0.00/0.00	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : app
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : 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 $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n066.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 08:10:53 CST 2018
1.22/1.42	% done 1273 iterations in 1.220s
1.22/1.42	% SZS status Theorem for 'stdin'
1.22/1.42	% SZS output start Refutation
1.22/1.42	tff(zf_stmt_28, axiom,
1.22/1.42	  (app_encode_app(int,$o,
1.22/1.42	                  app_encode_app(int,app_encode_fun(int,$o),ord_less(int),
1.22/1.42	                                 one_one(int)),
1.22/1.42	                  t))).
1.22/1.42	tff('0', plain,
1.22/1.42	    app_encode_app(int, $o, 
1.22/1.42	      app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
1.22/1.42	        one_one(int)), t),
1.22/1.42	    inference('cnf', [status(esa)], [zf_stmt_28])).
1.22/1.42	tff(zf_stmt_114, axiom,
1.22/1.42	  (![Z2:int,Z1:int]:
1.22/1.42	     (app_encode_app(int,$o,
1.22/1.42	                     app_encode_app(int,app_encode_fun(int,$o),
1.22/1.42	                                    ord_less_eq(int),zero_zero(int)),
1.22/1.42	                     Z1) =>
1.22/1.42	      (app_encode_app(int,$o,
1.22/1.42	                      app_encode_app(int,app_encode_fun(int,$o),
1.22/1.42	                                     ord_less_eq(int),Z1),
1.22/1.42	                      Z2) =>
1.22/1.42	       (app_encode_app(int,nat,nat1,
1.22/1.42	                       app_encode_app(int,int,
1.22/1.42	                                      app_encode_app(int,
1.22/1.42	                                                     app_encode_fun(int,int),
1.22/1.42	                                                     minus_minus(int),Z2),
1.22/1.42	                                      Z1)) =
1.22/1.42	        app_encode_app(nat,nat,
1.22/1.42	                       app_encode_app(nat,app_encode_fun(nat,nat),
1.22/1.42	                                      minus_minus(nat),
1.22/1.42	                                      app_encode_app(int,nat,nat1,Z2)),
1.22/1.42	                       app_encode_app(int,nat,nat1,Z1))))))).
1.22/1.42	tff('1', plain,
1.22/1.42	    ![X180 : int, X181 : int]:
1.22/1.42	      (~ app_encode_app(int, $o, 
1.22/1.42	           app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
1.22/1.42	             X180), X181)
1.22/1.42	       | app_encode_app(int, nat, nat1, 
1.22/1.42	           app_encode_app(int, int, 
1.22/1.42	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
1.22/1.42	               X181), X180))
1.22/1.42	          = app_encode_app(nat, nat, 
1.22/1.42	              app_encode_app(nat, app_encode_fun(nat, nat), 
1.22/1.42	                minus_minus(nat), app_encode_app(int, nat, nat1, X181)), 
1.22/1.42	              app_encode_app(int, nat, nat1, X180))
1.22/1.42	       | ~ app_encode_app(int, $o, 
1.22/1.42	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
1.22/1.42	               zero_zero(int)), X180)),
1.22/1.42	    inference('cnf', [status(esa)], [zf_stmt_114])).
1.22/1.42	tff(zf_stmt_32, axiom,
1.22/1.42	  (![N1:nat]:
1.22/1.42	     ((N1 != zero_zero(nat)) <=>
1.22/1.42	      app_encode_app(nat,$o,
1.22/1.42	                     app_encode_app(nat,app_encode_fun(nat,$o),ord_less(nat),
1.22/1.42	                                    zero_zero(nat)),
1.22/1.42	                     N1)))).
1.22/1.42	tff('2', plain,
1.22/1.42	    ![X5 : nat]:
1.22/1.42	      (app_encode_app(nat, $o, 
1.22/1.42	         app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), 
1.22/1.42	           zero_zero(nat)), X5)
1.22/1.42	       | X5 = zero_zero(nat)),
1.22/1.42	    inference('cnf', [status(esa)], [zf_stmt_32])).
