0.00/0.01	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.01	% app-encoded or not : appext
0.00/0.01	% Variant    : fo
0.00/0.01	% Ordering    : rpo6
0.00/0.01	% 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 $2 \
0.00/0.01	  --simultaneous-sup false \
0.00/0.01	  --no-max-vars \
0.00/0.01	  --no-fool
0.00/0.20	% Computer   : n088.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 08:10:38 CST 2018
1.26/1.49	% done 1281 iterations in 1.277s
1.26/1.49	% SZS status Theorem for 'stdin'
1.26/1.49	% SZS output start Refutation
1.26/1.49	tff(zf_stmt_29, axiom,
1.26/1.49	  (app_encode_app(int,$o,
1.26/1.49	                  app_encode_app(int,app_encode_fun(int,$o),ord_less(int),
1.26/1.49	                                 one_one(int)),
1.26/1.49	                  t))).
1.26/1.49	tff('0', plain,
1.26/1.49	    app_encode_app(int, $o, 
1.26/1.49	      app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
1.26/1.49	        one_one(int)), t),
1.26/1.49	    inference('cnf', [status(esa)], [zf_stmt_29])).
1.26/1.49	tff(zf_stmt_115, axiom,
1.26/1.49	  (![Z2:int,Z1:int]:
1.26/1.49	     (app_encode_app(int,$o,
1.26/1.49	                     app_encode_app(int,app_encode_fun(int,$o),
1.26/1.49	                                    ord_less_eq(int),zero_zero(int)),
1.26/1.49	                     Z1) =>
1.26/1.49	      (app_encode_app(int,$o,
1.26/1.49	                      app_encode_app(int,app_encode_fun(int,$o),
1.26/1.49	                                     ord_less_eq(int),Z1),
1.26/1.49	                      Z2) =>
1.26/1.49	       (app_encode_app(int,nat,nat1,
1.26/1.49	                       app_encode_app(int,int,
1.26/1.49	                                      app_encode_app(int,
1.26/1.49	                                                     app_encode_fun(int,int),
1.26/1.49	                                                     minus_minus(int),Z2),
1.26/1.49	                                      Z1)) =
1.26/1.49	        app_encode_app(nat,nat,
1.26/1.49	                       app_encode_app(nat,app_encode_fun(nat,nat),
1.26/1.49	                                      minus_minus(nat),
1.26/1.49	                                      app_encode_app(int,nat,nat1,Z2)),
1.26/1.49	                       app_encode_app(int,nat,nat1,Z1))))))).
1.26/1.49	tff('1', plain,
1.26/1.49	    ![X184 : int, X185 : int]:
1.26/1.49	      (~ app_encode_app(int, $o, 
1.26/1.49	           app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
1.26/1.49	             X184), X185)
1.26/1.49	       | app_encode_app(int, nat, nat1, 
1.26/1.49	           app_encode_app(int, int, 
1.26/1.49	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
1.26/1.49	               X185), X184))
1.26/1.49	          = app_encode_app(nat, nat, 
1.26/1.49	              app_encode_app(nat, app_encode_fun(nat, nat), 
1.26/1.49	                minus_minus(nat), app_encode_app(int, nat, nat1, X185)), 
1.26/1.49	              app_encode_app(int, nat, nat1, X184))
1.26/1.49	       | ~ app_encode_app(int, $o, 
1.26/1.49	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
1.26/1.49	               zero_zero(int)), X184)),
1.26/1.49	    inference('cnf', [status(esa)], [zf_stmt_115])).
1.26/1.49	tff(zf_stmt_33, axiom,
1.26/1.49	  (![N1:nat]:
1.26/1.49	     ((N1 != zero_zero(nat)) <=>
1.26/1.49	      app_encode_app(nat,$o,
1.26/1.49	                     app_encode_app(nat,app_encode_fun(nat,$o),ord_less(nat),
1.26/1.49	                                    zero_zero(nat)),
1.26/1.49	                     N1)))).
1.26/1.49	tff('2', plain,
1.26/1.49	    ![X9 : nat]:
1.26/1.49	      (app_encode_app(nat, $o, 
1.26/1.49	         app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), 
1.26/1.49	           zero_zero(nat)), X9)
1.26/1.49	       | X9 = zero_zero(nat)),
1.26/1.49	    inference('cnf', [status(esa)], [zf_stmt_33])).
