0.00/0.00	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : app
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : kbo
0.00/0.00	% Command    : 
0.00/0.01	#!/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 $2 \
0.00/0.01	  --simultaneous-sup false \
0.00/0.01	  --no-max-vars \
0.00/0.01	  --no-fool
0.00/0.20	% Computer   : n050.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 08:10:38 CST 2018
1.04/1.27	% done 1471 iterations in 1.066s
1.04/1.27	% SZS status Theorem for 'stdin'
1.04/1.27	% SZS output start Refutation
1.04/1.27	tff(zf_stmt_28, axiom,
1.04/1.27	  (app_encode_app(int,$o,
1.04/1.27	                  app_encode_app(int,app_encode_fun(int,$o),ord_less(int),
1.04/1.27	                                 one_one(int)),
1.04/1.27	                  t))).
1.04/1.27	tff('0', plain,
1.04/1.27	    app_encode_app(int, $o, 
1.04/1.27	      app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
1.04/1.27	        one_one(int)), t),
1.04/1.27	    inference('cnf', [status(esa)], [zf_stmt_28])).
1.04/1.27	tff(zf_stmt_84, axiom,
1.04/1.27	  (zero_zero(int) =
1.04/1.27	   app_encode_app(nat,int,semiring_1_of_nat(int),zero_zero(nat)))).
1.04/1.27	tff('1', plain,
1.04/1.27	    zero_zero(int)
1.04/1.27	     = app_encode_app(nat, int, semiring_1_of_nat(int), zero_zero(nat)),
1.04/1.27	    inference('cnf', [status(esa)], [zf_stmt_84])).
1.04/1.27	tff(zf_stmt_32, axiom,
1.04/1.27	  (![N1:nat]:
1.04/1.27	     ((N1 != zero_zero(nat)) <=>
1.04/1.27	      app_encode_app(nat,$o,
1.04/1.27	                     app_encode_app(nat,app_encode_fun(nat,$o),ord_less(nat),
1.04/1.27	                                    zero_zero(nat)),
1.04/1.27	                     N1)))).
1.04/1.27	tff('2', plain,
1.04/1.27	    ![X5 : nat]:
1.04/1.27	      (app_encode_app(nat, $o, 
1.04/1.27	         app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), 
1.04/1.27	           zero_zero(nat)), X5)
1.04/1.27	       | X5 = zero_zero(nat)),
1.04/1.27	    inference('cnf', [status(esa)], [zf_stmt_32])).
1.04/1.27	tff(zf_stmt_29, axiom,
1.04/1.27	  (![Ma:nat,N1:nat]:
1.04/1.27	     (app_encode_app(nat,$o,
1.04/1.27	                     app_encode_app(nat,app_encode_fun(nat,$o),ord_less(nat),
1.04/1.27	                                    zero_zero(nat)),
1.04/1.27	                     app_encode_app(nat,nat,
1.04/1.27	                                    app_encode_app(nat,
1.04/1.27	                                                   app_encode_fun(nat,nat),
1.04/1.27	                                                   minus_minus(nat),N1),
1.04/1.27	                                    Ma)) <=>
1.04/1.27	      app_encode_app(nat,$o,
1.04/1.27	                     app_encode_app(nat,app_encode_fun(nat,$o),ord_less(nat),
1.04/1.27	                                    Ma),
1.04/1.27	                     N1)))).
1.04/1.27	tff('3', plain,
1.04/1.27	    ![X0 : nat, X1 : nat]:
1.04/1.27	      (app_encode_app(nat, $o, 
1.04/1.27	         app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), X0), X1)
1.04/1.27	       | ~ app_encode_app(nat, $o, 
1.04/1.27	             app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), 
1.04/1.27	               zero_zero(nat)), 
1.04/1.27	             app_encode_app(nat, nat, 
1.04/1.27	               app_encode_app(nat, app_encode_fun(nat, nat), 
1.04/1.27	                 minus_minus(nat), X1), X0))),
1.04/1.27	    inference('cnf', [status(esa)], [zf_stmt_29])).
1.04/1.27	tff('4', plain,
1.04/1.27	    ![X0 : nat, X1 : nat]:
1.04/1.27	      (~ $true
1.04/1.27	       | app_encode_app(nat, nat, 
1.04/1.27	           app_encode_app(nat, app_encode_fun(nat, nat), minus_minus(nat), 
1.04/1.27	             X1), X0)
1.04/1.27	          = zero_zero(nat)
1.04/1.27	       | app_encode_app(nat, $o, 
1.04/1.27	           app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), X0), 
1.04/1.27	           X1)),
1.04/1.27	    inference('sup-', [status(thm)], ['2', '3'])).
