0.00/0.00	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : app
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : rpo6
0.00/0.00	% Command    : 
0.00/0.01	#!/bin/sh
0.00/0.01	
0.00/0.01	./zipperposition.native ${1:+"$1"} \
0.00/0.01	  -i tptp \
0.00/0.01	  -o tptp \
0.00/0.01	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.01	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.01	  --no-ho \
0.00/0.01	  --no-avatar \
0.00/0.01	  --no-induction \
0.00/0.01	  --no-unif-pattern \
0.00/0.01	  --ord $2 \
0.00/0.01	  --simultaneous-sup false \
0.00/0.01	  --no-max-vars \
0.00/0.01	  --no-fool
0.00/0.20	% Computer   : n091.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 08:00:08 CST 2018
29.42/29.67	% done 13439 iterations in 29.467s
29.42/29.67	% SZS status Theorem for 'stdin'
29.42/29.67	% SZS output start Refutation
29.49/29.68	tff(zf_stmt_38, axiom,
29.49/29.68	  (app_encode_app(int,$o,
29.49/29.68	                  app_encode_app(int,app_encode_fun(int,$o),ord_less(int),t),
29.49/29.68	                  zero_zero(int)) =>
29.49/29.68	   app_encode_app(int,$o,
29.49/29.68	                  app_encode_app(int,app_encode_fun(int,$o),ord_less(int),
29.49/29.68	                                 app_encode_app(int,int,
29.49/29.68	                                                app_encode_app(int,
29.49/29.68	                                                               app_encode_fun(
29.49/29.68	                                                               int,int),
29.49/29.68	                                                               plus_plus(int),
29.49/29.68	                                                               app_encode_app(
29.49/29.68	                                                               nat,int,
29.49/29.68	                                                               app_encode_app(
29.49/29.68	                                                               int,
29.49/29.68	                                                               app_encode_fun(
29.49/29.68	                                                               nat,int),
29.49/29.68	                                                               power_power(
29.49/29.68	                                                               int),s),
29.49/29.68	                                                               app_encode_app(
29.49/29.68	                                                               int,nat,
29.49/29.68	                                                               number_number_of(
29.49/29.68	                                                               nat),
29.49/29.68	                                                               app_encode_app(
29.49/29.68	                                                               int,int,bit0,
29.49/29.68	                                                               app_encode_app(
29.49/29.68	                                                               int,int,bit1,
29.49/29.68	                                                               pls))))),
29.49/29.68	                                                one_one(int))),
29.49/29.68	                  zero_zero(int)))).
29.49/29.68	tff('0', plain,
29.49/29.68	    (app_encode_app(int, $o, 
29.49/29.68	       app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
29.49/29.68	         app_encode_app(int, int, 
29.49/29.68	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
29.49/29.68	             app_encode_app(nat, int, 
29.49/29.68	               app_encode_app(int, app_encode_fun(nat, int), 
29.49/29.68	                 power_power(int), s), 
29.49/29.68	               app_encode_app(int, nat, number_number_of(nat), 
29.49/29.68	                 app_encode_app(int, int, bit0, 
29.49/29.68	                   app_encode_app(int, int, bit1, pls))))), one_one(int))), 
29.49/29.68	       zero_zero(int))
29.49/29.68	     | ~ app_encode_app(int, $o, 
29.49/29.68	           app_encode_app(int, app_encode_fun(int, $o), ord_less(int), t), 
29.49/29.68	           zero_zero(int))),
29.49/29.68	    inference('cnf', [status(esa)], [zf_stmt_38])).
29.49/29.68	tff(zf_stmt_106, axiom,
29.49/29.68	  (zero_zero(int) = app_encode_app(int,int,number_number_of(int),pls))).
29.49/29.68	tff('1', plain,
29.49/29.68	    zero_zero(int) = app_encode_app(int, int, number_number_of(int), pls),
29.49/29.68	    inference('cnf', [status(esa)], [zf_stmt_106])).
29.49/29.68	tff('2', plain,
29.49/29.68	    (app_encode_app(int, $o, 
29.49/29.68	       app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
29.49/29.68	         app_encode_app(int, int, 
29.49/29.68	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
29.49/29.68	             app_encode_app(nat, int, 
29.49/29.68	               app_encode_app(int, app_encode_fun(nat, int), 
29.49/29.68	                 power_power(int), s), 
29.49/29.68	               app_encode_app(int, nat, number_number_of(nat), 
29.49/29.68	                 app_encode_app(int, int, bit0, 
29.49/29.68	                   app_encode_app(int, int, bit1, pls))))), one_one(int))), 
29.49/29.68	       app_encode_app(int, int, number_number_of(int), pls))
29.49/29.68	     | ~ app_encode_app(int, $o, 
29.49/29.68	           app_encode_app(int, app_encode_fun(int, $o), ord_less(int), t), 
29.49/29.68	           app_encode_app(int, int, number_number_of(int), pls))),
29.49/29.68	    inference('demod', [status(thm)], ['0', '1', '1'])).
29.49/29.68	tff(zf_stmt_114, axiom,
29.49/29.68	  (one_one(int) =
29.49/29.68	   app_encode_app(int,int,number_number_of(int),
29.49/29.68	                  app_encode_app(int,int,bit1,pls)))).
29.49/29.68	tff('3', plain,
29.49/29.68	    one_one(int)
29.49/29.68	     = app_encode_app(int, int, number_number_of(int), 
29.49/29.68	         app_encode_app(int, int, bit1, pls)),
29.49/29.68	    inference('cnf', [status(esa)], [zf_stmt_114])).
29.49/29.68	tff('4', plain,
29.49/29.68	    (app_encode_app(int, $o, 
29.49/29.68	       app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
29.49/29.68	         app_encode_app(int, int, 
29.49/29.68	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
29.49/29.68	             app_encode_app(nat, int, 
29.49/29.68	               app_encode_app(int, app_encode_fun(nat, int), 
29.49/29.68	                 power_power(int), s), 
29.49/29.68	               app_encode_app(int, nat, number_number_of(nat), 
29.49/29.68	                 app_encode_app(int, int, bit0, 
29.49/29.68	                   app_encode_app(int, int, bit1, pls))))), 
29.49/29.68	           app_encode_app(int, int, number_number_of(int), 
29.49/29.68	             app_encode_app(int, int, bit1, pls)))), 
29.49/29.68	       app_encode_app(int, int, number_number_of(int), pls))
29.49/29.68	     | ~ app_encode_app(int, $o, 
29.49/29.68	           app_encode_app(int, app_encode_fun(int, $o), ord_less(int), t), 
29.49/29.68	           app_encode_app(int, int, number_number_of(int), pls))),
29.49/29.68	    inference('demod', [status(thm)], ['2', '3'])).
29.49/29.68	tff(zf_stmt_108, axiom,
29.49/29.68	  (![K:int]:
29.49/29.68	     (app_encode_app(int,int,
29.49/29.68	                     app_encode_app(int,app_encode_fun(int,int),
29.49/29.68	                                    plus_plus(int),K),
29.49/29.68	                     pls) =
29.49/29.68	      K))).
29.49/29.68	tff('5', plain,
29.49/29.68	    ![X157 : int]:
29.49/29.68	      app_encode_app(int, int, 
29.49/29.68	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X157), 
29.49/29.68	        pls)
29.49/29.68	       = X157,
29.49/29.68	    inference('cnf', [status(esa)], [zf_stmt_108])).
29.49/29.68	tff(zf_stmt_127, axiom,
29.49/29.68	  (![K:int]:
29.49/29.68	     (app_encode_app(int,int,bit1,K) =
29.49/29.68	      app_encode_app(int,int,
29.49/29.68	                     app_encode_app(int,app_encode_fun(int,int),
29.49/29.68	                                    plus_plus(int),
29.49/29.68	                                    app_encode_app(int,int,
29.49/29.68	                                                   app_encode_app(int,
29.49/29.68	                                                                  app_encode_fun(
29.49/29.68	                                                                  int,int),
29.49/29.68	                                                                  plus_plus(
29.49/29.68	                                                                  int),
29.49/29.68	                                                                  one_one(
29.49/29.68	                                                                  int)),
29.49/29.68	                                                   K)),
29.49/29.68	                     K)))).
29.49/29.68	tff('6', plain,
29.49/29.68	    ![X195 : int]:
29.49/29.68	      app_encode_app(int, int, bit1, X195)
29.49/29.68	       = app_encode_app(int, int, 
29.49/29.68	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
29.49/29.68	             app_encode_app(int, int, 
29.49/29.68	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
29.49/29.68	                 one_one(int)), X195)), X195),
29.49/29.68	    inference('cnf', [status(esa)], [zf_stmt_127])).