1.22/1.42	tff(zf_stmt_143, axiom,
1.22/1.42	  (![Tn:nat]:
1.22/1.42	     ((Tn =
1.22/1.42	       app_encode_app(nat,nat,
1.22/1.42	                      app_encode_app(nat,app_encode_fun(nat,nat),
1.22/1.42	                                     minus_minus(nat),
1.22/1.42	                                     app_encode_app(int,nat,nat1,t)),
1.22/1.42	                      one_one(nat))) =>
1.22/1.42	      (app_encode_app(nat,$o,
1.22/1.42	                      app_encode_app(nat,app_encode_fun(nat,$o),
1.22/1.42	                                     ord_less(nat),zero_zero(nat)),
1.22/1.42	                      Tn) =>
1.22/1.42	       thesis)))).
1.22/1.42	tff('3', plain,
1.22/1.42	    ![X209 : nat]:
1.22/1.42	      (thesis
1.22/1.42	       | X209
1.22/1.42	          != app_encode_app(nat, nat, 
1.22/1.42	               app_encode_app(nat, app_encode_fun(nat, nat), 
1.22/1.42	                 minus_minus(nat), app_encode_app(int, nat, nat1, t)), 
1.22/1.42	               one_one(nat))
1.22/1.42	       | ~ app_encode_app(nat, $o, 
1.22/1.42	             app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), 
1.22/1.42	               zero_zero(nat)), X209)),
1.22/1.42	    inference('cnf', [status(esa)], [zf_stmt_143])).
1.22/1.42	tff('4', plain,
1.22/1.42	    (~ app_encode_app(nat, $o, 
1.22/1.42	         app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), 
1.22/1.42	           zero_zero(nat)), 
1.22/1.42	         app_encode_app(nat, nat, 
1.22/1.42	           app_encode_app(nat, app_encode_fun(nat, nat), minus_minus(nat), 
1.22/1.42	             app_encode_app(int, nat, nat1, t)), one_one(nat)))
1.22/1.42	     | thesis),
1.22/1.42	    inference('simplify', [status(thm)], ['3'])).
1.22/1.42	tff(zf_stmt_68, axiom,
1.22/1.42	  (one_one(nat) = app_encode_app(int,nat,nat1,one_one(int)))).
1.22/1.42	tff('5', plain, one_one(nat) = app_encode_app(int, nat, nat1, one_one(int)),
1.22/1.42	    inference('cnf', [status(esa)], [zf_stmt_68])).
1.22/1.42	tff('6', plain,
1.22/1.42	    (~ app_encode_app(nat, $o, 
1.22/1.42	         app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), 
1.22/1.42	           zero_zero(nat)), 
1.22/1.42	         app_encode_app(nat, nat, 
1.22/1.42	           app_encode_app(nat, app_encode_fun(nat, nat), minus_minus(nat), 
1.22/1.42	             app_encode_app(int, nat, nat1, t)), 
1.22/1.42	           app_encode_app(int, nat, nat1, one_one(int))))
1.22/1.42	     | thesis),
1.22/1.42	    inference('demod', [status(thm)], ['4', '5'])).
1.22/1.42	tff(zf_stmt_144, conjecture, (thesis)).
1.22/1.42	tff(zf_stmt_0, negated_conjecture, (~thesis)).
1.22/1.42	tff('7', plain, ~ thesis, inference('cnf', [status(esa)], [zf_stmt_0])).
1.22/1.42	tff('8', plain,
1.22/1.42	    ~ app_encode_app(nat, $o, 
1.22/1.42	        app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), 
1.22/1.42	          zero_zero(nat)), 
1.22/1.42	        app_encode_app(nat, nat, 
1.22/1.42	          app_encode_app(nat, app_encode_fun(nat, nat), minus_minus(nat), 
1.22/1.42	            app_encode_app(int, nat, nat1, t)), 
1.22/1.42	          app_encode_app(int, nat, nat1, one_one(int)))),
1.22/1.42	    inference('clc', [status(thm)], ['6', '7'])).
1.22/1.42	tff('9', plain,
1.22/1.42	    (~ $true
1.22/1.42	     | app_encode_app(nat, nat, 
1.22/1.42	         app_encode_app(nat, app_encode_fun(nat, nat), minus_minus(nat), 
1.22/1.42	           app_encode_app(int, nat, nat1, t)), 
1.22/1.42	         app_encode_app(int, nat, nat1, one_one(int)))
1.22/1.42	        = zero_zero(nat)),
1.22/1.42	    inference('sup-', [status(thm)], ['2', '8'])).
