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    : kbo
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 $2 \
0.00/0.01	  --simultaneous-sup false \
0.00/0.01	  --no-max-vars \
0.00/0.01	  --no-fool
0.00/0.20	% Computer   : n158.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 08:07:08 CST 2018
1.12/1.32	% done 655 iterations in 1.112s
1.12/1.32	% SZS status Theorem for 'stdin'
1.12/1.32	% SZS output start Refutation
1.12/1.32	tff(zf_stmt_99, axiom,
1.12/1.32	  (![Na:nat]:
1.12/1.32	     (app_encode_app(int,$o,
1.12/1.32	                     app_encode_app(int,app_encode_fun(int,$o),ord_less(int),
1.12/1.32	                                    zero_zero(int)),
1.12/1.32	                     app_encode_app(nat,int,semiring_1_of_nat(int),Na)) <=>
1.12/1.32	      app_encode_app(nat,$o,
1.12/1.32	                     app_encode_app(nat,app_encode_fun(nat,$o),ord_less(nat),
1.12/1.32	                                    zero_zero(nat)),
1.12/1.32	                     Na)))).
1.12/1.32	tff('0', plain,
1.12/1.32	    ![X169 : nat]:
1.12/1.32	      (app_encode_app(int, $o, 
1.12/1.32	         app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
1.12/1.32	           zero_zero(int)), 
1.12/1.32	         app_encode_app(nat, int, semiring_1_of_nat(int), X169))
1.12/1.32	       | ~ app_encode_app(nat, $o, 
1.12/1.32	             app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), 
1.12/1.32	               zero_zero(nat)), X169)),
1.12/1.32	    inference('cnf', [status(esa)], [zf_stmt_99])).
1.12/1.32	tff(zf_stmt_169, conjecture,
1.12/1.32	  (app_encode_app(int,$o,
1.12/1.32	                  app_encode_app(int,app_encode_fun(int,$o),ord_less(int),
1.12/1.32	                                 zero_zero(int)),
1.12/1.32	                  app_encode_app(int,int,
1.12/1.32	                                 app_encode_app(int,app_encode_fun(int,int),
1.12/1.32	                                                plus_plus(int),one_one(int)),
1.12/1.32	                                 app_encode_app(nat,int,
1.12/1.32	                                                semiring_1_of_nat(int),n))))).
1.12/1.32	tff(zf_stmt_0, negated_conjecture,
1.12/1.32	  (~
1.12/1.32	    app_encode_app(int,$o,
1.12/1.32	                   app_encode_app(int,app_encode_fun(int,$o),ord_less(int),
1.12/1.32	                                  zero_zero(int)),
1.12/1.32	                   app_encode_app(int,int,
1.12/1.32	                                  app_encode_app(int,app_encode_fun(int,int),
1.12/1.32	                                                 plus_plus(int),one_one(int)),
1.12/1.32	                                  app_encode_app(nat,int,
1.12/1.32	                                                 semiring_1_of_nat(int),n))))).
1.12/1.32	tff('1', plain,
1.12/1.32	    ~ app_encode_app(int, $o, 
1.12/1.32	        app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
1.12/1.32	          zero_zero(int)), 
1.12/1.32	        app_encode_app(int, int, 
1.12/1.32	          app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.12/1.32	            one_one(int)), 
1.12/1.32	          app_encode_app(nat, int, semiring_1_of_nat(int), n))),
1.12/1.32	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.12/1.32	tff(zf_stmt_88, axiom,
1.12/1.32	  (app_encode_app(nat,int,semiring_1_of_nat(int),one_one(nat)) = one_one(int))).
1.12/1.32	tff('2', plain,
1.12/1.32	    app_encode_app(nat, int, semiring_1_of_nat(int), one_one(nat))
1.12/1.32	     = one_one(int),
1.12/1.32	    inference('cnf', [status(esa)], [zf_stmt_88])).