1.04/1.27	tff('5', plain,
1.04/1.27	    ![X0 : nat, X1 : nat]:
1.04/1.27	      (app_encode_app(nat, $o, 
1.04/1.27	         app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), X0), X1)
1.04/1.27	       | app_encode_app(nat, nat, 
1.04/1.27	           app_encode_app(nat, app_encode_fun(nat, nat), minus_minus(nat), 
1.04/1.27	             X1), X0)
1.04/1.27	          = zero_zero(nat)),
1.04/1.27	    inference('simplify', [status(thm)], ['4'])).
1.04/1.27	tff(zf_stmt_143, axiom,
1.04/1.27	  (![Tn:nat]:
1.04/1.27	     ((Tn =
1.04/1.27	       app_encode_app(nat,nat,
1.04/1.27	                      app_encode_app(nat,app_encode_fun(nat,nat),
1.04/1.27	                                     minus_minus(nat),
1.04/1.27	                                     app_encode_app(int,nat,nat1,t)),
1.04/1.27	                      one_one(nat))) =>
1.04/1.27	      (app_encode_app(nat,$o,
1.04/1.27	                      app_encode_app(nat,app_encode_fun(nat,$o),
1.04/1.27	                                     ord_less(nat),zero_zero(nat)),
1.04/1.27	                      Tn) =>
1.04/1.27	       thesis)))).
1.04/1.27	tff('6', plain,
1.04/1.27	    ![X209 : nat]:
1.04/1.27	      (thesis
1.04/1.27	       | X209
1.04/1.27	          != app_encode_app(nat, nat, 
1.04/1.27	               app_encode_app(nat, app_encode_fun(nat, nat), 
1.04/1.27	                 minus_minus(nat), app_encode_app(int, nat, nat1, t)), 
1.04/1.27	               one_one(nat))
1.04/1.27	       | ~ app_encode_app(nat, $o, 
1.04/1.27	             app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), 
1.04/1.27	               zero_zero(nat)), X209)),
1.04/1.27	    inference('cnf', [status(esa)], [zf_stmt_143])).
1.04/1.27	tff('7', plain,
1.04/1.27	    (~ app_encode_app(nat, $o, 
1.04/1.27	         app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), 
1.04/1.27	           zero_zero(nat)), 
1.04/1.27	         app_encode_app(nat, nat, 
1.04/1.27	           app_encode_app(nat, app_encode_fun(nat, nat), minus_minus(nat), 
1.04/1.27	             app_encode_app(int, nat, nat1, t)), one_one(nat)))
1.04/1.27	     | thesis),
1.04/1.27	    inference('simplify', [status(thm)], ['6'])).
1.04/1.27	tff(zf_stmt_144, conjecture, (thesis)).
1.04/1.27	tff(zf_stmt_0, negated_conjecture, (~thesis)).
1.04/1.27	tff('8', plain, ~ thesis, inference('cnf', [status(esa)], [zf_stmt_0])).
1.04/1.27	tff('9', plain,
1.04/1.27	    ~ app_encode_app(nat, $o, 
1.04/1.27	        app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), 
1.04/1.27	          zero_zero(nat)), 
1.04/1.27	        app_encode_app(nat, nat, 
1.04/1.27	          app_encode_app(nat, app_encode_fun(nat, nat), minus_minus(nat), 
1.04/1.27	            app_encode_app(int, nat, nat1, t)), one_one(nat))),
1.04/1.27	    inference('clc', [status(thm)], ['7', '8'])).
1.04/1.27	tff('10', plain,
1.04/1.27	    (~ $true
1.04/1.27	     | app_encode_app(nat, nat, 
1.04/1.27	         app_encode_app(nat, app_encode_fun(nat, nat), minus_minus(nat), 
1.04/1.27	           app_encode_app(int, nat, nat1, t)), one_one(nat))
1.04/1.27	        = zero_zero(nat)),
1.04/1.27	    inference('sup-', [status(thm)], ['2', '9'])).
1.04/1.27	tff('11', plain,
1.04/1.27	    app_encode_app(nat, nat, 
1.04/1.27	      app_encode_app(nat, app_encode_fun(nat, nat), minus_minus(nat), 
1.04/1.27	        app_encode_app(int, nat, nat1, t)), one_one(nat))
1.04/1.27	     = zero_zero(nat),
1.04/1.27	    inference('simplify', [status(thm)], ['10'])).
