0.00/0.00	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : appext
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : rpo6
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n115.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 08:00:08 CST 2018
29.55/29.79	% done 13535 iterations in 29.587s
29.55/29.79	% SZS status Theorem for 'stdin'
29.55/29.79	% SZS output start Refutation
29.55/29.79	tff(zf_stmt_39, axiom,
29.55/29.79	  (app_encode_app(int,$o,
29.55/29.79	                  app_encode_app(int,app_encode_fun(int,$o),ord_less(int),t),
29.55/29.79	                  zero_zero(int)) =>
29.55/29.79	   app_encode_app(int,$o,
29.55/29.79	                  app_encode_app(int,app_encode_fun(int,$o),ord_less(int),
29.55/29.79	                                 app_encode_app(int,int,
29.55/29.79	                                                app_encode_app(int,
29.55/29.79	                                                               app_encode_fun(
29.55/29.79	                                                               int,int),
29.55/29.79	                                                               plus_plus(int),
29.55/29.79	                                                               app_encode_app(
29.55/29.79	                                                               nat,int,
29.55/29.79	                                                               app_encode_app(
29.55/29.79	                                                               int,
29.55/29.79	                                                               app_encode_fun(
29.55/29.79	                                                               nat,int),
29.55/29.79	                                                               power_power(
29.55/29.79	                                                               int),s),
29.55/29.79	                                                               app_encode_app(
29.55/29.79	                                                               int,nat,
29.55/29.79	                                                               number_number_of(
29.55/29.79	                                                               nat),
29.55/29.79	                                                               app_encode_app(
29.55/29.79	                                                               int,int,bit0,
29.55/29.79	                                                               app_encode_app(
29.55/29.79	                                                               int,int,bit1,
29.55/29.79	                                                               pls))))),
29.55/29.79	                                                one_one(int))),
29.55/29.79	                  zero_zero(int)))).
29.55/29.79	tff('0', plain,
29.55/29.79	    (app_encode_app(int, $o, 
29.55/29.79	       app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
29.55/29.79	         app_encode_app(int, int, 
29.55/29.79	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
29.55/29.79	             app_encode_app(nat, int, 
29.55/29.79	               app_encode_app(int, app_encode_fun(nat, int), 
29.55/29.79	                 power_power(int), s), 
29.55/29.79	               app_encode_app(int, nat, number_number_of(nat), 
29.55/29.79	                 app_encode_app(int, int, bit0, 
29.55/29.79	                   app_encode_app(int, int, bit1, pls))))), one_one(int))), 
29.55/29.79	       zero_zero(int))
29.55/29.79	     | ~ app_encode_app(int, $o, 
29.55/29.79	           app_encode_app(int, app_encode_fun(int, $o), ord_less(int), t), 
29.55/29.79	           zero_zero(int))),
29.55/29.79	    inference('cnf', [status(esa)], [zf_stmt_39])).
29.55/29.79	tff(zf_stmt_115, axiom,
29.55/29.79	  (one_one(int) =
29.55/29.79	   app_encode_app(int,int,number_number_of(int),
29.55/29.79	                  app_encode_app(int,int,bit1,pls)))).
29.55/29.79	tff('1', plain,
29.55/29.79	    one_one(int)
29.55/29.79	     = app_encode_app(int, int, number_number_of(int), 
29.55/29.79	         app_encode_app(int, int, bit1, pls)),
29.55/29.79	    inference('cnf', [status(esa)], [zf_stmt_115])).
29.55/29.79	tff(zf_stmt_107, axiom,
29.55/29.79	  (zero_zero(int) = app_encode_app(int,int,number_number_of(int),pls))).
29.55/29.79	tff('2', plain,
29.55/29.79	    zero_zero(int) = app_encode_app(int, int, number_number_of(int), pls),
29.55/29.79	    inference('cnf', [status(esa)], [zf_stmt_107])).
29.55/29.79	tff('3', plain,
29.55/29.79	    (app_encode_app(int, $o, 
29.55/29.79	       app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
29.55/29.79	         app_encode_app(int, int, 
29.55/29.79	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
29.55/29.79	             app_encode_app(nat, int, 
29.55/29.79	               app_encode_app(int, app_encode_fun(nat, int), 
29.55/29.79	                 power_power(int), s), 
29.55/29.79	               app_encode_app(int, nat, number_number_of(nat), 
29.55/29.79	                 app_encode_app(int, int, bit0, 
29.55/29.79	                   app_encode_app(int, int, bit1, pls))))), 
29.55/29.79	           app_encode_app(int, int, number_number_of(int), 
29.55/29.79	             app_encode_app(int, int, bit1, pls)))), 
29.55/29.79	       app_encode_app(int, int, number_number_of(int), pls))
29.55/29.79	     | ~ app_encode_app(int, $o, 
29.55/29.79	           app_encode_app(int, app_encode_fun(int, $o), ord_less(int), t), 
29.55/29.79	           app_encode_app(int, int, number_number_of(int), pls))),
29.55/29.79	    inference('demod', [status(thm)], ['0', '1', '2', '2'])).
29.55/29.79	tff(zf_stmt_109, axiom,
29.55/29.79	  (![K:int]:
29.55/29.79	     (app_encode_app(int,int,
29.55/29.79	                     app_encode_app(int,app_encode_fun(int,int),
29.55/29.79	                                    plus_plus(int),K),
29.55/29.79	                     pls) =
29.55/29.79	      K))).
29.55/29.79	tff('4', plain,
29.55/29.79	    ![X161 : int]:
29.55/29.79	      app_encode_app(int, int, 
29.55/29.79	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), X161), 
29.55/29.79	        pls)
29.55/29.79	       = X161,
29.55/29.79	    inference('cnf', [status(esa)], [zf_stmt_109])).
29.55/29.79	tff(zf_stmt_128, axiom,
29.55/29.79	  (![K:int]:
29.55/29.79	     (app_encode_app(int,int,bit1,K) =
29.55/29.79	      app_encode_app(int,int,
29.55/29.79	                     app_encode_app(int,app_encode_fun(int,int),
29.55/29.79	                                    plus_plus(int),
29.55/29.79	                                    app_encode_app(int,int,
29.55/29.79	                                                   app_encode_app(int,
29.55/29.79	                                                                  app_encode_fun(
29.55/29.79	                                                                  int,int),
29.55/29.79	                                                                  plus_plus(
29.55/29.79	                                                                  int),
29.55/29.79	                                                                  one_one(
29.55/29.79	                                                                  int)),
29.55/29.79	                                                   K)),
29.55/29.79	                     K)))).
29.55/29.79	tff('5', plain,
29.55/29.79	    ![X199 : int]:
29.55/29.79	      app_encode_app(int, int, bit1, X199)
29.55/29.79	       = app_encode_app(int, int, 
29.55/29.79	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
29.55/29.79	             app_encode_app(int, int, 
29.55/29.79	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
29.55/29.79	                 one_one(int)), X199)), X199),
29.55/29.79	    inference('cnf', [status(esa)], [zf_stmt_128])).
29.55/29.79	tff('6', plain,
29.55/29.79	    ![X199 : int]:
29.55/29.79	      app_encode_app(int, int, bit1, X199)
29.55/29.79	       = app_encode_app(int, int, 
29.55/29.79	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
29.55/29.79	             app_encode_app(int, int, 
29.55/29.79	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
29.55/29.79	                 app_encode_app(int, int, number_number_of(int), 
29.55/29.79	                   app_encode_app(int, int, bit1, pls))), X199)), X199),
29.55/29.79	    inference('demod', [status(thm)], ['5', '1'])).
29.55/29.79	tff('7', plain,
29.55/29.79	    app_encode_app(int, int, bit1, pls)
29.55/29.79	     = app_encode_app(int, int, 
29.55/29.79	         app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
29.55/29.79	           app_encode_app(int, int, number_number_of(int), 
29.55/29.79	             app_encode_app(int, int, bit1, pls))), pls),
29.55/29.79	    inference('sup+', [status(thm)], ['4', '6'])).
29.55/29.79	tff('8', plain,
29.55/29.79	    app_encode_app(int, int, bit1, pls)
29.55/29.79	     = app_encode_app(int, int, number_number_of(int), 
29.55/29.79	         app_encode_app(int, int, bit1, pls)),
29.55/29.79	    inference('demod', [status(thm)], ['7', '4'])).