29.49/29.68	tff('7', plain,
29.49/29.68	    ![X195 : int]:
29.49/29.68	      app_encode_app(int, int, bit1, X195)
29.49/29.68	       = app_encode_app(int, int, 
29.49/29.68	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
29.49/29.68	             app_encode_app(int, int, 
29.49/29.68	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
29.49/29.68	                 app_encode_app(int, int, number_number_of(int), 
29.49/29.68	                   app_encode_app(int, int, bit1, pls))), X195)), X195),
29.49/29.68	    inference('demod', [status(thm)], ['6', '3'])).
29.49/29.68	tff('8', plain,
29.49/29.68	    app_encode_app(int, int, bit1, pls)
29.49/29.68	     = app_encode_app(int, int, 
29.49/29.68	         app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
29.49/29.68	           app_encode_app(int, int, number_number_of(int), 
29.49/29.68	             app_encode_app(int, int, bit1, pls))), pls),
29.49/29.68	    inference('sup+', [status(thm)], ['5', '7'])).
29.49/29.68	tff('9', plain,
29.49/29.68	    app_encode_app(int, int, bit1, pls)
29.49/29.68	     = app_encode_app(int, int, number_number_of(int), 
29.49/29.68	         app_encode_app(int, int, bit1, pls)),
29.49/29.68	    inference('demod', [status(thm)], ['8', '5'])).
29.49/29.68	tff(zf_stmt_143, axiom, (number_ring(int))).
29.49/29.68	tff('10', plain, number_ring(int),
29.49/29.68	    inference('cnf', [status(esa)], [zf_stmt_143])).
29.49/29.68	tff(zf_stmt_121, axiom,
29.49/29.68	  (![A:$tType]:
29.49/29.68	     (number_ring(A) =>
29.49/29.68	      (![A1:A]:
29.49/29.68	         (app_encode_app(A,A,
29.49/29.68	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
29.49/29.68	                                        app_encode_app(int,A,
29.49/29.68	                                                       number_number_of(A),
29.49/29.68	                                                       pls)),
29.49/29.68	                         A1) =
29.49/29.68	          A1))))).
29.49/29.68	tff('11', plain,
29.49/29.68	    ![X184 : $tType, X185 : X184]:
29.49/29.68	      (app_encode_app(X184, X184, 
29.49/29.68	         app_encode_app(X184, app_encode_fun(X184, X184), plus_plus(X184), 
29.49/29.68	           app_encode_app(int, X184, number_number_of(X184), pls)), X185)
29.49/29.68	        = X185
29.49/29.68	       | ~ number_ring(X184)),
29.49/29.68	    inference('cnf', [status(esa)], [zf_stmt_121])).
29.49/29.68	tff('12', plain,
29.49/29.68	    ![X0 : int]:
29.49/29.68	      (~ $true
29.49/29.68	       | app_encode_app(int, int, 
29.49/29.68	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
29.49/29.68	             app_encode_app(int, int, number_number_of(int), pls)), X0)
29.49/29.68	          = X0),
29.49/29.68	    inference('sup-', [status(thm)], ['10', '11'])).
29.49/29.68	tff('13', plain,
29.49/29.68	    ![X0 : int]:
29.49/29.68	      app_encode_app(int, int, 
29.49/29.68	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
29.49/29.68	          app_encode_app(int, int, number_number_of(int), pls)), X0)
29.49/29.68	       = X0,
29.49/29.68	    inference('simplify', [status(thm)], ['12'])).
29.49/29.68	tff('14', plain, pls = app_encode_app(int, int, number_number_of(int), pls),
29.49/29.68	    inference('sup+', [status(thm)], ['13', '5'])).
29.49/29.68	tff('15', plain,
29.49/29.68	    (app_encode_app(int, $o, 
29.49/29.68	       app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
29.49/29.68	         app_encode_app(int, int, 
29.49/29.68	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
29.49/29.68	             app_encode_app(nat, int, 
29.49/29.68	               app_encode_app(int, app_encode_fun(nat, int), 
29.49/29.68	                 power_power(int), s), 
29.49/29.68	               app_encode_app(int, nat, number_number_of(nat), 
29.49/29.68	                 app_encode_app(int, int, bit0, 
29.49/29.68	                   app_encode_app(int, int, bit1, pls))))), 
29.49/29.68	           app_encode_app(int, int, bit1, pls))), pls)
29.49/29.68	     | ~ app_encode_app(int, $o, 
29.49/29.68	           app_encode_app(int, app_encode_fun(int, $o), ord_less(int), t), 
29.49/29.68	           pls)),
29.49/29.68	    inference('demod', [status(thm)], ['4', '9', '14', '14'])).
29.49/29.68	tff(zf_stmt_113, axiom,
29.49/29.68	  (![W:int,Z1:int]:
29.49/29.68	     (app_encode_app(int,$o,
29.49/29.68	                     app_encode_app(int,app_encode_fun(int,$o),ord_less(int),
29.49/29.68	                                    Z1),
29.49/29.68	                     W) <=>
29.49/29.68	      (app_encode_app(int,$o,
29.49/29.68	                      app_encode_app(int,app_encode_fun(int,$o),
29.49/29.68	                                     ord_less_eq(int),Z1),
29.49/29.68	                      W) & 
29.49/29.68	       (Z1 != W))))).
29.49/29.68	tff('16', plain,
29.49/29.68	    ![X166 : int, X167 : int]:
29.49/29.68	      (app_encode_app(int, $o, 
29.49/29.68	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), X166), 
29.49/29.68	         X167)
29.49/29.68	       | ~ app_encode_app(int, $o, 
29.49/29.68	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
29.49/29.68	               X166), X167)),
29.49/29.68	    inference('cnf', [status(esa)], [zf_stmt_113])).
29.49/29.68	tff(zf_stmt_118, axiom,
29.49/29.68	  (![Z1:int,W:int]:
29.49/29.68	     (app_encode_app(int,$o,
29.49/29.68	                     app_encode_app(int,app_encode_fun(int,$o),
29.49/29.68	                                    ord_less_eq(int),
29.49/29.68	                                    app_encode_app(int,int,
29.49/29.68	                                                   app_encode_app(int,
29.49/29.68	                                                                  app_encode_fun(
29.49/29.68	                                                                  int,int),
29.49/29.68	                                                                  plus_plus(
29.49/29.68	                                                                  int),W),
29.49/29.68	                                                   one_one(int))),
29.49/29.68	                     Z1) <=>
29.49/29.68	      app_encode_app(int,$o,
29.49/29.68	                     app_encode_app(int,app_encode_fun(int,$o),ord_less(int),
29.49/29.68	                                    W),
29.49/29.68	                     Z1)))).
29.49/29.68	tff('17', plain,
29.49/29.68	    ![X173 : int, X174 : int]:
29.49/29.68	      (app_encode_app(int, $o, 
29.49/29.68	         app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X173), 
29.49/29.68	         X174)
29.49/29.68	       | ~ app_encode_app(int, $o, 
29.49/29.68	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
29.49/29.68	               app_encode_app(int, int, 
29.49/29.68	                 app_encode_app(int, app_encode_fun(int, int), 
29.49/29.68	                   plus_plus(int), X173), one_one(int))), X174)),
29.49/29.68	    inference('cnf', [status(esa)], [zf_stmt_118])).
29.49/29.68	tff('18', plain, one_one(int) = app_encode_app(int, int, bit1, pls),
29.49/29.68	    inference('demod', [status(thm)], ['3', '9'])).
29.49/29.68	tff('19', plain,
29.49/29.68	    ![X173 : int, X174 : int]:
29.49/29.68	      (app_encode_app(int, $o, 
29.49/29.68	         app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X173), 
29.49/29.68	         X174)
29.49/29.68	       | ~ app_encode_app(int, $o, 
29.49/29.68	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
29.49/29.68	               app_encode_app(int, int, 
29.49/29.68	                 app_encode_app(int, app_encode_fun(int, int), 
29.49/29.68	                   plus_plus(int), X173), 
29.49/29.68	                 app_encode_app(int, int, bit1, pls))), X174)),
29.49/29.68	    inference('demod', [status(thm)], ['17', '18'])).
29.49/29.68	tff('20', plain,
29.49/29.68	    ![X0 : int, X1 : int]:
29.49/29.68	      (~ $true
29.49/29.68	       | ~ app_encode_app(int, $o, 
29.49/29.68	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
29.49/29.68	               app_encode_app(int, int, 
29.49/29.68	                 app_encode_app(int, app_encode_fun(int, int), 
29.49/29.68	                   plus_plus(int), X1), app_encode_app(int, int, bit1, pls))), 
29.49/29.68	             X0)
29.49/29.68	       | app_encode_app(int, $o, 
29.49/29.68	           app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X1), 
29.49/29.68	           X0)),
29.49/29.68	    inference('sup-', [status(thm)], ['16', '19'])).