1.12/1.32	tff(zf_stmt_43, axiom,
1.12/1.32	  (![A:$tType]:
1.12/1.32	     (semiring_1(A) =>
1.12/1.32	      (![N1:nat,M:nat]:
1.12/1.32	         (app_encode_app(nat,A,semiring_1_of_nat(A),
1.12/1.32	                         app_encode_app(nat,nat,
1.12/1.32	                                        app_encode_app(nat,
1.12/1.32	                                                       app_encode_fun(
1.12/1.32	                                                       nat,nat),
1.12/1.32	                                                       plus_plus(nat),M),
1.12/1.32	                                        N1)) =
1.12/1.32	          app_encode_app(A,A,
1.12/1.32	                         app_encode_app(A,app_encode_fun(A,A),plus_plus(A),
1.12/1.32	                                        app_encode_app(nat,A,
1.12/1.32	                                                       semiring_1_of_nat(A),M)),
1.12/1.32	                         app_encode_app(nat,A,semiring_1_of_nat(A),N1))))))).
1.12/1.32	tff('3', plain,
1.12/1.32	    ![X14 : $tType, X15 : nat, X16 : nat]:
1.12/1.32	      (app_encode_app(nat, X14, semiring_1_of_nat(X14), 
1.12/1.32	         app_encode_app(nat, nat, 
1.12/1.32	           app_encode_app(nat, app_encode_fun(nat, nat), plus_plus(nat), X15), 
1.12/1.32	           X16))
1.12/1.32	        = app_encode_app(X14, X14, 
1.12/1.32	            app_encode_app(X14, app_encode_fun(X14, X14), plus_plus(X14), 
1.12/1.32	              app_encode_app(nat, X14, semiring_1_of_nat(X14), X15)), 
1.12/1.32	            app_encode_app(nat, X14, semiring_1_of_nat(X14), X16))
1.12/1.32	       | ~ semiring_1(X14)),
1.12/1.32	    inference('cnf', [status(esa)], [zf_stmt_43])).
1.12/1.32	tff('4', plain,
1.12/1.32	    ![X0 : nat]:
1.12/1.32	      (app_encode_app(nat, int, semiring_1_of_nat(int), 
1.12/1.32	         app_encode_app(nat, nat, 
1.12/1.32	           app_encode_app(nat, app_encode_fun(nat, nat), plus_plus(nat), 
1.12/1.32	             one_one(nat)), X0))
1.12/1.32	        = app_encode_app(int, int, 
1.12/1.32	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.12/1.32	              one_one(int)), 
1.12/1.32	            app_encode_app(nat, int, semiring_1_of_nat(int), X0))
1.12/1.32	       | ~ semiring_1(int)),
1.12/1.32	    inference('sup+', [status(thm)], ['2', '3'])).
1.12/1.32	tff(zf_stmt_147, axiom, (semiring_1(int))).
1.12/1.32	tff('5', plain, semiring_1(int),
1.12/1.32	    inference('cnf', [status(esa)], [zf_stmt_147])).
1.12/1.32	tff('6', plain,
1.12/1.32	    ![X0 : nat]:
1.12/1.32	      (app_encode_app(nat, int, semiring_1_of_nat(int), 
1.12/1.32	         app_encode_app(nat, nat, 
1.12/1.32	           app_encode_app(nat, app_encode_fun(nat, nat), plus_plus(nat), 
1.12/1.32	             one_one(nat)), X0))
1.12/1.32	        = app_encode_app(int, int, 
1.12/1.32	            app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.12/1.32	              one_one(int)), 
1.12/1.32	            app_encode_app(nat, int, semiring_1_of_nat(int), X0))
1.12/1.32	       | ~ $true),
1.12/1.32	    inference('demod', [status(thm)], ['4', '5'])).