1.04/1.27	tff(zf_stmt_61, axiom,
1.04/1.27	  (![N2:nat,M:nat]:
1.04/1.27	     ((app_encode_app(nat,nat,
1.04/1.27	                      app_encode_app(nat,app_encode_fun(nat,nat),
1.04/1.27	                                     minus_minus(nat),M),
1.04/1.27	                      N2) =
1.04/1.27	       zero_zero(nat)) =>
1.04/1.27	      ((app_encode_app(nat,nat,
1.04/1.27	                       app_encode_app(nat,app_encode_fun(nat,nat),
1.04/1.27	                                      minus_minus(nat),N2),
1.04/1.27	                       M) =
1.04/1.27	        zero_zero(nat)) =>
1.04/1.27	       (M = N2))))).
1.04/1.27	tff('12', plain,
1.04/1.27	    ![X74 : nat, X75 : nat]:
1.04/1.27	      (app_encode_app(nat, nat, 
1.04/1.27	         app_encode_app(nat, app_encode_fun(nat, nat), minus_minus(nat), X74), 
1.04/1.27	         X75)
1.04/1.27	        != zero_zero(nat)
1.04/1.27	       | X75 = X74
1.04/1.27	       | app_encode_app(nat, nat, 
1.04/1.27	           app_encode_app(nat, app_encode_fun(nat, nat), minus_minus(nat), 
1.04/1.27	             X75), X74)
1.04/1.27	          != zero_zero(nat)),
1.04/1.27	    inference('cnf', [status(esa)], [zf_stmt_61])).
1.04/1.27	tff('13', plain,
1.04/1.27	    (zero_zero(nat) != zero_zero(nat)
1.04/1.27	     | app_encode_app(nat, nat, 
1.04/1.27	         app_encode_app(nat, app_encode_fun(nat, nat), minus_minus(nat), 
1.04/1.27	           one_one(nat)), app_encode_app(int, nat, nat1, t))
1.04/1.27	        != zero_zero(nat)
1.04/1.27	     | one_one(nat) = app_encode_app(int, nat, nat1, t)),
1.04/1.27	    inference('sup-', [status(thm)], ['11', '12'])).
1.04/1.27	tff('14', plain,
1.04/1.27	    (one_one(nat) = app_encode_app(int, nat, nat1, t)
1.04/1.27	     | app_encode_app(nat, nat, 
1.04/1.27	         app_encode_app(nat, app_encode_fun(nat, nat), minus_minus(nat), 
1.04/1.27	           one_one(nat)), app_encode_app(int, nat, nat1, t))
1.04/1.27	        != zero_zero(nat)),
1.04/1.27	    inference('simplify', [status(thm)], ['13'])).
1.04/1.27	tff('15', plain,
1.04/1.27	    (zero_zero(nat) != zero_zero(nat)
1.04/1.27	     | app_encode_app(nat, $o, 
1.04/1.27	         app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), 
1.04/1.27	           app_encode_app(int, nat, nat1, t)), one_one(nat))
1.04/1.27	     | one_one(nat) = app_encode_app(int, nat, nat1, t)),
1.04/1.27	    inference('sup-', [status(thm)], ['5', '14'])).
1.04/1.27	tff('16', plain,
1.04/1.27	    (one_one(nat) = app_encode_app(int, nat, nat1, t)
1.04/1.27	     | app_encode_app(nat, $o, 
1.04/1.27	         app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), 
1.04/1.27	           app_encode_app(int, nat, nat1, t)), one_one(nat))),
1.04/1.27	    inference('simplify', [status(thm)], ['15'])).
1.04/1.27	tff(zf_stmt_122, axiom,
1.04/1.27	  (![Z:int,Ma:nat]:
1.04/1.27	     (app_encode_app(nat,$o,
1.04/1.27	                     app_encode_app(nat,app_encode_fun(nat,$o),ord_less(nat),
1.04/1.27	                                    Ma),
1.04/1.27	                     app_encode_app(int,nat,nat1,Z)) <=>
1.04/1.27	      app_encode_app(int,$o,
1.04/1.27	                     app_encode_app(int,app_encode_fun(int,$o),ord_less(int),
1.04/1.27	                                    app_encode_app(nat,int,
1.04/1.27	                                                   semiring_1_of_nat(int),Ma)),
1.04/1.27	                     Z)))).
1.04/1.27	tff('17', plain,
1.04/1.27	    ![X198 : nat, X199 : int]:
1.04/1.27	      (app_encode_app(int, $o, 
1.04/1.27	         app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
1.04/1.27	           app_encode_app(nat, int, semiring_1_of_nat(int), X198)), X199)
1.04/1.27	       | ~ app_encode_app(nat, $o, 
1.04/1.27	             app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), 
1.04/1.27	               X198), app_encode_app(int, nat, nat1, X199))),
1.04/1.27	    inference('cnf', [status(esa)], [zf_stmt_122])).
