0.00/0.00	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : app
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : kbo
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n159.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
0.00/0.20	% DateTime   : Fri Feb  2 14:28:10 CST 2018
2.04/2.23	% done 1231 iterations in 2.028s
2.04/2.23	% SZS status Theorem for 'stdin'
2.04/2.23	% SZS output start Refutation
2.04/2.24	tff(zf_stmt_168, conjecture,
2.04/2.24	  (app_encode_app(complex,complex,
2.04/2.24	                  app_encode_app(complex,app_encode_fun(complex,complex),
2.04/2.24	                                 inverse_divide(complex),
2.04/2.24	                                 app_encode_app(complex,complex,
2.04/2.24	                                                app_encode_app(complex,
2.04/2.24	                                                               app_encode_fun(
2.04/2.24	                                                               complex,
2.04/2.24	                                                               complex),
2.04/2.24	                                                               minus_minus(
2.04/2.24	                                                               complex),
2.04/2.24	                                                               app_encode_app(
2.04/2.24	                                                               nat,complex,
2.04/2.24	                                                               app_encode_app(
2.04/2.24	                                                               complex,
2.04/2.24	                                                               app_encode_fun(
2.04/2.24	                                                               nat,complex),
2.04/2.24	                                                               power_power(
2.04/2.24	                                                               complex),
2.04/2.24	                                                               app_encode_app(
2.04/2.24	                                                               nat,complex,
2.04/2.24	                                                               app_encode_app(
2.04/2.24	                                                               complex,
2.04/2.24	                                                               app_encode_fun(
2.04/2.24	                                                               nat,complex),
2.04/2.24	                                                               power_power(
2.04/2.24	                                                               complex),
2.04/2.24	                                                               app_encode_app(
2.04/2.24	                                                               nat,complex,
2.04/2.24	                                                               fFT_Mirabelle_root,
2.04/2.24	                                                               n)),n)),k)),
2.04/2.24	                                                one_one(complex))),
2.04/2.24	                  app_encode_app(complex,complex,
2.04/2.24	                                 app_encode_app(complex,
2.04/2.24	                                                app_encode_fun(complex,
2.04/2.24	                                                               complex),
2.04/2.24	                                                minus_minus(complex),
2.04/2.24	                                                app_encode_app(nat,complex,
2.04/2.24	                                                               app_encode_app(
2.04/2.24	                                                               complex,
2.04/2.24	                                                               app_encode_fun(
2.04/2.24	                                                               nat,complex),
2.04/2.24	                                                               power_power(
2.04/2.24	                                                               complex),
2.04/2.24	                                                               app_encode_app(
2.04/2.24	                                                               nat,complex,
2.04/2.24	                                                               fFT_Mirabelle_root,
2.04/2.24	                                                               n)),k)),
2.04/2.24	                                 one_one(complex))) =
2.04/2.24	   zero_zero(complex))).
2.04/2.24	tff(zf_stmt_0, negated_conjecture,
2.04/2.24	  (app_encode_app(complex,complex,
2.04/2.24	                  app_encode_app(complex,app_encode_fun(complex,complex),
2.04/2.24	                                 inverse_divide(complex),
2.04/2.24	                                 app_encode_app(complex,complex,
2.04/2.24	                                                app_encode_app(complex,
2.04/2.24	                                                               app_encode_fun(
2.04/2.24	                                                               complex,
2.04/2.24	                                                               complex),
2.04/2.24	                                                               minus_minus(
2.04/2.24	                                                               complex),
2.04/2.24	                                                               app_encode_app(
2.04/2.24	                                                               nat,complex,
2.04/2.24	                                                               app_encode_app(
2.04/2.24	                                                               complex,
2.04/2.24	                                                               app_encode_fun(
2.04/2.24	                                                               nat,complex),
2.04/2.24	                                                               power_power(
2.04/2.24	                                                               complex),
2.04/2.24	                                                               app_encode_app(
2.04/2.24	                                                               nat,complex,
2.04/2.24	                                                               app_encode_app(
2.04/2.24	                                                               complex,
2.04/2.24	                                                               app_encode_fun(
2.04/2.24	                                                               nat,complex),
2.04/2.24	                                                               power_power(
2.04/2.24	                                                               complex),
2.04/2.24	                                                               app_encode_app(
2.04/2.24	                                                               nat,complex,
2.04/2.24	                                                               fFT_Mirabelle_root,
2.04/2.24	                                                               n)),n)),k)),
2.04/2.24	                                                one_one(complex))),
2.04/2.24	                  app_encode_app(complex,complex,
2.04/2.24	                                 app_encode_app(complex,
2.04/2.24	                                                app_encode_fun(complex,
2.04/2.24	                                                               complex),
2.04/2.24	                                                minus_minus(complex),
2.04/2.24	                                                app_encode_app(nat,complex,
2.04/2.24	                                                               app_encode_app(
2.04/2.24	                                                               complex,
2.04/2.24	                                                               app_encode_fun(
2.04/2.24	                                                               nat,complex),
2.04/2.24	                                                               power_power(
2.04/2.24	                                                               complex),
2.04/2.24	                                                               app_encode_app(
2.04/2.24	                                                               nat,complex,
2.04/2.24	                                                               fFT_Mirabelle_root,
2.04/2.24	                                                               n)),k)),
2.04/2.24	                                 one_one(complex))) !=
2.04/2.24	   zero_zero(complex))).
2.04/2.24	tff('0', plain,
2.04/2.24	    app_encode_app(complex, complex, 
2.04/2.24	      app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	        inverse_divide(complex), 
2.04/2.24	        app_encode_app(complex, complex, 
2.04/2.24	          app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	            minus_minus(complex), 
2.04/2.24	            app_encode_app(nat, complex, 
2.04/2.24	              app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	                power_power(complex), 
2.04/2.24	                app_encode_app(nat, complex, 
2.04/2.24	                  app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	                    power_power(complex), 
2.04/2.24	                    app_encode_app(nat, complex, fFT_Mirabelle_root, n)), n)), 
2.04/2.24	              k)), one_one(complex))), 
2.04/2.24	      app_encode_app(complex, complex, 
2.04/2.24	        app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	          minus_minus(complex), 
2.04/2.24	          app_encode_app(nat, complex, 
2.04/2.24	            app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	              power_power(complex), 
2.04/2.24	              app_encode_app(nat, complex, fFT_Mirabelle_root, n)), k)), 
2.04/2.24	        one_one(complex)))
2.04/2.24	     != zero_zero(complex),
2.04/2.24	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.04/2.24	tff(zf_stmt_45, axiom,
2.04/2.24	  (![N:nat]:
2.04/2.24	     (app_encode_app(nat,complex,
2.04/2.24	                     app_encode_app(complex,app_encode_fun(nat,complex),
2.04/2.24	                                    power_power(complex),
2.04/2.24	                                    app_encode_app(nat,complex,
2.04/2.24	                                                   fFT_Mirabelle_root,N)),
2.04/2.24	                     N) =
2.04/2.24	      one_one(complex)))).
2.04/2.24	tff('1', plain,
2.04/2.24	    ![X1 : nat]:
2.04/2.24	      app_encode_app(nat, complex, 
2.04/2.24	        app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	          power_power(complex), 
2.04/2.24	          app_encode_app(nat, complex, fFT_Mirabelle_root, X1)), X1)
2.04/2.24	       = one_one(complex),
2.04/2.24	    inference('cnf', [status(esa)], [zf_stmt_45])).
2.04/2.24	tff(zf_stmt_52, axiom,
2.04/2.24	  (![A:$tType]:
2.04/2.24	     (field_inverse_zero(A) =>
2.04/2.24	      (![N:nat,A1:A]:
2.04/2.24	         (app_encode_app(A,A,
2.04/2.24	                         app_encode_app(A,app_encode_fun(A,A),
2.04/2.24	                                        inverse_divide(A),one_one(A)),
2.04/2.24	                         app_encode_app(nat,A,
2.04/2.24	                                        app_encode_app(A,
2.04/2.24	                                                       app_encode_fun(nat,A),
2.04/2.24	                                                       power_power(A),A1),
2.04/2.24	                                        N)) =
2.04/2.24	          app_encode_app(nat,A,
2.04/2.24	                         app_encode_app(A,app_encode_fun(nat,A),
2.04/2.24	                                        power_power(A),
2.04/2.24	                                        app_encode_app(A,A,
2.04/2.24	                                                       app_encode_app(
2.04/2.24	                                                       A,app_encode_fun(A,A),
2.04/2.24	                                                       inverse_divide(A),
2.04/2.24	                                                       one_one(A)),A1)),
2.04/2.24	                         N)))))).
2.04/2.24	tff('2', plain,
2.04/2.24	    ![X17 : $tType, X18 : X17, X19 : nat]:
2.04/2.24	      (app_encode_app(X17, X17, 
2.04/2.24	         app_encode_app(X17, app_encode_fun(X17, X17), inverse_divide(X17), 
2.04/2.24	           one_one(X17)), 
2.04/2.24	         app_encode_app(nat, X17, 
2.04/2.24	           app_encode_app(X17, app_encode_fun(nat, X17), power_power(X17), 
2.04/2.24	             X18), X19))
2.04/2.24	        = app_encode_app(nat, X17, 
2.04/2.24	            app_encode_app(X17, app_encode_fun(nat, X17), power_power(X17), 
2.04/2.24	              app_encode_app(X17, X17, 
2.04/2.24	                app_encode_app(X17, app_encode_fun(X17, X17), 
2.04/2.24	                  inverse_divide(X17), one_one(X17)), X18)), X19)
2.04/2.24	       | ~ field_inverse_zero(X17)),
2.04/2.24	    inference('cnf', [status(esa)], [zf_stmt_52])).