1.26/1.49	tff(zf_stmt_144, axiom,
1.26/1.49	  (![Tn:nat]:
1.26/1.49	     ((Tn =
1.26/1.49	       app_encode_app(nat,nat,
1.26/1.49	                      app_encode_app(nat,app_encode_fun(nat,nat),
1.26/1.49	                                     minus_minus(nat),
1.26/1.49	                                     app_encode_app(int,nat,nat1,t)),
1.26/1.49	                      one_one(nat))) =>
1.26/1.49	      (app_encode_app(nat,$o,
1.26/1.49	                      app_encode_app(nat,app_encode_fun(nat,$o),
1.26/1.49	                                     ord_less(nat),zero_zero(nat)),
1.26/1.49	                      Tn) =>
1.26/1.49	       thesis)))).
1.26/1.49	tff('3', plain,
1.26/1.49	    ![X213 : nat]:
1.26/1.49	      (thesis
1.26/1.49	       | X213
1.26/1.49	          != app_encode_app(nat, nat, 
1.26/1.49	               app_encode_app(nat, app_encode_fun(nat, nat), 
1.26/1.49	                 minus_minus(nat), app_encode_app(int, nat, nat1, t)), 
1.26/1.49	               one_one(nat))
1.26/1.49	       | ~ app_encode_app(nat, $o, 
1.26/1.49	             app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), 
1.26/1.49	               zero_zero(nat)), X213)),
1.26/1.49	    inference('cnf', [status(esa)], [zf_stmt_144])).
1.26/1.49	tff('4', plain,
1.26/1.49	    (~ app_encode_app(nat, $o, 
1.26/1.49	         app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), 
1.26/1.49	           zero_zero(nat)), 
1.26/1.49	         app_encode_app(nat, nat, 
1.26/1.49	           app_encode_app(nat, app_encode_fun(nat, nat), minus_minus(nat), 
1.26/1.49	             app_encode_app(int, nat, nat1, t)), one_one(nat)))
1.26/1.49	     | thesis),
1.26/1.49	    inference('simplify', [status(thm)], ['3'])).
1.26/1.49	tff(zf_stmt_69, axiom,
1.26/1.49	  (one_one(nat) = app_encode_app(int,nat,nat1,one_one(int)))).
1.26/1.49	tff('5', plain, one_one(nat) = app_encode_app(int, nat, nat1, one_one(int)),
1.26/1.49	    inference('cnf', [status(esa)], [zf_stmt_69])).
1.26/1.49	tff('6', plain,
1.26/1.49	    (~ app_encode_app(nat, $o, 
1.26/1.49	         app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), 
1.26/1.49	           zero_zero(nat)), 
1.26/1.49	         app_encode_app(nat, nat, 
1.26/1.49	           app_encode_app(nat, app_encode_fun(nat, nat), minus_minus(nat), 
1.26/1.49	             app_encode_app(int, nat, nat1, t)), 
1.26/1.49	           app_encode_app(int, nat, nat1, one_one(int))))
1.26/1.49	     | thesis),
1.26/1.49	    inference('demod', [status(thm)], ['4', '5'])).
1.26/1.49	tff(zf_stmt_145, conjecture, (thesis)).
1.26/1.49	tff(zf_stmt_0, negated_conjecture, (~thesis)).
1.26/1.49	tff('7', plain, ~ thesis, inference('cnf', [status(esa)], [zf_stmt_0])).
1.26/1.49	tff('8', plain,
1.26/1.49	    ~ app_encode_app(nat, $o, 
1.26/1.49	        app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), 
1.26/1.49	          zero_zero(nat)), 
1.26/1.49	        app_encode_app(nat, nat, 
1.26/1.49	          app_encode_app(nat, app_encode_fun(nat, nat), minus_minus(nat), 
1.26/1.49	            app_encode_app(int, nat, nat1, t)), 
1.26/1.49	          app_encode_app(int, nat, nat1, one_one(int)))),
1.26/1.49	    inference('clc', [status(thm)], ['6', '7'])).