1.04/1.27	tff(zf_stmt_35, axiom,
1.04/1.27	  (![A:$tType]:
1.04/1.27	     (group_add(A) =>
1.04/1.27	      (![A2:A]:
1.04/1.27	         (app_encode_app(A,A,
1.04/1.27	                         app_encode_app(A,app_encode_fun(A,A),minus_minus(A),
1.04/1.27	                                        A2),
1.04/1.27	                         A2) =
1.04/1.27	          zero_zero(A)))))).
1.04/1.27	tff('18', plain,
1.04/1.27	    ![X9 : $tType, X10 : X9]:
1.04/1.27	      (app_encode_app(X9, X9, 
1.04/1.27	         app_encode_app(X9, app_encode_fun(X9, X9), minus_minus(X9), X10), 
1.04/1.27	         X10)
1.04/1.27	        = zero_zero(X9)
1.04/1.27	       | ~ group_add(X9)),
1.04/1.27	    inference('cnf', [status(esa)], [zf_stmt_35])).
1.04/1.27	tff(zf_stmt_81, axiom,
1.04/1.27	  (![Z:int,W:int]:
1.04/1.27	     (app_encode_app(int,$o,
1.04/1.27	                     app_encode_app(int,app_encode_fun(int,$o),
1.04/1.27	                                    ord_less_eq(int),W),
1.04/1.27	                     app_encode_app(int,int,
1.04/1.27	                                    app_encode_app(int,
1.04/1.27	                                                   app_encode_fun(int,int),
1.04/1.27	                                                   minus_minus(int),Z),
1.04/1.27	                                    one_one(int))) <=>
1.04/1.27	      app_encode_app(int,$o,
1.04/1.27	                     app_encode_app(int,app_encode_fun(int,$o),ord_less(int),
1.04/1.27	                                    W),
1.04/1.27	                     Z)))).
1.04/1.27	tff('19', plain,
1.04/1.27	    ![X114 : int, X115 : int]:
1.04/1.27	      (app_encode_app(int, $o, 
1.04/1.27	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), X115), 
1.04/1.27	         app_encode_app(int, int, 
1.04/1.27	           app_encode_app(int, app_encode_fun(int, int), minus_minus(int), 
1.04/1.27	             X114), one_one(int)))
1.04/1.27	       | ~ app_encode_app(int, $o, 
1.04/1.27	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
1.04/1.27	               X115), X114)),
1.04/1.27	    inference('cnf', [status(esa)], [zf_stmt_81])).
1.04/1.27	tff('20', plain,
1.04/1.27	    ![X0 : int]:
1.04/1.27	      (app_encode_app(int, $o, 
1.04/1.27	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), X0), 
1.04/1.27	         zero_zero(int))
1.04/1.27	       | ~ group_add(int)
1.04/1.27	       | ~ app_encode_app(int, $o, 
1.04/1.27	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X0), 
1.04/1.27	             one_one(int))),
1.04/1.27	    inference('sup+', [status(thm)], ['18', '19'])).
1.04/1.27	tff(zf_stmt_132, axiom, (group_add(int))).
1.04/1.27	tff('21', plain, group_add(int),
1.04/1.27	    inference('cnf', [status(esa)], [zf_stmt_132])).
1.04/1.27	tff('22', plain,
1.04/1.27	    ![X0 : int]:
1.04/1.27	      (app_encode_app(int, $o, 
1.04/1.27	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), X0), 
1.04/1.27	         zero_zero(int))
1.04/1.27	       | ~ $true
1.04/1.27	       | ~ app_encode_app(int, $o, 
1.04/1.27	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X0), 
1.04/1.27	             one_one(int))),
1.04/1.27	    inference('demod', [status(thm)], ['20', '21'])).
1.04/1.27	tff('23', plain,
1.04/1.27	    ![X0 : int]:
1.04/1.27	      (~ app_encode_app(int, $o, 
1.04/1.27	           app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X0), 
1.04/1.27	           one_one(int))
1.04/1.27	       | app_encode_app(int, $o, 
1.04/1.27	           app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), X0), 
1.04/1.27	           zero_zero(int))),
1.04/1.27	    inference('simplify', [status(thm)], ['22'])).
1.04/1.27	tff(zf_stmt_80, axiom,
1.04/1.27	  (![I:int]:
1.04/1.27	     ((app_encode_app(int,nat,nat1,I) = zero_zero(nat)) <=>
1.04/1.27	      app_encode_app(int,$o,
1.04/1.27	                     app_encode_app(int,app_encode_fun(int,$o),
1.04/1.27	                                    ord_less_eq(int),I),
1.04/1.27	                     zero_zero(int))))).