2.04/2.24	tff('3', plain,
2.04/2.24	    ![X0 : nat]:
2.04/2.24	      (app_encode_app(complex, complex, 
2.04/2.24	         app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	           inverse_divide(complex), one_one(complex)), one_one(complex))
2.04/2.24	        = app_encode_app(nat, complex, 
2.04/2.24	            app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	              power_power(complex), 
2.04/2.24	              app_encode_app(complex, complex, 
2.04/2.24	                app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	                  inverse_divide(complex), one_one(complex)), 
2.04/2.24	                app_encode_app(nat, complex, fFT_Mirabelle_root, X0))), X0)
2.04/2.24	       | ~ field_inverse_zero(complex)),
2.04/2.24	    inference('sup+', [status(thm)], ['1', '2'])).
2.04/2.24	tff(zf_stmt_153, axiom, (field_inverse_zero(complex))).
2.04/2.24	tff('4', plain, field_inverse_zero(complex),
2.04/2.24	    inference('cnf', [status(esa)], [zf_stmt_153])).
2.04/2.24	tff('5', plain,
2.04/2.24	    ![X0 : nat]:
2.04/2.24	      (app_encode_app(complex, complex, 
2.04/2.24	         app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	           inverse_divide(complex), one_one(complex)), one_one(complex))
2.04/2.24	        = app_encode_app(nat, complex, 
2.04/2.24	            app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	              power_power(complex), 
2.04/2.24	              app_encode_app(complex, complex, 
2.04/2.24	                app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	                  inverse_divide(complex), one_one(complex)), 
2.04/2.24	                app_encode_app(nat, complex, fFT_Mirabelle_root, X0))), X0)
2.04/2.24	       | ~ $true),
2.04/2.24	    inference('demod', [status(thm)], ['3', '4'])).
2.04/2.24	tff('6', plain,
2.04/2.24	    ![X0 : nat]:
2.04/2.24	      app_encode_app(complex, complex, 
2.04/2.24	        app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	          inverse_divide(complex), one_one(complex)), one_one(complex))
2.04/2.24	       = app_encode_app(nat, complex, 
2.04/2.24	           app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	             power_power(complex), 
2.04/2.24	             app_encode_app(complex, complex, 
2.04/2.24	               app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	                 inverse_divide(complex), one_one(complex)), 
2.04/2.24	               app_encode_app(nat, complex, fFT_Mirabelle_root, X0))), X0),
2.04/2.24	    inference('simplify', [status(thm)], ['5'])).
2.04/2.24	tff(zf_stmt_87, axiom,
2.04/2.24	  (![A:$tType]:
2.04/2.24	     (division_ring(A) =>
2.04/2.24	      (![A1:A]:
2.04/2.24	         (app_encode_app(A,A,
2.04/2.24	                         app_encode_app(A,app_encode_fun(A,A),
2.04/2.24	                                        inverse_divide(A),A1),
2.04/2.24	                         one_one(A)) =
2.04/2.24	          A1))))).
2.04/2.24	tff('7', plain,
2.04/2.24	    ![X134 : $tType, X135 : X134]:
2.04/2.24	      (app_encode_app(X134, X134, 
2.04/2.24	         app_encode_app(X134, app_encode_fun(X134, X134), 
2.04/2.24	           inverse_divide(X134), X135), one_one(X134))
2.04/2.24	        = X135
2.04/2.24	       | ~ division_ring(X134)),
2.04/2.24	    inference('cnf', [status(esa)], [zf_stmt_87])).
2.04/2.24	tff(zf_stmt_63, axiom,
2.04/2.24	  (![A:$tType]:
2.04/2.24	     (monoid_mult(A) =>
2.04/2.24	      (![A1:A]:
2.04/2.24	         (app_encode_app(nat,A,
2.04/2.24	                         app_encode_app(A,app_encode_fun(nat,A),
2.04/2.24	                                        power_power(A),A1),
2.04/2.24	                         one_one(nat)) =
2.04/2.24	          A1))))).
2.04/2.24	tff('8', plain,
2.04/2.24	    ![X48 : $tType, X49 : X48]:
2.04/2.24	      (app_encode_app(nat, X48, 
2.04/2.24	         app_encode_app(X48, app_encode_fun(nat, X48), power_power(X48), X49), 
2.04/2.24	         one_one(nat))
2.04/2.24	        = X49
2.04/2.24	       | ~ monoid_mult(X48)),
2.04/2.24	    inference('cnf', [status(esa)], [zf_stmt_63])).
2.04/2.24	tff('9', plain,
2.04/2.24	    (one_one(complex)
2.04/2.24	      = app_encode_app(nat, complex, fFT_Mirabelle_root, one_one(nat))
2.04/2.24	     | ~ monoid_mult(complex)),
2.04/2.24	    inference('sup+', [status(thm)], ['1', '8'])).
2.04/2.24	tff(zf_stmt_158, axiom, (monoid_mult(complex))).
2.04/2.24	tff('10', plain, monoid_mult(complex),
2.04/2.24	    inference('cnf', [status(esa)], [zf_stmt_158])).
2.04/2.24	tff('11', plain,
2.04/2.24	    (one_one(complex)
2.04/2.24	      = app_encode_app(nat, complex, fFT_Mirabelle_root, one_one(nat))
2.04/2.24	     | ~ $true),
2.04/2.24	    inference('demod', [status(thm)], ['9', '10'])).
2.04/2.24	tff('12', plain,
2.04/2.24	    one_one(complex)
2.04/2.24	     = app_encode_app(nat, complex, fFT_Mirabelle_root, one_one(nat)),
2.04/2.24	    inference('simplify', [status(thm)], ['11'])).
2.04/2.24	tff('13', plain,
2.04/2.24	    app_encode_app(nat, complex, 
2.04/2.24	      app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	        power_power(complex), one_one(complex)), one_one(nat))
2.04/2.24	     = one_one(complex),
2.04/2.24	    inference('sup+', [status(thm)], ['12', '1'])).
2.04/2.24	tff('14', plain,
2.04/2.24	    (app_encode_app(complex, complex, 
2.04/2.24	       app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	         inverse_divide(complex), one_one(complex)), one_one(complex))
2.04/2.24	      = app_encode_app(nat, complex, 
2.04/2.24	          app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	            power_power(complex), 
2.04/2.24	            app_encode_app(complex, complex, 
2.04/2.24	              app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	                inverse_divide(complex), one_one(complex)), one_one(complex))), 
2.04/2.24	          one_one(nat))
2.04/2.24	     | ~ field_inverse_zero(complex)),
2.04/2.24	    inference('sup+', [status(thm)], ['13', '2'])).
2.04/2.24	tff('15', plain,
2.04/2.24	    (app_encode_app(complex, complex, 
2.04/2.24	       app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	         inverse_divide(complex), one_one(complex)), one_one(complex))
2.04/2.24	      = app_encode_app(nat, complex, 
2.04/2.24	          app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	            power_power(complex), 
2.04/2.24	            app_encode_app(complex, complex, 
2.04/2.24	              app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	                inverse_divide(complex), one_one(complex)), one_one(complex))), 
2.04/2.24	          one_one(nat))
2.04/2.24	     | ~ $true),
2.04/2.24	    inference('demod', [status(thm)], ['14', '4'])).
2.04/2.24	tff('16', plain,
2.04/2.24	    app_encode_app(complex, complex, 
2.04/2.24	      app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	        inverse_divide(complex), one_one(complex)), one_one(complex))
2.04/2.24	     = app_encode_app(nat, complex, 
2.04/2.24	         app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	           power_power(complex), 
2.04/2.24	           app_encode_app(complex, complex, 
2.04/2.24	             app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	               inverse_divide(complex), one_one(complex)), one_one(complex))), 
2.04/2.24	         one_one(nat)),
2.04/2.24	    inference('simplify', [status(thm)], ['15'])).
2.04/2.24	tff('17', plain,
2.04/2.24	    (app_encode_app(complex, complex, 
2.04/2.24	       app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	         inverse_divide(complex), one_one(complex)), one_one(complex))
2.04/2.24	      = app_encode_app(nat, complex, 
2.04/2.24	          app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	            power_power(complex), one_one(complex)), one_one(nat))
2.04/2.24	     | ~ division_ring(complex)),
2.04/2.24	    inference('sup+', [status(thm)], ['7', '16'])).
2.04/2.24	tff(zf_stmt_156, axiom, (division_ring(complex))).
2.04/2.24	tff('18', plain, division_ring(complex),
2.04/2.24	    inference('cnf', [status(esa)], [zf_stmt_156])).
2.04/2.24	tff('19', plain,
2.04/2.24	    (app_encode_app(complex, complex, 
2.04/2.24	       app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	         inverse_divide(complex), one_one(complex)), one_one(complex))
2.04/2.24	      = one_one(complex)
2.04/2.24	     | ~ $true),
2.04/2.24	    inference('demod', [status(thm)], ['17', '13', '18'])).
2.04/2.24	tff('20', plain,
2.04/2.24	    app_encode_app(complex, complex, 
2.04/2.24	      app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	        inverse_divide(complex), one_one(complex)), one_one(complex))
2.04/2.24	     = one_one(complex),
2.04/2.24	    inference('simplify', [status(thm)], ['19'])).
2.04/2.24	tff('21', plain,
2.04/2.24	    ![X0 : nat]:
2.04/2.24	      one_one(complex)
2.04/2.24	       = app_encode_app(nat, complex, 
2.04/2.24	           app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	             power_power(complex), 
2.04/2.24	             app_encode_app(complex, complex, 
2.04/2.24	               app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	                 inverse_divide(complex), one_one(complex)), 
2.04/2.24	               app_encode_app(nat, complex, fFT_Mirabelle_root, X0))), X0),
2.04/2.24	    inference('demod', [status(thm)], ['6', '20'])).