29.55/29.79	tff('9', plain,
29.55/29.79	    (app_encode_app(int, $o, 
29.55/29.79	       app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
29.55/29.79	         app_encode_app(int, int, 
29.55/29.79	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
29.55/29.79	             app_encode_app(nat, int, 
29.55/29.79	               app_encode_app(int, app_encode_fun(nat, int), 
29.55/29.79	                 power_power(int), s), 
29.55/29.79	               app_encode_app(int, nat, number_number_of(nat), 
29.55/29.79	                 app_encode_app(int, int, bit0, 
29.55/29.79	                   app_encode_app(int, int, bit1, pls))))), 
29.55/29.79	           app_encode_app(int, int, bit1, pls))), 
29.55/29.79	       app_encode_app(int, int, number_number_of(int), pls))
29.55/29.79	     | ~ app_encode_app(int, $o, 
29.55/29.79	           app_encode_app(int, app_encode_fun(int, $o), ord_less(int), t), 
29.55/29.79	           app_encode_app(int, int, number_number_of(int), pls))),
29.55/29.79	    inference('demod', [status(thm)], ['3', '8'])).
29.55/29.79	tff(zf_stmt_144, axiom, (number_ring(int))).
29.55/29.79	tff('10', plain, number_ring(int),
29.55/29.79	    inference('cnf', [status(esa)], [zf_stmt_144])).
29.55/29.79	tff(zf_stmt_122, axiom,
29.55/29.79	  (![A:$tType]:
29.55/29.79	     (number_ring(A) =>
29.55/29.79	      (![A1:A]:
29.55/29.79	         (app_encode_app(A,A,
29.55/29.79	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
29.55/29.79	                                        app_encode_app(int,A,
29.55/29.79	                                                       number_number_of(A),
29.55/29.79	                                                       pls)),
29.55/29.79	                         A1) =
29.55/29.79	          A1))))).
29.55/29.79	tff('11', plain,
29.55/29.79	    ![X188 : $tType, X189 : X188]:
29.55/29.79	      (app_encode_app(X188, X188, 
29.55/29.79	         app_encode_app(X188, app_encode_fun(X188, X188), plus_plus(X188), 
29.55/29.79	           app_encode_app(int, X188, number_number_of(X188), pls)), X189)
29.55/29.79	        = X189
29.55/29.79	       | ~ number_ring(X188)),
29.55/29.79	    inference('cnf', [status(esa)], [zf_stmt_122])).
29.55/29.79	tff('12', plain,
29.55/29.79	    ![X0 : int]:
29.55/29.79	      (~ $true
29.55/29.79	       | app_encode_app(int, int, 
29.55/29.79	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
29.55/29.79	             app_encode_app(int, int, number_number_of(int), pls)), X0)
29.55/29.79	          = X0),
29.55/29.79	    inference('sup-', [status(thm)], ['10', '11'])).
29.55/29.79	tff('13', plain,
29.55/29.79	    ![X0 : int]:
29.55/29.79	      app_encode_app(int, int, 
29.55/29.79	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
29.55/29.79	          app_encode_app(int, int, number_number_of(int), pls)), X0)
29.55/29.79	       = X0,
29.55/29.79	    inference('simplify', [status(thm)], ['12'])).
29.55/29.79	tff('14', plain, pls = app_encode_app(int, int, number_number_of(int), pls),
29.55/29.79	    inference('sup+', [status(thm)], ['13', '4'])).
29.55/29.79	tff('15', plain,
29.55/29.79	    (app_encode_app(int, $o, 
29.55/29.79	       app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
29.55/29.79	         app_encode_app(int, int, 
29.55/29.79	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
29.55/29.79	             app_encode_app(nat, int, 
29.55/29.79	               app_encode_app(int, app_encode_fun(nat, int), 
29.55/29.79	                 power_power(int), s), 
29.55/29.79	               app_encode_app(int, nat, number_number_of(nat), 
29.55/29.79	                 app_encode_app(int, int, bit0, 
29.55/29.79	                   app_encode_app(int, int, bit1, pls))))), 
29.55/29.79	           app_encode_app(int, int, bit1, pls))), pls)
29.55/29.79	     | ~ app_encode_app(int, $o, 
29.55/29.79	           app_encode_app(int, app_encode_fun(int, $o), ord_less(int), t), 
29.55/29.79	           pls)),
29.55/29.79	    inference('demod', [status(thm)], ['9', '14', '14'])).
29.55/29.79	tff(zf_stmt_114, axiom,
29.55/29.79	  (![W:int,Z1:int]:
29.55/29.79	     (app_encode_app(int,$o,
29.55/29.79	                     app_encode_app(int,app_encode_fun(int,$o),ord_less(int),
29.55/29.79	                                    Z1),
29.55/29.79	                     W) <=>
29.55/29.79	      (app_encode_app(int,$o,
29.55/29.79	                      app_encode_app(int,app_encode_fun(int,$o),
29.55/29.79	                                     ord_less_eq(int),Z1),
29.55/29.79	                      W) & 
29.55/29.79	       (Z1 != W))))).
29.55/29.79	tff('16', plain,
29.55/29.79	    ![X170 : int, X171 : int]:
29.55/29.79	      (app_encode_app(int, $o, 
29.55/29.79	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), X170), 
29.55/29.79	         X171)
29.55/29.79	       | ~ app_encode_app(int, $o, 
29.55/29.79	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
29.55/29.79	               X170), X171)),
29.55/29.79	    inference('cnf', [status(esa)], [zf_stmt_114])).
29.55/29.79	tff(zf_stmt_119, axiom,
29.55/29.79	  (![Z1:int,W:int]:
29.55/29.79	     (app_encode_app(int,$o,
29.55/29.79	                     app_encode_app(int,app_encode_fun(int,$o),
29.55/29.79	                                    ord_less_eq(int),
29.55/29.79	                                    app_encode_app(int,int,
29.55/29.79	                                                   app_encode_app(int,
29.55/29.79	                                                                  app_encode_fun(
29.55/29.79	                                                                  int,int),
29.55/29.79	                                                                  plus_plus(
29.55/29.79	                                                                  int),W),
29.55/29.79	                                                   one_one(int))),
29.55/29.79	                     Z1) <=>
29.55/29.79	      app_encode_app(int,$o,
29.55/29.79	                     app_encode_app(int,app_encode_fun(int,$o),ord_less(int),
29.55/29.79	                                    W),
29.55/29.79	                     Z1)))).
29.55/29.79	tff('17', plain,
29.55/29.79	    ![X177 : int, X178 : int]:
29.55/29.79	      (app_encode_app(int, $o, 
29.55/29.79	         app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X177), 
29.55/29.79	         X178)
29.55/29.79	       | ~ app_encode_app(int, $o, 
29.55/29.79	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
29.55/29.79	               app_encode_app(int, int, 
29.55/29.79	                 app_encode_app(int, app_encode_fun(int, int), 
29.55/29.79	                   plus_plus(int), X177), one_one(int))), X178)),
29.55/29.79	    inference('cnf', [status(esa)], [zf_stmt_119])).
29.55/29.79	tff('18', plain, one_one(int) = app_encode_app(int, int, bit1, pls),
29.55/29.79	    inference('demod', [status(thm)], ['1', '8'])).
29.55/29.79	tff('19', plain,
29.55/29.79	    ![X177 : int, X178 : int]:
29.55/29.79	      (app_encode_app(int, $o, 
29.55/29.79	         app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X177), 
29.55/29.79	         X178)
29.55/29.79	       | ~ app_encode_app(int, $o, 
29.55/29.79	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
29.55/29.79	               app_encode_app(int, int, 
29.55/29.79	                 app_encode_app(int, app_encode_fun(int, int), 
29.55/29.79	                   plus_plus(int), X177), 
29.55/29.79	                 app_encode_app(int, int, bit1, pls))), X178)),
29.55/29.79	    inference('demod', [status(thm)], ['17', '18'])).
29.55/29.79	tff('20', plain,
29.55/29.79	    ![X0 : int, X1 : int]:
29.55/29.79	      (~ $true
29.55/29.79	       | ~ app_encode_app(int, $o, 
29.55/29.80	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
29.55/29.80	               app_encode_app(int, int, 
29.55/29.80	                 app_encode_app(int, app_encode_fun(int, int), 
29.55/29.80	                   plus_plus(int), X1), app_encode_app(int, int, bit1, pls))), 
29.55/29.80	             X0)
29.55/29.80	       | app_encode_app(int, $o, 
29.55/29.80	           app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X1), 
29.55/29.80	           X0)),
29.55/29.80	    inference('sup-', [status(thm)], ['16', '19'])).
29.55/29.80	tff('21', plain,
29.55/29.80	    ![X0 : int, X1 : int]:
29.55/29.80	      (app_encode_app(int, $o, 
29.55/29.80	         app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X1), X0)
29.55/29.80	       | ~ app_encode_app(int, $o, 
29.55/29.80	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
29.55/29.80	               app_encode_app(int, int, 
29.55/29.80	                 app_encode_app(int, app_encode_fun(int, int), 
29.55/29.80	                   plus_plus(int), X1), app_encode_app(int, int, bit1, pls))), 
29.55/29.80	             X0)),
29.55/29.80	    inference('simplify', [status(thm)], ['20'])).