1.12/1.32	tff('7', plain,
1.12/1.32	    ![X0 : nat]:
1.12/1.32	      app_encode_app(nat, int, semiring_1_of_nat(int), 
1.12/1.32	        app_encode_app(nat, nat, 
1.12/1.32	          app_encode_app(nat, app_encode_fun(nat, nat), plus_plus(nat), 
1.12/1.32	            one_one(nat)), X0))
1.12/1.32	       = app_encode_app(int, int, 
1.12/1.32	           app_encode_app(int, app_encode_fun(int, int), plus_plus(int), 
1.12/1.32	             one_one(int)), 
1.12/1.32	           app_encode_app(nat, int, semiring_1_of_nat(int), X0)),
1.12/1.32	    inference('simplify', [status(thm)], ['6'])).
1.12/1.32	tff(zf_stmt_69, axiom,
1.12/1.32	  (![N1:nat,M:nat]:
1.12/1.32	     (app_encode_app(nat,nat,
1.12/1.32	                     app_encode_app(nat,app_encode_fun(nat,nat),
1.12/1.32	                                    plus_plus(nat),M),
1.12/1.32	                     N1) =
1.12/1.32	      app_encode_app(nat,nat,
1.12/1.32	                     app_encode_app(nat,app_encode_fun(nat,nat),
1.12/1.32	                                    plus_plus(nat),N1),
1.12/1.32	                     M)))).
1.12/1.32	tff('8', plain,
1.12/1.32	    ![X87 : nat, X88 : nat]:
1.12/1.32	      app_encode_app(nat, nat, 
1.12/1.32	        app_encode_app(nat, app_encode_fun(nat, nat), plus_plus(nat), X88), 
1.12/1.32	        X87)
1.12/1.32	       = app_encode_app(nat, nat, 
1.12/1.32	           app_encode_app(nat, app_encode_fun(nat, nat), plus_plus(nat), X87), 
1.12/1.32	           X88),
1.12/1.32	    inference('cnf', [status(esa)], [zf_stmt_69])).
1.12/1.32	tff('9', plain,
1.12/1.32	    ~ app_encode_app(int, $o, 
1.12/1.32	        app_encode_app(int, app_encode_fun(int, $o), ord_less(int), 
1.12/1.32	          zero_zero(int)), 
1.12/1.32	        app_encode_app(nat, int, semiring_1_of_nat(int), 
1.12/1.32	          app_encode_app(nat, nat, 
1.12/1.32	            app_encode_app(nat, app_encode_fun(nat, nat), plus_plus(nat), n), 
1.12/1.32	            one_one(nat)))),
1.12/1.32	    inference('demod', [status(thm)], ['1', '7', '8'])).
1.12/1.32	tff('10', plain,
1.12/1.32	    (~ $true
1.12/1.32	     | ~ app_encode_app(nat, $o, 
1.12/1.32	           app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), 
1.12/1.32	             zero_zero(nat)), 
1.12/1.32	           app_encode_app(nat, nat, 
1.12/1.32	             app_encode_app(nat, app_encode_fun(nat, nat), plus_plus(nat), n), 
1.12/1.32	             one_one(nat)))),
1.12/1.32	    inference('sup-', [status(thm)], ['0', '9'])).
1.12/1.32	tff(zf_stmt_67, axiom,
1.12/1.33	  (![N1:nat]:
1.12/1.33	     (app_encode_app(nat,nat,
1.12/1.33	                     app_encode_app(nat,app_encode_fun(nat,nat),
1.12/1.33	                                    plus_plus(nat),zero_zero(nat)),
1.12/1.33	                     N1) =
1.12/1.33	      N1))).
1.12/1.33	tff('11', plain,
1.12/1.33	    ![X85 : nat]:
1.12/1.33	      app_encode_app(nat, nat, 
1.12/1.33	        app_encode_app(nat, app_encode_fun(nat, nat), plus_plus(nat), 
1.12/1.33	          zero_zero(nat)), X85)
1.12/1.33	       = X85,
1.12/1.33	    inference('cnf', [status(esa)], [zf_stmt_67])).
1.12/1.33	tff(zf_stmt_37, axiom,
1.12/1.33	  (app_encode_app(nat,$o,
1.12/1.33	                  app_encode_app(nat,app_encode_fun(nat,$o),ord_less(nat),
1.12/1.33	                                 zero_zero(nat)),
1.12/1.33	                  n))).