29.49/29.68	tff('21', plain,
29.49/29.68	    ![X0 : int, X1 : int]:
29.49/29.68	      (app_encode_app(int, $o, 
29.49/29.68	         app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X1), X0)
29.49/29.68	       | ~ app_encode_app(int, $o, 
29.49/29.68	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
29.49/29.68	               app_encode_app(int, int, 
29.49/29.68	                 app_encode_app(int, app_encode_fun(int, int), 
29.49/29.68	                   plus_plus(int), X1), app_encode_app(int, int, bit1, pls))), 
29.49/29.68	             X0)),
29.49/29.68	    inference('simplify', [status(thm)], ['20'])).
29.49/29.68	tff('22', plain,
29.49/29.68	    (~ $true
29.49/29.68	     | ~ app_encode_app(int, $o, 
29.49/29.68	           app_encode_app(int, app_encode_fun(int, $o), ord_less(int), t), 
29.49/29.68	           pls)
29.49/29.68	     | app_encode_app(int, $o, 
29.49/29.68	         app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
29.49/29.68	           app_encode_app(nat, int, 
29.49/29.68	             app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
29.49/29.68	               s), 
29.49/29.68	             app_encode_app(int, nat, number_number_of(nat), 
29.49/29.68	               app_encode_app(int, int, bit0, 
29.49/29.68	                 app_encode_app(int, int, bit1, pls))))), pls)),
29.49/29.68	    inference('sup-', [status(thm)], ['15', '21'])).
29.49/29.68	tff(zf_stmt_36, axiom,
29.49/29.68	  (app_encode_app(int,$o,
29.49/29.68	                  app_encode_app(int,app_encode_fun(int,$o),ord_less(int),t),
29.49/29.68	                  one_one(int)))).
29.49/29.68	tff('23', plain,
29.49/29.68	    app_encode_app(int, $o, 
29.49/29.68	      app_encode_app(int, app_encode_fun(int, $o), ord_less(int), t), 
29.49/29.68	      one_one(int)),
29.49/29.68	    inference('cnf', [status(esa)], [zf_stmt_36])).
29.49/29.68	tff('24', plain,
29.49/29.68	    app_encode_app(int, $o, 
29.49/29.68	      app_encode_app(int, app_encode_fun(int, $o), ord_less(int), t), 
29.49/29.68	      app_encode_app(int, int, number_number_of(int), 
29.49/29.68	        app_encode_app(int, int, bit1, pls))),
29.49/29.68	    inference('demod', [status(thm)], ['23', '3'])).
29.49/29.68	tff('25', plain,
29.49/29.68	    app_encode_app(int, $o, 
29.49/29.68	      app_encode_app(int, app_encode_fun(int, $o), ord_less(int), t), 
29.49/29.68	      app_encode_app(int, int, bit1, pls)),
29.49/29.68	    inference('demod', [status(thm)], ['24', '9'])).
29.49/29.68	tff(zf_stmt_109, axiom,
29.49/29.68	  (![K:int]:
29.49/29.68	     (app_encode_app(int,int,
29.49/29.68	                     app_encode_app(int,app_encode_fun(int,int),
29.49/29.68	                                    plus_plus(int),pls),
29.49/29.68	                     K) =
29.49/29.68	      K))).
29.49/29.68	tff('26', plain,
29.49/29.68	    ![X158 : int]:
29.49/29.68	      app_encode_app(int, int, 
29.49/29.68	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
29.49/29.68	        X158)
29.49/29.68	       = X158,
29.49/29.68	    inference('cnf', [status(esa)], [zf_stmt_109])).
29.49/29.68	tff(zf_stmt_91, axiom,
29.49/29.68	  (![Z1:int,W:int]:
29.49/29.68	     (app_encode_app(int,$o,
29.49/29.68	                     app_encode_app(int,app_encode_fun(int,$o),ord_less(int),
29.49/29.68	                                    W),
29.49/29.68	                     app_encode_app(int,int,
29.49/29.68	                                    app_encode_app(int,
29.49/29.68	                                                   app_encode_fun(int,int),
29.49/29.68	                                                   plus_plus(int),Z1),
29.49/29.68	                                    one_one(int))) <=>
29.49/29.68	      app_encode_app(int,$o,
29.49/29.68	                     app_encode_app(int,app_encode_fun(int,$o),
29.49/29.68	                                    ord_less_eq(int),W),
29.49/29.68	                     Z1)))).
29.49/29.68	tff('27', plain,
29.49/29.68	    ![X117 : int, X118 : int]:
29.49/29.68	      (app_encode_app(int, $o, 
29.49/29.68	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), X117), 
29.49/29.68	         X118)
29.49/29.68	       | ~ app_encode_app(int, $o, 
29.49/29.68	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
29.49/29.68	               X117), 
29.49/29.68	             app_encode_app(int, int, 
29.49/29.68	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
29.49/29.68	                 X118), one_one(int)))),
29.49/29.68	    inference('cnf', [status(esa)], [zf_stmt_91])).
29.49/29.68	tff('28', plain,
29.49/29.68	    ![X117 : int, X118 : int]:
29.49/29.68	      (app_encode_app(int, $o, 
29.49/29.68	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), X117), 
29.49/29.68	         X118)
29.49/29.68	       | ~ app_encode_app(int, $o, 
29.49/29.68	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
29.49/29.68	               X117), 
29.49/29.68	             app_encode_app(int, int, 
29.49/29.68	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
29.49/29.68	                 X118), app_encode_app(int, int, bit1, pls)))),
29.49/29.68	    inference('demod', [status(thm)], ['27', '18'])).
29.49/29.68	tff('29', plain,
29.49/29.68	    ![X0 : int]:
29.49/29.68	      (~ app_encode_app(int, $o, 
29.49/29.68	           app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X0), 
29.49/29.68	           app_encode_app(int, int, bit1, pls))
29.49/29.68	       | app_encode_app(int, $o, 
29.49/29.68	           app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), X0), 
29.49/29.68	           pls)),
29.49/29.68	    inference('sup-', [status(thm)], ['26', '28'])).
29.49/29.68	tff('30', plain,
29.49/29.68	    (~ $true
29.49/29.68	     | app_encode_app(int, $o, 
29.49/29.68	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), t), 
29.49/29.68	         pls)),
29.49/29.68	    inference('sup-', [status(thm)], ['25', '29'])).
29.49/29.68	tff('31', plain,
29.49/29.68	    app_encode_app(int, $o, 
29.49/29.68	      app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), t), pls),
29.49/29.68	    inference('simplify', [status(thm)], ['30'])).
29.49/29.68	tff('32', plain,
29.49/29.68	    ![X167 : int, X168 : int]:
29.49/29.68	      (app_encode_app(int, $o, 
29.49/29.68	         app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X168), 
29.49/29.68	         X167)
29.49/29.68	       | X168 = X167
29.49/29.68	       | ~ app_encode_app(int, $o, 
29.49/29.68	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
29.49/29.68	               X168), X167)),
29.49/29.68	    inference('cnf', [status(esa)], [zf_stmt_113])).
29.49/29.68	tff('33', plain,
29.49/29.68	    (~ $true
29.49/29.68	     | t = pls
29.49/29.68	     | app_encode_app(int, $o, 
29.49/29.68	         app_encode_app(int, app_encode_fun(int, $o), ord_less(int), t), pls)),
29.49/29.68	    inference('sup-', [status(thm)], ['31', '32'])).
29.49/29.68	tff('34', plain,
29.49/29.68	    (app_encode_app(int, $o, 
29.49/29.68	       app_encode_app(int, app_encode_fun(int, $o), ord_less(int), t), pls)
29.49/29.68	     | t = pls),
29.49/29.68	    inference('simplify', [status(thm)], ['33'])).
29.49/29.68	tff(zf_stmt_37, axiom,
29.49/29.68	  ((t = zero_zero(int)) =>
29.49/29.68	   (app_encode_app(int,int,
29.49/29.68	                   app_encode_app(int,app_encode_fun(int,int),plus_plus(int),
29.49/29.68	                                  app_encode_app(nat,int,
29.49/29.68	                                                 app_encode_app(int,
29.49/29.68	                                                                app_encode_fun(
29.49/29.68	                                                                nat,int),
29.49/29.68	                                                                power_power(
29.49/29.68	                                                                int),s),
29.49/29.68	                                                 app_encode_app(int,nat,
29.49/29.68	                                                                number_number_of(
29.49/29.68	                                                                nat),
29.49/29.68	                                                                app_encode_app(
29.49/29.68	                                                                int,int,bit0,
29.49/29.68	                                                                app_encode_app(
29.49/29.68	                                                                int,int,bit1,
29.49/29.68	                                                                pls))))),
29.49/29.68	                   one_one(int)) =
29.49/29.68	    zero_zero(int)))).