29.55/29.80	tff('22', plain,
29.55/29.80	    (~ $true
29.55/29.80	     | ~ app_encode_app(int, $o, 
29.55/29.80	           app_encode_app(int, app_encode_fun(int, $o), ord_less(int), t), 
29.55/29.80	           pls)
29.55/29.80	     | app_encode_app(int, $o, 
29.55/29.80	         app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
29.55/29.80	           app_encode_app(nat, int, 
29.55/29.80	             app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
29.55/29.80	               s), 
29.55/29.80	             app_encode_app(int, nat, number_number_of(nat), 
29.55/29.80	               app_encode_app(int, int, bit0, 
29.55/29.80	                 app_encode_app(int, int, bit1, pls))))), pls)),
29.55/29.80	    inference('sup-', [status(thm)], ['15', '21'])).
29.55/29.80	tff(zf_stmt_37, axiom,
29.55/29.80	  (app_encode_app(int,$o,
29.55/29.80	                  app_encode_app(int,app_encode_fun(int,$o),ord_less(int),t),
29.55/29.80	                  one_one(int)))).
29.55/29.80	tff('23', plain,
29.55/29.80	    app_encode_app(int, $o, 
29.55/29.80	      app_encode_app(int, app_encode_fun(int, $o), ord_less(int), t), 
29.55/29.80	      one_one(int)),
29.55/29.80	    inference('cnf', [status(esa)], [zf_stmt_37])).
29.55/29.80	tff('24', plain,
29.55/29.80	    app_encode_app(int, $o, 
29.55/29.80	      app_encode_app(int, app_encode_fun(int, $o), ord_less(int), t), 
29.55/29.80	      app_encode_app(int, int, number_number_of(int), 
29.55/29.80	        app_encode_app(int, int, bit1, pls))),
29.55/29.80	    inference('demod', [status(thm)], ['23', '1'])).
29.55/29.80	tff('25', plain,
29.55/29.80	    app_encode_app(int, $o, 
29.55/29.80	      app_encode_app(int, app_encode_fun(int, $o), ord_less(int), t), 
29.55/29.80	      app_encode_app(int, int, bit1, pls)),
29.55/29.80	    inference('demod', [status(thm)], ['24', '8'])).
29.55/29.80	tff(zf_stmt_110, axiom,
29.55/29.80	  (![K:int]:
29.55/29.80	     (app_encode_app(int,int,
29.55/29.80	                     app_encode_app(int,app_encode_fun(int,int),
29.55/29.80	                                    plus_plus(int),pls),
29.55/29.80	                     K) =
29.55/29.80	      K))).
29.55/29.80	tff('26', plain,
29.55/29.80	    ![X162 : int]:
29.55/29.80	      app_encode_app(int, int, 
29.55/29.80	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
29.55/29.80	        X162)
29.55/29.80	       = X162,
29.55/29.80	    inference('cnf', [status(esa)], [zf_stmt_110])).
29.55/29.80	tff(zf_stmt_92, axiom,
29.55/29.80	  (![Z1:int,W:int]:
29.55/29.80	     (app_encode_app(int,$o,
29.55/29.80	                     app_encode_app(int,app_encode_fun(int,$o),ord_less(int),
29.55/29.80	                                    W),
29.55/29.80	                     app_encode_app(int,int,
29.55/29.80	                                    app_encode_app(int,
29.55/29.80	                                                   app_encode_fun(int,int),
29.55/29.80	                                                   plus_plus(int),Z1),
29.55/29.80	                                    one_one(int))) <=>
29.55/29.80	      app_encode_app(int,$o,
29.55/29.80	                     app_encode_app(int,app_encode_fun(int,$o),
29.55/29.80	                                    ord_less_eq(int),W),
29.55/29.80	                     Z1)))).
29.55/29.80	tff('27', plain,
29.55/29.80	    ![X121 : int, X122 : int]:
29.55/29.80	      (app_encode_app(int, $o, 
29.55/29.80	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), X121), 
29.55/29.80	         X122)
29.55/29.80	       | ~ app_encode_app(int, $o, 
29.55/29.80	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
29.55/29.80	               X121), 
29.55/29.80	             app_encode_app(int, int, 
29.55/29.80	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
29.55/29.80	                 X122), one_one(int)))),
29.55/29.80	    inference('cnf', [status(esa)], [zf_stmt_92])).
29.55/29.80	tff('28', plain,
29.55/29.80	    ![X121 : int, X122 : int]:
29.55/29.80	      (app_encode_app(int, $o, 
29.55/29.80	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), X121), 
29.55/29.80	         X122)
29.55/29.80	       | ~ app_encode_app(int, $o, 
29.55/29.80	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
29.55/29.80	               X121), 
29.55/29.80	             app_encode_app(int, int, 
29.55/29.80	               app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
29.55/29.80	                 X122), app_encode_app(int, int, bit1, pls)))),
29.55/29.80	    inference('demod', [status(thm)], ['27', '18'])).
29.55/29.80	tff('29', plain,
29.55/29.80	    ![X0 : int]:
29.55/29.80	      (~ app_encode_app(int, $o, 
29.55/29.80	           app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X0), 
29.55/29.80	           app_encode_app(int, int, bit1, pls))
29.55/29.80	       | app_encode_app(int, $o, 
29.55/29.80	           app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), X0), 
29.55/29.80	           pls)),
29.55/29.80	    inference('sup-', [status(thm)], ['26', '28'])).
29.55/29.80	tff('30', plain,
29.55/29.80	    (~ $true
29.55/29.80	     | app_encode_app(int, $o, 
29.55/29.80	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), t), 
29.55/29.80	         pls)),
29.55/29.80	    inference('sup-', [status(thm)], ['25', '29'])).
29.55/29.80	tff('31', plain,
29.55/29.80	    app_encode_app(int, $o, 
29.55/29.80	      app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), t), pls),
29.55/29.80	    inference('simplify', [status(thm)], ['30'])).
29.55/29.80	tff('32', plain,
29.55/29.80	    ![X171 : int, X172 : int]:
29.55/29.80	      (app_encode_app(int, $o, 
29.55/29.80	         app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X172), 
29.55/29.80	         X171)
29.55/29.80	       | X172 = X171
29.55/29.80	       | ~ app_encode_app(int, $o, 
29.55/29.80	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
29.55/29.80	               X172), X171)),
29.55/29.80	    inference('cnf', [status(esa)], [zf_stmt_114])).
29.55/29.80	tff('33', plain,
29.55/29.80	    (~ $true
29.55/29.80	     | t = pls
29.55/29.80	     | app_encode_app(int, $o, 
29.55/29.80	         app_encode_app(int, app_encode_fun(int, $o), ord_less(int), t), pls)),
29.55/29.80	    inference('sup-', [status(thm)], ['31', '32'])).
29.55/29.80	tff('34', plain,
29.55/29.80	    (app_encode_app(int, $o, 
29.55/29.80	       app_encode_app(int, app_encode_fun(int, $o), ord_less(int), t), pls)
29.55/29.80	     | t = pls),
29.55/29.80	    inference('simplify', [status(thm)], ['33'])).
29.55/29.80	tff(zf_stmt_38, axiom,
29.55/29.80	  ((t = zero_zero(int)) =>
29.55/29.80	   (app_encode_app(int,int,
29.55/29.80	                   app_encode_app(int,app_encode_fun(int,int),plus_plus(int),
29.55/29.80	                                  app_encode_app(nat,int,
29.55/29.80	                                                 app_encode_app(int,
29.55/29.80	                                                                app_encode_fun(
29.55/29.80	                                                                nat,int),
29.55/29.80	                                                                power_power(
29.55/29.80	                                                                int),s),
29.55/29.80	                                                 app_encode_app(int,nat,
29.55/29.80	                                                                number_number_of(
29.55/29.80	                                                                nat),
29.55/29.80	                                                                app_encode_app(
29.55/29.80	                                                                int,int,bit0,
29.55/29.80	                                                                app_encode_app(
29.55/29.80	                                                                int,int,bit1,
29.55/29.80	                                                                pls))))),
29.55/29.80	                   one_one(int)) =
29.55/29.80	    zero_zero(int)))).