1.26/1.49	tff('9', plain,
1.26/1.49	    (~ $true
1.26/1.49	     | app_encode_app(nat, nat, 
1.26/1.49	         app_encode_app(nat, app_encode_fun(nat, nat), minus_minus(nat), 
1.26/1.49	           app_encode_app(int, nat, nat1, t)), 
1.26/1.49	         app_encode_app(int, nat, nat1, one_one(int)))
1.26/1.49	        = zero_zero(nat)),
1.26/1.49	    inference('sup-', [status(thm)], ['2', '8'])).
1.26/1.49	tff('10', plain,
1.26/1.49	    app_encode_app(nat, nat, 
1.26/1.49	      app_encode_app(nat, app_encode_fun(nat, nat), minus_minus(nat), 
1.26/1.49	        app_encode_app(int, nat, nat1, t)), 
1.26/1.49	      app_encode_app(int, nat, nat1, one_one(int)))
1.26/1.49	     = zero_zero(nat),
1.26/1.49	    inference('simplify', [status(thm)], ['9'])).
1.26/1.49	tff('11', plain,
1.26/1.49	    (app_encode_app(int, nat, nat1, 
1.26/1.49	       app_encode_app(int, int, 
1.26/1.49	         app_encode_app(int, app_encode_fun(int, int), minus_minus(int), t), 
1.26/1.49	         one_one(int)))
1.26/1.49	      = zero_zero(nat)
1.26/1.49	     | ~ app_encode_app(int, $o, 
1.26/1.49	           app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
1.26/1.49	             zero_zero(int)), one_one(int))
1.26/1.49	     | ~ app_encode_app(int, $o, 
1.26/1.49	           app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
1.26/1.49	             one_one(int)), t)),
1.26/1.49	    inference('sup+', [status(thm)], ['1', '10'])).
1.26/1.49	tff(zf_stmt_100, axiom,
1.26/1.49	  (app_encode_app(int,$o,
1.26/1.49	                  app_encode_app(int,app_encode_fun(int,$o),ord_less_eq(int),
1.26/1.49	                                 zero_zero(int)),
1.26/1.49	                  one_one(int)))).
1.26/1.49	tff('12', plain,
1.26/1.49	    app_encode_app(int, $o, 
1.26/1.49	      app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
1.26/1.49	        zero_zero(int)), one_one(int)),
1.26/1.49	    inference('cnf', [status(esa)], [zf_stmt_100])).
1.26/1.49	tff(zf_stmt_71, axiom,
1.26/1.49	  (app_encode_app(int,$o,
1.26/1.49	                  app_encode_app(int,app_encode_fun(int,$o),ord_less_eq(int),
1.26/1.49	                                 one_one(int)),
1.26/1.49	                  t))).
1.26/1.49	tff('13', plain,
1.26/1.49	    app_encode_app(int, $o, 
1.26/1.49	      app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
1.26/1.49	        one_one(int)), t),
1.26/1.49	    inference('cnf', [status(esa)], [zf_stmt_71])).
1.26/1.49	tff('14', plain,
1.26/1.49	    (app_encode_app(int, nat, nat1, 
1.26/1.49	       app_encode_app(int, int, 
1.26/1.49	         app_encode_app(int, app_encode_fun(int, int), minus_minus(int), t), 
1.26/1.49	         one_one(int)))
1.26/1.49	      = zero_zero(nat)
1.26/1.49	     | ~ $true
1.26/1.49	     | ~ $true),
1.26/1.49	    inference('demod', [status(thm)], ['11', '12', '13'])).
1.26/1.49	tff('15', plain,
1.26/1.49	    app_encode_app(int, nat, nat1, 
1.26/1.49	      app_encode_app(int, int, 
1.26/1.49	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), t), 
1.26/1.49	        one_one(int)))
1.26/1.49	     = zero_zero(nat),
1.26/1.49	    inference('simplify', [status(thm)], ['14'])).
1.26/1.49	tff(zf_stmt_81, axiom,
1.26/1.49	  (![I:int]:
1.26/1.49	     ((app_encode_app(int,nat,nat1,I) = zero_zero(nat)) <=>
1.26/1.49	      app_encode_app(int,$o,
1.26/1.49	                     app_encode_app(int,app_encode_fun(int,$o),
1.26/1.49	                                    ord_less_eq(int),I),
1.26/1.49	                     zero_zero(int))))).