1.22/1.42	tff('10', plain,
1.22/1.42	    app_encode_app(nat, nat, 
1.22/1.42	      app_encode_app(nat, app_encode_fun(nat, nat), minus_minus(nat), 
1.22/1.42	        app_encode_app(int, nat, nat1, t)), 
1.22/1.42	      app_encode_app(int, nat, nat1, one_one(int)))
1.22/1.42	     = zero_zero(nat),
1.22/1.42	    inference('simplify', [status(thm)], ['9'])).
1.22/1.42	tff('11', plain,
1.22/1.42	    (app_encode_app(int, nat, nat1, 
1.22/1.42	       app_encode_app(int, int, 
1.22/1.42	         app_encode_app(int, app_encode_fun(int, int), minus_minus(int), t), 
1.22/1.42	         one_one(int)))
1.22/1.42	      = zero_zero(nat)
1.22/1.42	     | ~ app_encode_app(int, $o, 
1.22/1.42	           app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
1.22/1.42	             zero_zero(int)), one_one(int))
1.22/1.42	     | ~ app_encode_app(int, $o, 
1.22/1.42	           app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
1.22/1.42	             one_one(int)), t)),
1.22/1.42	    inference('sup+', [status(thm)], ['1', '10'])).
1.22/1.42	tff(zf_stmt_99, axiom,
1.22/1.42	  (app_encode_app(int,$o,
1.22/1.42	                  app_encode_app(int,app_encode_fun(int,$o),ord_less_eq(int),
1.22/1.42	                                 zero_zero(int)),
1.22/1.42	                  one_one(int)))).
1.22/1.42	tff('12', plain,
1.22/1.42	    app_encode_app(int, $o, 
1.22/1.42	      app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
1.22/1.42	        zero_zero(int)), one_one(int)),
1.22/1.42	    inference('cnf', [status(esa)], [zf_stmt_99])).
1.22/1.42	tff(zf_stmt_70, axiom,
1.22/1.42	  (app_encode_app(int,$o,
1.22/1.42	                  app_encode_app(int,app_encode_fun(int,$o),ord_less_eq(int),
1.22/1.42	                                 one_one(int)),
1.22/1.42	                  t))).
1.22/1.42	tff('13', plain,
1.22/1.42	    app_encode_app(int, $o, 
1.22/1.42	      app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
1.22/1.42	        one_one(int)), t),
1.22/1.42	    inference('cnf', [status(esa)], [zf_stmt_70])).
1.22/1.42	tff('14', plain,
1.22/1.42	    (app_encode_app(int, nat, nat1, 
1.22/1.42	       app_encode_app(int, int, 
1.22/1.42	         app_encode_app(int, app_encode_fun(int, int), minus_minus(int), t), 
1.22/1.42	         one_one(int)))
1.22/1.42	      = zero_zero(nat)
1.22/1.42	     | ~ $true
1.22/1.42	     | ~ $true),
1.22/1.42	    inference('demod', [status(thm)], ['11', '12', '13'])).
1.22/1.42	tff('15', plain,
1.22/1.42	    app_encode_app(int, nat, nat1, 
1.22/1.42	      app_encode_app(int, int, 
1.22/1.42	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), t), 
1.22/1.42	        one_one(int)))
1.22/1.42	     = zero_zero(nat),
1.22/1.42	    inference('simplify', [status(thm)], ['14'])).
1.22/1.42	tff(zf_stmt_80, axiom,
1.22/1.42	  (![I:int]:
1.22/1.42	     ((app_encode_app(int,nat,nat1,I) = zero_zero(nat)) <=>
1.22/1.42	      app_encode_app(int,$o,
1.22/1.42	                     app_encode_app(int,app_encode_fun(int,$o),
1.22/1.42	                                    ord_less_eq(int),I),
1.22/1.42	                     zero_zero(int))))).
1.22/1.42	tff('16', plain,
1.22/1.42	    ![X111 : int]:
1.22/1.43	      (app_encode_app(int, $o, 
1.22/1.43	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), X111), 
1.22/1.43	         zero_zero(int))
1.22/1.43	       | app_encode_app(int, nat, nat1, X111) != zero_zero(nat)),
1.22/1.43	    inference('cnf', [status(esa)], [zf_stmt_80])).