1.04/1.27	tff('24', plain,
1.04/1.27	    ![X112 : int]:
1.04/1.27	      (app_encode_app(int, nat, nat1, X112) = zero_zero(nat)
1.04/1.27	       | ~ app_encode_app(int, $o, 
1.04/1.27	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
1.04/1.27	               X112), zero_zero(int))),
1.04/1.27	    inference('cnf', [status(esa)], [zf_stmt_80])).
1.04/1.27	tff('25', plain,
1.04/1.27	    ![X0 : int]:
1.04/1.27	      (~ $true
1.04/1.27	       | ~ app_encode_app(int, $o, 
1.04/1.27	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X0), 
1.04/1.27	             one_one(int))
1.04/1.27	       | app_encode_app(int, nat, nat1, X0) = zero_zero(nat)),
1.04/1.27	    inference('sup-', [status(thm)], ['23', '24'])).
1.04/1.27	tff('26', plain,
1.04/1.27	    ![X0 : int]:
1.04/1.27	      (app_encode_app(int, nat, nat1, X0) = zero_zero(nat)
1.04/1.27	       | ~ app_encode_app(int, $o, 
1.04/1.27	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X0), 
1.04/1.27	             one_one(int))),
1.04/1.27	    inference('simplify', [status(thm)], ['25'])).
1.04/1.27	tff('27', plain,
1.04/1.27	    ![X0 : nat]:
1.04/1.27	      (~ $true
1.04/1.27	       | ~ app_encode_app(nat, $o, 
1.04/1.27	             app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), X0), 
1.04/1.27	             app_encode_app(int, nat, nat1, one_one(int)))
1.04/1.27	       | app_encode_app(int, nat, nat1, 
1.04/1.27	           app_encode_app(nat, int, semiring_1_of_nat(int), X0))
1.04/1.27	          = zero_zero(nat)),
1.04/1.27	    inference('sup-', [status(thm)], ['17', '26'])).
1.04/1.27	tff(zf_stmt_68, axiom,
1.04/1.27	  (one_one(nat) = app_encode_app(int,nat,nat1,one_one(int)))).
1.04/1.27	tff('28', plain, one_one(nat) = app_encode_app(int, nat, nat1, one_one(int)),
1.04/1.27	    inference('cnf', [status(esa)], [zf_stmt_68])).
1.04/1.27	tff(zf_stmt_96, axiom,
1.04/1.27	  (![N2:nat]:
1.04/1.27	     (app_encode_app(int,nat,nat1,
1.04/1.27	                     app_encode_app(nat,int,semiring_1_of_nat(int),N2)) =
1.04/1.27	      N2))).
1.04/1.27	tff('29', plain,
1.04/1.27	    ![X139 : nat]:
1.04/1.27	      app_encode_app(int, nat, nat1, 
1.04/1.27	        app_encode_app(nat, int, semiring_1_of_nat(int), X139))
1.04/1.27	       = X139,
1.04/1.27	    inference('cnf', [status(esa)], [zf_stmt_96])).
1.04/1.27	tff('30', plain,
1.04/1.27	    ![X0 : nat]:
1.04/1.27	      (~ $true
1.04/1.27	       | ~ app_encode_app(nat, $o, 
1.04/1.27	             app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), X0), 
1.04/1.27	             one_one(nat))
1.04/1.27	       | X0 = zero_zero(nat)),
1.04/1.27	    inference('demod', [status(thm)], ['27', '28', '29'])).
1.04/1.27	tff('31', plain,
1.04/1.27	    ![X0 : nat]:
1.04/1.27	      (X0 = zero_zero(nat)
1.04/1.27	       | ~ app_encode_app(nat, $o, 
1.04/1.27	             app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), X0), 
1.04/1.27	             one_one(nat))),
1.04/1.27	    inference('simplify', [status(thm)], ['30'])).
1.04/1.27	tff('32', plain,
1.04/1.27	    (~ $true
1.04/1.27	     | one_one(nat) = app_encode_app(int, nat, nat1, t)
1.04/1.27	     | app_encode_app(int, nat, nat1, t) = zero_zero(nat)),
1.04/1.27	    inference('sup-', [status(thm)], ['16', '31'])).
1.04/1.27	tff('33', plain,
1.04/1.27	    (app_encode_app(int, nat, nat1, t) = zero_zero(nat)
1.04/1.27	     | one_one(nat) = app_encode_app(int, nat, nat1, t)),
1.04/1.27	    inference('simplify', [status(thm)], ['32'])).