29.49/29.68	tff('35', plain,
29.49/29.68	    (app_encode_app(int, int, 
29.49/29.68	       app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
29.49/29.68	         app_encode_app(nat, int, 
29.49/29.68	           app_encode_app(int, app_encode_fun(nat, int), power_power(int), s), 
29.49/29.68	           app_encode_app(int, nat, number_number_of(nat), 
29.49/29.68	             app_encode_app(int, int, bit0, 
29.49/29.68	               app_encode_app(int, int, bit1, pls))))), one_one(int))
29.49/29.68	      = zero_zero(int)
29.49/29.68	     | t != zero_zero(int)),
29.49/29.68	    inference('cnf', [status(esa)], [zf_stmt_37])).
29.49/29.68	tff('36', plain,
29.49/29.68	    (app_encode_app(int, int, 
29.49/29.68	       app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
29.49/29.68	         app_encode_app(nat, int, 
29.49/29.68	           app_encode_app(int, app_encode_fun(nat, int), power_power(int), s), 
29.49/29.68	           app_encode_app(int, nat, number_number_of(nat), 
29.49/29.68	             app_encode_app(int, int, bit0, 
29.49/29.68	               app_encode_app(int, int, bit1, pls))))), one_one(int))
29.49/29.68	      = app_encode_app(int, int, number_number_of(int), pls)
29.49/29.68	     | t != app_encode_app(int, int, number_number_of(int), pls)),
29.49/29.68	    inference('demod', [status(thm)], ['35', '1', '1'])).
29.49/29.68	tff('37', plain,
29.49/29.68	    (app_encode_app(int, int, 
29.49/29.68	       app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
29.49/29.68	         app_encode_app(nat, int, 
29.49/29.68	           app_encode_app(int, app_encode_fun(nat, int), power_power(int), s), 
29.49/29.68	           app_encode_app(int, nat, number_number_of(nat), 
29.49/29.68	             app_encode_app(int, int, bit0, 
29.49/29.68	               app_encode_app(int, int, bit1, pls))))), 
29.49/29.68	       app_encode_app(int, int, bit1, pls))
29.49/29.68	      = pls
29.49/29.68	     | t != pls),
29.49/29.68	    inference('demod', [status(thm)], ['36', '18', '14', '14'])).
29.49/29.68	tff(zf_stmt_35, axiom,
29.49/29.68	  (app_encode_app(int,$o,
29.49/29.68	                  app_encode_app(int,app_encode_fun(int,$o),ord_less_eq(int),
29.49/29.68	                                 zero_zero(int)),
29.49/29.68	                  app_encode_app(nat,int,
29.49/29.68	                                 app_encode_app(int,app_encode_fun(nat,int),
29.49/29.68	                                                power_power(int),s),
29.49/29.68	                                 app_encode_app(int,nat,
29.49/29.68	                                                number_number_of(nat),
29.49/29.68	                                                app_encode_app(int,int,bit0,
29.49/29.68	                                                               app_encode_app(
29.49/29.68	                                                               int,int,bit1,
29.49/29.68	                                                               pls))))))).
29.49/29.68	tff('38', plain,
29.49/29.68	    app_encode_app(int, $o, 
29.49/29.68	      app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
29.49/29.68	        zero_zero(int)), 
29.49/29.68	      app_encode_app(nat, int, 
29.49/29.68	        app_encode_app(int, app_encode_fun(nat, int), power_power(int), s), 
29.49/29.68	        app_encode_app(int, nat, number_number_of(nat), 
29.49/29.68	          app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls))))),
29.49/29.68	    inference('cnf', [status(esa)], [zf_stmt_35])).
29.49/29.68	tff('39', plain,
29.49/29.68	    app_encode_app(int, $o, 
29.49/29.68	      app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
29.49/29.68	        app_encode_app(int, int, number_number_of(int), pls)), 
29.49/29.68	      app_encode_app(nat, int, 
29.49/29.68	        app_encode_app(int, app_encode_fun(nat, int), power_power(int), s), 
29.49/29.68	        app_encode_app(int, nat, number_number_of(nat), 
29.49/29.68	          app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls))))),
29.49/29.68	    inference('demod', [status(thm)], ['38', '1'])).
29.49/29.68	tff('40', plain,
29.49/29.68	    app_encode_app(int, $o, 
29.49/29.68	      app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), pls), 
29.49/29.68	      app_encode_app(nat, int, 
29.49/29.68	        app_encode_app(int, app_encode_fun(nat, int), power_power(int), s), 
29.49/29.68	        app_encode_app(int, nat, number_number_of(nat), 
29.49/29.68	          app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls))))),
29.49/29.68	    inference('demod', [status(thm)], ['39', '14'])).
29.49/29.68	tff('41', plain,
29.49/29.68	    ![X118 : int, X119 : int]:
29.49/29.68	      (app_encode_app(int, $o, 
29.49/29.68	         app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X119), 
29.49/29.68	         app_encode_app(int, int, 
29.49/29.68	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
29.49/29.68	             X118), one_one(int)))
29.49/29.68	       | ~ app_encode_app(int, $o, 
29.49/29.68	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
29.49/29.68	               X119), X118)),
29.49/29.68	    inference('cnf', [status(esa)], [zf_stmt_91])).
29.49/29.68	tff('42', plain,
29.49/29.68	    ![X118 : int, X119 : int]:
29.49/29.68	      (app_encode_app(int, $o, 
29.49/29.68	         app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X119), 
29.49/29.68	         app_encode_app(int, int, 
29.49/29.68	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
29.49/29.68	             X118), app_encode_app(int, int, bit1, pls)))
29.49/29.68	       | ~ app_encode_app(int, $o, 
29.49/29.68	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
29.49/29.68	               X119), X118)),
29.49/29.68	    inference('demod', [status(thm)], ['41', '18'])).
29.49/29.68	tff('43', plain,
29.49/29.68	    (~ $true
29.49/29.68	     | app_encode_app(int, $o, 
29.49/29.68	         app_encode_app(int, app_encode_fun(int, $o), ord_less(int), pls), 
29.49/29.68	         app_encode_app(int, int, 
29.49/29.68	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
29.49/29.68	             app_encode_app(nat, int, 
29.49/29.68	               app_encode_app(int, app_encode_fun(nat, int), 
29.49/29.68	                 power_power(int), s), 
29.49/29.68	               app_encode_app(int, nat, number_number_of(nat), 
29.49/29.68	                 app_encode_app(int, int, bit0, 
29.49/29.68	                   app_encode_app(int, int, bit1, pls))))), 
29.49/29.68	           app_encode_app(int, int, bit1, pls)))),
29.49/29.68	    inference('sup-', [status(thm)], ['40', '42'])).
29.49/29.68	tff('44', plain,
29.49/29.68	    app_encode_app(int, $o, 
29.49/29.68	      app_encode_app(int, app_encode_fun(int, $o), ord_less(int), pls), 
29.49/29.68	      app_encode_app(int, int, 
29.49/29.68	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
29.49/29.68	          app_encode_app(nat, int, 
29.49/29.68	            app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
29.49/29.68	              s), 
29.49/29.68	            app_encode_app(int, nat, number_number_of(nat), 
29.49/29.68	              app_encode_app(int, int, bit0, 
29.49/29.68	                app_encode_app(int, int, bit1, pls))))), 
29.49/29.68	        app_encode_app(int, int, bit1, pls))),
29.49/29.68	    inference('simplify', [status(thm)], ['43'])).
29.49/29.68	tff('45', plain,
29.49/29.68	    (app_encode_app(int, $o, 
29.49/29.68	       app_encode_app(int, app_encode_fun(int, $o), ord_less(int), pls), pls)
29.49/29.68	     | t != pls),
29.49/29.68	    inference('sup+', [status(thm)], ['37', '44'])).
29.49/29.68	tff('46', plain,
29.49/29.68	    ![X166 : int, X167 : int]:
29.49/29.68	      (X166 != X167
29.49/29.68	       | ~ app_encode_app(int, $o, 
29.49/29.68	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
29.49/29.68	               X166), X167)),
29.49/29.68	    inference('cnf', [status(esa)], [zf_stmt_113])).