1.22/1.43	tff('17', plain,
1.22/1.43	    (zero_zero(nat) != zero_zero(nat)
1.22/1.43	     | app_encode_app(int, $o, 
1.22/1.43	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
1.22/1.43	           app_encode_app(int, int, 
1.22/1.43	             app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
1.22/1.43	               t), one_one(int))), zero_zero(int))),
1.22/1.43	    inference('sup-', [status(thm)], ['15', '16'])).
1.22/1.43	tff('18', plain,
1.22/1.43	    app_encode_app(int, $o, 
1.22/1.43	      app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
1.22/1.43	        app_encode_app(int, int, 
1.22/1.43	          app_encode_app(int, app_encode_fun(int, int), minus_minus(int), t), 
1.22/1.43	          one_one(int))), zero_zero(int)),
1.22/1.43	    inference('simplify', [status(thm)], ['17'])).
1.22/1.43	tff(zf_stmt_123, axiom,
1.22/1.43	  (![A:$tType]:
1.22/1.43	     (ordered_ab_group_add(A) =>
1.22/1.43	      (![B:A,A1:A]:
1.22/1.43	         (app_encode_app(A,$o,
1.22/1.43	                         app_encode_app(A,app_encode_fun(A,$o),
1.22/1.43	                                        ord_less_eq(A),A1),
1.22/1.43	                         B) <=>
1.22/1.43	          app_encode_app(A,$o,
1.22/1.43	                         app_encode_app(A,app_encode_fun(A,$o),
1.22/1.43	                                        ord_less_eq(A),
1.22/1.43	                                        app_encode_app(A,A,
1.22/1.43	                                                       app_encode_app(
1.22/1.43	                                                       A,app_encode_fun(A,A),
1.22/1.43	                                                       minus_minus(A),A1),B)),
1.22/1.43	                         zero_zero(A))))))).
1.22/1.43	tff('19', plain,
1.22/1.43	    ![X201 : $tType, X202 : X201, X203 : X201]:
1.22/1.43	      (~ app_encode_app(X201, $o, 
1.22/1.43	           app_encode_app(X201, app_encode_fun(X201, $o), ord_less_eq(X201), 
1.22/1.43	             app_encode_app(X201, X201, 
1.22/1.43	               app_encode_app(X201, app_encode_fun(X201, X201), 
1.22/1.43	                 minus_minus(X201), X202), X203)), zero_zero(X201))
1.22/1.43	       | app_encode_app(X201, $o, 
1.22/1.43	           app_encode_app(X201, app_encode_fun(X201, $o), ord_less_eq(X201), 
1.22/1.43	             X202), X203)
1.22/1.43	       | ~ ordered_ab_group_add(X201)),
1.22/1.43	    inference('cnf', [status(esa)], [zf_stmt_123])).
1.22/1.43	tff('20', plain,
1.22/1.43	    (~ $true
1.22/1.43	     | ~ ordered_ab_group_add(int)
1.22/1.43	     | app_encode_app(int, $o, 
1.22/1.43	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), t), 
1.22/1.43	         one_one(int))),
1.22/1.43	    inference('sup-', [status(thm)], ['18', '19'])).
1.22/1.43	tff(zf_stmt_126, axiom, (ordered_ab_group_add(int))).
1.22/1.43	tff('21', plain, ordered_ab_group_add(int),
1.22/1.43	    inference('cnf', [status(esa)], [zf_stmt_126])).
1.22/1.43	tff('22', plain,
1.22/1.43	    (~ $true
1.22/1.43	     | ~ $true
1.22/1.43	     | app_encode_app(int, $o, 
1.22/1.43	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), t), 
1.22/1.43	         one_one(int))),
1.22/1.43	    inference('demod', [status(thm)], ['20', '21'])).
1.22/1.43	tff('23', plain,
1.22/1.43	    app_encode_app(int, $o, 
1.22/1.43	      app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), t), 
1.22/1.43	      one_one(int)),
1.22/1.43	    inference('simplify', [status(thm)], ['22'])).