2.04/2.24	tff(zf_stmt_53, axiom,
2.04/2.24	  (![A:$tType]:
2.04/2.24	     (field(A) =>
2.04/2.24	      (![N:nat,A1:A,B:A]:
2.04/2.24	         ((B != zero_zero(A)) =>
2.04/2.24	          (app_encode_app(nat,A,
2.04/2.24	                          app_encode_app(A,app_encode_fun(nat,A),
2.04/2.24	                                         power_power(A),
2.04/2.24	                                         app_encode_app(A,A,
2.04/2.24	                                                        app_encode_app(
2.04/2.24	                                                        A,
2.04/2.24	                                                        app_encode_fun(A,A),
2.04/2.24	                                                        inverse_divide(A),A1),
2.04/2.24	                                                        B)),
2.04/2.24	                          N) =
2.04/2.24	           app_encode_app(A,A,
2.04/2.24	                          app_encode_app(A,app_encode_fun(A,A),
2.04/2.24	                                         inverse_divide(A),
2.04/2.24	                                         app_encode_app(nat,A,
2.04/2.24	                                                        app_encode_app(
2.04/2.24	                                                        A,
2.04/2.24	                                                        app_encode_fun(nat,A),
2.04/2.24	                                                        power_power(A),A1),N)),
2.04/2.24	                          app_encode_app(nat,A,
2.04/2.24	                                         app_encode_app(A,
2.04/2.24	                                                        app_encode_fun(nat,A),
2.04/2.24	                                                        power_power(A),B),
2.04/2.24	                                         N)))))))).
2.04/2.24	tff('22', plain,
2.04/2.24	    ![X20 : $tType, X21 : X20, X22 : X20, X23 : nat]:
2.04/2.24	      (X21 = zero_zero(X20)
2.04/2.24	       | app_encode_app(nat, X20, 
2.04/2.24	           app_encode_app(X20, app_encode_fun(nat, X20), power_power(X20), 
2.04/2.24	             app_encode_app(X20, X20, 
2.04/2.24	               app_encode_app(X20, app_encode_fun(X20, X20), 
2.04/2.24	                 inverse_divide(X20), X22), X21)), X23)
2.04/2.24	          = app_encode_app(X20, X20, 
2.04/2.24	              app_encode_app(X20, app_encode_fun(X20, X20), 
2.04/2.24	                inverse_divide(X20), 
2.04/2.24	                app_encode_app(nat, X20, 
2.04/2.24	                  app_encode_app(X20, app_encode_fun(nat, X20), 
2.04/2.24	                    power_power(X20), X22), X23)), 
2.04/2.24	              app_encode_app(nat, X20, 
2.04/2.24	                app_encode_app(X20, app_encode_fun(nat, X20), 
2.04/2.24	                  power_power(X20), X21), X23))
2.04/2.24	       | ~ field(X20)),
2.04/2.24	    inference('cnf', [status(esa)], [zf_stmt_53])).
2.04/2.24	tff('23', plain,
2.04/2.24	    ![X0 : nat, X1 : complex]:
2.04/2.24	      (app_encode_app(nat, complex, 
2.04/2.24	         app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	           power_power(complex), 
2.04/2.24	           app_encode_app(complex, complex, 
2.04/2.24	             app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	               inverse_divide(complex), X1), 
2.04/2.24	             app_encode_app(nat, complex, fFT_Mirabelle_root, X0))), X0)
2.04/2.24	        = app_encode_app(complex, complex, 
2.04/2.24	            app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	              inverse_divide(complex), 
2.04/2.24	              app_encode_app(nat, complex, 
2.04/2.24	                app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	                  power_power(complex), X1), X0)), one_one(complex))
2.04/2.24	       | ~ field(complex)
2.04/2.24	       | app_encode_app(nat, complex, fFT_Mirabelle_root, X0)
2.04/2.24	          = zero_zero(complex)),
2.04/2.24	    inference('sup+', [status(thm)], ['1', '22'])).
2.04/2.24	tff(zf_stmt_162, axiom, (field(complex))).
2.04/2.24	tff('24', plain, field(complex),
2.04/2.24	    inference('cnf', [status(esa)], [zf_stmt_162])).
2.04/2.24	tff('25', plain,
2.04/2.24	    ![X0 : nat, X1 : complex]:
2.04/2.24	      (app_encode_app(nat, complex, 
2.04/2.24	         app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	           power_power(complex), 
2.04/2.24	           app_encode_app(complex, complex, 
2.04/2.24	             app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	               inverse_divide(complex), X1), 
2.04/2.24	             app_encode_app(nat, complex, fFT_Mirabelle_root, X0))), X0)
2.04/2.24	        = app_encode_app(complex, complex, 
2.04/2.24	            app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	              inverse_divide(complex), 
2.04/2.24	              app_encode_app(nat, complex, 
2.04/2.24	                app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	                  power_power(complex), X1), X0)), one_one(complex))
2.04/2.24	       | ~ $true
2.04/2.24	       | app_encode_app(nat, complex, fFT_Mirabelle_root, X0)
2.04/2.24	          = zero_zero(complex)),
2.04/2.24	    inference('demod', [status(thm)], ['23', '24'])).
2.04/2.24	tff('26', plain,
2.04/2.24	    ![X0 : nat, X1 : complex]:
2.04/2.24	      (app_encode_app(nat, complex, fFT_Mirabelle_root, X0)
2.04/2.24	        = zero_zero(complex)
2.04/2.24	       | app_encode_app(nat, complex, 
2.04/2.24	           app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	             power_power(complex), 
2.04/2.24	             app_encode_app(complex, complex, 
2.04/2.24	               app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	                 inverse_divide(complex), X1), 
2.04/2.24	               app_encode_app(nat, complex, fFT_Mirabelle_root, X0))), X0)
2.04/2.24	          = app_encode_app(complex, complex, 
2.04/2.24	              app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	                inverse_divide(complex), 
2.04/2.24	                app_encode_app(nat, complex, 
2.04/2.24	                  app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	                    power_power(complex), X1), X0)), one_one(complex))),
2.04/2.24	    inference('simplify', [status(thm)], ['25'])).
2.04/2.24	tff(zf_stmt_44, axiom,
2.04/2.24	  (![N:nat]:
2.04/2.24	     (app_encode_app(nat,complex,fFT_Mirabelle_root,N) != zero_zero(complex)))).
2.04/2.24	tff('27', plain,
2.04/2.24	    ![X0 : nat]:
2.04/2.24	      app_encode_app(nat, complex, fFT_Mirabelle_root, X0)
2.04/2.24	       != zero_zero(complex),
2.04/2.24	    inference('cnf', [status(esa)], [zf_stmt_44])).
2.04/2.24	tff('28', plain,
2.04/2.24	    ![X0 : nat, X1 : complex]:
2.04/2.24	      app_encode_app(nat, complex, 
2.04/2.24	        app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	          power_power(complex), 
2.04/2.24	          app_encode_app(complex, complex, 
2.04/2.24	            app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	              inverse_divide(complex), X1), 
2.04/2.24	            app_encode_app(nat, complex, fFT_Mirabelle_root, X0))), X0)
2.04/2.24	       = app_encode_app(complex, complex, 
2.04/2.24	           app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	             inverse_divide(complex), 
2.04/2.24	             app_encode_app(nat, complex, 
2.04/2.24	               app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	                 power_power(complex), X1), X0)), one_one(complex)),
2.04/2.24	    inference('simplify_reflect-', [status(thm)], ['26', '27'])).
2.04/2.24	tff('29', plain,
2.04/2.24	    ![X0 : complex]:
2.04/2.24	      (app_encode_app(nat, complex, 
2.04/2.24	         app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	           power_power(complex), 
2.04/2.24	           app_encode_app(complex, complex, 
2.04/2.24	             app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	               inverse_divide(complex), X0), one_one(complex))), 
2.04/2.24	         one_one(nat))
2.04/2.24	        = app_encode_app(complex, complex, 
2.04/2.24	            app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	              inverse_divide(complex), 
2.04/2.24	              app_encode_app(nat, complex, 
2.04/2.24	                app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	                  power_power(complex), X0), one_one(nat))), 
2.04/2.24	            one_one(complex))
2.04/2.24	       | ~ field(complex)
2.04/2.24	       | one_one(complex) = zero_zero(complex)),
2.04/2.24	    inference('sup+', [status(thm)], ['13', '22'])).
2.04/2.24	tff('30', plain,
2.04/2.24	    ![X0 : complex]:
2.04/2.24	      (app_encode_app(nat, complex, 
2.04/2.24	         app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	           power_power(complex), 
2.04/2.24	           app_encode_app(complex, complex, 
2.04/2.24	             app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	               inverse_divide(complex), X0), one_one(complex))), 
2.04/2.24	         one_one(nat))
2.04/2.24	        = app_encode_app(complex, complex, 
2.04/2.24	            app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	              inverse_divide(complex), 
2.04/2.24	              app_encode_app(nat, complex, 
2.04/2.24	                app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	                  power_power(complex), X0), one_one(nat))), 
2.04/2.24	            one_one(complex))
2.04/2.24	       | ~ $true
2.04/2.24	       | one_one(complex) = zero_zero(complex)),
2.04/2.24	    inference('demod', [status(thm)], ['29', '24'])).