29.55/29.80	tff('35', plain,
29.55/29.80	    (app_encode_app(int, int, 
29.55/29.80	       app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
29.55/29.80	         app_encode_app(nat, int, 
29.55/29.80	           app_encode_app(int, app_encode_fun(nat, int), power_power(int), s), 
29.55/29.80	           app_encode_app(int, nat, number_number_of(nat), 
29.55/29.80	             app_encode_app(int, int, bit0, 
29.55/29.80	               app_encode_app(int, int, bit1, pls))))), one_one(int))
29.55/29.80	      = zero_zero(int)
29.55/29.80	     | t != zero_zero(int)),
29.55/29.80	    inference('cnf', [status(esa)], [zf_stmt_38])).
29.55/29.80	tff('36', plain,
29.55/29.80	    (app_encode_app(int, int, 
29.55/29.80	       app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
29.55/29.80	         app_encode_app(nat, int, 
29.55/29.80	           app_encode_app(int, app_encode_fun(nat, int), power_power(int), s), 
29.55/29.80	           app_encode_app(int, nat, number_number_of(nat), 
29.55/29.80	             app_encode_app(int, int, bit0, 
29.55/29.80	               app_encode_app(int, int, bit1, pls))))), one_one(int))
29.55/29.80	      = app_encode_app(int, int, number_number_of(int), pls)
29.55/29.80	     | t != app_encode_app(int, int, number_number_of(int), pls)),
29.55/29.80	    inference('demod', [status(thm)], ['35', '2', '2'])).
29.55/29.80	tff('37', plain,
29.55/29.80	    (app_encode_app(int, int, 
29.55/29.80	       app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
29.55/29.80	         app_encode_app(nat, int, 
29.55/29.80	           app_encode_app(int, app_encode_fun(nat, int), power_power(int), s), 
29.55/29.80	           app_encode_app(int, nat, number_number_of(nat), 
29.55/29.80	             app_encode_app(int, int, bit0, 
29.55/29.80	               app_encode_app(int, int, bit1, pls))))), 
29.55/29.80	       app_encode_app(int, int, number_number_of(int), 
29.55/29.80	         app_encode_app(int, int, bit1, pls)))
29.55/29.80	      = app_encode_app(int, int, number_number_of(int), pls)
29.55/29.80	     | t != app_encode_app(int, int, number_number_of(int), pls)),
29.55/29.80	    inference('demod', [status(thm)], ['36', '1'])).
29.55/29.80	tff('38', plain,
29.55/29.80	    (app_encode_app(int, int, 
29.55/29.80	       app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
29.55/29.80	         app_encode_app(nat, int, 
29.55/29.80	           app_encode_app(int, app_encode_fun(nat, int), power_power(int), s), 
29.55/29.80	           app_encode_app(int, nat, number_number_of(nat), 
29.55/29.80	             app_encode_app(int, int, bit0, 
29.55/29.80	               app_encode_app(int, int, bit1, pls))))), 
29.55/29.80	       app_encode_app(int, int, bit1, pls))
29.55/29.80	      = pls
29.55/29.80	     | t != pls),
29.55/29.80	    inference('demod', [status(thm)], ['37', '8', '14', '14'])).
29.55/29.80	tff(zf_stmt_36, axiom,
29.55/29.80	  (app_encode_app(int,$o,
29.55/29.80	                  app_encode_app(int,app_encode_fun(int,$o),ord_less_eq(int),
29.55/29.80	                                 zero_zero(int)),
29.55/29.80	                  app_encode_app(nat,int,
29.55/29.80	                                 app_encode_app(int,app_encode_fun(nat,int),
29.55/29.80	                                                power_power(int),s),
29.55/29.80	                                 app_encode_app(int,nat,
29.55/29.80	                                                number_number_of(nat),
29.55/29.80	                                                app_encode_app(int,int,bit0,
29.55/29.80	                                                               app_encode_app(
29.55/29.80	                                                               int,int,bit1,
29.55/29.80	                                                               pls))))))).
29.55/29.80	tff('39', plain,
29.55/29.80	    app_encode_app(int, $o, 
29.55/29.80	      app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
29.55/29.80	        zero_zero(int)), 
29.55/29.80	      app_encode_app(nat, int, 
29.55/29.80	        app_encode_app(int, app_encode_fun(nat, int), power_power(int), s), 
29.55/29.80	        app_encode_app(int, nat, number_number_of(nat), 
29.55/29.80	          app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls))))),
29.55/29.80	    inference('cnf', [status(esa)], [zf_stmt_36])).
29.55/29.80	tff('40', plain,
29.55/29.80	    app_encode_app(int, $o, 
29.55/29.80	      app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
29.55/29.80	        app_encode_app(int, int, number_number_of(int), pls)), 
29.55/29.80	      app_encode_app(nat, int, 
29.55/29.80	        app_encode_app(int, app_encode_fun(nat, int), power_power(int), s), 
29.55/29.80	        app_encode_app(int, nat, number_number_of(nat), 
29.55/29.80	          app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls))))),
29.55/29.80	    inference('demod', [status(thm)], ['39', '2'])).
29.55/29.80	tff('41', plain,
29.55/29.80	    app_encode_app(int, $o, 
29.55/29.80	      app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), pls), 
29.55/29.80	      app_encode_app(nat, int, 
29.55/29.80	        app_encode_app(int, app_encode_fun(nat, int), power_power(int), s), 
29.55/29.80	        app_encode_app(int, nat, number_number_of(nat), 
29.55/29.80	          app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls))))),
29.55/29.80	    inference('demod', [status(thm)], ['40', '14'])).
29.55/29.80	tff('42', plain,
29.55/29.80	    ![X122 : int, X123 : int]:
29.55/29.80	      (app_encode_app(int, $o, 
29.55/29.80	         app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X123), 
29.55/29.80	         app_encode_app(int, int, 
29.55/29.80	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
29.55/29.80	             X122), one_one(int)))
29.55/29.80	       | ~ app_encode_app(int, $o, 
29.55/29.80	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
29.55/29.80	               X123), X122)),
29.55/29.80	    inference('cnf', [status(esa)], [zf_stmt_92])).
29.55/29.80	tff('43', plain,
29.55/29.80	    ![X122 : int, X123 : int]:
29.55/29.80	      (app_encode_app(int, $o, 
29.55/29.80	         app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X123), 
29.55/29.80	         app_encode_app(int, int, 
29.55/29.80	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
29.55/29.80	             X122), app_encode_app(int, int, bit1, pls)))
29.55/29.80	       | ~ app_encode_app(int, $o, 
29.55/29.80	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
29.55/29.80	               X123), X122)),
29.55/29.80	    inference('demod', [status(thm)], ['42', '18'])).
29.55/29.80	tff('44', plain,
29.55/29.80	    (~ $true
29.55/29.80	     | app_encode_app(int, $o, 
29.55/29.80	         app_encode_app(int, app_encode_fun(int, $o), ord_less(int), pls), 
29.55/29.80	         app_encode_app(int, int, 
29.55/29.80	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
29.55/29.80	             app_encode_app(nat, int, 
29.55/29.80	               app_encode_app(int, app_encode_fun(nat, int), 
29.55/29.80	                 power_power(int), s), 
29.55/29.80	               app_encode_app(int, nat, number_number_of(nat), 
29.55/29.80	                 app_encode_app(int, int, bit0, 
29.55/29.80	                   app_encode_app(int, int, bit1, pls))))), 
29.55/29.80	           app_encode_app(int, int, bit1, pls)))),
29.55/29.80	    inference('sup-', [status(thm)], ['41', '43'])).
29.55/29.80	tff('45', plain,
29.55/29.80	    app_encode_app(int, $o, 
29.55/29.80	      app_encode_app(int, app_encode_fun(int, $o), ord_less(int), pls), 
29.55/29.80	      app_encode_app(int, int, 
29.55/29.80	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
29.55/29.80	          app_encode_app(nat, int, 
29.55/29.80	            app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
29.55/29.80	              s), 
29.55/29.80	            app_encode_app(int, nat, number_number_of(nat), 
29.55/29.80	              app_encode_app(int, int, bit0, 
29.55/29.80	                app_encode_app(int, int, bit1, pls))))), 
29.55/29.80	        app_encode_app(int, int, bit1, pls))),
29.55/29.80	    inference('simplify', [status(thm)], ['44'])).
29.55/29.80	tff('46', plain,
29.55/29.80	    (app_encode_app(int, $o, 
29.55/29.80	       app_encode_app(int, app_encode_fun(int, $o), ord_less(int), pls), pls)
29.55/29.80	     | t != pls),
29.55/29.80	    inference('sup+', [status(thm)], ['38', '45'])).
29.55/29.80	tff('47', plain,
29.55/29.80	    ![X170 : int, X171 : int]:
29.55/29.80	      (X170 != X171
29.55/29.80	       | ~ app_encode_app(int, $o, 
29.55/29.80	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
29.55/29.80	               X170), X171)),
29.55/29.80	    inference('cnf', [status(esa)], [zf_stmt_114])).
