0.00/0.00	% File    : /export/starexec/sandbox/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    : 
0.00/0.00	#!/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
0.00/0.20	% Computer   : n091.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 10:08:23 CST 2018
3.35/3.56	% done 1225 iterations in 3.354s
3.35/3.56	% SZS status Theorem for 'stdin'
3.35/3.56	% SZS output start Refutation
3.35/3.56	tff(zf_stmt_176, axiom,
3.35/3.56	  (app_encode_app(a,nat,
3.35/3.56	                  app_encode_app(huffma1450048681e_tree(a),
3.35/3.56	                                 app_encode_fun(a,nat),
3.35/3.56	                                 huffma410068972_depth(a),t_2),
3.35/3.56	                  a1) =
3.35/3.56	   app_encode_app(nat,nat,
3.35/3.56	                  app_encode_app(nat,app_encode_fun(nat,nat),ord_max(nat),
3.35/3.56	                                 app_encode_app(huffma1450048681e_tree(b),
3.35/3.56	                                                nat,huffma945805758height(b),
3.35/3.56	                                                t_1)),
3.35/3.56	                  app_encode_app(huffma1450048681e_tree(a),nat,
3.35/3.56	                                 huffma945805758height(a),t_2)))).
3.35/3.56	tff('0', plain,
3.35/3.56	    app_encode_app(a, nat, 
3.35/3.56	      app_encode_app(huffma1450048681e_tree(a), app_encode_fun(a, nat), 
3.35/3.56	        huffma410068972_depth(a), t_2), a1)
3.35/3.56	     = app_encode_app(nat, nat, 
3.35/3.56	         app_encode_app(nat, app_encode_fun(nat, nat), ord_max(nat), 
3.35/3.56	           app_encode_app(huffma1450048681e_tree(b), nat, 
3.35/3.56	             huffma945805758height(b), t_1)), 
3.35/3.56	         app_encode_app(huffma1450048681e_tree(a), nat, 
3.35/3.56	           huffma945805758height(a), t_2)),
3.35/3.56	    inference('cnf', [status(esa)], [zf_stmt_176])).
3.35/3.56	tff(zf_stmt_77, axiom,
3.35/3.56	  (![A:$tType]:
3.35/3.56	     (linorder(A) =>
3.35/3.56	      (![Y:A,X:A]:
3.35/3.56	         (app_encode_app(A,A,
3.35/3.56	                         app_encode_app(A,app_encode_fun(A,A),ord_max(A),X),Y) =
3.35/3.56	          app_encode_app(A,A,
3.35/3.56	                         app_encode_app(A,app_encode_fun(A,A),ord_max(A),Y),X)))))).
3.35/3.56	tff('1', plain,
3.35/3.56	    ![X113 : $tType, X114 : X113, X115 : X113]:
3.35/3.56	      (app_encode_app(X113, X113, 
3.35/3.56	         app_encode_app(X113, app_encode_fun(X113, X113), ord_max(X113), 
3.35/3.56	           X115), X114)
3.35/3.56	        = app_encode_app(X113, X113, 
3.35/3.56	            app_encode_app(X113, app_encode_fun(X113, X113), ord_max(X113), 
3.35/3.56	              X114), X115)
3.35/3.56	       | ~ linorder(X113)),
3.35/3.56	    inference('cnf', [status(esa)], [zf_stmt_77])).
3.35/3.56	tff(zf_stmt_93, axiom,
3.35/3.56	  (![N:nat]:
3.35/3.56	     app_encode_app(nat,$o,
3.35/3.56	                    app_encode_app(nat,app_encode_fun(nat,$o),
3.35/3.56	                                   ord_less_eq(nat),N),
3.35/3.56	                    N))).
3.35/3.56	tff('2', plain,
3.35/3.56	    ![X176 : nat]:
3.35/3.56	      app_encode_app(nat, $o, 
3.35/3.56	        app_encode_app(nat, app_encode_fun(nat, $o), ord_less_eq(nat), X176), 
3.35/3.56	        X176),
3.35/3.56	    inference('cnf', [status(esa)], [zf_stmt_93])).