1.26/1.49	tff('16', plain,
1.26/1.49	    ![X115 : int]:
1.26/1.49	      (app_encode_app(int, $o, 
1.26/1.49	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), X115), 
1.26/1.49	         zero_zero(int))
1.26/1.49	       | app_encode_app(int, nat, nat1, X115) != zero_zero(nat)),
1.26/1.49	    inference('cnf', [status(esa)], [zf_stmt_81])).
1.26/1.49	tff('17', plain,
1.26/1.49	    (zero_zero(nat) != zero_zero(nat)
1.26/1.49	     | app_encode_app(int, $o, 
1.26/1.49	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
1.26/1.49	           app_encode_app(int, int, 
1.26/1.49	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
1.26/1.49	               t), one_one(int))), zero_zero(int))),
1.26/1.49	    inference('sup-', [status(thm)], ['15', '16'])).
1.26/1.49	tff('18', plain,
1.26/1.49	    app_encode_app(int, $o, 
1.26/1.49	      app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
1.26/1.49	        app_encode_app(int, int, 
1.26/1.49	          app_encode_app(int, app_encode_fun(int, int), minus_minus(int), t), 
1.26/1.49	          one_one(int))), zero_zero(int)),
1.26/1.49	    inference('simplify', [status(thm)], ['17'])).
1.26/1.49	tff(zf_stmt_124, axiom,
1.26/1.49	  (![A:$tType]:
1.26/1.49	     (ordered_ab_group_add(A) =>
1.26/1.49	      (![B:A,A1:A]:
1.26/1.49	         (app_encode_app(A,$o,
1.26/1.49	                         app_encode_app(A,app_encode_fun(A,$o),
1.26/1.49	                                        ord_less_eq(A),A1),
1.26/1.49	                         B) <=>
1.26/1.49	          app_encode_app(A,$o,
1.26/1.49	                         app_encode_app(A,app_encode_fun(A,$o),
1.26/1.49	                                        ord_less_eq(A),
1.26/1.49	                                        app_encode_app(A,A,
1.26/1.49	                                                       app_encode_app(
1.26/1.49	                                                       A,app_encode_fun(A,A),
1.26/1.49	                                                       minus_minus(A),A1),B)),
1.26/1.49	                         zero_zero(A))))))).
1.26/1.49	tff('19', plain,
1.26/1.49	    ![X205 : $tType, X206 : X205, X207 : X205]:
1.26/1.49	      (~ app_encode_app(X205, $o, 
1.26/1.49	           app_encode_app(X205, app_encode_fun(X205, $o), ord_less_eq(X205), 
1.26/1.49	             app_encode_app(X205, X205, 
1.26/1.49	               app_encode_app(X205, app_encode_fun(X205, X205), 
1.26/1.49	                 minus_minus(X205), X206), X207)), zero_zero(X205))
1.26/1.49	       | app_encode_app(X205, $o, 
1.26/1.49	           app_encode_app(X205, app_encode_fun(X205, $o), ord_less_eq(X205), 
1.26/1.49	             X206), X207)
1.26/1.49	       | ~ ordered_ab_group_add(X205)),
1.26/1.49	    inference('cnf', [status(esa)], [zf_stmt_124])).
1.26/1.49	tff('20', plain,
1.26/1.49	    (~ $true
1.26/1.49	     | ~ ordered_ab_group_add(int)
1.26/1.49	     | app_encode_app(int, $o, 
1.26/1.49	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), t), 
1.26/1.49	         one_one(int))),
1.26/1.49	    inference('sup-', [status(thm)], ['18', '19'])).
1.26/1.49	tff(zf_stmt_127, axiom, (ordered_ab_group_add(int))).
1.26/1.49	tff('21', plain, ordered_ab_group_add(int),
1.26/1.49	    inference('cnf', [status(esa)], [zf_stmt_127])).
1.26/1.49	tff('22', plain,
1.26/1.49	    (~ $true
1.26/1.49	     | ~ $true
1.26/1.49	     | app_encode_app(int, $o, 
1.26/1.49	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), t), 
1.26/1.49	         one_one(int))),
1.26/1.49	    inference('demod', [status(thm)], ['20', '21'])).
1.26/1.49	tff('23', plain,
1.26/1.49	    app_encode_app(int, $o, 
1.26/1.49	      app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), t), 
1.26/1.49	      one_one(int)),
1.26/1.49	    inference('simplify', [status(thm)], ['22'])).