2.04/2.24	tff('31', plain,
2.04/2.24	    ![X0 : complex]:
2.04/2.24	      (one_one(complex) = zero_zero(complex)
2.04/2.24	       | app_encode_app(nat, complex, 
2.04/2.24	           app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	             power_power(complex), 
2.04/2.24	             app_encode_app(complex, complex, 
2.04/2.24	               app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	                 inverse_divide(complex), X0), one_one(complex))), 
2.04/2.24	           one_one(nat))
2.04/2.24	          = app_encode_app(complex, complex, 
2.04/2.24	              app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	                inverse_divide(complex), 
2.04/2.24	                app_encode_app(nat, complex, 
2.04/2.24	                  app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	                    power_power(complex), X0), one_one(nat))), 
2.04/2.24	              one_one(complex))),
2.04/2.24	    inference('simplify', [status(thm)], ['30'])).
2.04/2.24	tff(zf_stmt_157, axiom, (zero_neq_one(complex))).
2.04/2.24	tff('32', plain, zero_neq_one(complex),
2.04/2.24	    inference('cnf', [status(esa)], [zf_stmt_157])).
2.04/2.24	tff(zf_stmt_113, axiom,
2.04/2.24	  (![A:$tType]: (zero_neq_one(A) => (one_one(A) != zero_zero(A))))).
2.04/2.24	tff('33', plain,
2.04/2.24	    ![X191 : $tType]:
2.04/2.24	      (one_one(X191) != zero_zero(X191) | ~ zero_neq_one(X191)),
2.04/2.24	    inference('cnf', [status(esa)], [zf_stmt_113])).
2.04/2.24	tff('34', plain, (~ $true | one_one(complex) != zero_zero(complex)),
2.04/2.24	    inference('sup-', [status(thm)], ['32', '33'])).
2.04/2.24	tff('35', plain, one_one(complex) != zero_zero(complex),
2.04/2.24	    inference('simplify', [status(thm)], ['34'])).
2.04/2.24	tff('36', plain,
2.04/2.24	    ![X0 : complex]:
2.04/2.24	      app_encode_app(nat, complex, 
2.04/2.24	        app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	          power_power(complex), 
2.04/2.24	          app_encode_app(complex, complex, 
2.04/2.24	            app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	              inverse_divide(complex), X0), one_one(complex))), one_one(nat))
2.04/2.24	       = app_encode_app(complex, complex, 
2.04/2.24	           app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	             inverse_divide(complex), 
2.04/2.24	             app_encode_app(nat, complex, 
2.04/2.24	               app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	                 power_power(complex), X0), one_one(nat))), one_one(complex)),
2.04/2.24	    inference('simplify_reflect-', [status(thm)], ['31', '35'])).
2.04/2.24	tff('37', plain,
2.04/2.24	    ![X0 : complex]:
2.04/2.24	      (app_encode_app(nat, complex, 
2.04/2.24	         app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	           power_power(complex), 
2.04/2.24	           app_encode_app(complex, complex, 
2.04/2.24	             app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	               inverse_divide(complex), X0), one_one(complex))), 
2.04/2.24	         one_one(nat))
2.04/2.24	        = app_encode_app(nat, complex, 
2.04/2.24	            app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	              power_power(complex), X0), one_one(nat))
2.04/2.24	       | ~ division_ring(complex)),
2.04/2.24	    inference('sup+', [status(thm)], ['7', '36'])).
2.04/2.24	tff('38', plain,
2.04/2.24	    ![X0 : complex]:
2.04/2.24	      (app_encode_app(nat, complex, 
2.04/2.24	         app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	           power_power(complex), 
2.04/2.24	           app_encode_app(complex, complex, 
2.04/2.24	             app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	               inverse_divide(complex), X0), one_one(complex))), 
2.04/2.24	         one_one(nat))
2.04/2.24	        = app_encode_app(nat, complex, 
2.04/2.24	            app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	              power_power(complex), X0), one_one(nat))
2.04/2.24	       | ~ $true),
2.04/2.24	    inference('demod', [status(thm)], ['37', '18'])).
2.04/2.24	tff('39', plain,
2.04/2.24	    ![X0 : complex]:
2.04/2.24	      app_encode_app(nat, complex, 
2.04/2.24	        app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	          power_power(complex), 
2.04/2.24	          app_encode_app(complex, complex, 
2.04/2.24	            app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	              inverse_divide(complex), X0), one_one(complex))), one_one(nat))
2.04/2.24	       = app_encode_app(nat, complex, 
2.04/2.24	           app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	             power_power(complex), X0), one_one(nat)),
2.04/2.24	    inference('simplify', [status(thm)], ['38'])).
2.04/2.24	tff('40', plain,
2.04/2.24	    ![X0 : complex]:
2.04/2.24	      (app_encode_app(complex, complex, 
2.04/2.24	         app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	           inverse_divide(complex), X0), one_one(complex))
2.04/2.24	        = app_encode_app(nat, complex, 
2.04/2.24	            app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	              power_power(complex), X0), one_one(nat))
2.04/2.24	       | ~ monoid_mult(complex)),
2.04/2.24	    inference('sup+', [status(thm)], ['8', '39'])).
2.04/2.24	tff('41', plain,
2.04/2.24	    ![X0 : complex]:
2.04/2.24	      (app_encode_app(complex, complex, 
2.04/2.24	         app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	           inverse_divide(complex), X0), one_one(complex))
2.04/2.24	        = app_encode_app(nat, complex, 
2.04/2.24	            app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	              power_power(complex), X0), one_one(nat))
2.04/2.24	       | ~ $true),
2.04/2.24	    inference('demod', [status(thm)], ['40', '10'])).
2.04/2.24	tff('42', plain,
2.04/2.24	    ![X0 : complex]:
2.04/2.24	      app_encode_app(complex, complex, 
2.04/2.24	        app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	          inverse_divide(complex), X0), one_one(complex))
2.04/2.24	       = app_encode_app(nat, complex, 
2.04/2.24	           app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	             power_power(complex), X0), one_one(nat)),
2.04/2.24	    inference('simplify', [status(thm)], ['41'])).
2.04/2.24	tff('43', plain,
2.04/2.24	    ![X0 : complex]:
2.04/2.24	      (X0
2.04/2.24	        = app_encode_app(nat, complex, 
2.04/2.24	            app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	              power_power(complex), X0), one_one(nat))
2.04/2.24	       | ~ division_ring(complex)),
2.04/2.24	    inference('sup+', [status(thm)], ['7', '42'])).
2.04/2.24	tff('44', plain,
2.04/2.24	    ![X0 : complex]:
2.04/2.24	      (X0
2.04/2.24	        = app_encode_app(nat, complex, 
2.04/2.24	            app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	              power_power(complex), X0), one_one(nat))
2.04/2.24	       | ~ $true),
2.04/2.24	    inference('demod', [status(thm)], ['43', '18'])).
2.04/2.24	tff('45', plain,
2.04/2.24	    ![X0 : complex]:
2.04/2.24	      X0
2.04/2.24	       = app_encode_app(nat, complex, 
2.04/2.24	           app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	             power_power(complex), X0), one_one(nat)),
2.04/2.24	    inference('simplify', [status(thm)], ['44'])).
2.04/2.24	tff('46', plain,
2.04/2.24	    ![X0 : complex]:
2.04/2.24	      app_encode_app(complex, complex, 
2.04/2.24	        app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	          inverse_divide(complex), X0), one_one(complex))
2.04/2.24	       = X0,
2.04/2.24	    inference('demod', [status(thm)], ['42', '45'])).
2.04/2.24	tff('47', plain,
2.04/2.24	    ![X0 : nat, X1 : complex]:
2.04/2.24	      app_encode_app(nat, complex, 
2.04/2.24	        app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	          power_power(complex), 
2.04/2.24	          app_encode_app(complex, complex, 
2.04/2.24	            app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	              inverse_divide(complex), X1), 
2.04/2.24	            app_encode_app(nat, complex, fFT_Mirabelle_root, X0))), X0)
2.04/2.24	       = app_encode_app(nat, complex, 
2.04/2.24	           app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	             power_power(complex), X1), X0),
2.04/2.24	    inference('demod', [status(thm)], ['28', '46'])).
2.04/2.24	tff('48', plain,
2.04/2.24	    ![X0 : nat]:
2.04/2.24	      one_one(complex)
2.04/2.24	       = app_encode_app(nat, complex, 
2.04/2.24	           app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	             power_power(complex), one_one(complex)), X0),
2.04/2.24	    inference('demod', [status(thm)], ['21', '47'])).
2.04/2.24	tff(zf_stmt_85, axiom,
2.04/2.24	  (![A:$tType]:
2.04/2.24	     (group_add(A) =>
2.04/2.24	      (![A1:A]:
2.04/2.24	         (app_encode_app(A,A,
2.04/2.24	                         app_encode_app(A,app_encode_fun(A,A),minus_minus(A),
2.04/2.24	                                        A1),
2.04/2.24	                         zero_zero(A)) =
2.04/2.24	          A1))))).
2.04/2.24	tff('49', plain,
2.04/2.24	    ![X129 : $tType, X130 : X129]:
2.04/2.24	      (app_encode_app(X129, X129, 
2.04/2.24	         app_encode_app(X129, app_encode_fun(X129, X129), minus_minus(X129), 
2.04/2.24	           X130), zero_zero(X129))
2.04/2.24	        = X130
2.04/2.24	       | ~ group_add(X129)),
2.04/2.24	    inference('cnf', [status(esa)], [zf_stmt_85])).
2.04/2.24	tff(zf_stmt_125, axiom,
2.04/2.24	  (![A:$tType]:
2.04/2.24	     (mult_zero(A) =>
2.04/2.24	      (![A1:A]:
2.04/2.24	         (app_encode_app(A,A,
2.04/2.24	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
2.04/2.24	                                        zero_zero(A)),
2.04/2.24	                         A1) =
2.04/2.24	          zero_zero(A)))))).