29.55/29.80	tff('48', plain,
29.55/29.80	    ![X171 : int]:
29.55/29.80	      ~ app_encode_app(int, $o, 
29.55/29.80	          app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X171), 
29.55/29.80	          X171),
29.55/29.80	    inference('simplify', [status(thm)], ['47'])).
29.55/29.80	tff('49', plain, t != pls, inference('clc', [status(thm)], ['46', '48'])).
29.55/29.80	tff('50', plain,
29.55/29.80	    app_encode_app(int, $o, 
29.55/29.80	      app_encode_app(int, app_encode_fun(int, $o), ord_less(int), t), pls),
29.55/29.80	    inference('simplify_reflect-', [status(thm)], ['34', '49'])).
29.55/29.80	tff('51', plain,
29.55/29.80	    (~ $true
29.55/29.80	     | ~ $true
29.55/29.80	     | app_encode_app(int, $o, 
29.55/29.80	         app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
29.55/29.80	           app_encode_app(nat, int, 
29.55/29.80	             app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
29.55/29.80	               s), 
29.55/29.80	             app_encode_app(int, nat, number_number_of(nat), 
29.55/29.80	               app_encode_app(int, int, bit0, 
29.55/29.80	                 app_encode_app(int, int, bit1, pls))))), pls)),
29.55/29.80	    inference('demod', [status(thm)], ['22', '50'])).
29.55/29.80	tff('52', plain,
29.55/29.80	    app_encode_app(int, $o, 
29.55/29.80	      app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
29.55/29.80	        app_encode_app(nat, int, 
29.55/29.80	          app_encode_app(int, app_encode_fun(nat, int), power_power(int), s), 
29.55/29.80	          app_encode_app(int, nat, number_number_of(nat), 
29.55/29.80	            app_encode_app(int, int, bit0, 
29.55/29.80	              app_encode_app(int, int, bit1, pls))))), pls),
29.55/29.80	    inference('simplify', [status(thm)], ['51'])).
29.55/29.80	tff(zf_stmt_88, axiom,
29.55/29.80	  (![V2:int]:
29.55/29.80	     ((app_encode_app(int,nat,number_number_of(nat),V2) = zero_zero(nat)) <=>
29.55/29.80	      app_encode_app(int,$o,
29.55/29.80	                     app_encode_app(int,app_encode_fun(int,$o),
29.55/29.80	                                    ord_less_eq(int),V2),
29.55/29.80	                     pls)))).
29.55/29.80	tff('53', plain,
29.55/29.80	    ![X112 : int]:
29.55/29.80	      (app_encode_app(int, nat, number_number_of(nat), X112) = zero_zero(nat)
29.55/29.80	       | ~ app_encode_app(int, $o, 
29.55/29.80	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
29.55/29.80	               X112), pls)),
29.55/29.80	    inference('cnf', [status(esa)], [zf_stmt_88])).
29.55/29.80	tff(zf_stmt_75, axiom,
29.55/29.80	  (app_encode_app(int,nat,number_number_of(nat),pls) = zero_zero(nat))).
29.55/29.80	tff('54', plain,
29.55/29.80	    app_encode_app(int, nat, number_number_of(nat), pls) = zero_zero(nat),
29.55/29.80	    inference('cnf', [status(esa)], [zf_stmt_75])).
29.55/29.80	tff('55', plain,
29.55/29.80	    ![X112 : int]:
29.55/29.80	      (app_encode_app(int, nat, number_number_of(nat), X112)
29.55/29.80	        = app_encode_app(int, nat, number_number_of(nat), pls)
29.55/29.80	       | ~ app_encode_app(int, $o, 
29.55/29.80	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
29.55/29.80	               X112), pls)),
29.55/29.80	    inference('demod', [status(thm)], ['53', '54'])).
29.55/29.80	tff('56', plain,
29.55/29.80	    ![X0 : int]:
29.55/29.80	      (~ $true
29.55/29.80	       | ~ app_encode_app(int, $o, 
29.55/29.80	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X0), 
29.55/29.80	             pls)
29.55/29.80	       | app_encode_app(int, nat, number_number_of(nat), X0)
29.55/29.80	          = app_encode_app(int, nat, number_number_of(nat), pls)),
29.55/29.80	    inference('sup-', [status(thm)], ['16', '55'])).
29.55/29.80	tff('57', plain,
29.55/29.80	    ![X0 : int]:
29.55/29.80	      (app_encode_app(int, nat, number_number_of(nat), X0)
29.55/29.80	        = app_encode_app(int, nat, number_number_of(nat), pls)
29.55/29.80	       | ~ app_encode_app(int, $o, 
29.55/29.80	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X0), 
29.55/29.80	             pls)),
29.55/29.80	    inference('simplify', [status(thm)], ['56'])).
29.55/29.80	tff('58', plain,
29.55/29.80	    (~ $true
29.55/29.80	     | app_encode_app(int, nat, number_number_of(nat), 
29.55/29.80	         app_encode_app(nat, int, 
29.55/29.80	           app_encode_app(int, app_encode_fun(nat, int), power_power(int), s), 
29.55/29.80	           app_encode_app(int, nat, number_number_of(nat), 
29.55/29.80	             app_encode_app(int, int, bit0, 
29.55/29.80	               app_encode_app(int, int, bit1, pls)))))
29.55/29.80	        = app_encode_app(int, nat, number_number_of(nat), pls)),
29.55/29.80	    inference('sup-', [status(thm)], ['52', '57'])).
29.55/29.80	tff('59', plain,
29.55/29.80	    app_encode_app(int, nat, number_number_of(nat), 
29.55/29.80	      app_encode_app(nat, int, 
29.55/29.80	        app_encode_app(int, app_encode_fun(nat, int), power_power(int), s), 
29.55/29.80	        app_encode_app(int, nat, number_number_of(nat), 
29.55/29.80	          app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls)))))
29.55/29.80	     = app_encode_app(int, nat, number_number_of(nat), pls),
29.55/29.80	    inference('simplify', [status(thm)], ['58'])).
29.55/29.80	tff('60', plain,
29.55/29.80	    ![X111 : int]:
29.55/29.80	      (app_encode_app(int, $o, 
29.55/29.80	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), X111), 
29.55/29.80	         pls)
29.55/29.80	       | app_encode_app(int, nat, number_number_of(nat), X111)
29.55/29.80	          != zero_zero(nat)),
29.55/29.80	    inference('cnf', [status(esa)], [zf_stmt_88])).
29.55/29.80	tff('61', plain,
29.55/29.80	    ![X111 : int]:
29.55/29.80	      (app_encode_app(int, $o, 
29.55/29.80	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), X111), 
29.55/29.80	         pls)
29.55/29.80	       | app_encode_app(int, nat, number_number_of(nat), X111)
29.55/29.80	          != app_encode_app(int, nat, number_number_of(nat), pls)),
29.55/29.80	    inference('demod', [status(thm)], ['60', '54'])).
29.55/29.80	tff('62', plain,
29.55/29.80	    (app_encode_app(int, nat, number_number_of(nat), pls)
29.55/29.80	      != app_encode_app(int, nat, number_number_of(nat), pls)
29.55/29.80	     | app_encode_app(int, $o, 
29.55/29.80	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
29.55/29.80	           app_encode_app(nat, int, 
29.55/29.80	             app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
29.55/29.80	               s), 
29.55/29.80	             app_encode_app(int, nat, number_number_of(nat), 
29.55/29.80	               app_encode_app(int, int, bit0, 
29.55/29.80	                 app_encode_app(int, int, bit1, pls))))), pls)),
29.55/29.80	    inference('sup-', [status(thm)], ['59', '61'])).
29.55/29.80	tff('63', plain,
29.55/29.80	    app_encode_app(int, $o, 
29.55/29.80	      app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
29.55/29.80	        app_encode_app(nat, int, 
29.55/29.80	          app_encode_app(int, app_encode_fun(nat, int), power_power(int), s), 
29.55/29.80	          app_encode_app(int, nat, number_number_of(nat), 
29.55/29.80	            app_encode_app(int, int, bit0, 
29.55/29.80	              app_encode_app(int, int, bit1, pls))))), pls),
29.55/29.80	    inference('simplify', [status(thm)], ['62'])).