3.35/3.56	tff(zf_stmt_49, axiom,
3.35/3.56	  (![C:$tType]:
3.35/3.56	     (linorder(C) =>
3.35/3.56	      (![Z:C,Y1:C,X1:C]:
3.35/3.56	         (app_encode_app(C,$o,
3.35/3.56	                         app_encode_app(C,app_encode_fun(C,$o),
3.35/3.56	                                        ord_less_eq(C),
3.35/3.56	                                        app_encode_app(C,C,
3.35/3.56	                                                       app_encode_app(
3.35/3.56	                                                       C,app_encode_fun(C,C),
3.35/3.56	                                                       ord_max(C),X1),Y1)),
3.35/3.56	                         Z) <=>
3.35/3.56	          (app_encode_app(C,$o,
3.35/3.56	                          app_encode_app(C,app_encode_fun(C,$o),
3.35/3.56	                                         ord_less_eq(C),X1),
3.35/3.56	                          Z) & 
3.35/3.56	           app_encode_app(C,$o,
3.35/3.56	                          app_encode_app(C,app_encode_fun(C,$o),
3.35/3.56	                                         ord_less_eq(C),Y1),
3.35/3.56	                          Z))))))).
3.35/3.56	tff('3', plain,
3.35/3.56	    ![X8 : $tType, X10 : X8, X11 : X8, X12 : X8]:
3.35/3.56	      (~ app_encode_app(X8, $o, 
3.35/3.56	           app_encode_app(X8, app_encode_fun(X8, $o), ord_less_eq(X8), 
3.35/3.56	             app_encode_app(X8, X8, 
3.35/3.56	               app_encode_app(X8, app_encode_fun(X8, X8), ord_max(X8), X12), 
3.35/3.56	               X11)), X10)
3.35/3.56	       | app_encode_app(X8, $o, 
3.35/3.56	           app_encode_app(X8, app_encode_fun(X8, $o), ord_less_eq(X8), X11), 
3.35/3.56	           X10)
3.35/3.56	       | ~ linorder(X8)),
3.35/3.56	    inference('cnf', [status(esa)], [zf_stmt_49])).
3.35/3.56	tff('4', plain,
3.35/3.56	    ![X0 : nat, X1 : nat]:
3.35/3.56	      (~ $true
3.35/3.56	       | ~ linorder(nat)
3.35/3.56	       | app_encode_app(nat, $o, 
3.35/3.56	           app_encode_app(nat, app_encode_fun(nat, $o), ord_less_eq(nat), X0), 
3.35/3.56	           app_encode_app(nat, nat, 
3.35/3.56	             app_encode_app(nat, app_encode_fun(nat, nat), ord_max(nat), X1), 
3.35/3.56	             X0))),
3.35/3.56	    inference('sup-', [status(thm)], ['2', '3'])).
3.35/3.56	tff(zf_stmt_163, axiom, (linorder(nat))).
3.35/3.56	tff('5', plain, linorder(nat), inference('cnf', [status(esa)], [zf_stmt_163])).
3.35/3.56	tff('6', plain,
3.35/3.56	    ![X0 : nat, X1 : nat]:
3.35/3.56	      (~ $true
3.35/3.56	       | ~ $true
3.35/3.56	       | app_encode_app(nat, $o, 
3.35/3.56	           app_encode_app(nat, app_encode_fun(nat, $o), ord_less_eq(nat), X0), 
3.35/3.56	           app_encode_app(nat, nat, 
3.35/3.56	             app_encode_app(nat, app_encode_fun(nat, nat), ord_max(nat), X1), 
3.35/3.56	             X0))),
3.35/3.56	    inference('demod', [status(thm)], ['4', '5'])).
3.35/3.56	tff('7', plain,
3.35/3.56	    ![X0 : nat, X1 : nat]:
3.35/3.56	      app_encode_app(nat, $o, 
3.35/3.56	        app_encode_app(nat, app_encode_fun(nat, $o), ord_less_eq(nat), X0), 
3.35/3.56	        app_encode_app(nat, nat, 
3.35/3.56	          app_encode_app(nat, app_encode_fun(nat, nat), ord_max(nat), X1), 
3.35/3.56	          X0)),
3.35/3.56	    inference('simplify', [status(thm)], ['6'])).