29.49/29.68	tff('47', plain,
29.49/29.68	    ![X167 : int]:
29.49/29.68	      ~ app_encode_app(int, $o, 
29.49/29.68	          app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X167), 
29.49/29.68	          X167),
29.49/29.68	    inference('simplify', [status(thm)], ['46'])).
29.49/29.68	tff('48', plain, t != pls, inference('clc', [status(thm)], ['45', '47'])).
29.49/29.68	tff('49', plain,
29.49/29.68	    app_encode_app(int, $o, 
29.49/29.68	      app_encode_app(int, app_encode_fun(int, $o), ord_less(int), t), pls),
29.49/29.68	    inference('simplify_reflect-', [status(thm)], ['34', '48'])).
29.49/29.68	tff('50', plain,
29.49/29.68	    (~ $true
29.49/29.68	     | ~ $true
29.49/29.68	     | app_encode_app(int, $o, 
29.49/29.68	         app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
29.49/29.68	           app_encode_app(nat, int, 
29.49/29.68	             app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
29.49/29.68	               s), 
29.49/29.68	             app_encode_app(int, nat, number_number_of(nat), 
29.49/29.68	               app_encode_app(int, int, bit0, 
29.49/29.68	                 app_encode_app(int, int, bit1, pls))))), pls)),
29.49/29.68	    inference('demod', [status(thm)], ['22', '49'])).
29.49/29.68	tff('51', plain,
29.49/29.68	    app_encode_app(int, $o, 
29.49/29.68	      app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
29.49/29.68	        app_encode_app(nat, int, 
29.49/29.68	          app_encode_app(int, app_encode_fun(nat, int), power_power(int), s), 
29.49/29.68	          app_encode_app(int, nat, number_number_of(nat), 
29.49/29.68	            app_encode_app(int, int, bit0, 
29.49/29.68	              app_encode_app(int, int, bit1, pls))))), pls),
29.49/29.68	    inference('simplify', [status(thm)], ['50'])).
29.49/29.68	tff(zf_stmt_87, axiom,
29.49/29.68	  (![V2:int]:
29.49/29.68	     ((app_encode_app(int,nat,number_number_of(nat),V2) = zero_zero(nat)) <=>
29.49/29.68	      app_encode_app(int,$o,
29.49/29.68	                     app_encode_app(int,app_encode_fun(int,$o),
29.49/29.68	                                    ord_less_eq(int),V2),
29.49/29.68	                     pls)))).
29.49/29.68	tff('52', plain,
29.49/29.68	    ![X108 : int]:
29.49/29.68	      (app_encode_app(int, nat, number_number_of(nat), X108) = zero_zero(nat)
29.49/29.68	       | ~ app_encode_app(int, $o, 
29.49/29.68	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
29.49/29.68	               X108), pls)),
29.49/29.68	    inference('cnf', [status(esa)], [zf_stmt_87])).
29.49/29.68	tff(zf_stmt_74, axiom,
29.49/29.68	  (app_encode_app(int,nat,number_number_of(nat),pls) = zero_zero(nat))).
29.49/29.68	tff('53', plain,
29.49/29.68	    app_encode_app(int, nat, number_number_of(nat), pls) = zero_zero(nat),
29.49/29.68	    inference('cnf', [status(esa)], [zf_stmt_74])).
29.49/29.68	tff('54', plain,
29.49/29.68	    ![X108 : int]:
29.49/29.68	      (app_encode_app(int, nat, number_number_of(nat), X108)
29.49/29.68	        = app_encode_app(int, nat, number_number_of(nat), pls)
29.49/29.68	       | ~ app_encode_app(int, $o, 
29.49/29.68	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
29.49/29.68	               X108), pls)),
29.49/29.68	    inference('demod', [status(thm)], ['52', '53'])).
29.49/29.68	tff('55', plain,
29.49/29.68	    ![X0 : int]:
29.49/29.68	      (~ $true
29.49/29.68	       | ~ app_encode_app(int, $o, 
29.49/29.68	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X0), 
29.49/29.68	             pls)
29.49/29.68	       | app_encode_app(int, nat, number_number_of(nat), X0)
29.49/29.68	          = app_encode_app(int, nat, number_number_of(nat), pls)),
29.49/29.68	    inference('sup-', [status(thm)], ['16', '54'])).
29.49/29.68	tff('56', plain,
29.49/29.68	    ![X0 : int]:
29.49/29.68	      (app_encode_app(int, nat, number_number_of(nat), X0)
29.49/29.68	        = app_encode_app(int, nat, number_number_of(nat), pls)
29.49/29.68	       | ~ app_encode_app(int, $o, 
29.49/29.68	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X0), 
29.49/29.68	             pls)),
29.49/29.68	    inference('simplify', [status(thm)], ['55'])).
29.49/29.68	tff('57', plain,
29.49/29.68	    (~ $true
29.49/29.68	     | app_encode_app(int, nat, number_number_of(nat), 
29.49/29.68	         app_encode_app(nat, int, 
29.49/29.68	           app_encode_app(int, app_encode_fun(nat, int), power_power(int), s), 
29.49/29.68	           app_encode_app(int, nat, number_number_of(nat), 
29.49/29.68	             app_encode_app(int, int, bit0, 
29.49/29.68	               app_encode_app(int, int, bit1, pls)))))
29.49/29.68	        = app_encode_app(int, nat, number_number_of(nat), pls)),
29.49/29.68	    inference('sup-', [status(thm)], ['51', '56'])).
29.49/29.68	tff('58', plain,
29.49/29.68	    app_encode_app(int, nat, number_number_of(nat), 
29.49/29.68	      app_encode_app(nat, int, 
29.49/29.68	        app_encode_app(int, app_encode_fun(nat, int), power_power(int), s), 
29.49/29.68	        app_encode_app(int, nat, number_number_of(nat), 
29.49/29.68	          app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls)))))
29.49/29.68	     = app_encode_app(int, nat, number_number_of(nat), pls),
29.49/29.68	    inference('simplify', [status(thm)], ['57'])).
29.49/29.68	tff('59', plain,
29.49/29.68	    ![X107 : int]:
29.49/29.68	      (app_encode_app(int, $o, 
29.49/29.68	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), X107), 
29.49/29.68	         pls)
29.49/29.68	       | app_encode_app(int, nat, number_number_of(nat), X107)
29.49/29.68	          != zero_zero(nat)),
29.49/29.68	    inference('cnf', [status(esa)], [zf_stmt_87])).
29.49/29.68	tff('60', plain,
29.49/29.68	    ![X107 : int]:
29.49/29.68	      (app_encode_app(int, $o, 
29.49/29.68	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), X107), 
29.49/29.68	         pls)
29.49/29.68	       | app_encode_app(int, nat, number_number_of(nat), X107)
29.49/29.68	          != app_encode_app(int, nat, number_number_of(nat), pls)),
29.49/29.68	    inference('demod', [status(thm)], ['59', '53'])).
29.49/29.68	tff('61', plain,
29.49/29.68	    (app_encode_app(int, nat, number_number_of(nat), pls)
29.49/29.68	      != app_encode_app(int, nat, number_number_of(nat), pls)
29.49/29.68	     | app_encode_app(int, $o, 
29.49/29.68	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
29.49/29.68	           app_encode_app(nat, int, 
29.49/29.68	             app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
29.49/29.68	               s), 
29.49/29.68	             app_encode_app(int, nat, number_number_of(nat), 
29.49/29.68	               app_encode_app(int, int, bit0, 
29.49/29.68	                 app_encode_app(int, int, bit1, pls))))), pls)),
29.49/29.68	    inference('sup-', [status(thm)], ['58', '60'])).
29.49/29.68	tff('62', plain,
29.49/29.68	    app_encode_app(int, $o, 
29.49/29.68	      app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
29.49/29.68	        app_encode_app(nat, int, 
29.49/29.68	          app_encode_app(int, app_encode_fun(nat, int), power_power(int), s), 
29.49/29.68	          app_encode_app(int, nat, number_number_of(nat), 
29.49/29.68	            app_encode_app(int, int, bit0, 
29.49/29.68	              app_encode_app(int, int, bit1, pls))))), pls),
29.49/29.68	    inference('simplify', [status(thm)], ['61'])).