29.55/29.80	tff('64', plain,
29.55/29.80	    (~ $true
29.55/29.80	     | app_encode_app(int, $o, 
29.55/29.80	         app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
29.55/29.80	           app_encode_app(nat, int, 
29.55/29.80	             app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
29.55/29.80	               s), 
29.55/29.80	             app_encode_app(int, nat, number_number_of(nat), 
29.55/29.80	               app_encode_app(int, int, bit0, 
29.55/29.80	                 app_encode_app(int, int, bit1, pls))))), 
29.55/29.80	         app_encode_app(int, int, 
29.55/29.80	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), pls), 
29.55/29.80	           app_encode_app(int, int, bit1, pls)))),
29.55/29.80	    inference('sup-', [status(thm)], ['63', '43'])).
29.55/29.80	tff('65', plain,
29.55/29.80	    (~ $true
29.55/29.80	     | app_encode_app(int, $o, 
29.55/29.80	         app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
29.55/29.80	           app_encode_app(nat, int, 
29.55/29.80	             app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
29.55/29.80	               s), 
29.55/29.80	             app_encode_app(int, nat, number_number_of(nat), 
29.55/29.80	               app_encode_app(int, int, bit0, 
29.55/29.80	                 app_encode_app(int, int, bit1, pls))))), 
29.55/29.80	         app_encode_app(int, int, bit1, pls))),
29.55/29.80	    inference('demod', [status(thm)], ['64', '26'])).
29.55/29.80	tff('66', plain,
29.55/29.80	    app_encode_app(int, $o, 
29.55/29.80	      app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
29.55/29.80	        app_encode_app(nat, int, 
29.55/29.80	          app_encode_app(int, app_encode_fun(nat, int), power_power(int), s), 
29.55/29.80	          app_encode_app(int, nat, number_number_of(nat), 
29.55/29.80	            app_encode_app(int, int, bit0, 
29.55/29.80	              app_encode_app(int, int, bit1, pls))))), 
29.55/29.80	      app_encode_app(int, int, bit1, pls)),
29.55/29.80	    inference('simplify', [status(thm)], ['65'])).
29.55/29.80	tff(zf_stmt_64, axiom,
29.55/29.80	  (![L:int,K3:int]:
29.55/29.80	     (app_encode_app(int,$o,
29.55/29.80	                     app_encode_app(int,app_encode_fun(int,$o),ord_less(int),
29.55/29.80	                                    app_encode_app(int,int,bit0,K3)),
29.55/29.80	                     app_encode_app(int,int,bit0,L)) <=>
29.55/29.80	      app_encode_app(int,$o,
29.55/29.80	                     app_encode_app(int,app_encode_fun(int,$o),ord_less(int),
29.55/29.80	                                    K3),
29.55/29.80	                     L)))).
29.55/29.80	tff('67', plain,
29.55/29.80	    ![X56 : int, X57 : int]:
29.55/29.80	      (app_encode_app(int, $o, 
29.55/29.80	         app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
29.55/29.80	           app_encode_app(int, int, bit0, X57)), 
29.55/29.80	         app_encode_app(int, int, bit0, X56))
29.55/29.80	       | ~ app_encode_app(int, $o, 
29.55/29.80	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X57), 
29.55/29.80	             X56)),
29.55/29.80	    inference('cnf', [status(esa)], [zf_stmt_64])).
29.55/29.80	tff(zf_stmt_132, axiom,
29.55/29.80	  (![X:int]:
29.55/29.80	     (app_encode_app(int,$o,
29.55/29.80	                     app_encode_app(int,app_encode_fun(int,$o),
29.55/29.80	                                    ord_less_eq(int),zero_zero(int)),
29.55/29.80	                     X) =>
29.55/29.80	      (app_encode_app(int,$o,
29.55/29.80	                      app_encode_app(int,app_encode_fun(int,$o),
29.55/29.80	                                     ord_less(int),X),
29.55/29.80	                      app_encode_app(int,int,number_number_of(int),
29.55/29.80	                                     app_encode_app(int,int,bit0,
29.55/29.80	                                                    app_encode_app(int,int,
29.55/29.80	                                                                   bit1,pls)))) =>
29.55/29.80	       ((X = zero_zero(int)) | (X = one_one(int))))))).
29.55/29.80	tff('68', plain,
29.55/29.80	    ![X205 : int]:
29.55/29.80	      (~ app_encode_app(int, $o, 
29.55/29.80	           app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X205), 
29.55/29.80	           app_encode_app(int, int, number_number_of(int), 
29.55/29.80	             app_encode_app(int, int, bit0, 
29.55/29.80	               app_encode_app(int, int, bit1, pls))))
29.55/29.80	       | X205 = zero_zero(int)
29.55/29.80	       | X205 = one_one(int)
29.55/29.80	       | ~ app_encode_app(int, $o, 
29.55/29.80	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
29.55/29.80	               zero_zero(int)), X205)),
29.55/29.80	    inference('cnf', [status(esa)], [zf_stmt_132])).
29.55/29.80	tff(zf_stmt_111, axiom,
29.55/29.80	  (![K:int]:
29.55/29.80	     (app_encode_app(int,int,bit0,K) =
29.55/29.80	      app_encode_app(int,int,
29.55/29.80	                     app_encode_app(int,app_encode_fun(int,int),
29.55/29.80	                                    plus_plus(int),K),
29.55/29.80	                     K)))).
29.55/29.80	tff('69', plain,
29.55/29.80	    ![X163 : int]:
29.55/29.80	      app_encode_app(int, int, bit0, X163)
29.55/29.80	       = app_encode_app(int, int, 
29.55/29.80	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
29.55/29.80	             X163), X163),
29.55/29.80	    inference('cnf', [status(esa)], [zf_stmt_111])).
29.55/29.80	tff(zf_stmt_101, axiom,
29.55/29.80	  (![W1:int,V:int]:
29.55/29.80	     (app_encode_app(int,int,
29.55/29.80	                     app_encode_app(int,app_encode_fun(int,int),
29.55/29.80	                                    plus_plus(int),
29.55/29.80	                                    app_encode_app(int,int,
29.55/29.80	                                                   number_number_of(int),V)),
29.55/29.80	                     app_encode_app(int,int,number_number_of(int),W1)) =
29.55/29.80	      app_encode_app(int,int,number_number_of(int),
29.55/29.80	                     app_encode_app(int,int,
29.55/29.80	                                    app_encode_app(int,
29.55/29.80	                                                   app_encode_fun(int,int),
29.55/29.80	                                                   plus_plus(int),V),
29.55/29.80	                                    W1))))).
29.55/29.80	tff('70', plain,
29.55/29.80	    ![X144 : int, X145 : int]:
29.55/29.80	      app_encode_app(int, int, 
29.55/29.80	        app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
29.55/29.80	          app_encode_app(int, int, number_number_of(int), X144)), 
29.55/29.80	        app_encode_app(int, int, number_number_of(int), X145))
29.55/29.80	       = app_encode_app(int, int, number_number_of(int), 
29.55/29.80	           app_encode_app(int, int, 
29.55/29.80	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
29.55/29.80	               X144), X145)),
29.55/29.80	    inference('cnf', [status(esa)], [zf_stmt_101])).
29.55/29.80	tff('71', plain,
29.55/29.80	    ![X0 : int]:
29.55/29.80	      app_encode_app(int, int, bit0, 
29.55/29.80	        app_encode_app(int, int, number_number_of(int), X0))
29.55/29.80	       = app_encode_app(int, int, number_number_of(int), 
29.55/29.80	           app_encode_app(int, int, 
29.55/29.80	             app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
29.55/29.80	               X0), X0)),
29.55/29.80	    inference('sup+', [status(thm)], ['69', '70'])).
29.55/29.80	tff('72', plain,
29.55/29.80	    ![X0 : int]:
29.55/29.80	      app_encode_app(int, int, bit0, 
29.55/29.80	        app_encode_app(int, int, number_number_of(int), X0))
29.55/29.80	       = app_encode_app(int, int, number_number_of(int), 
29.55/29.80	           app_encode_app(int, int, bit0, X0)),
29.55/29.80	    inference('demod', [status(thm)], ['71', '69'])).
29.55/29.80	tff('73', plain,
29.55/29.80	    app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls))
29.55/29.80	     = app_encode_app(int, int, number_number_of(int), 
29.55/29.80	         app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls))),
29.55/29.80	    inference('sup+', [status(thm)], ['8', '72'])).
29.55/29.80	tff('74', plain, zero_zero(int) = pls,
29.55/29.80	    inference('demod', [status(thm)], ['2', '14'])).
29.55/29.80	tff('75', plain,
29.55/29.80	    ![X205 : int]:
29.55/29.80	      (~ app_encode_app(int, $o, 
29.55/29.80	           app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X205), 
29.55/29.80	           app_encode_app(int, int, bit0, 
29.55/29.80	             app_encode_app(int, int, bit1, pls)))
29.55/29.80	       | X205 = pls
29.55/29.80	       | X205 = app_encode_app(int, int, bit1, pls)
29.55/29.80	       | ~ app_encode_app(int, $o, 
29.55/29.80	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
29.55/29.80	               pls), X205)),
29.55/29.80	    inference('demod', [status(thm)], ['68', '73', '74', '18', '74'])).