1.12/1.33	tff('12', plain,
1.12/1.33	    app_encode_app(nat, $o, 
1.12/1.33	      app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), 
1.12/1.33	        zero_zero(nat)), n),
1.12/1.33	    inference('cnf', [status(esa)], [zf_stmt_37])).
1.12/1.33	tff(zf_stmt_81, axiom,
1.12/1.33	  (![N1:nat,M:nat,L:nat,K2:nat]:
1.12/1.33	     (app_encode_app(nat,$o,
1.12/1.33	                     app_encode_app(nat,app_encode_fun(nat,$o),ord_less(nat),
1.12/1.33	                                    K2),
1.12/1.33	                     L) =>
1.12/1.33	      ((app_encode_app(nat,nat,
1.12/1.33	                       app_encode_app(nat,app_encode_fun(nat,nat),
1.12/1.33	                                      plus_plus(nat),M),
1.12/1.33	                       L) =
1.12/1.33	        app_encode_app(nat,nat,
1.12/1.33	                       app_encode_app(nat,app_encode_fun(nat,nat),
1.12/1.33	                                      plus_plus(nat),K2),
1.12/1.33	                       N1)) =>
1.12/1.33	       app_encode_app(nat,$o,
1.12/1.33	                      app_encode_app(nat,app_encode_fun(nat,$o),
1.12/1.33	                                     ord_less(nat),M),
1.12/1.33	                      N1))))).
1.12/1.33	tff('13', plain,
1.12/1.33	    ![X117 : nat, X118 : nat, X119 : nat, X120 : nat]:
1.12/1.33	      (app_encode_app(nat, $o, 
1.12/1.33	         app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), X117), 
1.12/1.33	         X118)
1.12/1.33	       | ~ app_encode_app(nat, $o, 
1.12/1.33	             app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), 
1.12/1.33	               X119), X120)
1.12/1.33	       | app_encode_app(nat, nat, 
1.12/1.33	           app_encode_app(nat, app_encode_fun(nat, nat), plus_plus(nat), 
1.12/1.33	             X117), X120)
1.12/1.33	          != app_encode_app(nat, nat, 
1.12/1.33	               app_encode_app(nat, app_encode_fun(nat, nat), plus_plus(nat), 
1.12/1.33	                 X119), X118)),
1.12/1.33	    inference('cnf', [status(esa)], [zf_stmt_81])).
1.12/1.33	tff('14', plain,
1.12/1.33	    ![X0 : nat, X1 : nat]:
1.12/1.33	      (~ $true
1.12/1.33	       | app_encode_app(nat, nat, 
1.12/1.33	           app_encode_app(nat, app_encode_fun(nat, nat), plus_plus(nat), X0), 
1.12/1.33	           n)
1.12/1.33	          != app_encode_app(nat, nat, 
1.12/1.33	               app_encode_app(nat, app_encode_fun(nat, nat), plus_plus(nat), 
1.12/1.33	                 zero_zero(nat)), X1)
1.12/1.33	       | app_encode_app(nat, $o, 
1.12/1.33	           app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), X0), 
1.12/1.33	           X1)),
1.12/1.33	    inference('sup-', [status(thm)], ['12', '13'])).
1.12/1.33	tff('15', plain,
1.12/1.33	    ![X0 : nat, X1 : nat]:
1.12/1.33	      (~ $true
1.12/1.33	       | app_encode_app(nat, nat, 
1.12/1.33	           app_encode_app(nat, app_encode_fun(nat, nat), plus_plus(nat), X0), 
1.12/1.33	           n)
1.12/1.33	          != X1
1.12/1.33	       | app_encode_app(nat, $o, 
1.12/1.33	           app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), X0), 
1.12/1.33	           X1)),
1.12/1.33	    inference('demod', [status(thm)], ['14', '11'])).