29.49/29.68	tff('63', plain,
29.49/29.68	    (~ $true
29.49/29.68	     | app_encode_app(int, $o, 
29.49/29.68	         app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
29.49/29.68	           app_encode_app(nat, int, 
29.49/29.68	             app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
29.49/29.68	               s), 
29.49/29.68	             app_encode_app(int, nat, number_number_of(nat), 
29.49/29.68	               app_encode_app(int, int, bit0, 
29.49/29.68	                 app_encode_app(int, int, bit1, pls))))), 
29.49/29.68	         app_encode_app(int, int, 
29.49/29.68	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
29.49/29.68	           app_encode_app(int, int, bit1, pls)))),
29.49/29.68	    inference('sup-', [status(thm)], ['62', '42'])).
29.49/29.68	tff('64', plain,
29.49/29.68	    (~ $true
29.49/29.68	     | app_encode_app(int, $o, 
29.49/29.68	         app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
29.49/29.68	           app_encode_app(nat, int, 
29.49/29.68	             app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
29.49/29.68	               s), 
29.49/29.68	             app_encode_app(int, nat, number_number_of(nat), 
29.49/29.68	               app_encode_app(int, int, bit0, 
29.49/29.68	                 app_encode_app(int, int, bit1, pls))))), 
29.49/29.68	         app_encode_app(int, int, bit1, pls))),
29.49/29.68	    inference('demod', [status(thm)], ['63', '26'])).
29.49/29.68	tff('65', plain,
29.49/29.68	    app_encode_app(int, $o, 
29.49/29.68	      app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
29.49/29.68	        app_encode_app(nat, int, 
29.49/29.68	          app_encode_app(int, app_encode_fun(nat, int), power_power(int), s), 
29.49/29.68	          app_encode_app(int, nat, number_number_of(nat), 
29.49/29.68	            app_encode_app(int, int, bit0, 
29.49/29.68	              app_encode_app(int, int, bit1, pls))))), 
29.49/29.68	      app_encode_app(int, int, bit1, pls)),
29.49/29.68	    inference('simplify', [status(thm)], ['64'])).
29.49/29.68	tff(zf_stmt_63, axiom,
29.49/29.68	  (![L:int,K3:int]:
29.49/29.68	     (app_encode_app(int,$o,
29.49/29.68	                     app_encode_app(int,app_encode_fun(int,$o),ord_less(int),
29.49/29.68	                                    app_encode_app(int,int,bit0,K3)),
29.49/29.68	                     app_encode_app(int,int,bit0,L)) <=>
29.49/29.68	      app_encode_app(int,$o,
29.49/29.68	                     app_encode_app(int,app_encode_fun(int,$o),ord_less(int),
29.49/29.68	                                    K3),
29.49/29.68	                     L)))).
29.49/29.68	tff('66', plain,
29.49/29.68	    ![X52 : int, X53 : int]:
29.49/29.68	      (app_encode_app(int, $o, 
29.49/29.68	         app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
29.49/29.68	           app_encode_app(int, int, bit0, X53)), 
29.49/29.68	         app_encode_app(int, int, bit0, X52))
29.49/29.68	       | ~ app_encode_app(int, $o, 
29.49/29.68	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X53), 
29.49/29.68	             X52)),
29.49/29.68	    inference('cnf', [status(esa)], [zf_stmt_63])).
29.49/29.68	tff(zf_stmt_131, axiom,
29.49/29.68	  (![X:int]:
29.49/29.68	     (app_encode_app(int,$o,
29.49/29.68	                     app_encode_app(int,app_encode_fun(int,$o),
29.49/29.68	                                    ord_less_eq(int),zero_zero(int)),
29.49/29.68	                     X) =>
29.49/29.68	      (app_encode_app(int,$o,
29.49/29.68	                      app_encode_app(int,app_encode_fun(int,$o),
29.49/29.68	                                     ord_less(int),X),
29.49/29.68	                      app_encode_app(int,int,number_number_of(int),
29.49/29.68	                                     app_encode_app(int,int,bit0,
29.49/29.68	                                                    app_encode_app(int,int,
29.49/29.68	                                                                   bit1,pls)))) =>
29.49/29.68	       ((X = zero_zero(int)) | (X = one_one(int))))))).
29.49/29.68	tff('67', plain,
29.49/29.68	    ![X201 : int]:
29.49/29.68	      (~ app_encode_app(int, $o, 
29.49/29.68	           app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X201), 
29.49/29.68	           app_encode_app(int, int, number_number_of(int), 
29.49/29.68	             app_encode_app(int, int, bit0, 
29.49/29.68	               app_encode_app(int, int, bit1, pls))))
29.49/29.68	       | X201 = zero_zero(int)
29.49/29.68	       | X201 = one_one(int)
29.49/29.68	       | ~ app_encode_app(int, $o, 
29.49/29.68	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
29.49/29.68	               zero_zero(int)), X201)),
29.49/29.68	    inference('cnf', [status(esa)], [zf_stmt_131])).
29.49/29.68	tff(zf_stmt_110, axiom,
29.49/29.68	  (![K:int]:
29.49/29.68	     (app_encode_app(int,int,bit0,K) =
29.49/29.68	      app_encode_app(int,int,
29.49/29.68	                     app_encode_app(int,app_encode_fun(int,int),
29.49/29.68	                                    plus_plus(int),K),
29.49/29.68	                     K)))).
29.49/29.68	tff('68', plain,
29.49/29.68	    ![X159 : int]:
29.49/29.68	      app_encode_app(int, int, bit0, X159)
29.49/29.68	       = app_encode_app(int, int, 
29.49/29.68	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
29.49/29.68	             X159), X159),
29.49/29.68	    inference('cnf', [status(esa)], [zf_stmt_110])).
29.49/29.68	tff(zf_stmt_100, axiom,
29.49/29.68	  (![W1:int,V:int]:
29.49/29.68	     (app_encode_app(int,int,
29.49/29.68	                     app_encode_app(int,app_encode_fun(int,int),
29.49/29.68	                                    plus_plus(int),
29.49/29.68	                                    app_encode_app(int,int,
29.49/29.68	                                                   number_number_of(int),V)),
29.49/29.68	                     app_encode_app(int,int,number_number_of(int),W1)) =
29.49/29.68	      app_encode_app(int,int,number_number_of(int),
29.49/29.68	                     app_encode_app(int,int,
29.49/29.68	                                    app_encode_app(int,
29.49/29.68	                                                   app_encode_fun(int,int),
29.49/29.68	                                                   plus_plus(int),V),
29.49/29.68	                                    W1))))).
29.49/29.68	tff('69', plain,
29.49/29.68	    ![X140 : int, X141 : int]:
29.49/29.68	      app_encode_app(int, int, 
29.49/29.68	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
29.49/29.68	          app_encode_app(int, int, number_number_of(int), X140)), 
29.49/29.68	        app_encode_app(int, int, number_number_of(int), X141))
29.49/29.68	       = app_encode_app(int, int, number_number_of(int), 
29.49/29.68	           app_encode_app(int, int, 
29.49/29.68	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
29.49/29.68	               X140), X141)),
29.49/29.68	    inference('cnf', [status(esa)], [zf_stmt_100])).
29.49/29.68	tff('70', plain,
29.49/29.68	    ![X0 : int]:
29.49/29.68	      app_encode_app(int, int, bit0, 
29.49/29.68	        app_encode_app(int, int, number_number_of(int), X0))
29.49/29.68	       = app_encode_app(int, int, number_number_of(int), 
29.49/29.68	           app_encode_app(int, int, 
29.49/29.68	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
29.49/29.68	               X0), X0)),
29.49/29.68	    inference('sup+', [status(thm)], ['68', '69'])).
29.49/29.68	tff('71', plain,
29.49/29.68	    ![X0 : int]:
29.49/29.68	      app_encode_app(int, int, bit0, 
29.49/29.68	        app_encode_app(int, int, number_number_of(int), X0))
29.49/29.68	       = app_encode_app(int, int, number_number_of(int), 
29.49/29.68	           app_encode_app(int, int, bit0, X0)),
29.49/29.68	    inference('demod', [status(thm)], ['70', '68'])).
29.49/29.68	tff('72', plain,
29.49/29.68	    app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls))
29.49/29.68	     = app_encode_app(int, int, number_number_of(int), 
29.49/29.68	         app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls))),
29.49/29.68	    inference('sup+', [status(thm)], ['9', '71'])).
29.49/29.68	tff('73', plain, zero_zero(int) = pls,
29.49/29.68	    inference('demod', [status(thm)], ['1', '14'])).
29.49/29.68	tff('74', plain,
29.49/29.68	    ![X201 : int]:
29.49/29.68	      (~ app_encode_app(int, $o, 
29.49/29.68	           app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X201), 
29.49/29.68	           app_encode_app(int, int, bit0, 
29.49/29.68	             app_encode_app(int, int, bit1, pls)))
29.49/29.68	       | X201 = pls
29.49/29.68	       | X201 = app_encode_app(int, int, bit1, pls)
29.49/29.68	       | ~ app_encode_app(int, $o, 
29.49/29.68	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
29.49/29.68	               pls), X201)),
29.49/29.68	    inference('demod', [status(thm)], ['67', '72', '73', '18', '73'])).