2.04/2.24	tff('50', plain,
2.04/2.24	    ![X213 : $tType, X214 : X213]:
2.04/2.24	      (app_encode_app(X213, X213, 
2.04/2.24	         app_encode_app(X213, app_encode_fun(X213, X213), times_times(X213), 
2.04/2.24	           zero_zero(X213)), X214)
2.04/2.24	        = zero_zero(X213)
2.04/2.24	       | ~ mult_zero(X213)),
2.04/2.24	    inference('cnf', [status(esa)], [zf_stmt_125])).
2.04/2.24	tff(zf_stmt_49, axiom,
2.04/2.24	  (![A:$tType]:
2.04/2.24	     (divisi14063676e_zero(A) =>
2.04/2.24	      (![A1:A]:
2.04/2.24	         (app_encode_app(A,A,
2.04/2.24	                         app_encode_app(A,app_encode_fun(A,A),
2.04/2.24	                                        inverse_divide(A),A1),
2.04/2.24	                         zero_zero(A)) =
2.04/2.24	          zero_zero(A)))))).
2.04/2.24	tff('51', plain,
2.04/2.24	    ![X9 : $tType, X10 : X9]:
2.04/2.24	      (app_encode_app(X9, X9, 
2.04/2.24	         app_encode_app(X9, app_encode_fun(X9, X9), inverse_divide(X9), X10), 
2.04/2.24	         zero_zero(X9))
2.04/2.24	        = zero_zero(X9)
2.04/2.24	       | ~ divisi14063676e_zero(X9)),
2.04/2.24	    inference('cnf', [status(esa)], [zf_stmt_49])).
2.04/2.24	tff(zf_stmt_89, axiom,
2.04/2.24	  (![A:$tType]:
2.04/2.24	     (field_inverse_zero(A) =>
2.04/2.24	      (![N:nat,B:A,A1:A]:
2.04/2.24	         (app_encode_app(nat,A,
2.04/2.24	                         app_encode_app(A,app_encode_fun(nat,A),
2.04/2.24	                                        power_power(A),
2.04/2.24	                                        app_encode_app(A,A,
2.04/2.24	                                                       app_encode_app(
2.04/2.24	                                                       A,app_encode_fun(A,A),
2.04/2.24	                                                       inverse_divide(A),A1),
2.04/2.24	                                                       B)),
2.04/2.24	                         N) =
2.04/2.24	          app_encode_app(A,A,
2.04/2.24	                         app_encode_app(A,app_encode_fun(A,A),
2.04/2.24	                                        inverse_divide(A),
2.04/2.24	                                        app_encode_app(nat,A,
2.04/2.24	                                                       app_encode_app(
2.04/2.24	                                                       A,
2.04/2.24	                                                       app_encode_fun(nat,A),
2.04/2.24	                                                       power_power(A),A1),N)),
2.04/2.24	                         app_encode_app(nat,A,
2.04/2.24	                                        app_encode_app(A,
2.04/2.24	                                                       app_encode_fun(nat,A),
2.04/2.24	                                                       power_power(A),B),
2.04/2.24	                                        N))))))).
2.04/2.24	tff('52', plain,
2.04/2.24	    ![X140 : $tType, X141 : X140, X142 : nat, X143 : X140]:
2.04/2.24	      (app_encode_app(nat, X140, 
2.04/2.24	         app_encode_app(X140, app_encode_fun(nat, X140), power_power(X140), 
2.04/2.24	           app_encode_app(X140, X140, 
2.04/2.24	             app_encode_app(X140, app_encode_fun(X140, X140), 
2.04/2.24	               inverse_divide(X140), X141), X143)), X142)
2.04/2.24	        = app_encode_app(X140, X140, 
2.04/2.24	            app_encode_app(X140, app_encode_fun(X140, X140), 
2.04/2.24	              inverse_divide(X140), 
2.04/2.24	              app_encode_app(nat, X140, 
2.04/2.24	                app_encode_app(X140, app_encode_fun(nat, X140), 
2.04/2.24	                  power_power(X140), X141), X142)), 
2.04/2.24	            app_encode_app(nat, X140, 
2.04/2.24	              app_encode_app(X140, app_encode_fun(nat, X140), 
2.04/2.24	                power_power(X140), X143), X142))
2.04/2.24	       | ~ field_inverse_zero(X140)),
2.04/2.24	    inference('cnf', [status(esa)], [zf_stmt_89])).
2.04/2.24	tff('53', plain,
2.04/2.24	    ![X0 : nat, X1 : complex]:
2.04/2.24	      (app_encode_app(nat, complex, 
2.04/2.24	         app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	           power_power(complex), 
2.04/2.24	           app_encode_app(complex, complex, 
2.04/2.24	             app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	               inverse_divide(complex), 
2.04/2.24	               app_encode_app(nat, complex, fFT_Mirabelle_root, X0)), X1)), 
2.04/2.24	         X0)
2.04/2.24	        = app_encode_app(complex, complex, 
2.04/2.24	            app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	              inverse_divide(complex), one_one(complex)), 
2.04/2.24	            app_encode_app(nat, complex, 
2.04/2.24	              app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	                power_power(complex), X1), X0))
2.04/2.24	       | ~ field_inverse_zero(complex)),
2.04/2.24	    inference('sup+', [status(thm)], ['1', '52'])).
2.04/2.24	tff('54', plain,
2.04/2.24	    ![X0 : nat, X1 : complex]:
2.04/2.24	      (app_encode_app(nat, complex, 
2.04/2.24	         app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	           power_power(complex), 
2.04/2.24	           app_encode_app(complex, complex, 
2.04/2.24	             app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	               inverse_divide(complex), 
2.04/2.24	               app_encode_app(nat, complex, fFT_Mirabelle_root, X0)), X1)), 
2.04/2.24	         X0)
2.04/2.24	        = app_encode_app(complex, complex, 
2.04/2.24	            app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	              inverse_divide(complex), one_one(complex)), 
2.04/2.24	            app_encode_app(nat, complex, 
2.04/2.24	              app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	                power_power(complex), X1), X0))
2.04/2.24	       | ~ $true),
2.04/2.24	    inference('demod', [status(thm)], ['53', '4'])).
2.04/2.24	tff('55', plain,
2.04/2.24	    ![X0 : nat, X1 : complex]:
2.04/2.24	      app_encode_app(nat, complex, 
2.04/2.24	        app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	          power_power(complex), 
2.04/2.24	          app_encode_app(complex, complex, 
2.04/2.24	            app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	              inverse_divide(complex), 
2.04/2.24	              app_encode_app(nat, complex, fFT_Mirabelle_root, X0)), X1)), 
2.04/2.24	        X0)
2.04/2.24	       = app_encode_app(complex, complex, 
2.04/2.24	           app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	             inverse_divide(complex), one_one(complex)), 
2.04/2.24	           app_encode_app(nat, complex, 
2.04/2.24	             app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	               power_power(complex), X1), X0)),
2.04/2.24	    inference('simplify', [status(thm)], ['54'])).
2.04/2.24	tff('56', plain,
2.04/2.24	    ![X0 : nat, X1 : complex]:
2.04/2.24	      (app_encode_app(nat, complex, 
2.04/2.24	         app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	           power_power(complex), 
2.04/2.24	           app_encode_app(complex, complex, 
2.04/2.24	             app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	               inverse_divide(complex), one_one(complex)), X1)), X0)
2.04/2.24	        = app_encode_app(complex, complex, 
2.04/2.24	            app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	              inverse_divide(complex), one_one(complex)), 
2.04/2.24	            app_encode_app(nat, complex, 
2.04/2.24	              app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	                power_power(complex), X1), X0))
2.04/2.24	       | ~ field_inverse_zero(complex)),
2.04/2.24	    inference('sup+', [status(thm)], ['48', '52'])).
2.04/2.24	tff('57', plain,
2.04/2.24	    ![X0 : nat, X1 : complex]:
2.04/2.24	      (app_encode_app(nat, complex, 
2.04/2.24	         app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	           power_power(complex), 
2.04/2.24	           app_encode_app(complex, complex, 
2.04/2.24	             app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	               inverse_divide(complex), one_one(complex)), X1)), X0)
2.04/2.24	        = app_encode_app(complex, complex, 
2.04/2.24	            app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	              inverse_divide(complex), one_one(complex)), 
2.04/2.24	            app_encode_app(nat, complex, 
2.04/2.24	              app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	                power_power(complex), X1), X0))
2.04/2.24	       | ~ $true),
2.04/2.24	    inference('demod', [status(thm)], ['56', '4'])).
2.04/2.24	tff('58', plain,
2.04/2.24	    ![X0 : nat, X1 : complex]:
2.04/2.24	      app_encode_app(nat, complex, 
2.04/2.24	        app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	          power_power(complex), 
2.04/2.24	          app_encode_app(complex, complex, 
2.04/2.24	            app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	              inverse_divide(complex), one_one(complex)), X1)), X0)
2.04/2.24	       = app_encode_app(complex, complex, 
2.04/2.24	           app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	             inverse_divide(complex), one_one(complex)), 
2.04/2.24	           app_encode_app(nat, complex, 
2.04/2.24	             app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	               power_power(complex), X1), X0)),
2.04/2.24	    inference('simplify', [status(thm)], ['57'])).
2.04/2.24	tff('59', plain,
2.04/2.24	    ![X0 : nat, X1 : complex]:
2.04/2.24	      app_encode_app(nat, complex, 
2.04/2.24	        app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	          power_power(complex), 
2.04/2.24	          app_encode_app(complex, complex, 
2.04/2.24	            app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	              inverse_divide(complex), 
2.04/2.24	              app_encode_app(nat, complex, fFT_Mirabelle_root, X0)), X1)), 
2.04/2.24	        X0)
2.04/2.24	       = app_encode_app(nat, complex, 
2.04/2.24	           app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	             power_power(complex), 
2.04/2.24	             app_encode_app(complex, complex, 
2.04/2.24	               app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	                 inverse_divide(complex), one_one(complex)), X1)), X0),
2.04/2.24	    inference('demod', [status(thm)], ['55', '58'])).
