complex, 
177.30/177.50	           app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	             plus_plus(complex), zero_zero(complex)), X0),
177.30/177.50	    inference('eq_res', [status(thm)], ['50'])).
177.30/177.50	tff('52', plain,
177.30/177.50	    ![X0 : complex, X1 : complex, X2 : complex]:
177.30/177.50	      ~ app_encode_app(real, $o, 
177.30/177.50	          app_encode_app(real, app_encode_fun(real, $o), ord_less(real), 
177.30/177.50	            app_encode_app(real, real, 
177.30/177.50	              app_encode_app(real, app_encode_fun(real, real), 
177.30/177.50	                plus_plus(real), 
177.30/177.50	                app_encode_app(complex, real, norm_norm(complex), X2)), 
177.30/177.50	              app_encode_app(real, real, 
177.30/177.50	                app_encode_app(real, app_encode_fun(real, real), 
177.30/177.50	                  times_times(real), 
177.30/177.50	                  app_encode_app(complex, real, norm_norm(complex), X1)), 
177.30/177.50	                app_encode_app(complex, real, norm_norm(complex), X0)))), 
177.30/177.50	          app_encode_app(complex, real, norm_norm(complex), 
177.30/177.50	            app_encode_app(complex, complex, 
177.30/177.50	              app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	                plus_plus(complex), X2), 
177.30/177.50	              app_encode_app(complex, complex, 
177.30/177.50	                app_encode_app(complex, app_encode_fun(complex, complex), 
177.30/177.50	                  times_times(complex), X1), X0)))),
177.30/177.50	    inference('demod', [status(thm)], ['35', '51', '51'])).
177.30/177.50	tff('53', plain, ~ $true, inference('sup-', [status(thm)], ['16', '52'])).
177.30/177.50	tff('54', plain, $false, inference('simplify', [status(thm)], ['53'])).
177.30/177.50	
177.30/177.50	% SZS output end Refutation
177.30/177.51	EOF