3.35/3.56	tff(zf_stmt_55, axiom,
3.35/3.56	  (![C:$tType]:
3.35/3.56	     (linorder(C) =>
3.35/3.56	      (![Y1:C,X1:C]:
3.35/3.56	         (app_encode_app(C,$o,
3.35/3.56	                         app_encode_app(C,app_encode_fun(C,$o),
3.35/3.56	                                        ord_less_eq(C),X1),
3.35/3.56	                         Y1) <=>
3.35/3.56	          (app_encode_app(C,C,
3.35/3.56	                          app_encode_app(C,app_encode_fun(C,C),ord_max(C),X1),
3.35/3.56	                          Y1) =
3.35/3.56	           Y1)))))).
3.35/3.56	tff('8', plain,
3.35/3.56	    ![X27 : $tType, X28 : X27, X30 : X27]:
3.35/3.56	      (~ app_encode_app(X27, $o, 
3.35/3.56	           app_encode_app(X27, app_encode_fun(X27, $o), ord_less_eq(X27), 
3.35/3.56	             X30), X28)
3.35/3.56	       | app_encode_app(X27, X27, 
3.35/3.56	           app_encode_app(X27, app_encode_fun(X27, X27), ord_max(X27), X30), 
3.35/3.56	           X28)
3.35/3.56	          = X28
3.35/3.56	       | ~ linorder(X27)),
3.35/3.56	    inference('cnf', [status(esa)], [zf_stmt_55])).
3.35/3.56	tff('9', plain,
3.35/3.56	    ![X0 : nat, X1 : nat]:
3.35/3.56	      (~ $true
3.35/3.56	       | ~ linorder(nat)
3.35/3.56	       | app_encode_app(nat, nat, 
3.35/3.56	           app_encode_app(nat, app_encode_fun(nat, nat), ord_max(nat), X0), 
3.35/3.56	           app_encode_app(nat, nat, 
3.35/3.56	             app_encode_app(nat, app_encode_fun(nat, nat), ord_max(nat), X1), 
3.35/3.56	             X0))
3.35/3.56	          = app_encode_app(nat, nat, 
3.35/3.56	              app_encode_app(nat, app_encode_fun(nat, nat), ord_max(nat), X1), 
3.35/3.56	              X0)),
3.35/3.56	    inference('sup-', [status(thm)], ['7', '8'])).
3.35/3.56	tff('10', plain,
3.35/3.56	    ![X0 : nat, X1 : nat]:
3.35/3.56	      (~ $true
3.35/3.56	       | ~ $true
3.35/3.56	       | app_encode_app(nat, nat, 
3.35/3.56	           app_encode_app(nat, app_encode_fun(nat, nat), ord_max(nat), X0), 
3.35/3.56	           app_encode_app(nat, nat, 
3.35/3.56	             app_encode_app(nat, app_encode_fun(nat, nat), ord_max(nat), X1), 
3.35/3.56	             X0))
3.35/3.56	          = app_encode_app(nat, nat, 
3.35/3.56	              app_encode_app(nat, app_encode_fun(nat, nat), ord_max(nat), X1), 
3.35/3.56	              X0)),
3.35/3.56	    inference('demod', [status(thm)], ['9', '5'])).
3.35/3.56	tff('11', plain,
3.35/3.56	    ![X0 : nat, X1 : nat]:
3.35/3.56	      app_encode_app(nat, nat, 
3.35/3.56	        app_encode_app(nat, app_encode_fun(nat, nat), ord_max(nat), X0), 
3.35/3.56	        app_encode_app(nat, nat, 
3.35/3.56	          app_encode_app(nat, app_encode_fun(nat, nat), ord_max(nat), X1), 
3.35/3.56	          X0))
3.35/3.56	       = app_encode_app(nat, nat, 
3.35/3.56	           app_encode_app(nat, app_encode_fun(nat, nat), ord_max(nat), X1), 
3.35/3.56	           X0),
3.35/3.56	    inference('simplify', [status(thm)], ['10'])).
3.35/3.56	tff('12', plain,
3.35/3.56	    ![X0 : nat, X1 : nat]:
3.35/3.56	      (app_encode_app(nat, nat, 
3.35/3.56	         app_encode_app(nat, app_encode_fun(nat, nat), ord_max(nat), X1), 
3.35/3.56	         app_encode_app(nat, nat, 
3.35/3.56	           app_encode_app(nat, app_encode_fun(nat, nat), ord_max(nat), X1), 
3.35/3.56	           X0))
3.35/3.56	        = app_encode_app(nat, nat, 
3.35/3.56	            app_encode_app(nat, app_encode_fun(nat, nat), ord_max(nat), X0), 
3.35/3.56	            X1)
3.35/3.56	       | ~ linorder(nat)),
3.35/3.56	    inference('sup+', [status(thm)], ['1', '11'])).