1.26/1.49	tff(zf_stmt_99, axiom,
1.26/1.49	  (![W:int,Z:int]:
1.26/1.49	     (app_encode_app(int,$o,
1.26/1.49	                     app_encode_app(int,app_encode_fun(int,$o),ord_less(int),
1.26/1.49	                                    Z),
1.26/1.49	                     W) <=>
1.26/1.49	      (app_encode_app(int,$o,
1.26/1.49	                      app_encode_app(int,app_encode_fun(int,$o),
1.26/1.49	                                     ord_less_eq(int),Z),
1.26/1.49	                      W) & 
1.26/1.49	       (Z != W))))).
1.26/1.49	tff('24', plain,
1.26/1.49	    ![X148 : int, X149 : int]:
1.26/1.49	      (app_encode_app(int, $o, 
1.26/1.49	         app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X149), 
1.26/1.49	         X148)
1.26/1.49	       | X149 = X148
1.26/1.49	       | ~ app_encode_app(int, $o, 
1.26/1.49	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
1.26/1.49	               X149), X148)),
1.26/1.49	    inference('cnf', [status(esa)], [zf_stmt_99])).
1.26/1.49	tff('25', plain,
1.26/1.49	    (~ $true
1.26/1.49	     | t = one_one(int)
1.26/1.49	     | app_encode_app(int, $o, 
1.26/1.49	         app_encode_app(int, app_encode_fun(int, $o), ord_less(int), t), 
1.26/1.49	         one_one(int))),
1.26/1.49	    inference('sup-', [status(thm)], ['23', '24'])).
1.26/1.49	tff('26', plain,
1.26/1.49	    (app_encode_app(int, $o, 
1.26/1.49	       app_encode_app(int, app_encode_fun(int, $o), ord_less(int), t), 
1.26/1.49	       one_one(int))
1.26/1.49	     | t = one_one(int)),
1.26/1.49	    inference('simplify', [status(thm)], ['25'])).
1.26/1.49	tff(zf_stmt_133, axiom, (group_add(int))).
1.26/1.49	tff('27', plain, group_add(int),
1.26/1.49	    inference('cnf', [status(esa)], [zf_stmt_133])).
1.26/1.49	tff(zf_stmt_36, axiom,
1.26/1.49	  (![A:$tType]:
1.26/1.49	     (group_add(A) =>
1.26/1.49	      (![A2:A]:
1.26/1.49	         (app_encode_app(A,A,
1.26/1.49	                         app_encode_app(A,app_encode_fun(A,A),minus_minus(A),
1.26/1.49	                                        A2),
1.26/1.49	                         A2) =
1.26/1.49	          zero_zero(A)))))).
1.26/1.49	tff('28', plain,
1.26/1.49	    ![X13 : $tType, X14 : X13]:
1.26/1.49	      (app_encode_app(X13, X13, 
1.26/1.49	         app_encode_app(X13, app_encode_fun(X13, X13), minus_minus(X13), X14), 
1.26/1.49	         X14)
1.26/1.49	        = zero_zero(X13)
1.26/1.49	       | ~ group_add(X13)),
1.26/1.49	    inference('cnf', [status(esa)], [zf_stmt_36])).
1.26/1.49	tff('29', plain,
1.26/1.49	    ![X0 : int]:
1.26/1.49	      (~ $true
1.26/1.49	       | app_encode_app(int, int, 
1.26/1.49	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
1.26/1.49	             X0), X0)
1.26/1.49	          = zero_zero(int)),
1.26/1.49	    inference('sup-', [status(thm)], ['27', '28'])).
1.26/1.49	tff('30', plain,
1.26/1.49	    ![X0 : int]:
1.26/1.49	      app_encode_app(int, int, 
1.26/1.49	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), X0), 
1.26/1.49	        X0)
1.26/1.49	       = zero_zero(int),
1.26/1.49	    inference('simplify', [status(thm)], ['29'])).
1.26/1.49	tff(zf_stmt_82, axiom,
1.26/1.49	  (![Z:int,W:int]:
1.26/1.49	     (app_encode_app(int,$o,
1.26/1.49	                     app_encode_app(int,app_encode_fun(int,$o),
1.26/1.49	                                    ord_less_eq(int),W),
1.26/1.49	                     app_encode_app(int,int,
1.26/1.49	                                    app_encode_app(int,
1.26/1.49	                                                   app_encode_fun(int,int),
1.26/1.49	                                                   minus_minus(int),Z),
1.26/1.49	                                    one_one(int))) <=>
1.26/1.49	      app_encode_app(int,$o,
1.26/1.49	                     app_encode_app(int,app_encode_fun(int,$o),ord_less(int),
1.26/1.49	                                    W),
1.26/1.49	                     Z)))).