29.49/29.68	tff('75', plain,
29.49/29.68	    ![X0 : int]:
29.49/29.68	      (~ $true
29.49/29.68	       | ~ app_encode_app(int, $o, 
29.49/29.68	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X0), 
29.49/29.68	             app_encode_app(int, int, bit1, pls))
29.49/29.68	       | ~ app_encode_app(int, $o, 
29.49/29.68	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
29.49/29.68	               pls), app_encode_app(int, int, bit0, X0))
29.49/29.68	       | app_encode_app(int, int, bit0, X0)
29.49/29.68	          = app_encode_app(int, int, bit1, pls)
29.49/29.68	       | app_encode_app(int, int, bit0, X0) = pls),
29.49/29.68	    inference('sup-', [status(thm)], ['66', '74'])).
29.49/29.68	tff('76', plain,
29.49/29.68	    ![X0 : int]:
29.49/29.68	      (app_encode_app(int, int, bit0, X0) = pls
29.49/29.68	       | app_encode_app(int, int, bit0, X0)
29.49/29.68	          = app_encode_app(int, int, bit1, pls)
29.49/29.68	       | ~ app_encode_app(int, $o, 
29.49/29.68	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
29.49/29.68	               pls), app_encode_app(int, int, bit0, X0))
29.49/29.68	       | ~ app_encode_app(int, $o, 
29.49/29.68	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X0), 
29.49/29.68	             app_encode_app(int, int, bit1, pls))),
29.49/29.68	    inference('simplify', [status(thm)], ['75'])).
29.49/29.68	tff(zf_stmt_56, axiom,
29.49/29.68	  (![L1:int,K:int]:
29.49/29.68	     (app_encode_app(int,int,bit1,K) != app_encode_app(int,int,bit0,L1)))).
29.49/29.68	tff('77', plain,
29.49/29.68	    ![X40 : int, X41 : int]:
29.49/29.68	      app_encode_app(int, int, bit1, X41)
29.49/29.68	       != app_encode_app(int, int, bit0, X40),
29.49/29.68	    inference('cnf', [status(esa)], [zf_stmt_56])).
29.49/29.68	tff('78', plain,
29.49/29.68	    ![X0 : int]:
29.49/29.68	      (~ app_encode_app(int, $o, 
29.49/29.68	           app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X0), 
29.49/29.68	           app_encode_app(int, int, bit1, pls))
29.49/29.68	       | ~ app_encode_app(int, $o, 
29.49/29.68	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
29.49/29.68	               pls), app_encode_app(int, int, bit0, X0))
29.49/29.68	       | app_encode_app(int, int, bit0, X0) = pls),
29.49/29.68	    inference('clc', [status(thm)], ['76', '77'])).
29.49/29.68	tff('79', plain,
29.49/29.68	    (~ $true
29.49/29.68	     | app_encode_app(int, int, bit0, 
29.49/29.68	         app_encode_app(nat, int, 
29.49/29.68	           app_encode_app(int, app_encode_fun(nat, int), power_power(int), s), 
29.49/29.68	           app_encode_app(int, nat, number_number_of(nat), 
29.49/29.68	             app_encode_app(int, int, bit0, 
29.49/29.68	               app_encode_app(int, int, bit1, pls)))))
29.49/29.68	        = pls
29.49/29.68	     | ~ app_encode_app(int, $o, 
29.49/29.68	           app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
29.49/29.68	             pls), 
29.49/29.68	           app_encode_app(int, int, bit0, 
29.49/29.68	             app_encode_app(nat, int, 
29.49/29.68	               app_encode_app(int, app_encode_fun(nat, int), 
29.49/29.68	                 power_power(int), s), 
29.49/29.68	               app_encode_app(int, nat, number_number_of(nat), 
29.49/29.68	                 app_encode_app(int, int, bit0, 
29.49/29.68	                   app_encode_app(int, int, bit1, pls))))))),
29.49/29.68	    inference('sup-', [status(thm)], ['65', '78'])).
29.49/29.68	tff(zf_stmt_66, axiom,
29.49/29.68	  (![L:int,K3:int]:
29.49/29.68	     (app_encode_app(int,$o,
29.49/29.68	                     app_encode_app(int,app_encode_fun(int,$o),
29.49/29.68	                                    ord_less_eq(int),
29.49/29.68	                                    app_encode_app(int,int,bit0,K3)),
29.49/29.68	                     app_encode_app(int,int,bit0,L)) <=>
29.49/29.68	      app_encode_app(int,$o,
29.49/29.68	                     app_encode_app(int,app_encode_fun(int,$o),
29.49/29.68	                                    ord_less_eq(int),K3),
29.49/29.68	                     L)))).
29.49/29.68	tff('80', plain,
29.49/29.68	    ![X58 : int, X59 : int]:
29.49/29.68	      (app_encode_app(int, $o, 
29.49/29.68	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
29.49/29.68	           app_encode_app(int, int, bit0, X59)), 
29.49/29.68	         app_encode_app(int, int, bit0, X58))
29.49/29.68	       | ~ app_encode_app(int, $o, 
29.49/29.68	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
29.49/29.68	               X59), X58)),
29.49/29.68	    inference('cnf', [status(esa)], [zf_stmt_66])).
29.49/29.68	tff(zf_stmt_90, axiom,
29.49/29.68	  (![L:int,K3:int]:
29.49/29.68	     (app_encode_app(int,$o,
29.49/29.68	                     app_encode_app(int,app_encode_fun(int,$o),ord_less(int),
29.49/29.68	                                    app_encode_app(int,int,bit0,K3)),
29.49/29.68	                     app_encode_app(int,int,bit1,L)) <=>
29.49/29.68	      app_encode_app(int,$o,
29.49/29.68	                     app_encode_app(int,app_encode_fun(int,$o),
29.49/29.68	                                    ord_less_eq(int),K3),
29.49/29.68	                     L)))).
29.49/29.68	tff('81', plain,
29.49/29.68	    ![X115 : int, X116 : int]:
29.49/29.68	      (app_encode_app(int, $o, 
29.49/29.68	         app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
29.49/29.68	           app_encode_app(int, int, bit0, X116)), 
29.49/29.68	         app_encode_app(int, int, bit1, X115))
29.49/29.68	       | ~ app_encode_app(int, $o, 
29.49/29.68	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
29.49/29.68	               X116), X115)),
29.49/29.68	    inference('cnf', [status(esa)], [zf_stmt_90])).
29.49/29.68	tff('82', plain,
29.49/29.68	    ![X0 : int, X1 : int]:
29.49/29.68	      (~ $true
29.49/29.68	       | ~ app_encode_app(int, $o, 
29.49/29.68	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
29.49/29.68	               X1), X0)
29.49/29.68	       | app_encode_app(int, $o, 
29.49/29.68	           app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
29.49/29.68	             app_encode_app(int, int, bit0, 
29.49/29.68	               app_encode_app(int, int, bit0, X1))), 
29.49/29.68	           app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, X0)))),
29.49/29.68	    inference('sup-', [status(thm)], ['80', '81'])).
29.49/29.68	tff('83', plain,
29.49/29.68	    ![X0 : int, X1 : int]:
29.49/29.68	      (app_encode_app(int, $o, 
29.49/29.68	         app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
29.49/29.68	           app_encode_app(int, int, bit0, app_encode_app(int, int, bit0, X1))), 
29.49/29.68	         app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, X0)))
29.49/29.68	       | ~ app_encode_app(int, $o, 
29.49/29.68	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
29.49/29.68	               X1), X0)),
29.49/29.68	    inference('simplify', [status(thm)], ['82'])).
29.49/29.68	tff('84', plain,
29.49/29.68	    (~ $true
29.49/29.68	     | app_encode_app(int, $o, 
29.49/29.68	         app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
29.49/29.68	           app_encode_app(int, int, bit0, 
29.49/29.68	             app_encode_app(int, int, bit0, pls))), 
29.49/29.68	         app_encode_app(int, int, bit1, 
29.49/29.68	           app_encode_app(int, int, bit0, 
29.49/29.68	             app_encode_app(nat, int, 
29.49/29.68	               app_encode_app(int, app_encode_fun(nat, int), 
29.49/29.68	                 power_power(int), s), 
29.49/29.68	               app_encode_app(int, nat, number_number_of(nat), 
29.49/29.68	                 app_encode_app(int, int, bit0, 
29.49/29.68	                   app_encode_app(int, int, bit1, pls)))))))),
29.49/29.68	    inference('sup-', [status(thm)], ['40', '83'])).