1.22/1.43	tff(zf_stmt_98, axiom,
1.22/1.43	  (![W:int,Z:int]:
1.22/1.43	     (app_encode_app(int,$o,
1.22/1.43	                     app_encode_app(int,app_encode_fun(int,$o),ord_less(int),
1.22/1.43	                                    Z),
1.22/1.43	                     W) <=>
1.22/1.43	      (app_encode_app(int,$o,
1.22/1.43	                      app_encode_app(int,app_encode_fun(int,$o),
1.22/1.43	                                     ord_less_eq(int),Z),
1.22/1.43	                      W) & 
1.22/1.43	       (Z != W))))).
1.22/1.43	tff('24', plain,
1.22/1.43	    ![X144 : int, X145 : int]:
1.22/1.43	      (app_encode_app(int, $o, 
1.22/1.43	         app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X145), 
1.22/1.43	         X144)
1.22/1.43	       | X145 = X144
1.22/1.43	       | ~ app_encode_app(int, $o, 
1.22/1.43	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
1.22/1.43	               X145), X144)),
1.22/1.43	    inference('cnf', [status(esa)], [zf_stmt_98])).
1.22/1.43	tff('25', plain,
1.22/1.43	    (~ $true
1.22/1.43	     | t = one_one(int)
1.22/1.43	     | app_encode_app(int, $o, 
1.22/1.43	         app_encode_app(int, app_encode_fun(int, $o), ord_less(int), t), 
1.22/1.43	         one_one(int))),
1.22/1.43	    inference('sup-', [status(thm)], ['23', '24'])).
1.22/1.43	tff('26', plain,
1.22/1.43	    (app_encode_app(int, $o, 
1.22/1.43	       app_encode_app(int, app_encode_fun(int, $o), ord_less(int), t), 
1.22/1.43	       one_one(int))
1.22/1.43	     | t = one_one(int)),
1.22/1.43	    inference('simplify', [status(thm)], ['25'])).
1.22/1.43	tff(zf_stmt_132, axiom, (group_add(int))).
1.22/1.43	tff('27', plain, group_add(int),
1.22/1.43	    inference('cnf', [status(esa)], [zf_stmt_132])).
1.22/1.43	tff(zf_stmt_35, axiom,
1.22/1.43	  (![A:$tType]:
1.22/1.43	     (group_add(A) =>
1.22/1.43	      (![A2:A]:
1.22/1.43	         (app_encode_app(A,A,
1.22/1.43	                         app_encode_app(A,app_encode_fun(A,A),minus_minus(A),
1.22/1.43	                                        A2),
1.22/1.43	                         A2) =
1.22/1.43	          zero_zero(A)))))).
1.22/1.43	tff('28', plain,
1.22/1.43	    ![X9 : $tType, X10 : X9]:
1.22/1.43	      (app_encode_app(X9, X9, 
1.22/1.43	         app_encode_app(X9, app_encode_fun(X9, X9), minus_minus(X9), X10), 
1.22/1.43	         X10)
1.22/1.43	        = zero_zero(X9)
1.22/1.43	       | ~ group_add(X9)),
1.22/1.43	    inference('cnf', [status(esa)], [zf_stmt_35])).
1.22/1.43	tff('29', plain,
1.22/1.43	    ![X0 : int]:
1.22/1.43	      (~ $true
1.22/1.43	       | app_encode_app(int, int, 
1.22/1.43	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
1.22/1.43	             X0), X0)
1.22/1.43	          = zero_zero(int)),
1.22/1.43	    inference('sup-', [status(thm)], ['27', '28'])).
1.22/1.43	tff('30', plain,
1.22/1.43	    ![X0 : int]:
1.22/1.43	      app_encode_app(int, int, 
1.22/1.43	        app_encode_app(int, app_encode_fun(int, int), minus_minus(int), X0), 
1.22/1.43	        X0)
1.22/1.43	       = zero_zero(int),
1.22/1.43	    inference('simplify', [status(thm)], ['29'])).
1.22/1.43	tff(zf_stmt_81, axiom,
1.22/1.43	  (![Z:int,W:int]:
1.22/1.43	     (app_encode_app(int,$o,
1.22/1.43	                     app_encode_app(int,app_encode_fun(int,$o),
1.22/1.43	                                    ord_less_eq(int),W),
1.22/1.43	                     app_encode_app(int,int,
1.22/1.43	                                    app_encode_app(int,
1.22/1.43	                                                   app_encode_fun(int,int),
1.22/1.43	                                                   minus_minus(int),Z),
1.22/1.43	                                    one_one(int))) <=>
1.22/1.43	      app_encode_app(int,$o,
1.22/1.43	                     app_encode_app(int,app_encode_fun(int,$o),ord_less(int),
1.22/1.43	                                    W),
1.22/1.43	                     Z)))).