1.12/1.33	tff('16', plain,
1.12/1.33	    ![X0 : nat]:
1.12/1.33	      app_encode_app(nat, $o, 
1.12/1.33	        app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), X0), 
1.12/1.33	        app_encode_app(nat, nat, 
1.12/1.33	          app_encode_app(nat, app_encode_fun(nat, nat), plus_plus(nat), X0), 
1.12/1.33	          n)),
1.12/1.33	    inference('simplify', [status(thm)], ['15'])).
1.12/1.33	tff(zf_stmt_83, axiom,
1.12/1.33	  (![K2:nat,J:nat,I:nat]:
1.12/1.33	     (app_encode_app(nat,$o,
1.12/1.33	                     app_encode_app(nat,app_encode_fun(nat,$o),ord_less(nat),
1.12/1.33	                                    app_encode_app(nat,nat,
1.12/1.33	                                                   app_encode_app(nat,
1.12/1.33	                                                                  app_encode_fun(
1.12/1.33	                                                                  nat,nat),
1.12/1.33	                                                                  plus_plus(
1.12/1.33	                                                                  nat),I),
1.12/1.33	                                                   J)),
1.12/1.33	                     K2) =>
1.12/1.33	      app_encode_app(nat,$o,
1.12/1.33	                     app_encode_app(nat,app_encode_fun(nat,$o),ord_less(nat),
1.12/1.33	                                    I),
1.12/1.33	                     K2)))).
1.12/1.33	tff('17', plain,
1.12/1.33	    ![X123 : nat, X124 : nat, X125 : nat]:
1.12/1.33	      (app_encode_app(nat, $o, 
1.12/1.33	         app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), X123), 
1.12/1.33	         X124)
1.12/1.33	       | ~ app_encode_app(nat, $o, 
1.12/1.33	             app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), 
1.12/1.33	               app_encode_app(nat, nat, 
1.12/1.33	                 app_encode_app(nat, app_encode_fun(nat, nat), 
1.12/1.33	                   plus_plus(nat), X123), X125)), X124)),
1.12/1.33	    inference('cnf', [status(esa)], [zf_stmt_83])).
1.12/1.33	tff('18', plain,
1.12/1.33	    ![X0 : nat, X1 : nat]:
1.12/1.33	      (~ $true
1.12/1.33	       | app_encode_app(nat, $o, 
1.12/1.33	           app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), X1), 
1.12/1.33	           app_encode_app(nat, nat, 
1.12/1.33	             app_encode_app(nat, app_encode_fun(nat, nat), plus_plus(nat), 
1.12/1.33	               app_encode_app(nat, nat, 
1.12/1.33	                 app_encode_app(nat, app_encode_fun(nat, nat), 
1.12/1.33	                   plus_plus(nat), X1), X0)), n))),
1.12/1.33	    inference('sup-', [status(thm)], ['16', '17'])).
1.12/1.33	tff(zf_stmt_71, axiom,
1.12/1.33	  (![K2:nat,N1:nat,M:nat]:
1.12/1.33	     (app_encode_app(nat,nat,
1.12/1.33	                     app_encode_app(nat,app_encode_fun(nat,nat),
1.12/1.33	                                    plus_plus(nat),
1.12/1.33	                                    app_encode_app(nat,nat,
1.12/1.33	                                                   app_encode_app(nat,
1.12/1.33	                                                                  app_encode_fun(
1.12/1.33	                                                                  nat,nat),
1.12/1.33	                                                                  plus_plus(
1.12/1.33	                                                                  nat),M),
1.12/1.33	                                                   N1)),
1.12/1.33	                     K2) =
1.12/1.33	      app_encode_app(nat,nat,
1.12/1.33	                     app_encode_app(nat,app_encode_fun(nat,nat),
1.12/1.33	                                    plus_plus(nat),M),
1.12/1.33	                     app_encode_app(nat,nat,
1.12/1.33	                                    app_encode_app(nat,
1.12/1.33	                                                   app_encode_fun(nat,nat),
1.12/1.33	                                                   plus_plus(nat),N1),
1.12/1.33	                                    K2))))).