2.04/2.24	tff('60', plain,
2.04/2.24	    ![X0 : nat]:
2.04/2.24	      (app_encode_app(nat, complex, 
2.04/2.24	         app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	           power_power(complex), zero_zero(complex)), X0)
2.04/2.24	        = app_encode_app(nat, complex, 
2.04/2.24	            app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	              power_power(complex), 
2.04/2.24	              app_encode_app(complex, complex, 
2.04/2.24	                app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	                  inverse_divide(complex), one_one(complex)), 
2.04/2.24	                zero_zero(complex))), X0)
2.04/2.24	       | ~ divisi14063676e_zero(complex)),
2.04/2.24	    inference('sup+', [status(thm)], ['51', '59'])).
2.04/2.24	tff(zf_stmt_150, axiom, (divisi14063676e_zero(complex))).
2.04/2.24	tff('61', plain, divisi14063676e_zero(complex),
2.04/2.24	    inference('cnf', [status(esa)], [zf_stmt_150])).
2.04/2.24	tff('62', plain,
2.04/2.24	    ![X0 : nat]:
2.04/2.24	      (app_encode_app(nat, complex, 
2.04/2.24	         app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	           power_power(complex), zero_zero(complex)), X0)
2.04/2.24	        = app_encode_app(nat, complex, 
2.04/2.24	            app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	              power_power(complex), 
2.04/2.24	              app_encode_app(complex, complex, 
2.04/2.24	                app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	                  inverse_divide(complex), one_one(complex)), 
2.04/2.24	                zero_zero(complex))), X0)
2.04/2.24	       | ~ $true),
2.04/2.24	    inference('demod', [status(thm)], ['60', '61'])).
2.04/2.24	tff('63', plain,
2.04/2.24	    ![X0 : nat]:
2.04/2.24	      app_encode_app(nat, complex, 
2.04/2.24	        app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	          power_power(complex), zero_zero(complex)), X0)
2.04/2.24	       = app_encode_app(nat, complex, 
2.04/2.24	           app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	             power_power(complex), 
2.04/2.24	             app_encode_app(complex, complex, 
2.04/2.24	               app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	                 inverse_divide(complex), one_one(complex)), 
2.04/2.24	               zero_zero(complex))), X0),
2.04/2.24	    inference('simplify', [status(thm)], ['62'])).
2.04/2.24	tff('64', plain,
2.04/2.24	    app_encode_app(nat, complex, 
2.04/2.24	      app_encode_app(complex, app_encode_fun(nat, complex), 
2.04/2.24	        power_power(complex), zero_zero(complex)), one_one(nat))
2.04/2.24	     = app_encode_app(complex, complex, 
2.04/2.24	         app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	           inverse_divide(complex), one_one(complex)), zero_zero(complex)),
2.04/2.24	    inference('sup+', [status(thm)], ['45', '63'])).
2.04/2.24	tff('65', plain,
2.04/2.24	    zero_zero(complex)
2.04/2.24	     = app_encode_app(complex, complex, 
2.04/2.24	         app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	           inverse_divide(complex), one_one(complex)), zero_zero(complex)),
2.04/2.24	    inference('demod', [status(thm)], ['64', '45'])).
2.04/2.24	tff(zf_stmt_88, axiom,
2.04/2.24	  (![A:$tType]:
2.04/2.24	     (division_ring(A) =>
2.04/2.24	      (![C:A,B:A,A1:A]:
2.04/2.24	         (app_encode_app(A,A,
2.04/2.24	                         app_encode_app(A,app_encode_fun(A,A),
2.04/2.24	                                        inverse_divide(A),
2.04/2.24	                                        app_encode_app(A,A,
2.04/2.24	                                                       app_encode_app(
2.04/2.24	                                                       A,app_encode_fun(A,A),
2.04/2.24	                                                       minus_minus(A),A1),B)),
2.04/2.24	                         C) =
2.04/2.24	          app_encode_app(A,A,
2.04/2.24	                         app_encode_app(A,app_encode_fun(A,A),minus_minus(A),
2.04/2.24	                                        app_encode_app(A,A,
2.04/2.24	                                                       app_encode_app(
2.04/2.24	                                                       A,app_encode_fun(A,A),
2.04/2.24	                                                       inverse_divide(A),A1),
2.04/2.24	                                                       C)),
2.04/2.24	                         app_encode_app(A,A,
2.04/2.24	                                        app_encode_app(A,app_encode_fun(A,A),
2.04/2.24	                                                       inverse_divide(A),B),
2.04/2.24	                                        C))))))).
2.04/2.24	tff('66', plain,
2.04/2.24	    ![X136 : $tType, X137 : X136, X138 : X136, X139 : X136]:
2.04/2.24	      (app_encode_app(X136, X136, 
2.04/2.24	         app_encode_app(X136, app_encode_fun(X136, X136), 
2.04/2.24	           inverse_divide(X136), 
2.04/2.24	           app_encode_app(X136, X136, 
2.04/2.24	             app_encode_app(X136, app_encode_fun(X136, X136), 
2.04/2.24	               minus_minus(X136), X137), X139)), X138)
2.04/2.24	        = app_encode_app(X136, X136, 
2.04/2.24	            app_encode_app(X136, app_encode_fun(X136, X136), 
2.04/2.24	              minus_minus(X136), 
2.04/2.24	              app_encode_app(X136, X136, 
2.04/2.24	                app_encode_app(X136, app_encode_fun(X136, X136), 
2.04/2.24	                  inverse_divide(X136), X137), X138)), 
2.04/2.24	            app_encode_app(X136, X136, 
2.04/2.24	              app_encode_app(X136, app_encode_fun(X136, X136), 
2.04/2.24	                inverse_divide(X136), X139), X138))
2.04/2.24	       | ~ division_ring(X136)),
2.04/2.24	    inference('cnf', [status(esa)], [zf_stmt_88])).
2.04/2.24	tff('67', plain,
2.04/2.24	    ![X0 : complex]:
2.04/2.24	      (app_encode_app(complex, complex, 
2.04/2.24	         app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	           inverse_divide(complex), 
2.04/2.24	           app_encode_app(complex, complex, 
2.04/2.24	             app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	               minus_minus(complex), one_one(complex)), X0)), 
2.04/2.24	         zero_zero(complex))
2.04/2.24	        = app_encode_app(complex, complex, 
2.04/2.24	            app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	              minus_minus(complex), zero_zero(complex)), 
2.04/2.24	            app_encode_app(complex, complex, 
2.04/2.24	              app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	                inverse_divide(complex), X0), zero_zero(complex)))
2.04/2.24	       | ~ division_ring(complex)),
2.04/2.24	    inference('sup+', [status(thm)], ['65', '66'])).
2.04/2.24	tff('68', plain,
2.04/2.24	    ![X0 : complex]:
2.04/2.24	      (app_encode_app(complex, complex, 
2.04/2.24	         app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	           inverse_divide(complex), 
2.04/2.24	           app_encode_app(complex, complex, 
2.04/2.24	             app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	               minus_minus(complex), one_one(complex)), X0)), 
2.04/2.24	         zero_zero(complex))
2.04/2.24	        = app_encode_app(complex, complex, 
2.04/2.24	            app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	              minus_minus(complex), zero_zero(complex)), 
2.04/2.24	            app_encode_app(complex, complex, 
2.04/2.24	              app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	                inverse_divide(complex), X0), zero_zero(complex)))
2.04/2.24	       | ~ $true),
2.04/2.24	    inference('demod', [status(thm)], ['67', '18'])).
2.04/2.24	tff('69', plain,
2.04/2.24	    ![X0 : complex]:
2.04/2.24	      app_encode_app(complex, complex, 
2.04/2.24	        app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	          inverse_divide(complex), 
2.04/2.24	          app_encode_app(complex, complex, 
2.04/2.24	            app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	              minus_minus(complex), one_one(complex)), X0)), 
2.04/2.24	        zero_zero(complex))
2.04/2.24	       = app_encode_app(complex, complex, 
2.04/2.24	           app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	             minus_minus(complex), zero_zero(complex)), 
2.04/2.24	           app_encode_app(complex, complex, 
2.04/2.24	             app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	               inverse_divide(complex), X0), zero_zero(complex))),
2.04/2.24	    inference('simplify', [status(thm)], ['68'])).
2.04/2.24	tff('70', plain,
2.04/2.24	    ![X0 : complex]:
2.04/2.24	      (zero_zero(complex)
2.04/2.24	        = app_encode_app(complex, complex, 
2.04/2.24	            app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	              minus_minus(complex), zero_zero(complex)), 
2.04/2.24	            app_encode_app(complex, complex, 
2.04/2.24	              app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	                inverse_divide(complex), X0), zero_zero(complex)))
2.04/2.24	       | ~ divisi14063676e_zero(complex)),
2.04/2.24	    inference('sup+', [status(thm)], ['51', '69'])).
2.04/2.24	tff('71', plain,
2.04/2.24	    ![X0 : complex]:
2.04/2.24	      (zero_zero(complex)
2.04/2.24	        = app_encode_app(complex, complex, 
2.04/2.24	            app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	              minus_minus(complex), zero_zero(complex)), 
2.04/2.24	            app_encode_app(complex, complex, 
2.04/2.24	              app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	                inverse_divide(complex), X0), zero_zero(complex)))
2.04/2.24	       | ~ $true),
2.04/2.24	    inference('demod', [status(thm)], ['70', '61'])).