3.35/3.56	tff('13', plain,
3.35/3.56	    ![X0 : nat, X1 : nat]:
3.35/3.56	      (app_encode_app(nat, nat, 
3.35/3.56	         app_encode_app(nat, app_encode_fun(nat, nat), ord_max(nat), X1), 
3.35/3.56	         app_encode_app(nat, nat, 
3.35/3.56	           app_encode_app(nat, app_encode_fun(nat, nat), ord_max(nat), X1), 
3.35/3.56	           X0))
3.35/3.56	        = app_encode_app(nat, nat, 
3.35/3.56	            app_encode_app(nat, app_encode_fun(nat, nat), ord_max(nat), X0), 
3.35/3.56	            X1)
3.35/3.56	       | ~ $true),
3.35/3.56	    inference('demod', [status(thm)], ['12', '5'])).
3.35/3.56	tff('14', plain,
3.35/3.56	    ![X0 : nat, X1 : nat]:
3.35/3.56	      app_encode_app(nat, nat, 
3.35/3.56	        app_encode_app(nat, app_encode_fun(nat, nat), ord_max(nat), X1), 
3.35/3.56	        app_encode_app(nat, nat, 
3.35/3.56	          app_encode_app(nat, app_encode_fun(nat, nat), ord_max(nat), X1), 
3.35/3.56	          X0))
3.35/3.56	       = app_encode_app(nat, nat, 
3.35/3.56	           app_encode_app(nat, app_encode_fun(nat, nat), ord_max(nat), X0), 
3.35/3.56	           X1),
3.35/3.56	    inference('simplify', [status(thm)], ['13'])).
3.35/3.56	tff('15', plain,
3.35/3.56	    ![X8 : $tType, X10 : X8, X11 : X8, X12 : X8]:
3.35/3.56	      (~ app_encode_app(X8, $o, 
3.35/3.56	           app_encode_app(X8, app_encode_fun(X8, $o), ord_less_eq(X8), 
3.35/3.56	             app_encode_app(X8, X8, 
3.35/3.56	               app_encode_app(X8, app_encode_fun(X8, X8), ord_max(X8), X12), 
3.35/3.56	               X11)), X10)
3.35/3.56	       | app_encode_app(X8, $o, 
3.35/3.56	           app_encode_app(X8, app_encode_fun(X8, $o), ord_less_eq(X8), X12), 
3.35/3.56	           X10)
3.35/3.56	       | ~ linorder(X8)),
3.35/3.56	    inference('cnf', [status(esa)], [zf_stmt_49])).
3.35/3.56	tff('16', plain,
3.35/3.56	    ![X0 : nat, X1 : nat]:
3.35/3.56	      (~ $true
3.35/3.56	       | ~ linorder(nat)
3.35/3.56	       | app_encode_app(nat, $o, 
3.35/3.56	           app_encode_app(nat, app_encode_fun(nat, $o), ord_less_eq(nat), X1), 
3.35/3.56	           app_encode_app(nat, nat, 
3.35/3.56	             app_encode_app(nat, app_encode_fun(nat, nat), ord_max(nat), X1), 
3.35/3.56	             X0))),
3.35/3.56	    inference('sup-', [status(thm)], ['2', '15'])).
3.35/3.56	tff('17', plain,
3.35/3.56	    ![X0 : nat, X1 : nat]:
3.35/3.56	      (~ $true
3.35/3.56	       | ~ $true
3.35/3.56	       | app_encode_app(nat, $o, 
3.35/3.56	           app_encode_app(nat, app_encode_fun(nat, $o), ord_less_eq(nat), X1), 
3.35/3.56	           app_encode_app(nat, nat, 
3.35/3.56	             app_encode_app(nat, app_encode_fun(nat, nat), ord_max(nat), X1), 
3.35/3.56	             X0))),
3.35/3.56	    inference('demod', [status(thm)], ['16', '5'])).