1.26/1.49	tff('31', plain,
1.26/1.49	    ![X118 : int, X119 : int]:
1.26/1.49	      (app_encode_app(int, $o, 
1.26/1.49	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), X119), 
1.26/1.49	         app_encode_app(int, int, 
1.26/1.49	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
1.26/1.49	             X118), one_one(int)))
1.26/1.49	       | ~ app_encode_app(int, $o, 
1.26/1.49	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
1.26/1.49	               X119), X118)),
1.26/1.49	    inference('cnf', [status(esa)], [zf_stmt_82])).
1.26/1.49	tff('32', plain,
1.26/1.49	    ![X0 : int]:
1.26/1.49	      (app_encode_app(int, $o, 
1.26/1.49	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), X0), 
1.26/1.49	         zero_zero(int))
1.26/1.49	       | ~ app_encode_app(int, $o, 
1.26/1.49	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X0), 
1.26/1.49	             one_one(int))),
1.26/1.49	    inference('sup+', [status(thm)], ['30', '31'])).
1.26/1.49	tff('33', plain,
1.26/1.49	    (~ $true
1.26/1.49	     | t = one_one(int)
1.26/1.49	     | app_encode_app(int, $o, 
1.26/1.49	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), t), 
1.26/1.49	         zero_zero(int))),
1.26/1.49	    inference('sup-', [status(thm)], ['26', '32'])).
1.26/1.49	tff('34', plain,
1.26/1.49	    (app_encode_app(int, $o, 
1.26/1.49	       app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), t), 
1.26/1.49	       zero_zero(int))
1.26/1.49	     | t = one_one(int)),
1.26/1.49	    inference('simplify', [status(thm)], ['33'])).
1.26/1.49	tff('35', plain,
1.26/1.49	    ![X116 : int]:
1.26/1.49	      (app_encode_app(int, nat, nat1, X116) = zero_zero(nat)
1.26/1.49	       | ~ app_encode_app(int, $o, 
1.26/1.49	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
1.26/1.49	               X116), zero_zero(int))),
1.26/1.49	    inference('cnf', [status(esa)], [zf_stmt_81])).
1.26/1.49	tff('36', plain,
1.26/1.49	    (~ $true
1.26/1.49	     | t = one_one(int)
1.26/1.49	     | app_encode_app(int, nat, nat1, t) = zero_zero(nat)),
1.26/1.49	    inference('sup-', [status(thm)], ['34', '35'])).
1.26/1.49	tff('37', plain,
1.26/1.49	    (app_encode_app(int, nat, nat1, t) = zero_zero(nat) | t = one_one(int)),
1.26/1.49	    inference('simplify', [status(thm)], ['36'])).
1.26/1.49	tff(zf_stmt_111, axiom,
1.26/1.49	  (one_one(int) = app_encode_app(nat,int,semiring_1_of_nat(int),one_one(nat)))).
1.26/1.49	tff('38', plain,
1.26/1.49	    one_one(int)
1.26/1.49	     = app_encode_app(nat, int, semiring_1_of_nat(int), one_one(nat)),
1.26/1.49	    inference('cnf', [status(esa)], [zf_stmt_111])).
1.26/1.49	tff('39', plain,
1.26/1.49	    one_one(int)
1.26/1.49	     = app_encode_app(nat, int, semiring_1_of_nat(int), 
1.26/1.49	         app_encode_app(int, nat, nat1, one_one(int))),
1.26/1.49	    inference('demod', [status(thm)], ['38', '5'])).
1.26/1.49	tff(zf_stmt_123, axiom,
1.26/1.49	  (![Z:int,Ma:nat]:
1.26/1.49	     (app_encode_app(nat,$o,
1.26/1.49	                     app_encode_app(nat,app_encode_fun(nat,$o),ord_less(nat),
1.26/1.49	                                    Ma),
1.26/1.49	                     app_encode_app(int,nat,nat1,Z)) <=>
1.26/1.49	      app_encode_app(int,$o,
1.26/1.49	                     app_encode_app(int,app_encode_fun(int,$o),ord_less(int),
1.26/1.49	                                    app_encode_app(nat,int,
1.26/1.49	                                                   semiring_1_of_nat(int),Ma)),
1.26/1.49	                     Z)))).