2.04/2.24	tff('72', plain,
2.04/2.24	    ![X0 : complex]:
2.04/2.24	      zero_zero(complex)
2.04/2.24	       = app_encode_app(complex, complex, 
2.04/2.24	           app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	             minus_minus(complex), zero_zero(complex)), 
2.04/2.24	           app_encode_app(complex, complex, 
2.04/2.24	             app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	               inverse_divide(complex), X0), zero_zero(complex))),
2.04/2.24	    inference('simplify', [status(thm)], ['71'])).
2.04/2.24	tff(zf_stmt_83, axiom,
2.04/2.24	  (![A:$tType]:
2.04/2.24	     (group_add(A) =>
2.04/2.24	      (![B1:A,A2:A]:
2.04/2.24	         ((app_encode_app(A,A,
2.04/2.24	                          app_encode_app(A,app_encode_fun(A,A),
2.04/2.24	                                         minus_minus(A),A2),
2.04/2.24	                          B1) =
2.04/2.24	           zero_zero(A)) <=>
2.04/2.24	          (A2 = B1)))))).
2.04/2.24	tff('73', plain,
2.04/2.24	    ![X121 : $tType, X122 : X121, X124 : X121]:
2.04/2.24	      (app_encode_app(X121, X121, 
2.04/2.24	         app_encode_app(X121, app_encode_fun(X121, X121), minus_minus(X121), 
2.04/2.24	           X124), X122)
2.04/2.24	        != zero_zero(X121)
2.04/2.24	       | X124 = X122
2.04/2.24	       | ~ group_add(X121)),
2.04/2.24	    inference('cnf', [status(esa)], [zf_stmt_83])).
2.04/2.24	tff('74', plain,
2.04/2.24	    ![X0 : complex]:
2.04/2.24	      (zero_zero(complex) != zero_zero(complex)
2.04/2.24	       | ~ group_add(complex)
2.04/2.24	       | zero_zero(complex)
2.04/2.24	          = app_encode_app(complex, complex, 
2.04/2.24	              app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	                inverse_divide(complex), X0), zero_zero(complex))),
2.04/2.24	    inference('sup-', [status(thm)], ['72', '73'])).
2.04/2.24	tff(zf_stmt_160, axiom, (group_add(complex))).
2.04/2.24	tff('75', plain, group_add(complex),
2.04/2.24	    inference('cnf', [status(esa)], [zf_stmt_160])).
2.04/2.24	tff('76', plain,
2.04/2.24	    ![X0 : complex]:
2.04/2.24	      (zero_zero(complex) != zero_zero(complex)
2.04/2.24	       | ~ $true
2.04/2.24	       | zero_zero(complex)
2.04/2.24	          = app_encode_app(complex, complex, 
2.04/2.24	              app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	                inverse_divide(complex), X0), zero_zero(complex))),
2.04/2.24	    inference('demod', [status(thm)], ['74', '75'])).
2.04/2.24	tff('77', plain,
2.04/2.24	    ![X0 : complex]:
2.04/2.24	      zero_zero(complex)
2.04/2.24	       = app_encode_app(complex, complex, 
2.04/2.24	           app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	             inverse_divide(complex), X0), zero_zero(complex)),
2.04/2.24	    inference('simplify', [status(thm)], ['76'])).
2.04/2.24	tff(zf_stmt_128, axiom,
2.04/2.24	  (![A:$tType]:
2.04/2.24	     (division_ring(A) =>
2.04/2.24	      (![C:A,B:A,A1:A]:
2.04/2.24	         (app_encode_app(A,A,
2.04/2.24	                         app_encode_app(A,app_encode_fun(A,A),times_times(A),
2.04/2.24	                                        A1),
2.04/2.24	                         app_encode_app(A,A,
2.04/2.24	                                        app_encode_app(A,app_encode_fun(A,A),
2.04/2.24	                                                       inverse_divide(A),B),
2.04/2.24	                                        C)) =
2.04/2.24	          app_encode_app(A,A,
2.04/2.24	                         app_encode_app(A,app_encode_fun(A,A),
2.04/2.24	                                        inverse_divide(A),
2.04/2.24	                                        app_encode_app(A,A,
2.04/2.24	                                                       app_encode_app(
2.04/2.24	                                                       A,app_encode_fun(A,A),
2.04/2.24	                                                       times_times(A),A1),B)),
2.04/2.24	                         C)))))).
2.04/2.24	tff('78', plain,
2.04/2.24	    ![X221 : $tType, X222 : X221, X223 : X221, X224 : X221]:
2.04/2.24	      (app_encode_app(X221, X221, 
2.04/2.24	         app_encode_app(X221, app_encode_fun(X221, X221), times_times(X221), 
2.04/2.24	           X222), 
2.04/2.24	         app_encode_app(X221, X221, 
2.04/2.24	           app_encode_app(X221, app_encode_fun(X221, X221), 
2.04/2.24	             inverse_divide(X221), X223), X224))
2.04/2.24	        = app_encode_app(X221, X221, 
2.04/2.24	            app_encode_app(X221, app_encode_fun(X221, X221), 
2.04/2.24	              inverse_divide(X221), 
2.04/2.24	              app_encode_app(X221, X221, 
2.04/2.24	                app_encode_app(X221, app_encode_fun(X221, X221), 
2.04/2.24	                  times_times(X221), X222), X223)), X224)
2.04/2.24	       | ~ division_ring(X221)),
2.04/2.24	    inference('cnf', [status(esa)], [zf_stmt_128])).
2.04/2.24	tff('79', plain,
2.04/2.24	    ![X0 : complex, X1 : complex]:
2.04/2.24	      (app_encode_app(complex, complex, 
2.04/2.24	         app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	           times_times(complex), X1), 
2.04/2.24	         app_encode_app(complex, complex, 
2.04/2.24	           app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	             inverse_divide(complex), X0), zero_zero(complex)))
2.04/2.24	        = zero_zero(complex)
2.04/2.24	       | ~ division_ring(complex)),
2.04/2.24	    inference('sup+', [status(thm)], ['77', '78'])).
2.04/2.24	tff('80', plain,
2.04/2.24	    ![X1 : complex]:
2.04/2.24	      (app_encode_app(complex, complex, 
2.04/2.24	         app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	           times_times(complex), X1), zero_zero(complex))
2.04/2.24	        = zero_zero(complex)
2.04/2.24	       | ~ $true),
2.04/2.24	    inference('demod', [status(thm)], ['79', '77', '18'])).
2.04/2.24	tff('81', plain,
2.04/2.24	    ![X1 : complex]:
2.04/2.24	      app_encode_app(complex, complex, 
2.04/2.24	        app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	          times_times(complex), X1), zero_zero(complex))
2.04/2.24	       = zero_zero(complex),
2.04/2.24	    inference('simplify', [status(thm)], ['80'])).
2.04/2.24	tff('82', plain,
2.04/2.24	    ![X0 : complex, X1 : complex]:
2.04/2.24	      (app_encode_app(complex, complex, 
2.04/2.24	         app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	           times_times(complex), X1), 
2.04/2.24	         app_encode_app(complex, complex, 
2.04/2.24	           app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	             inverse_divide(complex), zero_zero(complex)), X0))
2.04/2.24	        = app_encode_app(complex, complex, 
2.04/2.24	            app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	              inverse_divide(complex), zero_zero(complex)), X0)
2.04/2.24	       | ~ division_ring(complex)),
2.04/2.24	    inference('sup+', [status(thm)], ['81', '78'])).
2.04/2.24	tff('83', plain,
2.04/2.24	    ![X0 : complex, X1 : complex]:
2.04/2.24	      (app_encode_app(complex, complex, 
2.04/2.24	         app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	           times_times(complex), X1), 
2.04/2.24	         app_encode_app(complex, complex, 
2.04/2.24	           app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	             inverse_divide(complex), zero_zero(complex)), X0))
2.04/2.24	        = app_encode_app(complex, complex, 
2.04/2.24	            app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	              inverse_divide(complex), zero_zero(complex)), X0)
2.04/2.24	       | ~ $true),
2.04/2.24	    inference('demod', [status(thm)], ['82', '18'])).
2.04/2.24	tff('84', plain,
2.04/2.24	    ![X0 : complex, X1 : complex]:
2.04/2.24	      app_encode_app(complex, complex, 
2.04/2.24	        app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	          times_times(complex), X1), 
2.04/2.24	        app_encode_app(complex, complex, 
2.04/2.24	          app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	            inverse_divide(complex), zero_zero(complex)), X0))
2.04/2.24	       = app_encode_app(complex, complex, 
2.04/2.24	           app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	             inverse_divide(complex), zero_zero(complex)), X0),
2.04/2.24	    inference('simplify', [status(thm)], ['83'])).
2.04/2.24	tff('85', plain,
2.04/2.24	    ![X0 : complex]:
2.04/2.24	      (zero_zero(complex)
2.04/2.24	        = app_encode_app(complex, complex, 
2.04/2.24	            app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	              inverse_divide(complex), zero_zero(complex)), X0)
2.04/2.24	       | ~ mult_zero(complex)),
2.04/2.24	    inference('sup+', [status(thm)], ['50', '84'])).
2.04/2.24	tff(zf_stmt_161, axiom, (mult_zero(complex))).
2.04/2.24	tff('86', plain, mult_zero(complex),
2.04/2.24	    inference('cnf', [status(esa)], [zf_stmt_161])).
2.04/2.24	tff('87', plain,
2.04/2.24	    ![X0 : complex]:
2.04/2.24	      (zero_zero(complex)
2.04/2.24	        = app_encode_app(complex, complex, 
2.04/2.24	            app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	              inverse_divide(complex), zero_zero(complex)), X0)
2.04/2.24	       | ~ $true),
2.04/2.24	    inference('demod', [status(thm)], ['85', '86'])).