3.35/3.56	tff('18', plain,
3.35/3.56	    ![X0 : nat, X1 : nat]:
3.35/3.56	      app_encode_app(nat, $o, 
3.35/3.56	        app_encode_app(nat, app_encode_fun(nat, $o), ord_less_eq(nat), X1), 
3.35/3.56	        app_encode_app(nat, nat, 
3.35/3.56	          app_encode_app(nat, app_encode_fun(nat, nat), ord_max(nat), X1), 
3.35/3.56	          X0)),
3.35/3.56	    inference('simplify', [status(thm)], ['17'])).
3.35/3.56	tff('19', plain,
3.35/3.56	    ![X0 : nat, X1 : nat]:
3.35/3.56	      (~ $true
3.35/3.56	       | ~ linorder(nat)
3.35/3.56	       | app_encode_app(nat, nat, 
3.35/3.56	           app_encode_app(nat, app_encode_fun(nat, nat), ord_max(nat), X1), 
3.35/3.56	           app_encode_app(nat, nat, 
3.35/3.56	             app_encode_app(nat, app_encode_fun(nat, nat), ord_max(nat), X1), 
3.35/3.56	             X0))
3.35/3.56	          = app_encode_app(nat, nat, 
3.35/3.56	              app_encode_app(nat, app_encode_fun(nat, nat), ord_max(nat), X1), 
3.35/3.56	              X0)),
3.35/3.56	    inference('sup-', [status(thm)], ['18', '8'])).
3.35/3.56	tff('20', plain,
3.35/3.56	    ![X0 : nat, X1 : nat]:
3.35/3.56	      (~ $true
3.35/3.56	       | ~ $true
3.35/3.56	       | app_encode_app(nat, nat, 
3.35/3.56	           app_encode_app(nat, app_encode_fun(nat, nat), ord_max(nat), X1), 
3.35/3.56	           app_encode_app(nat, nat, 
3.35/3.56	             app_encode_app(nat, app_encode_fun(nat, nat), ord_max(nat), X1), 
3.35/3.56	             X0))
3.35/3.56	          = app_encode_app(nat, nat, 
3.35/3.56	              app_encode_app(nat, app_encode_fun(nat, nat), ord_max(nat), X1), 
3.35/3.56	              X0)),
3.35/3.56	    inference('demod', [status(thm)], ['19', '5'])).
3.35/3.56	tff('21', plain,
3.35/3.56	    ![X0 : nat, X1 : nat]:
3.35/3.56	      app_encode_app(nat, nat, 
3.35/3.56	        app_encode_app(nat, app_encode_fun(nat, nat), ord_max(nat), X1), 
3.35/3.56	        app_encode_app(nat, nat, 
3.35/3.56	          app_encode_app(nat, app_encode_fun(nat, nat), ord_max(nat), X1), 
3.35/3.56	          X0))
3.35/3.56	       = app_encode_app(nat, nat, 
3.35/3.56	           app_encode_app(nat, app_encode_fun(nat, nat), ord_max(nat), X1), 
3.35/3.56	           X0),
3.35/3.56	    inference('simplify', [status(thm)], ['20'])).
3.35/3.56	tff('22', plain,
3.35/3.56	    ![X0 : nat, X1 : nat]:
3.35/3.56	      app_encode_app(nat, nat, 
3.35/3.56	        app_encode_app(nat, app_encode_fun(nat, nat), ord_max(nat), X1), X0)
3.35/3.56	       = app_encode_app(nat, nat, 
3.35/3.56	           app_encode_app(nat, app_encode_fun(nat, nat), ord_max(nat), X0), 
3.35/3.56	           X1),
3.35/3.56	    inference('sup+', [status(thm)], ['14', '21'])).
3.35/3.56	tff('23', plain,
3.35/3.56	    app_encode_app(a, nat, 
3.35/3.56	      app_encode_app(huffma1450048681e_tree(a), app_encode_fun(a, nat), 
3.35/3.56	        huffma410068972_depth(a), t_2), a1)
3.35/3.56	     = app_encode_app(nat, nat, 
3.35/3.56	         app_encode_app(nat, app_encode_fun(nat, nat), ord_max(nat), 
3.35/3.56	           app_encode_app(huffma1450048681e_tree(a), nat, 
3.35/3.56	             huffma945805758height(a), t_2)), 
3.35/3.56	         app_encode_app(huffma1450048681e_tree(b), nat, 
3.35/3.56	           huffma945805758height(b), t_1)),
3.35/3.56	    inference('demod', [status(thm)], ['0', '22'])).