1.12/1.33	tff('19', plain,
1.12/1.33	    ![X92 : nat, X93 : nat, X94 : nat]:
1.12/1.33	      app_encode_app(nat, nat, 
1.12/1.33	        app_encode_app(nat, app_encode_fun(nat, nat), plus_plus(nat), 
1.12/1.33	          app_encode_app(nat, nat, 
1.12/1.33	            app_encode_app(nat, app_encode_fun(nat, nat), plus_plus(nat), 
1.12/1.33	              X92), X93)), X94)
1.12/1.33	       = app_encode_app(nat, nat, 
1.12/1.33	           app_encode_app(nat, app_encode_fun(nat, nat), plus_plus(nat), X92), 
1.12/1.33	           app_encode_app(nat, nat, 
1.12/1.33	             app_encode_app(nat, app_encode_fun(nat, nat), plus_plus(nat), 
1.12/1.33	               X93), X94)),
1.12/1.33	    inference('cnf', [status(esa)], [zf_stmt_71])).
1.12/1.33	tff('20', plain,
1.12/1.33	    ![X0 : nat, X1 : nat]:
1.12/1.33	      (~ $true
1.12/1.33	       | app_encode_app(nat, $o, 
1.12/1.33	           app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), X1), 
1.12/1.33	           app_encode_app(nat, nat, 
1.12/1.33	             app_encode_app(nat, app_encode_fun(nat, nat), plus_plus(nat), 
1.12/1.33	               X1), 
1.12/1.33	             app_encode_app(nat, nat, 
1.12/1.33	               app_encode_app(nat, app_encode_fun(nat, nat), plus_plus(nat), 
1.12/1.33	                 X0), n)))),
1.12/1.33	    inference('demod', [status(thm)], ['18', '19'])).
1.12/1.33	tff('21', plain,
1.12/1.33	    ![X0 : nat, X1 : nat]:
1.12/1.33	      app_encode_app(nat, $o, 
1.12/1.33	        app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), X1), 
1.12/1.33	        app_encode_app(nat, nat, 
1.12/1.33	          app_encode_app(nat, app_encode_fun(nat, nat), plus_plus(nat), X1), 
1.12/1.33	          app_encode_app(nat, nat, 
1.12/1.33	            app_encode_app(nat, app_encode_fun(nat, nat), plus_plus(nat), X0), 
1.12/1.33	            n))),
1.12/1.33	    inference('simplify', [status(thm)], ['20'])).
1.12/1.33	tff('22', plain,
1.12/1.33	    ![X0 : nat]:
1.12/1.33	      app_encode_app(nat, $o, 
1.12/1.33	        app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), 
1.12/1.33	          zero_zero(nat)), 
1.12/1.33	        app_encode_app(nat, nat, 
1.12/1.33	          app_encode_app(nat, app_encode_fun(nat, nat), plus_plus(nat), X0), 
1.12/1.33	          n)),
1.12/1.33	    inference('sup+', [status(thm)], ['11', '21'])).
1.12/1.33	tff('23', plain,
1.12/1.33	    ![X0 : nat]:
1.12/1.33	      app_encode_app(nat, $o, 
1.12/1.33	        app_encode_app(nat, app_encode_fun(nat, $o), ord_less(nat), 
1.12/1.33	          zero_zero(nat)), 
1.12/1.33	        app_encode_app(nat, nat, 
1.12/1.33	          app_encode_app(nat, app_encode_fun(nat, nat), plus_plus(nat), n), 
1.12/1.33	          X0)),
1.12/1.33	    inference('sup+', [status(thm)], ['8', '22'])).
1.12/1.33	tff('24', plain, (~ $true | ~ $true),
1.12/1.33	    inference('demod', [status(thm)], ['10', '23'])).
1.12/1.33	tff('25', plain, $false, inference('simplify', [status(thm)], ['24'])).
1.12/1.33	
1.12/1.33	% SZS output end Refutation
1.12/1.33	EOF