1.26/1.49	tff('40', plain,
1.26/1.49	    ![X203 : int, X204 : nat]:
1.26/1.49	      (app_encode_app(nat, $o, 
1.26/1.49	         app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), X204), 
1.26/1.49	         app_encode_app(int, nat, nat1, X203))
1.26/1.49	       | ~ app_encode_app(int, $o, 
1.26/1.49	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
1.26/1.49	               app_encode_app(nat, int, semiring_1_of_nat(int), X204)), X203)),
1.26/1.49	    inference('cnf', [status(esa)], [zf_stmt_123])).
1.26/1.49	tff('41', plain,
1.26/1.49	    ![X0 : int]:
1.26/1.49	      (~ app_encode_app(int, $o, 
1.26/1.49	           app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
1.26/1.49	             one_one(int)), X0)
1.26/1.49	       | app_encode_app(nat, $o, 
1.26/1.49	           app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), 
1.26/1.49	             app_encode_app(int, nat, nat1, one_one(int))), 
1.26/1.49	           app_encode_app(int, nat, nat1, X0))),
1.26/1.49	    inference('sup-', [status(thm)], ['39', '40'])).
1.26/1.49	tff(zf_stmt_32, axiom,
1.26/1.49	  (![M:nat]:
1.26/1.49	     (app_encode_app(nat,nat,
1.26/1.49	                     app_encode_app(nat,app_encode_fun(nat,nat),
1.26/1.49	                                    minus_minus(nat),M),
1.26/1.49	                     M) =
1.26/1.49	      zero_zero(nat)))).
1.26/1.49	tff('42', plain,
1.26/1.49	    ![X8 : nat]:
1.26/1.49	      app_encode_app(nat, nat, 
1.26/1.49	        app_encode_app(nat, app_encode_fun(nat, nat), minus_minus(nat), X8), 
1.26/1.49	        X8)
1.26/1.49	       = zero_zero(nat),
1.26/1.49	    inference('cnf', [status(esa)], [zf_stmt_32])).
1.26/1.49	tff(zf_stmt_65, axiom,
1.26/1.49	  (![N2:nat,K:nat,J:nat]:
1.26/1.49	     (app_encode_app(nat,$o,
1.26/1.49	                     app_encode_app(nat,app_encode_fun(nat,$o),ord_less(nat),
1.26/1.49	                                    J),
1.26/1.49	                     K) =>
1.26/1.49	      app_encode_app(nat,$o,
1.26/1.49	                     app_encode_app(nat,app_encode_fun(nat,$o),ord_less(nat),
1.26/1.49	                                    app_encode_app(nat,nat,
1.26/1.49	                                                   app_encode_app(nat,
1.26/1.49	                                                                  app_encode_fun(
1.26/1.49	                                                                  nat,nat),
1.26/1.49	                                                                  minus_minus(
1.26/1.49	                                                                  nat),J),
1.26/1.49	                                                   N2)),
1.26/1.49	                     K)))).
1.26/1.49	tff('43', plain,
1.26/1.49	    ![X84 : nat, X85 : nat, X86 : nat]:
1.26/1.49	      (app_encode_app(nat, $o, 
1.26/1.49	         app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), 
1.26/1.49	           app_encode_app(nat, nat, 
1.26/1.49	             app_encode_app(nat, app_encode_fun(nat, nat), minus_minus(nat), 
1.26/1.49	               X84), X85)), X86)
1.26/1.49	       | ~ app_encode_app(nat, $o, 
1.26/1.49	             app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), X84), 
1.26/1.49	             X86)),
1.26/1.49	    inference('cnf', [status(esa)], [zf_stmt_65])).
1.26/1.49	tff('44', plain,
1.26/1.49	    ![X0 : nat, X1 : nat]:
1.26/1.49	      (app_encode_app(nat, $o, 
1.26/1.49	         app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), 
1.26/1.49	           zero_zero(nat)), X0)
1.26/1.49	       | ~ app_encode_app(nat, $o, 
1.26/1.49	             app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), X1), 
1.26/1.49	             X0)),
1.26/1.49	    inference('sup+', [status(thm)], ['42', '43'])).