3.35/3.56	tff('24', plain,
3.35/3.56	    app_encode_app(nat, $o, 
3.35/3.56	      app_encode_app(nat, app_encode_fun(nat, $o), ord_less_eq(nat), 
3.35/3.56	        app_encode_app(huffma1450048681e_tree(b), nat, 
3.35/3.56	          huffma945805758height(b), t_1)), 
3.35/3.56	      app_encode_app(a, nat, 
3.35/3.56	        app_encode_app(huffma1450048681e_tree(a), app_encode_fun(a, nat), 
3.35/3.56	          huffma410068972_depth(a), t_2), a1)),
3.35/3.56	    inference('sup+', [status(thm)], ['23', '7'])).
3.35/3.56	tff('25', plain,
3.35/3.56	    app_encode_app(nat, $o, 
3.35/3.56	      app_encode_app(nat, app_encode_fun(nat, $o), ord_less_eq(nat), 
3.35/3.56	        app_encode_app(huffma1450048681e_tree(a), nat, 
3.35/3.56	          huffma945805758height(a), t_2)), 
3.35/3.56	      app_encode_app(a, nat, 
3.35/3.56	        app_encode_app(huffma1450048681e_tree(a), app_encode_fun(a, nat), 
3.35/3.56	          huffma410068972_depth(a), t_2), a1)),
3.35/3.56	    inference('sup+', [status(thm)], ['23', '18'])).
3.35/3.56	tff(zf_stmt_92, axiom,
3.35/3.56	  (![N:nat,M:nat]:
3.35/3.56	     (app_encode_app(nat,$o,
3.35/3.56	                     app_encode_app(nat,app_encode_fun(nat,$o),
3.35/3.56	                                    ord_less_eq(nat),M),
3.35/3.56	                     N) =>
3.35/3.56	      (app_encode_app(nat,$o,
3.35/3.56	                      app_encode_app(nat,app_encode_fun(nat,$o),
3.35/3.56	                                     ord_less_eq(nat),N),
3.35/3.56	                      M) =>
3.35/3.56	       (M = N))))).
3.35/3.56	tff('26', plain,
3.35/3.56	    ![X174 : nat, X175 : nat]:
3.35/3.56	      (~ app_encode_app(nat, $o, 
3.35/3.56	           app_encode_app(nat, app_encode_fun(nat, $o), ord_less_eq(nat), 
3.35/3.56	             X174), X175)
3.35/3.56	       | X175 = X174
3.35/3.56	       | ~ app_encode_app(nat, $o, 
3.35/3.56	             app_encode_app(nat, app_encode_fun(nat, $o), ord_less_eq(nat), 
3.35/3.56	               X175), X174)),
3.35/3.56	    inference('cnf', [status(esa)], [zf_stmt_92])).
3.35/3.56	tff('27', plain,
3.35/3.56	    (~ $true
3.35/3.56	     | ~ app_encode_app(nat, $o, 
3.35/3.56	           app_encode_app(nat, app_encode_fun(nat, $o), ord_less_eq(nat), 
3.35/3.56	             app_encode_app(a, nat, 
3.35/3.56	               app_encode_app(huffma1450048681e_tree(a), 
3.35/3.56	                 app_encode_fun(a, nat), huffma410068972_depth(a), t_2), a1)), 
3.35/3.56	           app_encode_app(huffma1450048681e_tree(a), nat, 
3.35/3.56	             huffma945805758height(a), t_2))
3.35/3.56	     | app_encode_app(a, nat, 
3.35/3.56	         app_encode_app(huffma1450048681e_tree(a), app_encode_fun(a, nat), 
3.35/3.56	           huffma410068972_depth(a), t_2), a1)
3.35/3.56	        = app_encode_app(huffma1450048681e_tree(a), nat, 
3.35/3.56	            huffma945805758height(a), t_2)),
3.35/3.56	    inference('sup-', [status(thm)], ['25', '26'])).