1.22/1.43	tff('31', plain,
1.22/1.43	    ![X114 : int, X115 : int]:
1.22/1.43	      (app_encode_app(int, $o, 
1.22/1.43	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), X115), 
1.22/1.43	         app_encode_app(int, int, 
1.22/1.43	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
1.22/1.43	             X114), one_one(int)))
1.22/1.43	       | ~ app_encode_app(int, $o, 
1.22/1.43	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
1.22/1.43	               X115), X114)),
1.22/1.43	    inference('cnf', [status(esa)], [zf_stmt_81])).
1.22/1.43	tff('32', plain,
1.22/1.43	    ![X0 : int]:
1.22/1.43	      (app_encode_app(int, $o, 
1.22/1.43	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), X0), 
1.22/1.43	         zero_zero(int))
1.22/1.43	       | ~ app_encode_app(int, $o, 
1.22/1.43	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X0), 
1.22/1.43	             one_one(int))),
1.22/1.43	    inference('sup+', [status(thm)], ['30', '31'])).
1.22/1.43	tff('33', plain,
1.22/1.43	    (~ $true
1.22/1.43	     | t = one_one(int)
1.22/1.43	     | app_encode_app(int, $o, 
1.22/1.43	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), t), 
1.22/1.43	         zero_zero(int))),
1.22/1.43	    inference('sup-', [status(thm)], ['26', '32'])).
1.22/1.43	tff('34', plain,
1.22/1.43	    (app_encode_app(int, $o, 
1.22/1.43	       app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), t), 
1.22/1.43	       zero_zero(int))
1.22/1.43	     | t = one_one(int)),
1.22/1.43	    inference('simplify', [status(thm)], ['33'])).
1.22/1.43	tff('35', plain,
1.22/1.43	    ![X112 : int]:
1.22/1.43	      (app_encode_app(int, nat, nat1, X112) = zero_zero(nat)
1.22/1.43	       | ~ app_encode_app(int, $o, 
1.22/1.43	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
1.22/1.43	               X112), zero_zero(int))),
1.22/1.43	    inference('cnf', [status(esa)], [zf_stmt_80])).
1.22/1.43	tff('36', plain,
1.22/1.43	    (~ $true
1.22/1.43	     | t = one_one(int)
1.22/1.43	     | app_encode_app(int, nat, nat1, t) = zero_zero(nat)),
1.22/1.43	    inference('sup-', [status(thm)], ['34', '35'])).
1.22/1.43	tff('37', plain,
1.22/1.43	    (app_encode_app(int, nat, nat1, t) = zero_zero(nat) | t = one_one(int)),
1.22/1.43	    inference('simplify', [status(thm)], ['36'])).
1.22/1.43	tff(zf_stmt_110, axiom,
1.22/1.43	  (one_one(int) = app_encode_app(nat,int,semiring_1_of_nat(int),one_one(nat)))).
1.22/1.43	tff('38', plain,
1.22/1.43	    one_one(int)
1.22/1.43	     = app_encode_app(nat, int, semiring_1_of_nat(int), one_one(nat)),
1.22/1.43	    inference('cnf', [status(esa)], [zf_stmt_110])).
1.22/1.43	tff('39', plain,
1.22/1.43	    one_one(int)
1.22/1.43	     = app_encode_app(nat, int, semiring_1_of_nat(int), 
1.22/1.43	         app_encode_app(int, nat, nat1, one_one(int))),
1.22/1.43	    inference('demod', [status(thm)], ['38', '5'])).
1.22/1.43	tff(zf_stmt_122, axiom,
1.22/1.43	  (![Z:int,Ma:nat]:
1.22/1.43	     (app_encode_app(nat,$o,
1.22/1.43	                     app_encode_app(nat,app_encode_fun(nat,$o),ord_less(nat),
1.22/1.43	                                    Ma),
1.22/1.43	                     app_encode_app(int,nat,nat1,Z)) <=>
1.22/1.43	      app_encode_app(int,$o,
1.22/1.43	                     app_encode_app(int,app_encode_fun(int,$o),ord_less(int),
1.22/1.43	                                    app_encode_app(nat,int,
1.22/1.43	                                                   semiring_1_of_nat(int),Ma)),
1.22/1.43	                     Z)))).