29.55/29.80	tff('76', plain,
29.55/29.80	    ![X0 : int]:
29.55/29.80	      (~ $true
29.55/29.80	       | ~ app_encode_app(int, $o, 
29.55/29.80	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X0), 
29.55/29.80	             app_encode_app(int, int, bit1, pls))
29.55/29.80	       | ~ app_encode_app(int, $o, 
29.55/29.80	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
29.55/29.80	               pls), app_encode_app(int, int, bit0, X0))
29.55/29.80	       | app_encode_app(int, int, bit0, X0)
29.55/29.80	          = app_encode_app(int, int, bit1, pls)
29.55/29.80	       | app_encode_app(int, int, bit0, X0) = pls),
29.55/29.80	    inference('sup-', [status(thm)], ['67', '75'])).
29.55/29.80	tff('77', plain,
29.55/29.80	    ![X0 : int]:
29.55/29.80	      (app_encode_app(int, int, bit0, X0) = pls
29.55/29.80	       | app_encode_app(int, int, bit0, X0)
29.55/29.80	          = app_encode_app(int, int, bit1, pls)
29.55/29.80	       | ~ app_encode_app(int, $o, 
29.55/29.80	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
29.55/29.80	               pls), app_encode_app(int, int, bit0, X0))
29.55/29.80	       | ~ app_encode_app(int, $o, 
29.55/29.80	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X0), 
29.55/29.80	             app_encode_app(int, int, bit1, pls))),
29.55/29.80	    inference('simplify', [status(thm)], ['76'])).
29.55/29.80	tff(zf_stmt_57, axiom,
29.55/29.80	  (![L1:int,K:int]:
29.55/29.80	     (app_encode_app(int,int,bit1,K) != app_encode_app(int,int,bit0,L1)))).
29.55/29.80	tff('78', plain,
29.55/29.80	    ![X44 : int, X45 : int]:
29.55/29.80	      app_encode_app(int, int, bit1, X45)
29.55/29.80	       != app_encode_app(int, int, bit0, X44),
29.55/29.80	    inference('cnf', [status(esa)], [zf_stmt_57])).
29.55/29.80	tff('79', plain,
29.55/29.80	    ![X0 : int]:
29.55/29.80	      (~ app_encode_app(int, $o, 
29.55/29.80	           app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X0), 
29.55/29.80	           app_encode_app(int, int, bit1, pls))
29.55/29.80	       | ~ app_encode_app(int, $o, 
29.55/29.80	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
29.55/29.80	               pls), app_encode_app(int, int, bit0, X0))
29.55/29.80	       | app_encode_app(int, int, bit0, X0) = pls),
29.55/29.80	    inference('clc', [status(thm)], ['77', '78'])).
29.55/29.80	tff('80', plain,
29.55/29.80	    (~ $true
29.55/29.80	     | app_encode_app(int, int, bit0, 
29.55/29.80	         app_encode_app(nat, int, 
29.55/29.80	           app_encode_app(int, app_encode_fun(nat, int), power_power(int), s), 
29.55/29.80	           app_encode_app(int, nat, number_number_of(nat), 
29.55/29.80	             app_encode_app(int, int, bit0, 
29.55/29.80	               app_encode_app(int, int, bit1, pls)))))
29.55/29.80	        = pls
29.55/29.80	     | ~ app_encode_app(int, $o, 
29.55/29.80	           app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
29.55/29.80	             pls), 
29.55/29.80	           app_encode_app(int, int, bit0, 
29.55/29.80	             app_encode_app(nat, int, 
29.55/29.80	               app_encode_app(int, app_encode_fun(nat, int), 
29.55/29.80	                 power_power(int), s), 
29.55/29.80	               app_encode_app(int, nat, number_number_of(nat), 
29.55/29.80	                 app_encode_app(int, int, bit0, 
29.55/29.80	                   app_encode_app(int, int, bit1, pls))))))),
29.55/29.80	    inference('sup-', [status(thm)], ['66', '79'])).
29.55/29.80	tff(zf_stmt_67, axiom,
29.55/29.80	  (![L:int,K3:int]:
29.55/29.80	     (app_encode_app(int,$o,
29.55/29.80	                     app_encode_app(int,app_encode_fun(int,$o),
29.55/29.80	                                    ord_less_eq(int),
29.55/29.80	                                    app_encode_app(int,int,bit0,K3)),
29.55/29.80	                     app_encode_app(int,int,bit0,L)) <=>
29.55/29.80	      app_encode_app(int,$o,
29.55/29.80	                     app_encode_app(int,app_encode_fun(int,$o),
29.55/29.80	                                    ord_less_eq(int),K3),
29.55/29.80	                     L)))).
29.55/29.80	tff('81', plain,
29.55/29.80	    ![X62 : int, X63 : int]:
29.55/29.80	      (app_encode_app(int, $o, 
29.55/29.80	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
29.55/29.80	           app_encode_app(int, int, bit0, X63)), 
29.55/29.80	         app_encode_app(int, int, bit0, X62))
29.55/29.80	       | ~ app_encode_app(int, $o, 
29.55/29.80	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
29.55/29.80	               X63), X62)),
29.55/29.80	    inference('cnf', [status(esa)], [zf_stmt_67])).
29.55/29.80	tff(zf_stmt_91, axiom,
29.55/29.80	  (![L:int,K3:int]:
29.55/29.80	     (app_encode_app(int,$o,
29.55/29.80	                     app_encode_app(int,app_encode_fun(int,$o),ord_less(int),
29.55/29.80	                                    app_encode_app(int,int,bit0,K3)),
29.55/29.80	                     app_encode_app(int,int,bit1,L)) <=>
29.55/29.80	      app_encode_app(int,$o,
29.55/29.80	                     app_encode_app(int,app_encode_fun(int,$o),
29.55/29.80	                                    ord_less_eq(int),K3),
29.55/29.80	                     L)))).
29.55/29.80	tff('82', plain,
29.55/29.80	    ![X119 : int, X120 : int]:
29.55/29.80	      (app_encode_app(int, $o, 
29.55/29.80	         app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
29.55/29.80	           app_encode_app(int, int, bit0, X120)), 
29.55/29.80	         app_encode_app(int, int, bit1, X119))
29.55/29.80	       | ~ app_encode_app(int, $o, 
29.55/29.80	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
29.55/29.80	               X120), X119)),
29.55/29.80	    inference('cnf', [status(esa)], [zf_stmt_91])).
29.55/29.80	tff('83', plain,
29.55/29.80	    ![X0 : int, X1 : int]:
29.55/29.80	      (~ $true
29.55/29.80	       | ~ app_encode_app(int, $o, 
29.55/29.80	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
29.55/29.80	               X1), X0)
29.55/29.80	       | app_encode_app(int, $o, 
29.55/29.80	           app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
29.55/29.80	             app_encode_app(int, int, bit0, 
29.55/29.80	               app_encode_app(int, int, bit0, X1))), 
29.55/29.80	           app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, X0)))),
29.55/29.80	    inference('sup-', [status(thm)], ['81', '82'])).
29.55/29.80	tff('84', plain,
29.55/29.80	    ![X0 : int, X1 : int]:
29.55/29.80	      (app_encode_app(int, $o, 
29.55/29.80	         app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
29.55/29.80	           app_encode_app(int, int, bit0, app_encode_app(int, int, bit0, X1))), 
29.55/29.80	         app_encode_app(int, int, bit1, app_encode_app(int, int, bit0, X0)))
29.55/29.80	       | ~ app_encode_app(int, $o, 
29.55/29.80	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
29.55/29.80	               X1), X0)),
29.55/29.80	    inference('simplify', [status(thm)], ['83'])).
29.55/29.80	tff('85', plain,
29.55/29.80	    (~ $true
29.55/29.80	     | app_encode_app(int, $o, 
29.55/29.80	         app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
29.55/29.80	           app_encode_app(int, int, bit0, 
29.55/29.80	             app_encode_app(int, int, bit0, pls))), 
29.55/29.80	         app_encode_app(int, int, bit1, 
29.55/29.80	           app_encode_app(int, int, bit0, 
29.55/29.80	             app_encode_app(nat, int, 
29.55/29.80	               app_encode_app(int, app_encode_fun(nat, int), 
29.55/29.80	                 power_power(int), s), 
29.55/29.80	               app_encode_app(int, nat, number_number_of(nat), 
29.55/29.80	                 app_encode_app(int, int, bit0, 
29.55/29.80	                   app_encode_app(int, int, bit1, pls)))))))),
29.55/29.80	    inference('sup-', [status(thm)], ['41', '84'])).