3.35/3.56	tff(zf_stmt_48, axiom,
3.35/3.56	  (![A:$tType,A3:A,T:huffma1450048681e_tree(A)]:
3.35/3.56	     app_encode_app(nat,$o,
3.35/3.56	                    app_encode_app(nat,app_encode_fun(nat,$o),
3.35/3.56	                                   ord_less_eq(nat),
3.35/3.56	                                   app_encode_app(A,nat,
3.35/3.56	                                                  app_encode_app(huffma1450048681e_tree(
3.35/3.56	                                                                 A),
3.35/3.56	                                                                 app_encode_fun(
3.35/3.56	                                                                 A,nat),
3.35/3.56	                                                                 huffma410068972_depth(
3.35/3.56	                                                                 A),T),
3.35/3.56	                                                  A3)),
3.35/3.56	                    app_encode_app(huffma1450048681e_tree(A),nat,
3.35/3.56	                                   huffma945805758height(A),T)))).
3.35/3.56	tff('28', plain,
3.35/3.56	    ![X5 : $tType, X6 : huffma1450048681e_tree(X5), X7 : X5]:
3.35/3.56	      app_encode_app(nat, $o, 
3.35/3.56	        app_encode_app(nat, app_encode_fun(nat, $o), ord_less_eq(nat), 
3.35/3.56	          app_encode_app(X5, nat, 
3.35/3.56	            app_encode_app(huffma1450048681e_tree(X5), 
3.35/3.56	              app_encode_fun(X5, nat), huffma410068972_depth(X5), X6), X7)), 
3.35/3.56	        app_encode_app(huffma1450048681e_tree(X5), nat, 
3.35/3.56	          huffma945805758height(X5), X6)),
3.35/3.56	    inference('cnf', [status(esa)], [zf_stmt_48])).
3.35/3.56	tff('29', plain,
3.35/3.56	    (~ $true
3.35/3.56	     | ~ $true
3.35/3.56	     | app_encode_app(a, nat, 
3.35/3.56	         app_encode_app(huffma1450048681e_tree(a), app_encode_fun(a, nat), 
3.35/3.56	           huffma410068972_depth(a), t_2), a1)
3.35/3.56	        = app_encode_app(huffma1450048681e_tree(a), nat, 
3.35/3.56	            huffma945805758height(a), t_2)),
3.35/3.56	    inference('demod', [status(thm)], ['27', '28'])).
3.35/3.56	tff('30', plain,
3.35/3.56	    app_encode_app(a, nat, 
3.35/3.56	      app_encode_app(huffma1450048681e_tree(a), app_encode_fun(a, nat), 
3.35/3.56	        huffma410068972_depth(a), t_2), a1)
3.35/3.56	     = app_encode_app(huffma1450048681e_tree(a), nat, 
3.35/3.56	         huffma945805758height(a), t_2),
3.35/3.56	    inference('simplify', [status(thm)], ['29'])).
3.35/3.56	tff('31', plain,
3.35/3.56	    app_encode_app(nat, $o, 
3.35/3.56	      app_encode_app(nat, app_encode_fun(nat, $o), ord_less_eq(nat), 
3.35/3.56	        app_encode_app(huffma1450048681e_tree(b), nat, 
3.35/3.56	          huffma945805758height(b), t_1)), 
3.35/3.56	      app_encode_app(huffma1450048681e_tree(a), nat, 
3.35/3.56	        huffma945805758height(a), t_2)),
3.35/3.56	    inference('demod', [status(thm)], ['24', '30'])).
3.35/3.56	tff(zf_stmt_177, axiom,
3.35/3.56	  ((app_encode_app(a,nat,
3.35/3.56	                   app_encode_app(huffma1450048681e_tree(a),
3.35/3.56	                                  app_encode_fun(a,nat),
3.35/3.56	                                  huffma410068972_depth(a),t_2),
3.35/3.56	                   a1) =
3.35/3.56	    app_encode_app(huffma1450048681e_tree(a),nat,huffma945805758height(a),t_2)) =>
3.35/3.56	   (app_encode_app(nat,$o,
3.35/3.56	                   app_encode_app(nat,app_encode_fun(nat,$o),
3.35/3.56	                                  ord_less_eq(nat),
3.35/3.56	                                  app_encode_app(huffma1450048681e_tree(b),
3.35/3.56	                                                 nat,
3.35/3.56	                                                 huffma945805758height(b),t_1)),
3.35/3.56	                   app_encode_app(huffma1450048681e_tree(a),nat,
3.35/3.56	                                  huffma945805758height(a),t_2)) =>
3.35/3.56	    p))).