1.22/1.43	tff('40', plain,
1.22/1.43	    ![X199 : int, X200 : nat]:
1.22/1.43	      (app_encode_app(nat, $o, 
1.22/1.43	         app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), X200), 
1.22/1.43	         app_encode_app(int, nat, nat1, X199))
1.22/1.43	       | ~ app_encode_app(int, $o, 
1.22/1.43	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
1.22/1.43	               app_encode_app(nat, int, semiring_1_of_nat(int), X200)), X199)),
1.22/1.43	    inference('cnf', [status(esa)], [zf_stmt_122])).
1.22/1.43	tff('41', plain,
1.22/1.43	    ![X0 : int]:
1.22/1.43	      (~ app_encode_app(int, $o, 
1.22/1.43	           app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
1.22/1.43	             one_one(int)), X0)
1.22/1.43	       | app_encode_app(nat, $o, 
1.22/1.43	           app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), 
1.22/1.43	             app_encode_app(int, nat, nat1, one_one(int))), 
1.22/1.43	           app_encode_app(int, nat, nat1, X0))),
1.22/1.43	    inference('sup-', [status(thm)], ['39', '40'])).
1.22/1.43	tff(zf_stmt_31, axiom,
1.22/1.43	  (![M:nat]:
1.22/1.43	     (app_encode_app(nat,nat,
1.22/1.43	                     app_encode_app(nat,app_encode_fun(nat,nat),
1.22/1.43	                                    minus_minus(nat),M),
1.22/1.43	                     M) =
1.22/1.43	      zero_zero(nat)))).
1.22/1.43	tff('42', plain,
1.22/1.43	    ![X4 : nat]:
1.22/1.43	      app_encode_app(nat, nat, 
1.22/1.43	        app_encode_app(nat, app_encode_fun(nat, nat), minus_minus(nat), X4), 
1.22/1.43	        X4)
1.22/1.43	       = zero_zero(nat),
1.22/1.43	    inference('cnf', [status(esa)], [zf_stmt_31])).
1.22/1.43	tff(zf_stmt_64, axiom,
1.22/1.43	  (![N2:nat,K:nat,J:nat]:
1.22/1.43	     (app_encode_app(nat,$o,
1.22/1.43	                     app_encode_app(nat,app_encode_fun(nat,$o),ord_less(nat),
1.22/1.43	                                    J),
1.22/1.43	                     K) =>
1.22/1.43	      app_encode_app(nat,$o,
1.22/1.43	                     app_encode_app(nat,app_encode_fun(nat,$o),ord_less(nat),
1.22/1.43	                                    app_encode_app(nat,nat,
1.22/1.43	                                                   app_encode_app(nat,
1.22/1.43	                                                                  app_encode_fun(
1.22/1.43	                                                                  nat,nat),
1.22/1.43	                                                                  minus_minus(
1.22/1.43	                                                                  nat),J),
1.22/1.43	                                                   N2)),
1.22/1.43	                     K)))).
1.22/1.43	tff('43', plain,
1.22/1.43	    ![X80 : nat, X81 : nat, X82 : nat]:
1.22/1.43	      (app_encode_app(nat, $o, 
1.22/1.43	         app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), 
1.22/1.43	           app_encode_app(nat, nat, 
1.22/1.43	             app_encode_app(nat, app_encode_fun(nat, nat), minus_minus(nat), 
1.22/1.43	               X80), X81)), X82)
1.22/1.43	       | ~ app_encode_app(nat, $o, 
1.22/1.43	             app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), X80), 
1.22/1.43	             X82)),
1.22/1.43	    inference('cnf', [status(esa)], [zf_stmt_64])).
1.22/1.43	tff('44', plain,
1.22/1.43	    ![X0 : nat, X1 : nat]:
1.22/1.43	      (app_encode_app(nat, $o, 
1.22/1.43	         app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), 
1.22/1.43	           zero_zero(nat)), X0)
1.22/1.43	       | ~ app_encode_app(nat, $o, 
1.22/1.43	             app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), X1), 
1.22/1.43	             X0)),
1.22/1.43	    inference('sup+', [status(thm)], ['42', '43'])).