1.04/1.27	tff(zf_stmt_70, axiom,
1.04/1.27	  (app_encode_app(int,$o,
1.04/1.27	                  app_encode_app(int,app_encode_fun(int,$o),ord_less_eq(int),
1.04/1.27	                                 one_one(int)),
1.04/1.27	                  t))).
1.04/1.27	tff('34', plain,
1.04/1.27	    app_encode_app(int, $o, 
1.04/1.27	      app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
1.04/1.27	        one_one(int)), t),
1.04/1.27	    inference('cnf', [status(esa)], [zf_stmt_70])).
1.04/1.27	tff(zf_stmt_112, axiom,
1.04/1.27	  (![Z:int]:
1.04/1.27	     (app_encode_app(int,$o,
1.04/1.27	                     app_encode_app(int,app_encode_fun(int,$o),
1.04/1.27	                                    ord_less_eq(int),one_one(int)),
1.04/1.27	                     Z) <=>
1.04/1.27	      app_encode_app(int,$o,
1.04/1.27	                     app_encode_app(int,app_encode_fun(int,$o),ord_less(int),
1.04/1.27	                                    zero_zero(int)),
1.04/1.27	                     Z)))).
1.04/1.27	tff('35', plain,
1.04/1.27	    ![X177 : int]:
1.04/1.27	      (app_encode_app(int, $o, 
1.04/1.27	         app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
1.04/1.27	           zero_zero(int)), X177)
1.04/1.27	       | ~ app_encode_app(int, $o, 
1.04/1.27	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
1.04/1.27	               one_one(int)), X177)),
1.04/1.27	    inference('cnf', [status(esa)], [zf_stmt_112])).
1.04/1.27	tff('36', plain,
1.04/1.27	    (~ $true
1.04/1.27	     | app_encode_app(int, $o, 
1.04/1.27	         app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
1.04/1.27	           zero_zero(int)), t)),
1.04/1.27	    inference('sup-', [status(thm)], ['34', '35'])).
1.04/1.27	tff('37', plain,
1.04/1.27	    app_encode_app(int, $o, 
1.04/1.27	      app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
1.04/1.27	        zero_zero(int)), t),
1.04/1.27	    inference('simplify', [status(thm)], ['36'])).
1.04/1.27	tff(zf_stmt_98, axiom,
1.04/1.27	  (![W:int,Z:int]:
1.04/1.27	     (app_encode_app(int,$o,
1.04/1.27	                     app_encode_app(int,app_encode_fun(int,$o),ord_less(int),
1.04/1.27	                                    Z),
1.04/1.27	                     W) <=>
1.04/1.27	      (app_encode_app(int,$o,
1.04/1.27	                      app_encode_app(int,app_encode_fun(int,$o),
1.04/1.27	                                     ord_less_eq(int),Z),
1.04/1.27	                      W) & 
1.04/1.27	       (Z != W))))).
1.04/1.27	tff('38', plain,
1.04/1.27	    ![X143 : int, X144 : int]:
1.04/1.27	      (app_encode_app(int, $o, 
1.04/1.27	         app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), X143), 
1.04/1.27	         X144)
1.04/1.27	       | ~ app_encode_app(int, $o, 
1.04/1.27	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
1.04/1.27	               X143), X144)),
1.04/1.27	    inference('cnf', [status(esa)], [zf_stmt_98])).
1.04/1.27	tff(zf_stmt_79, axiom,
1.04/1.27	  (![Z2:int]:
1.04/1.27	     ((app_encode_app(int,$o,
1.04/1.27	                      app_encode_app(int,app_encode_fun(int,$o),
1.04/1.27	                                     ord_less_eq(int),zero_zero(int)),
1.04/1.27	                      Z2) =>
1.04/1.27	       (app_encode_app(nat,int,semiring_1_of_nat(int),
1.04/1.27	                       app_encode_app(int,nat,nat1,Z2)) =
1.04/1.27	        Z2)) & 
1.04/1.27	      ((~
1.04/1.27	         app_encode_app(int,$o,
1.04/1.27	                        app_encode_app(int,app_encode_fun(int,$o),
1.04/1.27	                                       ord_less_eq(int),zero_zero(int)),
1.04/1.27	                        Z2)) =>
1.04/1.27	       (app_encode_app(nat,int,semiring_1_of_nat(int),
1.04/1.27	                       app_encode_app(int,nat,nat1,Z2)) =
1.04/1.27	        zero_zero(int)))))).
1.04/1.27	tff('39', plain,
1.04/1.27	    ![X110 : int]:
1.04/1.27	      (app_encode_app(nat, int, semiring_1_of_nat(int), 
1.04/1.27	         app_encode_app(int, nat, nat1, X110))
1.04/1.27	        = X110
1.04/1.27	       | ~ app_encode_app(int, $o, 
1.04/1.27	             app_encode_app(int, app_encode_fun(int, $o), ord_less_eq(int), 
1.04/1.27	               zero_zero(int)), X110)),
1.04/1.27	    inference('cnf', [status(esa)], [zf_stmt_79])).