1.26/1.49	tff('45', plain,
1.26/1.49	    ![X0 : int]:
1.26/1.49	      (~ $true
1.26/1.49	       | ~ app_encode_app(int, $o, 
1.26/1.49	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
1.26/1.49	               one_one(int)), X0)
1.26/1.49	       | app_encode_app(nat, $o, 
1.26/1.49	           app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), 
1.26/1.49	             zero_zero(nat)), app_encode_app(int, nat, nat1, X0))),
1.26/1.49	    inference('sup-', [status(thm)], ['41', '44'])).
1.26/1.49	tff('46', plain,
1.26/1.49	    ![X0 : int]:
1.26/1.49	      (app_encode_app(nat, $o, 
1.26/1.49	         app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), 
1.26/1.49	           zero_zero(nat)), app_encode_app(int, nat, nat1, X0))
1.26/1.49	       | ~ app_encode_app(int, $o, 
1.26/1.49	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
1.26/1.49	               one_one(int)), X0)),
1.26/1.49	    inference('simplify', [status(thm)], ['45'])).
1.26/1.49	tff('47', plain,
1.26/1.49	    (~ $true
1.26/1.49	     | app_encode_app(nat, $o, 
1.26/1.49	         app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), 
1.26/1.49	           zero_zero(nat)), app_encode_app(int, nat, nat1, t))),
1.26/1.49	    inference('sup-', [status(thm)], ['0', '46'])).
1.26/1.49	tff('48', plain,
1.26/1.49	    app_encode_app(nat, $o, 
1.26/1.49	      app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), 
1.26/1.49	        zero_zero(nat)), app_encode_app(int, nat, nat1, t)),
1.26/1.49	    inference('simplify', [status(thm)], ['47'])).
1.26/1.49	tff('49', plain,
1.26/1.49	    (app_encode_app(nat, $o, 
1.26/1.49	       app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), 
1.26/1.49	         zero_zero(nat)), zero_zero(nat))
1.26/1.49	     | t = one_one(int)),
1.26/1.49	    inference('sup+', [status(thm)], ['37', '48'])).
1.26/1.49	tff(zf_stmt_48, axiom,
1.26/1.49	  (![N2:nat]:
1.26/1.49	     (~
1.26/1.49	       app_encode_app(nat,$o,
1.26/1.49	                      app_encode_app(nat,app_encode_fun(nat,$o),
1.26/1.49	                                     ord_less(nat),N2),
1.26/1.49	                      N2)))).
1.26/1.49	tff('50', plain,
1.26/1.49	    ![X47 : nat]:
1.26/1.49	      ~ app_encode_app(nat, $o, 
1.26/1.49	          app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), X47), 
1.26/1.49	          X47),
1.26/1.49	    inference('cnf', [status(esa)], [zf_stmt_48])).
1.26/1.49	tff('51', plain, t = one_one(int),
1.26/1.49	    inference('clc', [status(thm)], ['49', '50'])).
1.26/1.49	tff('52', plain,
1.26/1.49	    app_encode_app(int, $o, 
1.26/1.49	      app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
1.26/1.49	        one_one(int)), one_one(int)),
1.26/1.49	    inference('demod', [status(thm)], ['0', '51'])).
1.26/1.49	tff('53', plain,
1.26/1.49	    ![X147 : int, X148 : int]:
1.26/1.49	      (X147 != X148
1.26/1.49	       | ~ app_encode_app(int, $o, 
1.26/1.49	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
1.26/1.49	               X147), X148)),
1.26/1.49	    inference('cnf', [status(esa)], [zf_stmt_99])).
1.26/1.49	tff('54', plain,
1.26/1.49	    ![X148 : int]:
1.26/1.49	      ~ app_encode_app(int, $o, 
1.26/1.49	          app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X148), 
1.26/1.49	          X148),
1.26/1.49	    inference('simplify', [status(thm)], ['53'])).
1.26/1.49	tff('55', plain, ~ $true, inference('sup-', [status(thm)], ['52', '54'])).
1.26/1.49	tff('56', plain, $false, inference('simplify', [status(thm)], ['55'])).
1.26/1.49	
1.26/1.49	% SZS output end Refutation
1.26/1.49	EOF