3.35/3.56	tff('32', plain,
3.35/3.56	    (~ app_encode_app(nat, $o, 
3.35/3.56	         app_encode_app(nat, app_encode_fun(nat, $o), ord_less_eq(nat), 
3.35/3.56	           app_encode_app(huffma1450048681e_tree(b), nat, 
3.35/3.56	             huffma945805758height(b), t_1)), 
3.35/3.56	         app_encode_app(huffma1450048681e_tree(a), nat, 
3.35/3.56	           huffma945805758height(a), t_2))
3.35/3.56	     | p
3.35/3.56	     | app_encode_app(a, nat, 
3.35/3.56	         app_encode_app(huffma1450048681e_tree(a), app_encode_fun(a, nat), 
3.35/3.56	           huffma410068972_depth(a), t_2), a1)
3.35/3.56	        != app_encode_app(huffma1450048681e_tree(a), nat, 
3.35/3.56	             huffma945805758height(a), t_2)),
3.35/3.56	    inference('cnf', [status(esa)], [zf_stmt_177])).
3.35/3.56	tff(zf_stmt_178, conjecture, (p)).
3.35/3.56	tff(zf_stmt_0, negated_conjecture, (~p)).
3.35/3.56	tff('33', plain, ~ p, inference('cnf', [status(esa)], [zf_stmt_0])).
3.35/3.56	tff('34', plain,
3.35/3.56	    (app_encode_app(a, nat, 
3.35/3.56	       app_encode_app(huffma1450048681e_tree(a), app_encode_fun(a, nat), 
3.35/3.56	         huffma410068972_depth(a), t_2), a1)
3.35/3.56	      != app_encode_app(huffma1450048681e_tree(a), nat, 
3.35/3.56	           huffma945805758height(a), t_2)
3.35/3.56	     | ~ app_encode_app(nat, $o, 
3.35/3.56	           app_encode_app(nat, app_encode_fun(nat, $o), ord_less_eq(nat), 
3.35/3.56	             app_encode_app(huffma1450048681e_tree(b), nat, 
3.35/3.56	               huffma945805758height(b), t_1)), 
3.35/3.56	           app_encode_app(huffma1450048681e_tree(a), nat, 
3.35/3.56	             huffma945805758height(a), t_2))),
3.35/3.56	    inference('clc', [status(thm)], ['32', '33'])).
3.35/3.56	tff('35', plain,
3.35/3.56	    (app_encode_app(huffma1450048681e_tree(a), nat, 
3.35/3.56	       huffma945805758height(a), t_2)
3.35/3.56	      != app_encode_app(huffma1450048681e_tree(a), nat, 
3.35/3.56	           huffma945805758height(a), t_2)
3.35/3.56	     | ~ app_encode_app(nat, $o, 
3.35/3.56	           app_encode_app(nat, app_encode_fun(nat, $o), ord_less_eq(nat), 
3.35/3.56	             app_encode_app(huffma1450048681e_tree(b), nat, 
3.35/3.56	               huffma945805758height(b), t_1)), 
3.35/3.56	           app_encode_app(huffma1450048681e_tree(a), nat, 
3.35/3.56	             huffma945805758height(a), t_2))),
3.35/3.56	    inference('demod', [status(thm)], ['34', '30'])).
3.35/3.56	tff('36', plain,
3.35/3.56	    ~ app_encode_app(nat, $o, 
3.35/3.56	        app_encode_app(nat, app_encode_fun(nat, $o), ord_less_eq(nat), 
3.35/3.56	          app_encode_app(huffma1450048681e_tree(b), nat, 
3.35/3.56	            huffma945805758height(b), t_1)), 
3.35/3.56	        app_encode_app(huffma1450048681e_tree(a), nat, 
3.35/3.56	          huffma945805758height(a), t_2)),
3.35/3.56	    inference('simplify', [status(thm)], ['35'])).
3.35/3.56	tff('37', plain, ~ $true, inference('sup-', [status(thm)], ['31', '36'])).
3.35/3.56	tff('38', plain, $false, inference('simplify', [status(thm)], ['37'])).
3.35/3.56	
3.35/3.56	% SZS output end Refutation
3.35/3.56	EOF