1.04/1.27	tff('40', plain,
1.04/1.27	    ![X0 : int]:
1.04/1.27	      (~ $true
1.04/1.27	       | ~ app_encode_app(int, $o, 
1.04/1.27	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
1.04/1.27	               zero_zero(int)), X0)
1.04/1.27	       | app_encode_app(nat, int, semiring_1_of_nat(int), 
1.04/1.27	           app_encode_app(int, nat, nat1, X0))
1.04/1.27	          = X0),
1.04/1.27	    inference('sup-', [status(thm)], ['38', '39'])).
1.04/1.27	tff('41', plain,
1.04/1.27	    ![X0 : int]:
1.04/1.27	      (app_encode_app(nat, int, semiring_1_of_nat(int), 
1.04/1.27	         app_encode_app(int, nat, nat1, X0))
1.04/1.27	        = X0
1.04/1.27	       | ~ app_encode_app(int, $o, 
1.04/1.27	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
1.04/1.27	               zero_zero(int)), X0)),
1.04/1.27	    inference('simplify', [status(thm)], ['40'])).
1.04/1.27	tff('42', plain,
1.04/1.27	    (~ $true
1.04/1.27	     | app_encode_app(nat, int, semiring_1_of_nat(int), 
1.04/1.27	         app_encode_app(int, nat, nat1, t))
1.04/1.27	        = t),
1.04/1.27	    inference('sup-', [status(thm)], ['37', '41'])).
1.04/1.27	tff('43', plain,
1.04/1.27	    app_encode_app(nat, int, semiring_1_of_nat(int), 
1.04/1.27	      app_encode_app(int, nat, nat1, t))
1.04/1.27	     = t,
1.04/1.27	    inference('simplify', [status(thm)], ['42'])).
1.04/1.27	tff('44', plain,
1.04/1.27	    (app_encode_app(nat, int, semiring_1_of_nat(int), one_one(nat)) = t
1.04/1.27	     | app_encode_app(int, nat, nat1, t) = zero_zero(nat)),
1.04/1.27	    inference('sup+', [status(thm)], ['33', '43'])).
1.04/1.27	tff(zf_stmt_110, axiom,
1.04/1.27	  (one_one(int) = app_encode_app(nat,int,semiring_1_of_nat(int),one_one(nat)))).
1.04/1.27	tff('45', plain,
1.04/1.27	    one_one(int)
1.04/1.27	     = app_encode_app(nat, int, semiring_1_of_nat(int), one_one(nat)),
1.04/1.27	    inference('cnf', [status(esa)], [zf_stmt_110])).
1.04/1.27	tff('46', plain,
1.04/1.27	    (one_one(int) = t | app_encode_app(int, nat, nat1, t) = zero_zero(nat)),
1.04/1.27	    inference('sup+', [status(thm)], ['44', '45'])).
1.04/1.27	tff('47', plain,
1.04/1.27	    (app_encode_app(nat, int, semiring_1_of_nat(int), zero_zero(nat)) = t
1.04/1.27	     | one_one(int) = t),
1.04/1.27	    inference('sup+', [status(thm)], ['46', '43'])).
1.04/1.27	tff('48', plain, (zero_zero(int) = t | one_one(int) = t),
1.04/1.27	    inference('sup+', [status(thm)], ['1', '47'])).
1.04/1.27	tff(zf_stmt_92, axiom,
1.04/1.27	  (![N1:nat]:
1.04/1.27	     ((app_encode_app(nat,int,semiring_1_of_nat(int),N1) = zero_zero(int)) <=>
1.04/1.27	      (N1 = zero_zero(nat))))).
1.04/1.27	tff('49', plain,
1.04/1.27	    ![X131 : nat]:
1.04/1.27	      (X131 = zero_zero(nat)
1.04/1.27	       | app_encode_app(nat, int, semiring_1_of_nat(int), X131)
1.04/1.27	          != zero_zero(int)),
1.04/1.27	    inference('cnf', [status(esa)], [zf_stmt_92])).
1.04/1.27	tff('50', plain,
1.04/1.27	    (t != zero_zero(int) | app_encode_app(int, nat, nat1, t) = zero_zero(nat)),
1.04/1.27	    inference('sup-', [status(thm)], ['43', '49'])).