29.49/29.68	tff(zf_stmt_60, axiom, (app_encode_app(int,int,bit0,pls) = pls)).
29.49/29.68	tff('85', plain, app_encode_app(int, int, bit0, pls) = pls,
29.49/29.68	    inference('cnf', [status(esa)], [zf_stmt_60])).
29.49/29.68	tff('86', plain,
29.49/29.68	    (~ $true
29.49/29.68	     | app_encode_app(int, $o, 
29.49/29.68	         app_encode_app(int, app_encode_fun(int, $o), ord_less(int), pls), 
29.49/29.68	         app_encode_app(int, int, bit1, 
29.49/29.68	           app_encode_app(int, int, bit0, 
29.49/29.68	             app_encode_app(nat, int, 
29.49/29.68	               app_encode_app(int, app_encode_fun(nat, int), 
29.49/29.68	                 power_power(int), s), 
29.49/29.68	               app_encode_app(int, nat, number_number_of(nat), 
29.49/29.68	                 app_encode_app(int, int, bit0, 
29.49/29.68	                   app_encode_app(int, int, bit1, pls)))))))),
29.49/29.68	    inference('demod', [status(thm)], ['84', '85', '85'])).
29.49/29.68	tff('87', plain,
29.49/29.68	    app_encode_app(int, $o, 
29.49/29.68	      app_encode_app(int, app_encode_fun(int, $o), ord_less(int), pls), 
29.49/29.68	      app_encode_app(int, int, bit1, 
29.49/29.68	        app_encode_app(int, int, bit0, 
29.49/29.68	          app_encode_app(nat, int, 
29.49/29.68	            app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
29.49/29.68	              s), 
29.49/29.68	            app_encode_app(int, nat, number_number_of(nat), 
29.49/29.68	              app_encode_app(int, int, bit0, 
29.49/29.68	                app_encode_app(int, int, bit1, pls))))))),
29.49/29.68	    inference('simplify', [status(thm)], ['86'])).
29.49/29.68	tff(zf_stmt_86, axiom,
29.49/29.68	  (![K3:int]:
29.49/29.68	     (app_encode_app(int,$o,
29.49/29.68	                     app_encode_app(int,app_encode_fun(int,$o),ord_less(int),
29.49/29.68	                                    pls),
29.49/29.68	                     app_encode_app(int,int,bit1,K3)) <=>
29.49/29.68	      app_encode_app(int,$o,
29.49/29.68	                     app_encode_app(int,app_encode_fun(int,$o),
29.49/29.68	                                    ord_less_eq(int),pls),
29.49/29.68	                     K3)))).
29.49/29.68	tff('88', plain,
29.49/29.68	    ![X105 : int]:
29.49/29.68	      (app_encode_app(int, $o, 
29.49/29.68	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), pls), 
29.49/29.68	         X105)
29.49/29.68	       | ~ app_encode_app(int, $o, 
29.49/29.68	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), pls), 
29.49/29.68	             app_encode_app(int, int, bit1, X105))),
29.49/29.68	    inference('cnf', [status(esa)], [zf_stmt_86])).
29.49/29.68	tff('89', plain,
29.49/29.68	    (~ $true
29.49/29.68	     | app_encode_app(int, $o, 
29.49/29.68	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), pls), 
29.49/29.68	         app_encode_app(int, int, bit0, 
29.49/29.68	           app_encode_app(nat, int, 
29.49/29.68	             app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
29.49/29.68	               s), 
29.49/29.68	             app_encode_app(int, nat, number_number_of(nat), 
29.49/29.68	               app_encode_app(int, int, bit0, 
29.49/29.68	                 app_encode_app(int, int, bit1, pls))))))),
29.49/29.68	    inference('sup-', [status(thm)], ['87', '88'])).
29.49/29.68	tff('90', plain,
29.49/29.68	    app_encode_app(int, $o, 
29.49/29.68	      app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), pls), 
29.49/29.68	      app_encode_app(int, int, bit0, 
29.49/29.68	        app_encode_app(nat, int, 
29.49/29.68	          app_encode_app(int, app_encode_fun(nat, int), power_power(int), s), 
29.49/29.68	          app_encode_app(int, nat, number_number_of(nat), 
29.49/29.68	            app_encode_app(int, int, bit0, 
29.49/29.68	              app_encode_app(int, int, bit1, pls)))))),
29.49/29.68	    inference('simplify', [status(thm)], ['89'])).
29.49/29.68	tff('91', plain,
29.49/29.68	    (~ $true
29.49/29.68	     | app_encode_app(int, int, bit0, 
29.49/29.68	         app_encode_app(nat, int, 
29.49/29.68	           app_encode_app(int, app_encode_fun(nat, int), power_power(int), s), 
29.49/29.68	           app_encode_app(int, nat, number_number_of(nat), 
29.49/29.68	             app_encode_app(int, int, bit0, 
29.49/29.68	               app_encode_app(int, int, bit1, pls)))))
29.49/29.68	        = pls
29.49/29.68	     | ~ $true),
29.49/29.68	    inference('demod', [status(thm)], ['79', '90'])).
29.49/29.68	tff('92', plain,
29.49/29.68	    app_encode_app(int, int, bit0, 
29.49/29.68	      app_encode_app(nat, int, 
29.49/29.68	        app_encode_app(int, app_encode_fun(nat, int), power_power(int), s), 
29.49/29.68	        app_encode_app(int, nat, number_number_of(nat), 
29.49/29.68	          app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls)))))
29.49/29.68	     = pls,
29.49/29.68	    inference('simplify', [status(thm)], ['91'])).
29.49/29.68	tff(zf_stmt_76, axiom,
29.49/29.68	  (![K3:int]:
29.49/29.68	     (app_encode_app(int,$o,
29.49/29.68	                     app_encode_app(int,app_encode_fun(int,$o),ord_less(int),
29.49/29.68	                                    app_encode_app(int,int,bit0,K3)),
29.49/29.68	                     pls) <=>
29.49/29.68	      app_encode_app(int,$o,
29.49/29.68	                     app_encode_app(int,app_encode_fun(int,$o),ord_less(int),
29.49/29.68	                                    K3),
29.49/29.68	                     pls)))).
29.49/29.68	tff('93', plain,
29.49/29.68	    ![X84 : int]:
29.49/29.68	      (app_encode_app(int, $o, 
29.49/29.68	         app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
29.49/29.68	           app_encode_app(int, int, bit0, X84)), pls)
29.49/29.68	       | ~ app_encode_app(int, $o, 
29.49/29.68	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X84), 
29.49/29.68	             pls)),
29.49/29.68	    inference('cnf', [status(esa)], [zf_stmt_76])).
29.49/29.68	tff('94', plain,
29.49/29.68	    (app_encode_app(int, $o, 
29.49/29.68	       app_encode_app(int, app_encode_fun(int, $o), ord_less(int), pls), pls)
29.49/29.68	     | ~ app_encode_app(int, $o, 
29.49/29.68	           app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
29.49/29.68	             app_encode_app(nat, int, 
29.49/29.68	               app_encode_app(int, app_encode_fun(nat, int), 
29.49/29.68	                 power_power(int), s), 
29.49/29.68	               app_encode_app(int, nat, number_number_of(nat), 
29.49/29.68	                 app_encode_app(int, int, bit0, 
29.49/29.68	                   app_encode_app(int, int, bit1, pls))))), pls)),
29.49/29.68	    inference('sup+', [status(thm)], ['92', '93'])).
29.49/29.68	tff('95', plain,
29.49/29.68	    (app_encode_app(int, $o, 
29.49/29.68	       app_encode_app(int, app_encode_fun(int, $o), ord_less(int), pls), pls)
29.49/29.68	     | ~ $true),
29.49/29.68	    inference('demod', [status(thm)], ['94', '51'])).
29.49/29.68	tff('96', plain,
29.49/29.68	    app_encode_app(int, $o, 
29.49/29.68	      app_encode_app(int, app_encode_fun(int, $o), ord_less(int), pls), pls),
29.49/29.68	    inference('simplify', [status(thm)], ['95'])).
29.49/29.68	tff('97', plain, ~ $true, inference('sup-', [status(thm)], ['96', '47'])).
29.49/29.68	tff('98', plain, $false, inference('simplify', [status(thm)], ['97'])).
29.49/29.68	
29.49/29.68	% SZS output end Refutation
29.49/29.68	EOF