2.04/2.24	tff('88', plain,
2.04/2.24	    ![X0 : complex]:
2.04/2.24	      zero_zero(complex)
2.04/2.24	       = app_encode_app(complex, complex, 
2.04/2.24	           app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	             inverse_divide(complex), zero_zero(complex)), X0),
2.04/2.24	    inference('simplify', [status(thm)], ['87'])).
2.04/2.24	tff('89', plain,
2.04/2.24	    ![X0 : complex, X1 : complex]:
2.04/2.24	      (app_encode_app(complex, complex, 
2.04/2.24	         app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	           inverse_divide(complex), 
2.04/2.24	           app_encode_app(complex, complex, 
2.04/2.24	             app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	               minus_minus(complex), X1), zero_zero(complex))), X0)
2.04/2.24	        = app_encode_app(complex, complex, 
2.04/2.24	            app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	              minus_minus(complex), 
2.04/2.24	              app_encode_app(complex, complex, 
2.04/2.24	                app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	                  inverse_divide(complex), X1), X0)), zero_zero(complex))
2.04/2.24	       | ~ division_ring(complex)),
2.04/2.24	    inference('sup+', [status(thm)], ['88', '66'])).
2.04/2.24	tff('90', plain,
2.04/2.24	    ![X0 : complex, X1 : complex]:
2.04/2.24	      (app_encode_app(complex, complex, 
2.04/2.24	         app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	           inverse_divide(complex), 
2.04/2.24	           app_encode_app(complex, complex, 
2.04/2.24	             app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	               minus_minus(complex), X1), zero_zero(complex))), X0)
2.04/2.24	        = app_encode_app(complex, complex, 
2.04/2.24	            app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	              minus_minus(complex), 
2.04/2.24	              app_encode_app(complex, complex, 
2.04/2.24	                app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	                  inverse_divide(complex), X1), X0)), zero_zero(complex))
2.04/2.24	       | ~ $true),
2.04/2.24	    inference('demod', [status(thm)], ['89', '18'])).
2.04/2.24	tff('91', plain,
2.04/2.24	    ![X0 : complex, X1 : complex]:
2.04/2.24	      app_encode_app(complex, complex, 
2.04/2.24	        app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	          inverse_divide(complex), 
2.04/2.24	          app_encode_app(complex, complex, 
2.04/2.24	            app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	              minus_minus(complex), X1), zero_zero(complex))), X0)
2.04/2.24	       = app_encode_app(complex, complex, 
2.04/2.24	           app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	             minus_minus(complex), 
2.04/2.24	             app_encode_app(complex, complex, 
2.04/2.24	               app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	                 inverse_divide(complex), X1), X0)), zero_zero(complex)),
2.04/2.24	    inference('simplify', [status(thm)], ['90'])).
2.04/2.24	tff('92', plain,
2.04/2.24	    ![X0 : complex, X1 : complex]:
2.04/2.24	      (app_encode_app(complex, complex, 
2.04/2.24	         app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	           inverse_divide(complex), X0), X1)
2.04/2.24	        = app_encode_app(complex, complex, 
2.04/2.24	            app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	              minus_minus(complex), 
2.04/2.24	              app_encode_app(complex, complex, 
2.04/2.24	                app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	                  inverse_divide(complex), X0), X1)), zero_zero(complex))
2.04/2.24	       | ~ group_add(complex)),
2.04/2.24	    inference('sup+', [status(thm)], ['49', '91'])).
2.04/2.24	tff('93', plain,
2.04/2.24	    ![X0 : complex, X1 : complex]:
2.04/2.24	      (app_encode_app(complex, complex, 
2.04/2.24	         app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	           inverse_divide(complex), X0), X1)
2.04/2.24	        = app_encode_app(complex, complex, 
2.04/2.24	            app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	              minus_minus(complex), 
2.04/2.24	              app_encode_app(complex, complex, 
2.04/2.24	                app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	                  inverse_divide(complex), X0), X1)), zero_zero(complex))
2.04/2.24	       | ~ $true),
2.04/2.24	    inference('demod', [status(thm)], ['92', '75'])).
2.04/2.24	tff('94', plain,
2.04/2.24	    ![X0 : complex, X1 : complex]:
2.04/2.24	      app_encode_app(complex, complex, 
2.04/2.24	        app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	          inverse_divide(complex), X0), X1)
2.04/2.24	       = app_encode_app(complex, complex, 
2.04/2.24	           app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	             minus_minus(complex), 
2.04/2.24	             app_encode_app(complex, complex, 
2.04/2.24	               app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	                 inverse_divide(complex), X0), X1)), zero_zero(complex)),
2.04/2.24	    inference('simplify', [status(thm)], ['93'])).
2.04/2.24	tff('95', plain,
2.04/2.24	    ![X0 : complex]:
2.04/2.24	      app_encode_app(complex, complex, 
2.04/2.24	        app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	          inverse_divide(complex), X0), one_one(complex))
2.04/2.24	       = app_encode_app(complex, complex, 
2.04/2.24	           app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	             minus_minus(complex), X0), zero_zero(complex)),
2.04/2.24	    inference('sup+', [status(thm)], ['46', '94'])).
2.04/2.24	tff('96', plain,
2.04/2.24	    ![X0 : complex]:
2.04/2.24	      X0
2.04/2.24	       = app_encode_app(complex, complex, 
2.04/2.24	           app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	             minus_minus(complex), X0), zero_zero(complex)),
2.04/2.24	    inference('demod', [status(thm)], ['95', '46'])).
2.04/2.24	tff(zf_stmt_82, axiom,
2.04/2.24	  (![A:$tType]:
2.04/2.24	     (group_add(A) =>
2.04/2.24	      (![D1:A,C1:A,B1:A,A2:A]:
2.04/2.24	         ((app_encode_app(A,A,
2.04/2.24	                          app_encode_app(A,app_encode_fun(A,A),
2.04/2.24	                                         minus_minus(A),A2),
2.04/2.24	                          B1) =
2.04/2.24	           app_encode_app(A,A,
2.04/2.24	                          app_encode_app(A,app_encode_fun(A,A),
2.04/2.24	                                         minus_minus(A),C1),
2.04/2.24	                          D1)) =>
2.04/2.24	          ((A2 = B1) <=> (C1 = D1))))))).
2.04/2.24	tff('97', plain,
2.04/2.24	    ![X116 : $tType, X117 : X116, X118 : X116, X119 : X116, X120 : X116]:
2.04/2.24	      (app_encode_app(X116, X116, 
2.04/2.24	         app_encode_app(X116, app_encode_fun(X116, X116), minus_minus(X116), 
2.04/2.24	           X119), X120)
2.04/2.24	        != app_encode_app(X116, X116, 
2.04/2.24	             app_encode_app(X116, app_encode_fun(X116, X116), 
2.04/2.24	               minus_minus(X116), X117), X118)
2.04/2.24	       | X119 != X120
2.04/2.24	       | X117 = X118
2.04/2.24	       | ~ group_add(X116)),
2.04/2.24	    inference('cnf', [status(esa)], [zf_stmt_82])).
2.04/2.24	tff('98', plain,
2.04/2.24	    ![X116 : $tType, X117 : X116, X118 : X116, X120 : X116]:
2.04/2.24	      (~ group_add(X116)
2.04/2.24	       | X117 = X118
2.04/2.24	       | app_encode_app(X116, X116, 
2.04/2.24	           app_encode_app(X116, app_encode_fun(X116, X116), 
2.04/2.24	             minus_minus(X116), X120), X120)
2.04/2.24	          != app_encode_app(X116, X116, 
2.04/2.24	               app_encode_app(X116, app_encode_fun(X116, X116), 
2.04/2.24	                 minus_minus(X116), X117), X118)),
2.04/2.24	    inference('simplify', [status(thm)], ['97'])).
2.04/2.24	tff('99', plain,
2.04/2.24	    ![X0 : complex, X1 : complex]:
2.04/2.24	      (app_encode_app(complex, complex, 
2.04/2.24	         app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	           minus_minus(complex), X1), X1)
2.04/2.24	        != X0
2.04/2.24	       | X0 = zero_zero(complex)
2.04/2.24	       | ~ group_add(complex)),
2.04/2.24	    inference('sup-', [status(thm)], ['96', '98'])).
2.04/2.24	tff('100', plain,
2.04/2.24	    ![X0 : complex, X1 : complex]:
2.04/2.24	      (app_encode_app(complex, complex, 
2.04/2.24	         app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	           minus_minus(complex), X1), X1)
2.04/2.24	        != X0
2.04/2.24	       | X0 = zero_zero(complex)
2.04/2.24	       | ~ $true),
2.04/2.24	    inference('demod', [status(thm)], ['99', '75'])).
2.04/2.24	tff('101', plain,
2.04/2.24	    ![X1 : complex]:
2.04/2.24	      app_encode_app(complex, complex, 
2.04/2.24	        app_encode_app(complex, app_encode_fun(complex, complex), 
2.04/2.24	          minus_minus(complex), X1), X1)
2.04/2.24	       = zero_zero(complex),
2.04/2.24	    inference('simplify', [status(thm)], ['100'])).
2.04/2.24	tff('102', plain, zero_zero(complex) != zero_zero(complex),
2.04/2.24	    inference('demod', [status(thm)], ['0', '1', '48', '101', '88'])).
2.04/2.24	tff('103', plain, $false, inference('simplify', [status(thm)], ['102'])).
2.04/2.24	
2.04/2.24	% SZS output end Refutation
2.04/2.24	EOF