29.55/29.80	tff(zf_stmt_61, axiom, (app_encode_app(int,int,bit0,pls) = pls)).
29.55/29.80	tff('86', plain, app_encode_app(int, int, bit0, pls) = pls,
29.55/29.80	    inference('cnf', [status(esa)], [zf_stmt_61])).
29.55/29.80	tff('87', plain,
29.55/29.80	    (~ $true
29.55/29.80	     | app_encode_app(int, $o, 
29.55/29.80	         app_encode_app(int, app_encode_fun(int, $o), ord_less(int), pls), 
29.55/29.80	         app_encode_app(int, int, bit1, 
29.55/29.80	           app_encode_app(int, int, bit0, 
29.55/29.80	             app_encode_app(nat, int, 
29.55/29.80	               app_encode_app(int, app_encode_fun(nat, int), 
29.55/29.80	                 power_power(int), s), 
29.55/29.80	               app_encode_app(int, nat, number_number_of(nat), 
29.55/29.80	                 app_encode_app(int, int, bit0, 
29.55/29.80	                   app_encode_app(int, int, bit1, pls)))))))),
29.55/29.80	    inference('demod', [status(thm)], ['85', '86', '86'])).
29.55/29.80	tff('88', plain,
29.55/29.80	    app_encode_app(int, $o, 
29.55/29.80	      app_encode_app(int, app_encode_fun(int, $o), ord_less(int), pls), 
29.55/29.80	      app_encode_app(int, int, bit1, 
29.55/29.80	        app_encode_app(int, int, bit0, 
29.55/29.80	          app_encode_app(nat, int, 
29.55/29.80	            app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
29.55/29.80	              s), 
29.55/29.80	            app_encode_app(int, nat, number_number_of(nat), 
29.55/29.80	              app_encode_app(int, int, bit0, 
29.55/29.80	                app_encode_app(int, int, bit1, pls))))))),
29.55/29.80	    inference('simplify', [status(thm)], ['87'])).
29.55/29.80	tff(zf_stmt_87, axiom,
29.55/29.80	  (![K3:int]:
29.55/29.80	     (app_encode_app(int,$o,
29.55/29.80	                     app_encode_app(int,app_encode_fun(int,$o),ord_less(int),
29.55/29.80	                                    pls),
29.55/29.80	                     app_encode_app(int,int,bit1,K3)) <=>
29.55/29.80	      app_encode_app(int,$o,
29.55/29.80	                     app_encode_app(int,app_encode_fun(int,$o),
29.55/29.80	                                    ord_less_eq(int),pls),
29.55/29.80	                     K3)))).
29.55/29.80	tff('89', plain,
29.55/29.80	    ![X109 : int]:
29.55/29.80	      (app_encode_app(int, $o, 
29.55/29.80	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), pls), 
29.55/29.80	         X109)
29.55/29.80	       | ~ app_encode_app(int, $o, 
29.55/29.80	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), pls), 
29.55/29.80	             app_encode_app(int, int, bit1, X109))),
29.55/29.80	    inference('cnf', [status(esa)], [zf_stmt_87])).
29.55/29.80	tff('90', plain,
29.55/29.80	    (~ $true
29.55/29.80	     | app_encode_app(int, $o, 
29.55/29.80	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), pls), 
29.55/29.80	         app_encode_app(int, int, bit0, 
29.55/29.80	           app_encode_app(nat, int, 
29.55/29.80	             app_encode_app(int, app_encode_fun(nat, int), power_power(int), 
29.55/29.80	               s), 
29.55/29.80	             app_encode_app(int, nat, number_number_of(nat), 
29.55/29.80	               app_encode_app(int, int, bit0, 
29.55/29.80	                 app_encode_app(int, int, bit1, pls))))))),
29.55/29.80	    inference('sup-', [status(thm)], ['88', '89'])).
29.55/29.80	tff('91', plain,
29.55/29.80	    app_encode_app(int, $o, 
29.55/29.80	      app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), pls), 
29.55/29.80	      app_encode_app(int, int, bit0, 
29.55/29.80	        app_encode_app(nat, int, 
29.55/29.80	          app_encode_app(int, app_encode_fun(nat, int), power_power(int), s), 
29.55/29.80	          app_encode_app(int, nat, number_number_of(nat), 
29.55/29.80	            app_encode_app(int, int, bit0, 
29.55/29.80	              app_encode_app(int, int, bit1, pls)))))),
29.55/29.80	    inference('simplify', [status(thm)], ['90'])).
29.55/29.80	tff('92', plain,
29.55/29.80	    (~ $true
29.55/29.80	     | app_encode_app(int, int, bit0, 
29.55/29.80	         app_encode_app(nat, int, 
29.55/29.80	           app_encode_app(int, app_encode_fun(nat, int), power_power(int), s), 
29.55/29.80	           app_encode_app(int, nat, number_number_of(nat), 
29.55/29.80	             app_encode_app(int, int, bit0, 
29.55/29.80	               app_encode_app(int, int, bit1, pls)))))
29.55/29.80	        = pls
29.55/29.80	     | ~ $true),
29.55/29.80	    inference('demod', [status(thm)], ['80', '91'])).
29.55/29.80	tff('93', plain,
29.55/29.80	    app_encode_app(int, int, bit0, 
29.55/29.80	      app_encode_app(nat, int, 
29.55/29.80	        app_encode_app(int, app_encode_fun(nat, int), power_power(int), s), 
29.55/29.80	        app_encode_app(int, nat, number_number_of(nat), 
29.55/29.80	          app_encode_app(int, int, bit0, app_encode_app(int, int, bit1, pls)))))
29.55/29.80	     = pls,
29.55/29.80	    inference('simplify', [status(thm)], ['92'])).
29.55/29.80	tff(zf_stmt_77, axiom,
29.55/29.80	  (![K3:int]:
29.55/29.80	     (app_encode_app(int,$o,
29.55/29.80	                     app_encode_app(int,app_encode_fun(int,$o),ord_less(int),
29.55/29.80	                                    app_encode_app(int,int,bit0,K3)),
29.55/29.80	                     pls) <=>
29.55/29.80	      app_encode_app(int,$o,
29.55/29.80	                     app_encode_app(int,app_encode_fun(int,$o),ord_less(int),
29.55/29.80	                                    K3),
29.55/29.80	                     pls)))).
29.55/29.80	tff('94', plain,
29.55/29.80	    ![X88 : int]:
29.55/29.80	      (app_encode_app(int, $o, 
29.55/29.80	         app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
29.55/29.80	           app_encode_app(int, int, bit0, X88)), pls)
29.55/29.80	       | ~ app_encode_app(int, $o, 
29.55/29.80	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X88), 
29.55/29.80	             pls)),
29.55/29.80	    inference('cnf', [status(esa)], [zf_stmt_77])).
29.55/29.80	tff('95', plain,
29.55/29.80	    (app_encode_app(int, $o, 
29.55/29.80	       app_encode_app(int, app_encode_fun(int, $o), ord_less(int), pls), pls)
29.55/29.80	     | ~ app_encode_app(int, $o, 
29.55/29.80	           app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
29.55/29.80	             app_encode_app(nat, int, 
29.55/29.80	               app_encode_app(int, app_encode_fun(nat, int), 
29.55/29.80	                 power_power(int), s), 
29.55/29.80	               app_encode_app(int, nat, number_number_of(nat), 
29.55/29.80	                 app_encode_app(int, int, bit0, 
29.55/29.80	                   app_encode_app(int, int, bit1, pls))))), pls)),
29.55/29.80	    inference('sup+', [status(thm)], ['93', '94'])).
29.55/29.80	tff('96', plain,
29.55/29.80	    (app_encode_app(int, $o, 
29.55/29.80	       app_encode_app(int, app_encode_fun(int, $o), ord_less(int), pls), pls)
29.55/29.80	     | ~ $true),
29.55/29.80	    inference('demod', [status(thm)], ['95', '52'])).
29.55/29.80	tff('97', plain,
29.55/29.80	    app_encode_app(int, $o, 
29.55/29.80	      app_encode_app(int, app_encode_fun(int, $o), ord_less(int), pls), pls),
29.55/29.80	    inference('simplify', [status(thm)], ['96'])).
29.55/29.80	tff('98', plain, ~ $true, inference('sup-', [status(thm)], ['97', '48'])).
29.55/29.80	tff('99', plain, $false, inference('simplify', [status(thm)], ['98'])).
29.55/29.80	
29.55/29.80	% SZS output end Refutation
29.55/29.80	EOF