1.04/1.27	tff(zf_stmt_65, axiom,
1.04/1.27	  (![Z:int]:
1.04/1.27	     (app_encode_app(nat,$o,
1.04/1.27	                     app_encode_app(nat,app_encode_fun(nat,$o),ord_less(nat),
1.04/1.27	                                    zero_zero(nat)),
1.04/1.27	                     app_encode_app(int,nat,nat1,Z)) <=>
1.04/1.27	      app_encode_app(int,$o,
1.04/1.27	                     app_encode_app(int,app_encode_fun(int,$o),ord_less(int),
1.04/1.27	                                    zero_zero(int)),
1.04/1.27	                     Z)))).
1.04/1.27	tff('51', plain,
1.04/1.27	    ![X84 : int]:
1.04/1.27	      (app_encode_app(nat, $o, 
1.04/1.27	         app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), 
1.04/1.27	           zero_zero(nat)), app_encode_app(int, nat, nat1, X84))
1.04/1.27	       | ~ app_encode_app(int, $o, 
1.04/1.27	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
1.04/1.27	               zero_zero(int)), X84)),
1.04/1.27	    inference('cnf', [status(esa)], [zf_stmt_65])).
1.04/1.27	tff('52', plain,
1.04/1.27	    (app_encode_app(nat, $o, 
1.04/1.27	       app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), 
1.04/1.27	         zero_zero(nat)), zero_zero(nat))
1.04/1.27	     | t != zero_zero(int)
1.04/1.27	     | ~ app_encode_app(int, $o, 
1.04/1.27	           app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
1.04/1.27	             zero_zero(int)), t)),
1.04/1.27	    inference('sup+', [status(thm)], ['50', '51'])).
1.04/1.27	tff('53', plain,
1.04/1.27	    (app_encode_app(nat, $o, 
1.04/1.27	       app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), 
1.04/1.27	         zero_zero(nat)), zero_zero(nat))
1.04/1.27	     | t != zero_zero(int)
1.04/1.27	     | ~ $true),
1.04/1.27	    inference('demod', [status(thm)], ['52', '37'])).
1.04/1.27	tff('54', plain,
1.04/1.27	    (t != zero_zero(int)
1.04/1.27	     | app_encode_app(nat, $o, 
1.04/1.27	         app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), 
1.04/1.27	           zero_zero(nat)), zero_zero(nat))),
1.04/1.27	    inference('simplify', [status(thm)], ['53'])).
1.04/1.27	tff(zf_stmt_47, axiom,
1.04/1.27	  (![N2:nat]:
1.04/1.27	     (~
1.04/1.27	       app_encode_app(nat,$o,
1.04/1.27	                      app_encode_app(nat,app_encode_fun(nat,$o),
1.04/1.27	                                     ord_less(nat),N2),
1.04/1.27	                      N2)))).
1.04/1.27	tff('55', plain,
1.04/1.27	    ![X43 : nat]:
1.04/1.27	      ~ app_encode_app(nat, $o, 
1.04/1.27	          app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), X43), 
1.04/1.27	          X43),
1.04/1.27	    inference('cnf', [status(esa)], [zf_stmt_47])).
1.04/1.27	tff('56', plain, t != zero_zero(int),
1.04/1.27	    inference('clc', [status(thm)], ['54', '55'])).
1.04/1.27	tff('57', plain, one_one(int) = t,
1.04/1.27	    inference('simplify_reflect-', [status(thm)], ['48', '56'])).
1.04/1.27	tff('58', plain,
1.04/1.27	    app_encode_app(int, $o, 
1.04/1.27	      app_encode_app(int, app_encode_fun(int, $o), ord_less(int), t), t),
1.04/1.27	    inference('demod', [status(thm)], ['0', '57'])).
1.04/1.27	tff('59', plain,
1.04/1.27	    ![X143 : int, X144 : int]:
1.04/1.27	      (X143 != X144
1.04/1.27	       | ~ app_encode_app(int, $o, 
1.04/1.27	             app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
1.04/1.27	               X143), X144)),
1.04/1.27	    inference('cnf', [status(esa)], [zf_stmt_98])).
1.04/1.27	tff('60', plain,
1.04/1.28	    ![X144 : int]:
1.04/1.28	      ~ app_encode_app(int, $o, 
1.04/1.28	          app_encode_app(int, app_encode_fun(int, $o), ord_less(int), X144), 
1.04/1.28	          X144),
1.04/1.28	    inference('simplify', [status(thm)], ['59'])).
1.04/1.28	tff('61', plain, ~ $true, inference('sup-', [status(thm)], ['58', '60'])).
1.04/1.28	tff('62', plain, $false, inference('simplify', [status(thm)], ['61'])).
1.04/1.28	
1.04/1.28	% SZS output end Refutation
1.04/1.28	EOF