1.22/1.43	tff('45', plain,
1.22/1.43	    ![X0 : int]:
1.22/1.43	      (~ $true
1.22/1.43	       | ~ app_encode_app(int, $o, 
1.22/1.43	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
1.22/1.43	               one_one(int)), X0)
1.22/1.43	       | app_encode_app(nat, $o, 
1.22/1.43	           app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), 
1.22/1.43	             zero_zero(nat)), app_encode_app(int, nat, nat1, X0))),
1.22/1.43	    inference('sup-', [status(thm)], ['41', '44'])).
1.22/1.43	tff('46', plain,
1.22/1.43	    ![X0 : int]:
1.22/1.43	      (app_encode_app(nat, $o, 
1.22/1.43	         app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), 
1.22/1.43	           zero_zero(nat)), app_encode_app(int, nat, nat1, X0))
1.22/1.43	       | ~ app_encode_app(int, $o, 
1.22/1.43	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
1.22/1.43	               one_one(int)), X0)),
1.22/1.43	    inference('simplify', [status(thm)], ['45'])).
1.22/1.43	tff('47', plain,
1.22/1.43	    (~ $true
1.22/1.43	     | app_encode_app(nat, $o, 
1.22/1.43	         app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), 
1.22/1.43	           zero_zero(nat)), app_encode_app(int, nat, nat1, t))),
1.22/1.43	    inference('sup-', [status(thm)], ['0', '46'])).
1.22/1.43	tff('48', plain,
1.22/1.43	    app_encode_app(nat, $o, 
1.22/1.43	      app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), 
1.22/1.43	        zero_zero(nat)), app_encode_app(int, nat, nat1, t)),
1.22/1.43	    inference('simplify', [status(thm)], ['47'])).
1.22/1.43	tff('49', plain,
1.22/1.43	    (app_encode_app(nat, $o, 
1.22/1.43	       app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), 
1.22/1.43	         zero_zero(nat)), zero_zero(nat))
1.22/1.43	     | t = one_one(int)),
1.22/1.43	    inference('sup+', [status(thm)], ['37', '48'])).
1.22/1.43	tff(zf_stmt_47, axiom,
1.22/1.43	  (![N2:nat]:
1.22/1.43	     (~
1.22/1.43	       app_encode_app(nat,$o,
1.22/1.43	                      app_encode_app(nat,app_encode_fun(nat,$o),
1.22/1.43	                                     ord_less(nat),N2),
1.22/1.43	                      N2)))).
1.22/1.43	tff('50', plain,
1.22/1.43	    ![X43 : nat]:
1.22/1.43	      ~ app_encode_app(nat, $o, 
1.22/1.43	          app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), X43), 
1.22/1.43	          X43),
1.22/1.43	    inference('cnf', [status(esa)], [zf_stmt_47])).
1.22/1.43	tff('51', plain, t = one_one(int),
1.22/1.43	    inference('clc', [status(thm)], ['49', '50'])).
1.22/1.43	tff('52', plain,
1.22/1.43	    app_encode_app(int, $o, 
1.22/1.43	      app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
1.22/1.43	        one_one(int)), one_one(int)),
1.22/1.43	    inference('demod', [status(thm)], ['0', '51'])).
1.22/1.43	tff('53', plain,
1.22/1.43	    ![X143 : int, X144 : int]:
1.22/1.43	      (X143 != X144
1.22/1.43	       | ~ app_encode_app(int, $o, 
1.22/1.43	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
1.22/1.43	               X143), X144)),
1.22/1.43	    inference('cnf', [status(esa)], [zf_stmt_98])).
1.22/1.43	tff('54', plain,
1.22/1.43	    ![X144 : int]:
1.22/1.43	      ~ app_encode_app(int, $o, 
1.22/1.43	          app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X144), 
1.22/1.43	          X144),
1.22/1.43	    inference('simplify', [status(thm)], ['53'])).
1.22/1.43	tff('55', plain, ~ $true, inference('sup-', [status(thm)], ['52', '54'])).
1.22/1.43	tff('56', plain, $false, inference('simplify', [status(thm)], ['55'])).
1.22/1.43	
1.22/1.43	% SZS output end Refutation
1.22/1.43	EOF
